@misc{DeuflhardSchuette, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7427}, number = {03-20}, abstract = {The paper surveys recent progress in the mathematical modelling and simulation of essential molecular dynamics. Particular emphasis is put on computational drug design wherein time scales of \$msec\$ up to \$min\$ play the dominant role. Classical long-term molecular dynamics computations, however, would run into ill-conditioned initial value problems already after time spans of only \$psec=10^{-12} sec\$. Therefore, in order to obtain results for times of pharmaceutical interest, a combined deterministic-stochastic model is needed. The concept advocated in this paper is the direct identification of metastable conformations together with their life times and their transition patterns. It can be interpreted as a {\em transfer operator} approach corresponding to some underlying hybrid Monte Carlo process, wherein short-term trajectories enter. Once this operator has been discretized, which is a hard problem of its own, a stochastic matrix arises. This matrix is then treated by {\em Perron cluster analysis}, a recently developed cluster analysis method involving the numerical solution of an eigenproblem for a Perron cluster of eigenvalues. In order to avoid the 'curse of dimension', the construction of appropriate boxes for the spatial discretization of the Markov operator requires careful consideration. As a biomolecular example we present a rather recent SARS protease inhibitor.}, language = {en} } @misc{SchuetteNettesheim, author = {Sch{\"u}tte, Christof and Nettesheim, Peter}, title = {Non-Adiabatic Effects in Quantum-Classical Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3817}, number = {SC-98-38}, abstract = {In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The article is concerned with the so-called QCMD model. This model describes most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of a wavefunction. We review the conditions under which the QCMD model is known to approximate the full quantum dynamical evolution of the system. In most quantum-classical simulations the {\em Born-Oppenheimer model} (BO) is used. In this model, the wavefunction is adiabatically coupled to the classical motion which leads to serious approximation deficiencies with respect to non-adiabatic effects in the fully quantum dynamical description of the system. In contrast to the BO model, the QCMD model does include non-adiabatic processes, e.g., transitions between the energy levels of the quantum system. It is demonstrated that, in mildly non-adiabatic scenarios, so-called {\em surface hopping} extensions of QCMD simulations yield good approximations of the non-adiabatic effects in full quantum dynamics. The algorithmic strategy of such extensions of QCMD is explained and the crucial steps of its realization are discussed with special emphasis on the numerical problems caused by highly oscillatory phase effects.}, language = {en} } @misc{SchuetteFischerHuisingaetal., author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3889}, number = {SC-98-45}, abstract = {Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator \$T\$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of \$T\$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix \$P\$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of \$T\$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted.}, language = {en} } @misc{BornemannSchuette, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {Adaptive Accuracy Control for Microcanonical Car-Parrinello Simulations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2311}, number = {SC-96-20}, abstract = {The Car-Parrinello (CP) approach to ab initio molecular dynamics serves as an approximation to time-dependent Born-Oppenheimer (BO) calculations. It replaces the explicit minimization of the energy functional by a fictitious Newtonian dynamics and therefore introduces an artificial mass parameter \$\mu\$ which controls the electronic motion. A recent theoretical investigation shows that the CP-error, i.e., the deviation of the CP--solution from the BO-solution {\em decreases} like \$\mu^{1/2}\$ asymptotically. Since the computational effort {\em increases} like \$\mu^{-1/2}\$, the choice of \$\mu\$ has to find a compromise between efficiency and accuracy. The asymptotical result is used in this paper to construct an easily implemented algorithm which automatically controls \$\mu\$: the parameter \$\mu\$ is repeatedly adapted during the simulation by choosing \$\mu\$ as large as possible while pushing an error measure below a user-given tolerance. The performance and reliability of the algorithm is illustrated by a typical example.}, language = {en} } @misc{SchuetteHuisinga, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {On Conformational Dynamics induced by Langevin Processes}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4130}, number = {SC-99-25}, abstract = {The function of many important biomolecules is related to their dynamic properties and their ability to switch between different {\em conformations}, which are understood as {\em almost invariant} or {\em metastable} subsets of the positional state space of the system. Recently, the present authors and their coworkers presented a novel algorithmic scheme for the direct numerical determination of such metastable subsets and the transition probability between them. Although being different in most aspects, this method exploits the same basic idea as {\sc Dellnitz} and {\sc Junge} in their approach to almost invariance in discrete dynamical systems: the almost invariant sets are computed via certain eigenvectors of the Markov operators associated with the dynamical behavior. In the present article we analyze the application of this approach to (high--friction) Langevin models describing the dynamical behavior of molecular systems coupled to a heat bath. We will see that this can be related to theoretical results for (symmetric) semigroups of Markov operators going back to {\sc Davies}. We concentrate on a comparison of our approach in respect to random perturbations of dynamical systems.}, language = {en} } @phdthesis{Schuette, author = {Sch{\"u}tte, Christof}, title = {A Quasiresonant Smoothing Algorithm for Solving Large Highly Differential Equations from Quantum Chemistry.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5090}, number = {TR-94-04}, abstract = {In Quantum Chemistry the field of Laser--Assisted Molecular Control'' has received a considerable amount of attention recently. One key problem in this new field is the simulation of the dynamical reaction of a molecule subjected to external radiation. This problem is described by the Schr{\"o}dinger equation, which, after eigenfunction expansion, can be written in the form of a large system of ordinary differential equations, the solutions of which show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. Standard smoothing techniques (averaging, filtering) would kill the whole process and thus, lead to wrong numerical results. To avoid this unwanted effect and nevertheless speed up computations, this paper presents a quasiresonant smoothing algorithm (QRS). In QRS, a natural splitting parameter \$\delta\$ controls the smoothing properties. An adaptive QRS--version (AQRS) is presented which includes an error estimation scheme for choosing this parameter \$\delta\$ in order to meet a given accuracy requirement. In AQRS \$\delta\$ is permanently adapted to the solution properties for computing the chemically necessary information'' only. The performance of AQRS is demonstrated in several test problems from the field Laser--Assisted Selective Excitation of Molecules'' in which the external radiation is a picosecond laser pulse. In comparison with standard methods speedup factors of the order of \$10^2\$ are observed.}, language = {en} } @misc{Schuette, author = {Sch{\"u}tte, Christof}, title = {Partial Wigner Transforms and the Quantum--Classical Liouville Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3983}, number = {SC-99-10}, abstract = {In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The {\em quantum-classical Liouville equation} (QCL) describes most atoms of the molecular system under consideration by means of classical phase space density but an important, small portion of the system by means of quantum mechanics. The QCL is derived from the full quantum dynamical (QD) description by applying the Wigner transform to the classical part'' of the system only. We discuss the conditions under which the QCL model approximates the full QD evolution of the system. First, analysis of the asymptotic properties of the Wigner transform shows that solving the QCL yields a first order approximation of full quantum dynamics. Second, we discuss the adiabatic limit of the QCL. This discussion shows that the QCL solutions may be interpretated as classical phase space densities, at least near the adiabatic limit. Third, it is demonstrated that the QCL yields good approximations of {\em non-adiabatic quantum effects,} especially near so-called {\em avoided crossings} where most quantum-classical models fail.}, language = {en} } @misc{BornemannNettesheimSchuette, author = {Bornemann, Folkmar A. and Nettesheim, Peter and Sch{\"u}tte, Christof}, title = {Quantum-Classical Molecular Dynamics as an Approximation to Full Quantum Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1922}, number = {SC-95-26}, abstract = {This paper presents a mathematical derivation of a model for quantum-classical molecular dynamics (QCMD) as a {\em partial} classical limit of the full Schr{\"o}dinger equation. This limit is achieved in two steps: separation of the full wavefunction and short wave asymptotics for its ``classical'' part. Both steps can be rigorously justified under certain smallness assumptions. Moreover, the results imply that neither the time-dependent self-consistent field method nor mixed quantum-semi-classical models lead to better approximations than QCMD since they depend on the separation step, too. On the other hand, the theory leads to a characterization of the critical situations in which the models are in danger of largely deviating from the solution of the full Schr{\"o}dinger equation. These critical situations are exemplified in an illustrative numerical simulation: the collinear collision of an Argon atom with a harmonic quantum oscillator.}, language = {en} } @misc{BornemannSchuette, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {A Mathematical Approach to Smoothed Molecular Dynamics: Correcting Potentials for Freezing Bond Angles}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1960}, number = {SC-95-30}, abstract = {The interaction potential of molecular systems which are typically used in molecular dynamics can be split into two parts of essentially different stiffness. The strong part of the potential forces the solution of the equations of motion to oscillate on a very small time scale. There is a strong need for eliminating the smallest time scales because they are a severe restriction for numerical long-term simulations of macromolecules. This leads to the idea of just freezing the high frequency degrees of freedom (bond stretching and bond angles). However, the naive way of doing this via holonomic constraints is bound to produce incorrect results. The paper presents a mathematically rigorous discussion of the limit situation in which the stiffness of the strong part of the potential is increased to infinity. It is demonstrated that the average of the limit solution indeed obeys a constrained Hamiltonian system but with a {\em corrected soft potential}. An explicit formula for the additive potential correction is given and its significant contribution is demonstrated in an illustrative example. It appears that this correcting potential is definitely not identical with the Fixman-potential as was repeatedly assumed in the literature.}, language = {en} } @misc{NettesheimSchuette, author = {Nettesheim, Peter and Sch{\"u}tte, Christof}, title = {Numerical Integrators for Quantum-Classical Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3111}, number = {SC-97-42}, abstract = {It was revealed that the QCMD model is of canonical Hamiltonian form with symplectic structure, which implies the conservation of energy. An efficient and reliable integrator for transfering these properties to the discrete solution is the symplectic and explicit {\sc Pickaback} algorithm. The only drawback of this kind of integrator is the small stepsize in time induced by the splitting techniques used to discretize the quantum evolution operator. Recent investigations concerning Krylov iteration techniques result in alternative approaches which overcome this difficulty for a wide range of problems. By using iterative methods in the evaluation of the quantum time propagator, these techniques allow for the stepsize to adapt to the coupling between the classical and the quantum mechanical subsystem. This yields a drastic reduction of the numerical effort. The pros and cons of both approaches as well as the suitable applications are discussed in the last part.}, language = {en} } @misc{SchuetteDinandZumbuschetal., author = {Sch{\"u}tte, Christof and Dinand, Manfred and Zumbusch, Gerhard and Brinkmann, Ralf}, title = {Dynamics of Erbium-doped Waveguide Lasers: Modelling, Reliable Simulation, and Comparison with Experiments}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1856}, number = {SC-95-19}, abstract = {A theoretical investigation of the dynamic properties of integrated optical Er--doped waveguide lasers is presented. It includes the construction of a physical model and of numerical techniques which allow reliable simulations of the dynamical behaviour of the laser signal depending on essential parameters of the laser device and on its external, time--dependent pump radiation. Therefore, a physical theory is developed which describes the propagation of light and its interaction with the active substrate in the laser cavity. This is realized in two steps. First, a {\em fundamental model} based on Maxwell's equations and on rate equations for the transitions in the active medium is constructed. Since this turns out to prohibit reliable simulations, it is, in a second step, reformulated via averaging in time and space which suppresses the fluctuations on the fastest time scales but represents them correctly. For this {\em reduced model} reliable and efficient simulation techniques using adaptive control schemes are designed and implemented. We apply the linear--implicit Euler discretization with extrapolation in time and a multilevel quadrature scheme in space. Finally, the model is justified in comparison with experimental observations in four cases of technological relevance.}, language = {en} } @misc{SchuetteHuisingaDeuflhard, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4247}, number = {SC-99-36}, abstract = {The article surveys the development of novel mathematical concepts and algorithmic approaches based thereon in view of their possible applicability to biomolecular design. Both a first deterministic approach, based on the Frobenius-Perron operator corresponding to the flow of the Hamiltonian dynamics, and later stochastic approaches, based on a spatial Markov operator or on Langevin dynamics, can be subsumed under the unified mathematical roof of the transfer operator approach to effective dynamics of molecular systems. The key idea of constructing specific transfer operators especially taylored for the purpose of conformational dynamics appears as the red line throughout the paper. Different steps of the algorithm are exemplified by a trinucleotide molecular system as a small representative of possible RNA drug molecules.}, language = {en} } @misc{SchuetteBornemann, author = {Sch{\"u}tte, Christof and Bornemann, Folkmar A.}, title = {Approximation Properties and Limits of the Quantum-Classical Molecular Dynamics Model}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3102}, number = {SC-97-41}, abstract = {In molecular dynamics applications there is a growing interest in including quantum effects for simulations of larger molecules. This paper is concerned with {\em mixed quantum-classical} models which are currently discussed: the so-called QCMD model with variants and the time-dependent Born-Oppenheimer approximation. All these models are known to approximate the full quantum dynamical evolution---under different assumptions, however. We review the meaning of these assumptions and the scope of the approximation. In particular, we characterize those typical problematic situations where a mixed model might largely deviate from the full quantum evolution. One such situation of specific interest, a non-adiabatic excitation at certain energy level crossings, can promisingly be dealt with by a modification of the QCMD model that we suggest.}, language = {en} } @misc{BornemannSchuette, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {On the Singular Limit of the Quantum-Classical Molecular Dynamics Model}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2761}, number = {SC-97-07}, abstract = {\noindent In molecular dynamics applications there is a growing interest in so-called {\em mixed quantum-classical} models. These models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of quantum mechanics. A particularly extensively used model, the QCMD model, consists of a {\em singularly perturbed}\/ Schr{\"o}dinger equation nonlinearly coupled to a classical Newtonian equation of motion. This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born-Oppenheimer model of quantum theory---provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the {\em quantum adiabatic theorem}. The proof uses the method of {\em weak convergence} by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly oscillatory phases. On the other hand, the limit of the QCMD model is of a different nature if the spectral decomposition of the Hamiltonian happens not to be smooth. We will present a generic example for which the limit set is not a unique trajectory of a limit dynamical system but rather a {\em funnel} consisting of infinitely many trajectories.}, language = {en} } @misc{HuisingaBestCordesetal., author = {Huisinga, Wilhelm and Best, Christoph and Cordes, Frank and Roitzsch, Rainer and Sch{\"u}tte, Christof}, title = {From Simulation Data to Conformational Ensembles: Structure and Dynamics based Methods}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3797}, number = {SC-98-36}, abstract = {Statistical methods for analyzing large data sets of molecular configurations within the chemical concept of molecular conformations are described. The strategies are based on dependencies between configurations of a molecular ensemble; the article concentrates on dependencies induces by a) correlations between the molecular degrees of freedom, b) geometrical similarities of configurations, and c) dynamical relations between subsets of configurations. The statistical technique realizing aspect a) is based on an approach suggested by {\sc Amadei et al.} (Proteins, 17 (1993)). It allows to identify essential degrees of freedom of a molecular system and is extended in order to determine single configurations as representatives for the crucial features related to these essential degrees of freedom. Aspects b) and c) are based on statistical cluster methods. They lead to a decomposition of the available simulation data into {\em conformational ensembles} or {\em subsets} with the property that all configurations in one of these subsets share a common chemical property. In contrast to the restriction to single representative conformations, conformational ensembles include information about, e.g., structural flexibility or dynamical connectivity. The conceptual similarities and differences of the three approaches are discussed in detail and are illustrated by application to simulation data originating from a hybrid Monte Carlo sampling of a triribonucleotide.}, language = {en} } @misc{SchuetteWulkow, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of RamanSpectroscopy.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-778}, number = {SC-92-07}, abstract = {Models for occupation dynamics in discrete quantum systems lead to large or even infinite systems of ordinary differential equations. Some new mathematical techniques, developed for the simulation of chemical processes, make a numerical solution of countable systems of ordinary differential equations possible. Both, a basic physical concept for the construction of such systems and the structure of the numerical tools for solving them are presented. These conceptual aspects are illustrated by a simulation of an occupation process from spectroscopy. In this example the structures of rotation spectra observed in infrared spectroscopy are explained and some possibilities for an extension of the model are shown.}, language = {en} } @misc{Schuette, author = {Sch{\"u}tte, Christof}, title = {A quasiresonant smoothing algorithm for the fast analysis of selective vibrational excitation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1066}, number = {SC-93-10}, abstract = {One key problem in modern chemistry is the simulation of the dynamical reaction of a molecule subjected to external radiation. This is described by the Schr{\"o}dinger equation, which, after eigenfunction expansion, can be written in form of a system of ordinary differential equations, whose solutions show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. This idea leads to the construction of a quasiresonant smoothing algorithm (QRS). In QRS, a natural and computationally available splitting parameter \$\delta\$ controls the smoothing properties. The performance of QRS is demonstrated in two applications treating the selective excitation of vibrational states by picosecond laser pulses. In comparison with standard methods a speedup factor of 60--100 is observed. A closer look to purely physically motivated quasiresonant approximations such as WFQRA shows some additional advantages of the above smoothing idea. Among these the possibility of an adaptive formulation of QRS via the parameter \$\delta\$ is of particular importance.}, language = {en} } @misc{SchuetteHohmannDinand, author = {Sch{\"u}tte, Christof and Hohmann, Andreas and Dinand, Manfred}, title = {Numerical Simulation of Relaxation Oscillations of Waveguide-Lasers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1106}, number = {SC-93-14}, abstract = {An analysis of relaxation oscillations in local Er-doped optically pumped lasers is reported. It is based on a time dependent rate equation model for a quasi-two-level-system with wavelength dependent emission- and absorption cross-sections. For the first time a numerically reliable simulation of the characteristic laser behaviour was possible: the onset and decay of the oscillations, the time-dependent repetition period and the steady state signal output power. The characteristic waveguide parameters, as the erbium-concentration profile, the polarization dependent pump- and signal mode intensity profiles, the scattering losses, the cavity length and the front and rear reflectivities were all taken into account. The basic formulas are general and can also be used for Er-doped fiber lasers. Mathematically the problem can be characterized as a large boundary value problem, which can approximately be replaced by a stiff initial value problem of ordinary differential equations. The used algorithmic replacement procedure is motivated and discussed in detail. Here, pump- and signal evolution versus time are presented for an planar Er-diffused \$\rm Ti\$:\$\rm LiNbO_{3}\$ waveguide laser. The numerically obtained results show a nearly quantitative agreement with experimental investigations. Simultanously they supply knowledge about non-measureable (space-dependent population dynamic of the Er-atoms) and till today not measured data (dynamical response of the laser by a sharp peak in the external pump).}, language = {en} } @misc{Schuette, author = {Sch{\"u}tte, Christof}, title = {Smoothed Molecular Dynamics for Thermally Embedded Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1809}, number = {SC-95-14}, abstract = {This paper makes use of statistical mechanics in order to construct effective potentials for Molecular Dynamics for systems with nonstationary thermal embedding. The usual approach requires the computation of a statistical ensemble of trajectories. In the context of the new model the evaluation of only one single trajectory is sufficient for the determination of all interesting quantities, which leads to an enormous reduction of computational effort. This single trajectory is the solution to a corrected Hamiltonian system with a new potential \$\tilde{V}\$. It turns out that \$\tilde{V}\$ can be defined as spatial average of the original potential \$V\$. Therefore, the Hamiltonian dynamics defined by \$\tilde{V}\$ is smoother than that effected by \$V\$, i.e. a numerical integration of its evolution in time allows larger stepsizes. Thus, the presented approach introduces a Molecular Dynamics with smoothed trajectories originating from spatial averaging. This is deeply connected to time--averaging in Molecular Dynamics. These two types of {\em smoothed Molecular Dynamics} share advantages (gain in efficiency, reduction of error amplification, increased stability) and problems (necessity of closing relations and adaptive control schemes) which will be explained in detail.}, language = {en} } @misc{BornemannSchuette, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {Homogenization of Highly Oscillatory Hamiltonian Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2050}, number = {SC-95-39}, abstract = {The paper studies Hamiltonian systems with a strong potential forcing the solutions to oscillate on a very small time scale. In particular, we are interested in the limit situation where the size \$\epsilon\$ of this small time scale tends to zero but the velocity components remain oscillating with an amplitude variation of order \${\rm O}(1)\$. The process of establishing an effective initial value problem for the limit positions will be called {\em homogenization} of the Hamiltonian system. This problem occurs in mechanics as the problem of realization of holonomic constraints, in plasma physics as the problem of guiding center motion, in the simulation of biomolecules as the so called smoothing problem. We suggest the systematic use of the notion of {\em weak convergence} in order to approach this problem. This methodology helps to establish unified and short proofs of the known results which throw light on the inherent structure of the problem. Moreover, we give a careful and critical review of the literature.}, language = {en} } @misc{FischerCordesSchuette, author = {Fischer, Alexander and Cordes, Frank and Sch{\"u}tte, Christof}, title = {Hybrid Monte Carlo with Adaptive Temperature in a Mixed-Canonical Ensemble: Efficient Conformational Analysis of RNA}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3364}, number = {SC-97-67}, abstract = {A hybrid Monte Carlo method with adaptive temperature choice is presented, which exactly generates the distribution of a mixed-canonical ensemble composed of two canonical ensembles at low and high temperature. The analysis of resulting Markov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature, whereas the high temperature component facilitates conformational transitions, which allows shorter simulation times. \\The algorithm was tested by comparing analytical and numerical results for the small n-butane molecule before simulations were performed for a triribonucleotide. Sampling the complex multi-minima energy landscape of these small RNA segments, we observed enforced crossing of energy barriers.}, language = {en} } @misc{DeuflhardDellnitzJungeetal., author = {Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of Essential Molecular Dynamics by Subdivision Techniques I: Basic Concept}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2553}, number = {SC-96-45}, abstract = {The paper presents the concept of a new type of algorithm for the numerical computation of what the authors call the {\em essential dynamics\/} of molecular systems. Mathematically speaking, such systems are described by Hamiltonian differential equations. In the bulk of applications, individual trajectories are of no specific interest. Rather, time averages of physical observables or relaxation times of conformational changes need to be actually computed. In the language of dynamical systems, such information is contained in the natural invariant measure (infinite relaxation time) or in almost invariant sets ("large" finite relaxation times). The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm. The advocated approach is different to both Monte-Carlo techniques on the one hand and long term trajectory simulation on the other hand: in our setup long term trajectories are replaced by short term sub-trajectories, Monte-Carlo techniques are just structurally connected via the underlying Frobenius-Perron theory. Numerical experiments with a first version of our suggested algorithm are included to illustrate certain distinguishing properties. A more advanced version of the algorithm will be presented in a second part of this paper.}, language = {en} } @misc{NettesheimHuisingaSchuette, author = {Nettesheim, Peter and Huisinga, Wilhelm and Sch{\"u}tte, Christof}, title = {Chebyshev-Approximation for Wavepacket-Dynamics: better than expected}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2575}, number = {SC-96-47}, abstract = {The aim of this work is to study the accuracy and stability of the Chebyshev--approximation method as a time--discretization for wavepacket dynamics. For this frequently used discretization we introduce estimates of the approximation and round--off error. These estimates mathematically confirm the stability of the Chebyshev--approximation with respect to round--off errors, especially for very large stepsizes. But the results also disclose threads to the stability due to large spatial dimensions. All theoretical statements are illustrated by numerical simulations of an analytically solvable example, the harmonic quantum oszillator.}, language = {en} } @misc{BornemannSchuette, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {A Mathematical Investigation of the Car-Parrinello Method}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2302}, number = {SC-96-19}, abstract = {The Car-Parrinello method for ab-initio molecular dynamics avoids the explicit minimization of energy functionals given by functional density theory in the context of the quantum adiabatic approximation (time-dependent Born-Oppenheimer approximation). Instead, it introduces a fictitious classical dynamics for the electronic orbitals. For many realistic systems this concept allowed first-principle computer simulations for the first time. In this paper we study the {\em quantitative} influence of the involved parameter \$\mu\$, the fictitious electronic mass of the method. In particular, we prove by use of a carefully chosen two-time-scale asymptotics that the deviation of the Car-Parrinello method from the adiabatic model is of order \${\rm O}(\mu^{1/2})\$ --- provided one starts in the ground state of the electronic system and the electronic excitation spectrum satisfies a certain non-degeneracy condition. Analyzing a two-level model problem we prove that our result cannot be improved in general. Finally, we show how to use the gained quantitative insight for an automatic control of the unphysical ``fake'' kinetic energy of the method.}, language = {en} } @misc{SchuetteBornemann, author = {Sch{\"u}tte, Christof and Bornemann, Folkmar A.}, title = {Homogenization Approach to Smoothed Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2410}, number = {SC-96-31}, abstract = {{\footnotesize In classical Molecular Dynamics a molecular system is modelled by classical Hamiltonian equations of motion. The potential part of the corresponding energy function of the system includes contributions of several types of atomic interaction. Among these, some interactions represent the bond structure of the molecule. Particularly these interactions lead to extremely stiff potentials which force the solution of the equations of motion to oscillate on a very small time scale. There is a strong need for eliminating the smallest time scales because they are a severe restriction for numerical long-term simulations of macromolecules. This leads to the idea of just freezing the high frequency degrees of freedom (bond stretching and bond angles) via increasing the stiffness of the strong part of the potential to infinity. However, the naive way of doing this via holonomic constraints mistakenly ignores the energy contribution of the fast oscillations. The paper presents a mathematically rigorous discussion of the limit situation of infinite stiffness. It is demonstrated that the average of the limit solution indeed obeys a constrained Hamiltonian system but with a {\em corrected soft potential}. An explicit formula for the additive potential correction is given via a careful inspection of the limit energy of the fast oscillations. Unfortunately, the theory is valid only as long as the system does not run into certain resonances of the fast motions. Behind those resonances, there is no unique limit solution but a kind of choatic scenario for which the notion ``Takens chaos'' was coined. For demonstrating the relevance of this observation for MD, the theory is applied to a realistic, but still simple system: a single butan molecule. The appearance of ``Takens chaos'' in smoothed MD is illustrated and the consequences are discussed.}}, language = {en} } @misc{DeuflhardHuisingaFischeretal., author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3469}, number = {SC-98-03}, abstract = {The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule.}, language = {en} } @misc{SchuetteFischerHuisingaetal., author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Hybrid Monte Carlo Method for Essential Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3474}, number = {SC-98-04}, abstract = {Recently, a novel concept for the computation of essential features of Hamiltonian systems (such as those arising in molecular dynamics) has been proposed. The realization of that concept was based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept based on statistical mechanics, which allows to attack realistic molecular systems. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator \$T\$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of \$T\$ via hybrid Monte Carlo techniques (based on short term subtrajectories only) is shown to lead to a stochastic matrix \$P\$. With these theoretical preparations, an identification algorithm for conformations is applicable (to be presented elsewhere). Numerical results for the n-pentane molecule are given and interpreted.}, language = {en} } @phdthesis{Schuette, author = {Sch{\"u}tte, Christof}, title = {Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4063}, number = {SC-99-18}, abstract = {The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric structure of the molecule is understood to be conserved, whereas on smaller scales the system may well rotate, oscillate or fluctuate. In a recent article [J. Comp. Phys., 151,1 (1999)], the present author and coworkers demonstrated that (a) conformations can be understood as almost invariant sets of some Markov chain being defined via the Hamiltonian system governing the molecular dynamics and that (b) these sets can efficiently be computed via eigenvectors of the corresponding Markov operator. The persent manuscript reviews the mathematical modelling steps behind the novel concept, includes a rigorous analytical justification of this approach and especially of the numerical details of the algorithm, and illustrates its performance when applied to realistic molecular systems.}, language = {en} } @misc{FischerSchuetteDeuflhardetal., author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6296}, number = {01-03}, abstract = {Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the \$n\$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.}, language = {en} } @incollection{SchuetteHuisingaDeuflhard2001, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer operator approach to conformational dynamics in biomolecular systems}, series = {Ergodic theory, analysis, and efficient simulation of dynamical systems}, booktitle = {Ergodic theory, analysis, and efficient simulation of dynamical systems}, editor = {Fiedler, Bernold}, publisher = {Berlin: Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo}, series = {J. Comput. Phys.}, volume = {151}, journal = {J. Comput. Phys.}, pages = {146 -- 168}, year = {1999}, language = {en} } @article{SarichSchuetteVandenEijnden2010, author = {Sarich, Marco and Sch{\"u}tte, Christof and Vanden-Eijnden, E.}, title = {Optimal Fuzzy Aggregation of Networks}, series = {Multiscale Modeling and Simulation}, volume = {8}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/090758519}, pages = {1535 -- 1561}, year = {2010}, language = {en} } @inproceedings{DeuflhardDellnitzJungeetal.1999, author = {Deuflhard, Peter and Dellnitz, M. and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of Essential Molecular Dynamics by Subdivision Techniques}, series = {Computational Molecular Dynamics}, volume = {4}, booktitle = {Computational Molecular Dynamics}, editor = {Deuflhard, Peter and Hermans, J. and Leimkuhler, Benedict and Marks, A. and Reich, Sebastian and Skeel, R.}, publisher = {Springer}, pages = {98 -- 115}, year = {1999}, language = {en} } @incollection{DeuflhardDellnitzJungeetal.1998, author = {Deuflhard, Peter and Dellnitz, M. and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of essential molecular dynamics by subdivision techniques}, series = {Computational molecular dynamics}, volume = {4}, booktitle = {Computational molecular dynamics}, editor = {Deuflhard, Peter}, publisher = {Berlin: Springer.}, pages = {98 -- 115}, year = {1998}, language = {en} } @article{FischerCordesSchuette1998, author = {Fischer, Alexander and Cordes, Frank and Sch{\"u}tte, Christof}, title = {Hybrid Monte Carlo with Adaptive Temperature in Mixed-Canonical Ensemble: Efficient conformational analysis of RNA}, series = {J. Comp. Chem.}, volume = {19}, journal = {J. Comp. Chem.}, number = {15}, doi = {10.1002/(SICI)1096-987X(19981130)19:15<1689::AID-JCC2>3.0.CO;2-J}, pages = {1689 -- 1697}, year = {1998}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, series = {Computational Methods for Macromolecules}, booktitle = {Computational Methods for Macromolecules}, number = {24}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @inproceedings{DeuflhardSchuette2004, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, series = {Applied Mathematics Entering the 21st Century}, booktitle = {Applied Mathematics Entering the 21st Century}, number = {116}, editor = {Hill, James and Moore, Ross}, publisher = {SIAM}, pages = {91 -- 119}, year = {2004}, language = {en} } @misc{DeuflhardSchuetteCordesetal.1999, author = {Deuflhard, Peter and Sch{\"u}tte, Christof and Cordes, Frank and M{\"u}ller-Kurth, L.}, title = {Konformationsdynamik. Mathematischer Entwurf hochspezifischer Biomolek{\"u}le}, publisher = {In: D. H{\"o}mberg (ed.), 8. Veranstaltungsreihe Forschungspolitische Dialoge in Berlin: Angewandte Mathematik - die verborgene Schl{\"u}sseltechnologie, 30. April 1999, Konrad-Zuse-Zentrum Berlin, pp. 30-34}, year = {1999}, language = {en} } @article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, series = {Lin. Alg. Appl.}, volume = {315}, journal = {Lin. Alg. Appl.}, pages = {39 -- 59}, year = {2000}, language = {en} } @article{MetznerWeberSchuette2010, author = {Metzner, Ph. and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Observation uncertainty in reversible Markov chains}, series = {Phys. Rev. E}, volume = {82}, journal = {Phys. Rev. E}, number = {3}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.82.031114}, pages = {031114}, year = {2010}, language = {en} } @article{HuisingaBestRoitzschetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Roitzsch, Rainer and Sch{\"u}tte, Christof and Cordes, Frank}, title = {From Simulation Data to Conformational Ensembles}, series = {J. Comp. Chem.}, volume = {20}, journal = {J. Comp. Chem.}, number = {16}, pages = {1760 -- 1774}, year = {1999}, language = {en} } @article{SarichSchuette2012, author = {Sarich, Marco and Sch{\"u}tte, Christof}, title = {Approximating Selected Non-dominant Timescales by Markov State Models}, series = {Comm. Math. Sci.}, volume = {10}, journal = {Comm. Math. Sci.}, number = {3}, doi = {10.4310/CMS.2012.v10.n3.a14}, pages = {1001 -- 1013}, year = {2012}, language = {en} } @article{SenneTrendelkampSchroerMeyetal.2012, author = {Senne, M. and Trendelkamp-Schroer, B. and Mey, A. and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {EMMA - A software package for Markov model building and analysis}, series = {Journal of Chemical Theory and Computation}, volume = {8}, journal = {Journal of Chemical Theory and Computation}, doi = {10.1021/ct300274u}, pages = {2223 -- 2238}, year = {2012}, language = {en} } @article{WinkelmannSchuettevonKleist2012, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control with Rare State Observation}, series = {International Journal of Biomathematics and Biostatistics}, journal = {International Journal of Biomathematics and Biostatistics}, year = {2012}, language = {en} } @misc{AgarwalWangSchuetteetal., author = {Agarwal, Animesh and Wang, Han and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Chemical potential of liquids and mixtures via Adaptive Resolution Simulation}, issn = {1438-0064}, doi = {10.1063/1.4886807}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50972}, abstract = {We employ the adaptive resolution approach AdResS, in its recently developed Grand Canonicallike version (GC-AdResS) [Wang et al. Phys.Rev.X 3, 011018 (2013)], to calculate the excess chemical potential, \$μ^{ex}\$, of various liquids and mixtures. We compare our results with those obtained from full atomistic simulations using the technique of thermodynamic integration and show a satisfactory agreement. In GC-AdResS the procedure to calculate \$μ^{ex}\$ corresponds to the process of standard initial equilibration of the system; this implies that, independently of the specific aim of the study, \$μ^{ex}\$, for each molecular species, is automatically calculated every time a GC-AdResS simulation is performed.}, language = {en} } @misc{DjurdjevacConradBanischSchuette, author = {Djurdjevac Conrad, Natasa and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Modularity of Directed Networks: Cycle Decomposition Approach}, issn = {1438-0064}, doi = {10.3934/jcd.2015.2.1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51166}, abstract = {The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.}, language = {en} } @misc{SarichSchuette, author = {Sarich, Marco and Sch{\"u}tte, Christof}, title = {Utilizing hitting times for finding metastable sets in non-reversible Markov chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51209}, abstract = {Techniques for finding metastable or almost invariant sets have been investigated, e.g., for deterministic dynamical systems in set-oriented numerics, for stochastic processes in molecular dynamics, and for random walks on complex networks. Most prominent algorithms are based on spectral apporaches and identify metastable sets via the doimant eigenvalues of the transfer operator associated with the dynamical system under consideration. These algorithms require the dominant eigenvalues to be real-valued. However, for many types of dynamics, e.g. for non-reversible Markov chains, this condition is not met. In this paper we utilize the hitting time apporach to metastable sets and demonstrate how the wellknown statements about optimal metastable decompositions of reversible chains can be reformulated for non-reversible chains if one switches from a spectral approach to an exit time approach. The performance of the resulting algorithm is illustrated by numerical experiments on random walks on complex networks.}, language = {en} } @article{SchuetteNielsenWeber, author = {Sch{\"u}tte, Christof and Nielsen, Adam and Weber, Marcus}, title = {Markov State Models and Molecular Alchemy}, series = {Molecular Physics}, volume = {113}, journal = {Molecular Physics}, number = {1}, doi = {10.1080/00268976.2014.944597}, pages = {69 -- 78}, abstract = {In recent years Markov State Models (MSMs) have attracted a consid- erable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g., for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under con- sideration. The performance of the reweighting scheme is illustrated for simple test cases including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.}, language = {en} } @article{AgarwalWangSchuetteetal., author = {Agarwal, Animesh and Wang, Han and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Chemical potential of liquids and mixtures via Adaptive Resolution Simulation}, series = {The Journal of Chemical Physics}, volume = {141}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.4886807}, pages = {034102}, language = {en} } @article{ZhangSchuette, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, series = {Entropy}, volume = {19}, journal = {Entropy}, number = {7}, doi = {10.3390/e19070367}, language = {en} } @article{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Objective priors in the empirical Bayes framework}, series = {Scandinavian Journal of Statistics}, volume = {48}, journal = {Scandinavian Journal of Statistics}, number = {4}, publisher = {Wiley Online Library}, doi = {10.1111/sjos.12485}, pages = {1212 -- 1233}, abstract = {When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies.}, language = {en} } @article{GulSchuetteBernhard, author = {Gul, Raheem and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries}, series = {Applied Mathematical Modelling}, journal = {Applied Mathematical Modelling}, doi = {10.1016/j.apm.2016.03.041}, language = {en} } @article{WinkelmannSchuette, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems}, series = {The Journal of Chemical Physics}, volume = {147}, journal = {The Journal of Chemical Physics}, number = {11}, doi = {10.1063/1.4986560}, pages = {114115-1 -- 114115-18}, abstract = {Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.}, language = {en} } @article{BennHiepenOsterlandetal., author = {Benn, Andreas and Hiepen, Christian and Osterland, Marc and Sch{\"u}tte, Christof and Zwijsen, An and Knaus, Petra}, title = {Role of bone morphogenetic proteins in sprouting angiogenesis: differential BMP receptor-dependent signaling pathways balance stalk vs. tip cell competence}, series = {FASEB Journal}, volume = {31}, journal = {FASEB Journal}, number = {11}, doi = {10.1096/fj.201700193RR}, pages = {4720 -- 4733}, abstract = {Before the onset of sprouting angiogenesis, the endothelium is prepatterned for the positioning of tip and stalk cells. Both cell identities are not static, as endothelial cells (ECs) constantly compete for the tip cell position in a dynamic fashion. Here, we show that both bone morphogenetic protein (BMP) 2 and BMP6 are proangiogenic in vitro and ex vivo and that the BMP type I receptors, activin receptor-like kinase (ALK)3 and ALK2, play crucial and distinct roles in this process. BMP2 activates the expression of tip cell-associated genes, such as DLL4 (delta-like ligand 4) and KDR (kinase insert domain receptor), and p38-heat shock protein 27 (HSP27)-dependent cell migration, thereby generating tip cell competence. Whereas BMP6 also triggers collective cell migration via the p38-HSP27 signaling axis, BMP6 induces in addition SMAD1/5 signaling, thereby promoting the expression of stalk cell-associated genes, such as HES1 (hairy and enhancer of split 1) and FLT1 (fms-like tyrosine kinase 1). Specifically, ALK3 is required for sprouting from HUVEC spheroids, whereas ALK2 represses sprout formation. We demonstrate that expression levels and respective complex formation of BMP type I receptors in ECs determine stalk vs. tip cell identity, thus contributing to endothelial plasticity during sprouting angiogenesis. As antiangiogenic monotherapies that target the VEGF or ALK1 pathways have not fulfilled efficacy objectives in clinical trials, the selective targeting of the ALK2/3 pathways may be an attractive new approach.}, language = {en} } @article{HuisingaBestCordesetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Cordes, Frank and Roitzsch, Rainer and Sch{\"u}tte, Christof}, title = {Identification of Molecular Conformations via Statistical Analysis of Simulation Data}, series = {Comp. Chem.}, volume = {20}, journal = {Comp. Chem.}, pages = {1760 -- 1774}, year = {1999}, language = {en} } @misc{SchuetteNielsenWeber, author = {Sch{\"u}tte, Christof and Nielsen, Adam and Weber, Marcus}, title = {Markov State Models and Molecular Alchemy}, issn = {1438-0064}, doi = {10.1080/00268976.2014.944597}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-46718}, abstract = {In recent years Markov State Models (MSMs) have attracted a consid- erable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g., for peptides including time-resolved spectroscopic ex- periments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multi- valent scenarios. In this article a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular proper- ties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under con- sideration. The performance of the reweighting scheme is illustrated for simple test cases including one where the main wells of the respective en- ergy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.}, language = {en} } @misc{SchuetteSarich, author = {Sch{\"u}tte, Christof and Sarich, Marco}, title = {A Critical Appraisal of Markov State Models}, issn = {1438-0064}, doi = {10.1140/epjst/e2015-02421-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54218}, abstract = {Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.}, language = {en} } @article{DjurdjevacConradWeberSchuette, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, series = {Multiscale Modeling and Simulation}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, language = {en} } @misc{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Prior estimation and Bayesian inference from large cohort data sets}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57475}, abstract = {One of the main goals of mathematical modelling in systems biology related to medical applications is to obtain patient-specific parameterisations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Using these population data, we propose an iterative algorithm for contructing an informative prior distribution, which then serves as the basis for computing patient-specific posteriors and obtaining individual predictions. We demonsrate the performance of our method by applying it to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.}, language = {en} } @misc{GuptaRoeblitzKrauseetal., author = {Gupta, Pooja and R{\"o}blitz, Susanna and Krause, Carola and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density}, series = {Computational Models in biology and medicine, 2013, Dresden, Germany}, journal = {Computational Models in biology and medicine, 2013, Dresden, Germany}, language = {en} } @inproceedings{GuptaKrauseRikeitetal., author = {Gupta, Pooja and Krause, Carola and Rikeit, Paul and R{\"o}blitz, Susanna and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density}, series = {10th International BMP conference, 2014, Berlin, Germany}, booktitle = {10th International BMP conference, 2014, Berlin, Germany}, language = {en} } @misc{KoltaiCiccottiSchuette, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On metastability and Markov state models for non-stationary molecular dynamics}, series = {The Journal of Chemical Physics}, volume = {174103}, journal = {The Journal of Chemical Physics}, edition = {145}, issn = {1438-0064}, doi = {10.1063/1.4966157}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57869}, abstract = {We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, "meta- stable" sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.}, language = {en} } @misc{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Empirical Bayes Methods for Prior Estimation in Systems Medicine}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61307}, abstract = {One of the main goals of mathematical modelling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Therefore, before applying Bayes' rule separately to the data of each patient (which is typically performed using a non-informative prior), it is meaningful to use empirical Bayes methods in order to construct an informative prior from all available data. We compare the performance of four priors - a non-informative prior and priors chosen by nonparametric maximum likelihood estimation (NPMLE), by maximum penalized lilelihood estimation (MPLE) and by doubly-smoothed maximum likelihood estimation (DS-MLE) - by applying them to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.}, language = {en} } @article{WinkelmannSchuette, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {The Spatiotemporal Master Equation: Approximation of Reaction-Diffusion Dynamics via Markov State Modeling}, series = {Journal of Chemical Physics}, volume = {145}, journal = {Journal of Chemical Physics}, number = {21}, doi = {10.1063/1.4971163}, abstract = {Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest.We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.}, language = {en} } @article{DuwalWinkelmannSchuetteetal., author = {Duwal, Sulav and Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV/1 in Resource-Poor Settings}, series = {PloS Computational Biology}, volume = {11}, journal = {PloS Computational Biology}, number = {4}, doi = {10.1371/journal.pcbi.1004200}, abstract = {An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention' may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention' for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that 'treatment-for-prevention' may be further improved using either of the two analyzed treatment paradigms.}, language = {en} } @misc{WinkelmannSchuette, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Hybrid Models for Chemical Reaction Networks: Multiscale Theory and Application to Gene Regulatory Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64264}, abstract = {Well-mixed stochastic chemical kinetics are properly modelled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows to express various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed.}, language = {en} } @misc{ZhangSchuette, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, issn = {1438-0064}, doi = {10.3390/e19070367}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63718}, abstract = {Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches.}, language = {en} } @article{KoltaiCiccottiSchuette, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On Markov state models for non-equilibrium molecular dynamics}, series = {The Journal of Chemical Physics}, volume = {145}, journal = {The Journal of Chemical Physics}, number = {174103}, doi = {10.1063/1.4966157}, language = {en} } @book{SchuetteSarich, author = {Sch{\"u}tte, Christof and Sarich, Marco}, title = {Metastability and Markov State Models in Molecular Dynamics: Modeling, Analysis, Algorithmic Approaches}, publisher = {American Mathematical Society}, language = {en} } @misc{BockmayrSiebertRoeblitzetal., author = {Bockmayr, Alexander and Siebert, Heike and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof and Deuflhard, Peter}, title = {Advanced mathematical modeling in systems biology}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutela, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {29 -- 44}, language = {en} } @misc{BanischSchuetteDjurdjevacConrad, author = {Banisch, Ralf and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Module Detection in Directed Real-World Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49849}, abstract = {We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network.}, language = {en} } @misc{SchuetteDeuflhardNoeetal., author = {Sch{\"u}tte, Christof and Deuflhard, Peter and No{\´e}, Frank and Weber, Marcus}, title = {Design of functional molecules}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {49 -- 65}, language = {en} } @misc{DeuflhardSchuette, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Life Sciences}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {1 -- 5}, language = {en} } @article{PaulusWeissSteinhilberetal., author = {Paulus, Florian and Weiss, Maximilian and Steinhilber, Dirk and Nikitin, Anatoly and Sch{\"u}tte, Christof and Haag, Rainer}, title = {Anionic Ring-Opening Polymerization Simulations for Hyperbranched Polyglycerols with Defined Molecular Weights}, series = {Macromolecules}, volume = {46}, journal = {Macromolecules}, number = {21}, doi = {10.1021/ma401712w}, pages = {8458 -- 8466}, language = {en} } @article{NikitinWulkowSchuette, author = {Nikitin, B. A. and Wulkow, Michael and Sch{\"u}tte, Christof}, title = {Modeling of Free Radical Styrene/Divinylbenzene Copolymerization with the Numerical Fractionation Technique}, series = {Macromolecular Theory and Simulation}, volume = {22}, journal = {Macromolecular Theory and Simulation}, number = {9}, doi = {10.1002/mats.201300125}, pages = {475 -- 489}, language = {en} } @article{EncisoSchuetteDelleSite, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {pH-dependent Response of Coiled Coils: A Coarse-Grained Molecular Simulation Study}, series = {Molecular Physics}, volume = {111}, journal = {Molecular Physics}, number = {22-23}, doi = {10.1080/00268976.2013.827254}, pages = {3363 -- 3371}, language = {en} } @article{WangSchuetteCiccottietal., author = {Wang, Han and Sch{\"u}tte, Christof and Ciccotti, Giovanni and Delle Site, Luigi}, title = {Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation}, series = {Journal of Chemical Theory and Computation}, volume = {10}, journal = {Journal of Chemical Theory and Computation}, number = {4}, doi = {10.1186/s12859-017-1565-4}, pages = {1376 -- 1386}, language = {en} } @misc{BittracherBanischSchuette, author = {Bittracher, Andreas and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Data-driven Computation of Molecular Reaction Coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66179}, abstract = {The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system.}, language = {en} } @article{BittracherKoltaiKlusetal., author = {Bittracher, Andreas and Koltai, P{\´e}ter and Klus, Stefan and Banisch, Ralf and Dellnitz, Michael and Sch{\"u}tte, Christof}, title = {Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics}, series = {Jounal of Nonlinear Science}, volume = {28}, journal = {Jounal of Nonlinear Science}, number = {2}, doi = {10.1007/s00332-017-9415-0}, pages = {471 -- 512}, abstract = {We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.}, language = {en} } @article{KoltaiWuNoeetal., author = {Koltai, Peter and Wu, Hao and No{\´e}, Frank and Sch{\"u}tte, Christof}, title = {Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics}, series = {Computation}, volume = {6}, journal = {Computation}, number = {1}, publisher = {MDPI}, address = {Basel, Switzerland}, doi = {10.3390/computation6010022}, pages = {22}, language = {en} } @article{DibakdelRazodeSanchoetal., author = {Dibak, Manuel and del Razo, Mauricio J. and de Sancho, David and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations}, series = {Journal of Chemical Physics}, volume = {148}, journal = {Journal of Chemical Physics}, number = {21}, doi = {10.1063/1.5020294}, abstract = {Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.}, language = {en} } @article{KlusSchuette, author = {Klus, Stefan and Sch{\"u}tte, Christof}, title = {Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator}, series = {Journal of Computational Dynamics}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {2}, doi = {10.3934/jcd.2016007}, pages = {139 -- 161}, abstract = {The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the system's behavior are the Perron-Frobenius operator and the Koopman operator. Due to the curse of dimensionality, computing the eigenfunctions of high-dimensional systems is in general infeasible. We will propose a tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional operators, namely Ulam's method and Extended Dynamic Mode Decomposition (EDMD). The aim of the tensor formulation is to approximate the eigenfunctions by low-rank tensors, potentially resulting in a significant reduction of the time and memory required to solve the resulting eigenvalue problems, provided that such a low-rank tensor decomposition exists. Typically, not all variables of a high-dimensional dynamical system contribute equally to the system's behavior, often the dynamics can be decomposed into slow and fast processes, which is also reflected in the eigenfunctions. Thus, the weak coupling between different variables might be approximated by low-rank tensor cores. We will illustrate the efficiency of the tensor-based formulation of Ulam's method and EDMD using simple stochastic differential equations.}, language = {en} } @article{KlusKoltaiSchuette, author = {Klus, Stefan and Koltai, Peter and Sch{\"u}tte, Christof}, title = {On the numerical approximation of the Perron-Frobenius and Koopman operator}, series = {Journal of Computational Dynamics}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2016003}, pages = {51 -- 77}, abstract = {Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review di� fferent methods that have been developed over the last decades to compute � infinite-dimensional approximations of these in� finite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and di� fferences between these approaches. The results will be illustrated using simple stochastic di� fferential equations and molecular dynamics examples.}, language = {en} } @article{RuedrichSarichSchuette, author = {R{\"u}drich, S. and Sarich, Marco and Sch{\"u}tte, Christof}, title = {Utilizing hitting times for finding metastable sets in non-reversible Markov chains}, series = {Journal of Comp. Dynamics}, journal = {Journal of Comp. Dynamics}, language = {en} } @article{GuptaGramatkeEinspanieretal.2017, author = {Gupta, Pooja and Gramatke, Annika and Einspanier, Ralf and Sch{\"u}tte, Christof and von Kleist, Max and Sharbati, Jutta}, title = {In silico cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, series = {Toxicology in Vitro}, volume = {41}, journal = {Toxicology in Vitro}, issn = {1438-0064}, pages = {179 -- 188}, year = {2017}, abstract = {Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence's real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50\% inhibitory concentration IC50 on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC50 values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA's in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master.}, language = {en} } @article{vonKleistSchuetteZhang, author = {von Kleist, Max and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Statistical analysis of the first passage path ensemble of jump processes}, series = {Journal of Statistical Physics}, volume = {170}, journal = {Journal of Statistical Physics}, doi = {10.1007/s10955-017-1949-x}, pages = {809 -- 843}, abstract = {The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.}, language = {en} } @article{HuttaryGoubergritsSchuetteetal., author = {Huttary, Rudolf and Goubergrits, Leonid and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Simulation, Identification and Statistical Variation in Cardiovascular Analysis (SISCA) - a Software Framework for Multi-compartment Lumped Modeling}, series = {Computers in Biology and Medicine}, volume = {87}, journal = {Computers in Biology and Medicine}, doi = {10.1016/j.compbiomed.2017.05.021}, pages = {104 -- 123}, language = {en} } @misc{GuptaGramatkeEinspanieretal., author = {Gupta, Pooja and Gramatke, Annika and Einspanier, Ralf and Sch{\"u}tte, Christof and von Kleist, Max and Sharbati, Jutta}, title = {In silicio cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62666}, abstract = {Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence's real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50\% inhibitory concentration IC_{50} on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC_{50} values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA's in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master.}, language = {en} } @article{KlusNueskeKoltaietal., author = {Klus, Stefan and N{\"u}ske, Feliks and Koltai, Peter and Wu, Hao and Kevrekidis, Ioannis and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Data-driven model reduction and transfer operator approximation}, series = {Journal of Nonlinear Science}, volume = {28}, journal = {Journal of Nonlinear Science}, number = {3}, doi = {10.1007/s00332-017-9437-7}, pages = {985 -- 1010}, language = {en} } @article{SchuetteWulkow2010, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {A hybrid Galerkin-Monte-Carlo approach to higher-dimensional population balances in polymerization kinetics}, series = {Macromol. React. Eng.}, volume = {4}, journal = {Macromol. React. Eng.}, pages = {562 -- 577}, year = {2010}, language = {en} } @misc{WinkelmannSchuettevonKleist, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1}, issn = {1438-0064}, doi = {10.4310/CMS.2014.v12.n5.a4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41955}, abstract = {Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are used for modelling situations in which the evolution of a process is partly random and partly controllable. These MDP theories allow for computing the optimal control policy for processes that can continuously or frequently be observed, even if only partially. However, they cannot be applied if state observation is very costly and therefore rare (in time). We present a novel MDP theory for rare, costly observations and derive the corresponding Bellman equation. In the new theory, state information can be derived for a particular cost after certain, rather long time intervals. The resulting information costs enter into the total cost and thus into the optimization criterion. This approach applies to many real world problems, particularly in the medical context, where the medical condition is examined rather rarely because examination costs are high. At the same time, the approach allows for efficient numerical realization. We demonstrate the usefulness of the novel theory by determining, from the national economic perspective, optimal therapeutic policies for the treatment of the human immunodefficiency virus (HIV) in resource-rich and resource-poor settings. Based on the developed theory and models, we discover that available drugs may not be utilized efficiently in resource-poor settings due to exorbitant diagnostic costs.}, language = {en} } @misc{OsterlandBennProhaskaetal., author = {Osterland, Marc and Benn, Andreas and Prohaska, Steffen and Sch{\"u}tte, Christof}, title = {Single Cell Tracking in Phase-Contrast Microscopy}, series = {EMBL Symposium 2015 - Seeing is Believing - Imaging the Processes of Life}, journal = {EMBL Symposium 2015 - Seeing is Believing - Imaging the Processes of Life}, abstract = {In this work, we developed an automatic algorithm to analyze cell migration in chemotaxis assays, based on phase-contrast time-lapse microscopy. While manual approaches are still widely used in recent publications, our algorithm is able to track hundreds of single cells per frame. The extracted paths are analysed with traditional geometrical approaches as well as diffusion-driven Markov state models (MSM). Based on these models, a detailed view on spatial and temporal effects is possible. Using our new approach on experimental data, we are able to distinguish between directed migration (e.g. towards a VEGF gradient) and random migration without favored direction. A calculation of the committor probabilities reveals that cells of the whole image area are more likely to migrate directly towards the VEGF than away from it during the first four hours. However, in absence of a chemoattractant, cells migrate more likely to their nearest image border. These conclusions are supported by the spatial mean directions. In a next step, the cell-cell interaction during migration and the migration of cell clusters will be analyzed. Furthermore, we want to observe phenotypical changes during migration based on fluorescence microscopy and machine learning. The algorithm is part of a collaborative platform which brings the experimental expertise of scientists from life sciences and the analytical knowledge of computer scientists together. This platform is built using web-based technologies with a responsive real-time user interface. All data, including raw and metadata as well as the accompanying results, will be stored in a secure and scalable compute cluster. The compute cluster provides sufficient space and computational power for modern image-based experiments and their analyses. Specific versions of data and results can be tagged to keep immutable records for archival.}, language = {en} } @article{KryvenRoeblitzSchuette, author = {Kryven, Ivan and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof}, title = {Solution of the chemical master equation by radial basis functions approximation with interface tracking}, series = {BMC Systems Biology}, volume = {9}, journal = {BMC Systems Biology}, number = {67}, doi = {10.1186/s12918-015-0210-y}, pages = {1 -- 12}, abstract = {Background. The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level. Results. We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time integration, the algorithm keeps track of the subset of states with significant probabilities (essential support). Secondly, the probability distribution that solves the equation is parametrised with a small number of coefficients using collocation on Gaussian radial basis functions. The system of basis functions is chosen in such a way that the solution is approximated only on the essential support instead of the whole state space. Discussion. In order to demonstrate the effectiveness of the method, we consider four application examples: a) the self-regulating gene model, b) the 2-dimensional bistable toggle switch, c) a generalisation of the bistable switch to a 3-dimensional tristable problem, and d) a 3-dimensional cell differentiation model that, depending on parameter values, may operate in bistable or tristable modes. In all multidimensional examples the manifold containing the system states with significant probabilities undergoes drastic transformations over time. This fact makes the examples especially challenging for numerical methods. Conclusions. The proposed method is a new numerical approach permitting to approximately solve a wide range of problems that have been hard to tackle until now. A full representation of multi-dimensional distributions is recovered. The method is especially attractive when dealing with models that yield solutions of a complex structure, for instance, featuring multi-stability. Electronic version: http://www.biomedcentral.com/1752-0509/9/67}, language = {en} } @article{SchuetteSarich, author = {Sch{\"u}tte, Christof and Sarich, Marco}, title = {A Critical Appraisal of Markov State Models}, series = {The European Physical Journal Special Topics}, volume = {224}, journal = {The European Physical Journal Special Topics}, number = {12}, doi = {10.1140/epjst/e2015-02421-0}, pages = {2445 -- 2462}, abstract = {Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.}, language = {en} } @misc{WillenbockelSchuette, author = {Willenbockel, Christian Tobias and Sch{\"u}tte, Christof}, title = {Variational Bayesian Inference and Model Selection for the Stochastic Block Model with Irrelevant Vertices}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57003}, abstract = {Real World networks often exhibit a significant number of vertices which are sparsely and irregularly connected to other vertices in the network. For clustering theses networks with a model based algorithm, we propose the Stochastic Block Model with Irrelevant Vertices (SBMIV) for weighted net- works. We propose an original Variational Bayesian Expectation Maximiza- tion inference algorithm for the SBMIV which is an advanced version of our Blockloading algorithm for the Stochastic Block Model. We introduce a model selection criterion for the number of clusters of the SBMIV which is based on the lower variational bound of the model likelihood. We propose a fully Bayesian inference process, based on plausible informative priors, which is independent of other algorithms for preprocessing start values for the cluster assignment of vertices. Our inference methods allow for a multi level identification of irrelevant vertices which are hard to cluster reliably ac- cording to the SBM. We demonstrate that our methods improve on the normal Stochastic Block model by applying it to to Earthquake Networks which are an example of networks with a large number of sparsely and irregularly con- nected vertices.}, language = {en} } @misc{DjurdjevacConradWeberSchuette, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, issn = {1438-0064}, doi = {10.1137/15M1032272}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55739}, abstract = {Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.}, language = {en} } @misc{EncisoSchuetteDelleSite, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Influence of pH and sequence in peptide aggregation via molecular simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55805}, abstract = {We employ a recently developed coarse-grained model for peptides and proteins where the effect of pH is automatically included. We explore the effect of pH in the aggregation process of the amyloidogenic peptide KTVIIE and two related sequences, using three different pH environments. Simulations using large systems (24 peptides chains per box) allow us to correctly account for the formation of realistic peptide aggregates. We evaluate the thermodynamic and kinetic implications of changes in sequence and pH upon peptide aggregation, and we discuss how a minimalistic coarse- grained model can account for these details.}, language = {en} } @article{EncisoSchuetteDelleSite, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Influence of pH and sequence in peptide aggregation via molecular simulation}, series = {Journal of Chemical Physics}, volume = {143}, journal = {Journal of Chemical Physics}, number = {24}, doi = {https://doi.org/10.1063/1.4935707}, language = {en} } @misc{HorenkoSchmidtEhrenbergSchuette2006, author = {Horenko, Illia and Schmidt-Ehrenberg, Johannes and Sch{\"u}tte, Christof}, title = {Set-oriented dimension reduction: Localizing principal component analysis via hidden Markov models}, series = {Computational Life Sciences II}, volume = {4216}, journal = {Computational Life Sciences II}, publisher = {Springer}, pages = {98 -- 115}, year = {2006}, language = {en} } @misc{SarichSchuette, author = {Sarich, Marco and Sch{\"u}tte, Christof}, title = {Markov Model Theory}, series = {An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation}, volume = {797}, journal = {An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation}, editor = {Bowman, Gregory R. and Pande, Vijay S. and No{\´e}, Frank}, publisher = {Springer}, doi = {10.1007/978-94-007-7606-7}, pages = {23 -- 44}, abstract = {This section reviews the relation between the continuous dynamics of a molecular system in thermal equilibrium and the kinetics given by a Markov State Model (MSM). We will introduce the dynamical propagator, an error-less, alternative description of the continuous dynamics, and show how MSMs result from its discretization. This allows for an precise understanding of the approximation quality of MSMs in comparison to the continuous dynamics. The results on the approximation quality are key for the design of good MSMs. While this section is important for understanding the theory of discretization and related systematic errors, practitioners wishing only to learn how to construct MSMs may skip directly to the discussion of Markov model estimation.}, language = {en} } @article{EncisoSchuetteDelleSite, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {A pH-dependent coarse-grained model for peptides}, series = {Soft Matter}, volume = {9}, journal = {Soft Matter}, number = {26}, doi = {10.1039/C3SM27893J}, pages = {6118 -- 6127}, abstract = {We propose the first, to our knowledge, coarse-grained modeling strategy for peptides where the effect of changes of the pH can be efficiently described. The idea is based on modeling the effects of the pH value on the main driving interactions. We use reference data from atomistic simulations and experimental databases and transfer their main physical features to the coarse-grained resolution according to the principle of "consistency across the scales". The coarse-grained model is refined by finding a set of parameters that, when applied to peptides with different sequences and experimental properties, reproduces the experimental and atomistic data of reference. We use such a parameterized model for performing several numerical tests to check its transferability to other systems and to prove the universality of the related modeling strategy. We have tried systems with rather different responses to pH variations, showing a highly satisfactory performance of the model.}, language = {en} } @article{WinkelmannSchuettevonKleist, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation: Sensitivity Analysis with Respect to Optimal Treatment Strategies against HIV-1}, series = {International Journal of Biomathematics and Biostatistics}, volume = {2}, journal = {International Journal of Biomathematics and Biostatistics}, number = {1}, abstract = {We present the theory of "Markov decision processes (MDP) with rare state observation" and apply it to optimal treatment scheduling and diagnostic testing to mitigate HIV-1 drug resistance development in resource-poor countries. The developed theory assumes that the state of the process is hidden and can only be determined by making an examination. Each examination produces costs which enter into the considered cost functional so that the resulting optimization problem includes finding optimal examination times. This is a realistic ansatz: In many real world applications, like HIV-1 treatment scheduling, the information about the disease evolution involves substantial costs, such that examination and control are intimately connected. However, a perfect compliance with the optimal strategy can rarely be achieved. This may be particularly true for HIV-1 resistance testing in resource-constrained countries. In the present work, we therefore analyze the sensitivity of the costs with respect to deviations from the optimal examination times both analytically and for the considered application. We discover continuity in the cost-functional with respect to the examination times. For the HIV-application, moreover, sensitivity towards small deviations from the optimal examination rule depends on the disease state. Furthermore, we compare the optimal rare-control strategy to (i) constant control strategies (one action for the remaining time) and to (ii) the permanent control of the original, fully observed MDP. This comparison is done in terms of expected costs and in terms of life-prolongation. The proposed rare-control strategy offers a clear benefit over a constant control, stressing the usefulness of medical testing and informed decision making. This indicates that lower-priced medical tests could improve HIV treatment in resource-constrained settings and warrants further investigation.}, language = {en} } @article{WangSchuetteCiccottietal., author = {Wang, Han and Sch{\"u}tte, Christof and Ciccotti, Giovanni and von Kleist, Max}, title = {Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation}, series = {Journal of Chemical Theory and Computation}, volume = {10}, journal = {Journal of Chemical Theory and Computation}, number = {4}, doi = {10.1021/ct400993e}, pages = {1376 -- 1386}, abstract = {In this paper, we investigate the conformational dynamics of alanine dipeptide under an external electric field by nonequilibrium molecular dynamics simulation. We consider the case of a constant and of an oscillatory field. In this context, we propose a procedure to implement the temperature control, which removes the irrelevant thermal effects of the field. For the constant field different time-scales are identified in the conformational, dipole moment, and orientational dynamics. Moreover, we prove that the solvent structure only marginally changes when the external field is switched on. In the case of oscillatory field, the conformational changes are shown to be as strong as in the previous case, and nontrivial nonequilibrium circular paths in the conformation space are revealed by calculating the integrated net probability fluxes.}, language = {en} } @article{WinkelmannSchuettevonKleist, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1}, series = {Communications in Mathematical Sciences}, volume = {12}, journal = {Communications in Mathematical Sciences}, number = {5}, doi = {10.4310/CMS.2014.v12.n5.a4}, pages = {859 -- 877}, abstract = {Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are used for modelling situations in which the evolution of a process is partly random and partly controllable. These MDP theories allow for computing the optimal control policy for processes that can continuously or frequently be observed, even if only partially. However, they cannot be applied if state observation is very costly and therefore rare (in time). We present a novel MDP theory for rare, costly observations and derive the corresponding Bellman equation. In the new theory, state information can be derived for a particular cost after certain, rather long time intervals. The resulting information costs enter into the total cost and thus into the optimization criterion. This approach applies to many real world problems, particularly in the medical context, where the medical condition is examined rather rarely because examination costs are high. At the same time, the approach allows for efficient numerical realization. We demonstrate the usefulness of the novel theory by determining, from the national economic perspective, optimal therapeutic policies for the treatment of the human immunodeficiency virus (HIV) in resource-rich and resource-poor settings. Based on the developed theory and models, we discover that available drugs may not be utilized efficiently in resource-poor settings due to exorbitant diagnostic costs.}, language = {en} } @misc{WillenbockelSchuette, author = {Willenbockel, Christian Tobias and Sch{\"u}tte, Christof}, title = {A Variational Bayesian Algorithm for Clustering of Large and Complex Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54588}, abstract = {We propose the Blockloading algorithm for the clustering of large and complex graphs with tens of thousands of vertices according to a Stochastic Block Model (SBM). Blockloading is based on generalized Variational Bayesian EM (VBEM) schemes and works for weighted and unweighted graphs. Existing Variational (Bayesian) EM methods have to consider each possible number of clusters sepa- rately to determine the optimal number of clusters and are prone to converge to local optima making multiple restarts necessary. These factors impose a severe restriction on the size and complexity of graphs these methods can handle. In con- trast, the Blockloading algorithm restricts restarts to subnetworks in a way that provides error correction of an existing cluster assignment. The number of clusters need not be specified in advance because Blockloading will return it as a result. We show that Blockloading outperforms all other variational methods regarding reliability of the results and computational efficiency.}, language = {en} } @misc{GulSchuetteBernhard, author = {Gul, Raheem and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54339}, abstract = {Cardiovascular diseases are one of the major problems in medicine today and the number of patients increases worldwide. To find the most efficient treatment, prior knowledge about function and dysfunction of the cardiovas- cular system is required and methods need to be developed that identify the disease in an early stage. Mathematical modeling is a powerful tool for prediction and investigation of cardiovascular diseases. It has been shown that the Windkessel model, being based on an analogy between electrical circuits and fluid flow, is a simple but effective method to model the human cardiovascular system. In this paper, we have applied parametric local sensitivity analysis (LSA) to a linear elastic model of the arm arteries, to find and rank sensitive param- eters that may be helpful in clinical diagnosis. A computational model for end-to-side anastomosis (superior ulnar collateral anastomosis with posterior ulnar recurrent, SUC-PUR) is carried out to study the effects of some clinically relevant haemodynamic parameters like blood flow resistance and terminal re- sistance on pressure and flow at different locations of the arm artery. In this context, we also discuss the spatio-temporal dependency of local sensitivities. The sensitivities with respect to cardiovascular parameters reveal the flow resistance and diameter of the vessels as most sensitive parameters. These parameters play a key role in diagnosis of severe stenosis and aneurysms. In contrast, wall thickness and elastic modulus are found to be less sensitive.}, language = {en} } @article{BanischDjurdjevacConradSchuette, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof}, title = {Reactive flows and unproductive cycles for random walks on complex networks}, series = {The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387}, journal = {The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387}, doi = {10.1140/epjst/e2015-02417-8}, language = {en} } @article{KostreSchuetteNoeetal.2021, author = {Kostre, Margarita and Sch{\"u}tte, Christof and No{\´e}, Frank and del Razo Sarmina, Mauricio}, title = {Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs}, series = {Multiscale Modeling \& Simulation}, volume = {19}, journal = {Multiscale Modeling \& Simulation}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/20M1352739}, pages = {1659 -- 1683}, year = {2021}, abstract = {Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications.}, language = {en} } @article{BeckerDjurdjevacConradEseretal., author = {Becker, Fabian and Djurdjevac Conrad, Natasa and Eser, Raphael A. and Helfmann, Luzie and Sch{\"u}tt, Brigitta and Sch{\"u}tte, Christof and Zonker, Johannes}, title = {The Furnace and the Goat—A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century CE}, series = {PLOS ONE}, volume = {15}, journal = {PLOS ONE}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0241133}, pages = {1 -- 37}, language = {en} } @article{SchulzYamamotoKlosseketal., author = {Schulz, Robert and Yamamoto, Kenji and Klossek, Andr{\´e} and Rancan, Fiorenza and Vogt, Annika and Sch{\"u}tte, Christof and R{\"u}hl, Eckart and Netz, Roland R.}, title = {Modeling of Drug Diffusion Based on Concentration Profiles in Healthy and Damaged Human Skin}, series = {Biophysical Journal}, volume = {117}, journal = {Biophysical Journal}, number = {5}, doi = {10.1016/j.bpj.2019.07.027}, pages = {998 -- 1008}, abstract = {Based on experimental drug concentration profiles in healthy as well as tape-stripped ex vivo human skin, we model the penetration of the antiinflammatory drug dexamethasone into the skin layers by the one-dimensional generalized diffusion equation. We estimate the position-dependent free-energy and diffusivity profiles by solving the conjugated minimization problem, in which the only inputs are concentration profiles of dexamethasone in skin at three consecutive penetration times. The resulting free-energy profiles for damaged and healthy skin show only minor differences. In contrast, the drug diffusivity in the first 10 μm of the upper skin layer of damaged skin is 200-fold increased compared to healthy skin, which reflects the corrupted barrier function of tape-stripped skin. For the case of healthy skin, we examine the robustness of our method by analyzing the behavior of the extracted skin parameters when the number of input and output parameters are reduced. We also discuss techniques for the regularization of our parameter extraction method.}, language = {en} } @article{delRazoDibakSchuetteetal., author = {del Razo, Mauricio J. and Dibak, Manuel and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics}, series = {The Journal of Chemical Physics}, volume = {155}, journal = {The Journal of Chemical Physics}, number = {12}, doi = {10.1063/5.0060314}, language = {en} } @article{SikorskiWeberSchuette, author = {Sikorski, Alexander and Weber, Marcus and Sch{\"u}tte, Christof}, title = {The Augmented Jump Chain}, series = {Advanced Theory and Simulations}, volume = {4}, journal = {Advanced Theory and Simulations}, number = {4}, publisher = {Wiley-VCH}, doi = {10.1002/adts.202000274}, abstract = {Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated.}, language = {en} } @article{DibakJdelRazoDeSanchoetal., author = {Dibak, Manuel and J. del Razo, Mauricio and De Sancho, David and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations}, series = {Journal of Chemical Physics}, volume = {148}, journal = {Journal of Chemical Physics}, number = {214107}, doi = {10.1063/1.5020294}, abstract = {Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B <--> C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.}, language = {en} } @article{DjurdjevacConradHelfmannZonkeretal., author = {Djurdjevac Conrad, Natasa and Helfmann, Luzie and Zonker, Johannes and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach}, series = {EPJ Data Science}, volume = {7}, journal = {EPJ Data Science}, number = {1}, edition = {EPJ Data Science}, publisher = {EPJ Data Science}, doi = {10.1140/epjds/s13688-018-0153-9}, pages = {24}, abstract = {Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.}, language = {en} } @article{HelfmannDjurdjevacConradDjurdjevacetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Djurdjevac, Ana and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {From interacting agents to density-based modeling with stochastic PDEs}, series = {Communications in Applied Mathematics and Computational Science}, volume = {16}, journal = {Communications in Applied Mathematics and Computational Science}, number = {1}, doi = {10.2140/camcos.2021.16.1}, pages = {1 -- 32}, abstract = {Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.}, language = {en} } @misc{HelfmannDjurdjevacConradDjurdjevacetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Djurdjevac, Ana and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {From interacting agents to density-based modeling with stochastic PDEs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73456}, abstract = {Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.}, language = {en} } @misc{CiccottiFerrarioSchuette, author = {Ciccotti, Giovanni and Ferrario, Mauro and Sch{\"u}tte, Christof}, title = {Molecular Dynamics vs. Stochastic Processes: Are We Heading Anywhere?}, series = {Special Issue: Understanding Molecular Dynamics via Stochastic Processes, Entropy}, volume = {20}, journal = {Special Issue: Understanding Molecular Dynamics via Stochastic Processes, Entropy}, number = {5}, doi = {10.3390/e20050348}, language = {en} } @article{KlusBittracherSchusteretal., author = {Klus, Stefan and Bittracher, Andreas and Schuster, Ingmar and Sch{\"u}tte, Christof}, title = {A kernel-based approach to molecular conformation analysis}, series = {Journal of Chemical Physics}, volume = {149}, journal = {Journal of Chemical Physics}, number = {24}, doi = {10.1063/1.5063533}, abstract = {We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecular dynamics simulation data. We show that many of the prominent methods like Markov State Models, EDMD, and TICA can be regarded as special cases of this approach and that new efficient algorithms can be constructed based on this derivation. The results of these new powerful methods will be illustrated with several examples, in particular the alanine dipeptide and the protein NTL9.}, language = {en} } @article{GuptaPeterJungetal., author = {Gupta, Pooja and Peter, Sarah and Jung, Markus and Lewin, Astrid and Hemmrich-Stanisak, Georg and Franke, Andre and von Kleist, Max and Sch{\"u}tte, Christof and Einspanier, Ralf and Sharbati, Soroush and zur Bruegge, Jennifer}, title = {Analysis of long non-coding RNA and mRNA expression in bovine macrophages brings up novel 2 aspects of Mycobacterium avium subspecies paratuberculosis infections}, series = {Scientific Reports in Nature}, volume = {9}, journal = {Scientific Reports in Nature}, doi = {10.1038/s41598-018-38141-x}, abstract = {Paratuberculosis is a major disease in cattle that severely affects animal welfare and causes huge economic losses worldwide. Development of alternative diagnostic methods is of urgent need to control the disease. Recent studies suggest that long non-coding RNAs (lncRNAs) play a crucial role in regulating immune function and may confer valuable information about the disease. However, their role has not yet been investigated in cattle with respect to infection towards Paratuberculosis. Therefore, we investigated the alteration in genomic expression profiles of mRNA and lncRNA in bovine macrophages in response to Paratuberculosis infection using RNA-Seq. We identified 397 potentially novel lncRNA candidates in macrophages of which 38 were differentially regulated by the infection. A total of 820 coding genes were also significantly altered by the infection. Co-expression analysis of lncRNAs and their neighbouring coding genes suggest regulatory functions of lncRNAs in pathways related to immune response. For example, this included protein coding genes such as TNIP3, TNFAIP3 and NF-κB2 that play a role in NF-κB2 signalling, a pathway associated with immune response. This study advances our understanding of lncRNA roles during Paratuberculosis infection.}, language = {en} } @article{KoltaiSchuette, author = {Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {A multiscale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics}, series = {SIAM J. Multiscale Model. Simul.}, volume = {16}, journal = {SIAM J. Multiscale Model. Simul.}, number = {4}, publisher = {SIAM}, doi = {10.1137/17M1146403}, pages = {1455 -- 1485}, abstract = {We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.}, language = {en} } @article{BittracherKlusHamzietal., author = {Bittracher, Andreas and Klus, Stefan and Hamzi, Boumediene and Sch{\"u}tte, Christof}, title = {Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds}, series = {Journal of Nonlinear Science}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09668-z}, abstract = {We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.}, language = {en} } @article{MoellerIsbilirSungkawornetal., author = {M{\"o}ller, Jan and Isbilir, Ali and Sungkaworn, Titiwat and Osberg, Brenda and Karathanasis, Christos and Sunkara, Vikram and Grushevsky, Eugene O and Bock, Andreas and Annibale, Paolo and Heilemann, Mike and Sch{\"u}tte, Christof and Lohse, Martin J.}, title = {Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision}, series = {Nature Chemical Biology}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, language = {en} } @misc{MollenhauerSchusterKlusetal., author = {Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces}, series = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, volume = {304}, journal = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, K.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_5}, pages = {109 -- 131}, language = {en} } @misc{BittracherSchuette, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A weak characterization of slow variables in stochastic dynamical systems}, series = {Advances in Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday}, volume = {304}, journal = {Advances in Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, E.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_6}, pages = {132 -- 150}, language = {en} } @article{BittracherMoschnerKokschetal., author = {Bittracher, Andreas and Moschner, Johann and Koksch, Beate and Netz, Roland and Sch{\"u}tte, Christof}, title = {Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis}, series = {The European Physical Journal B}, volume = {94}, journal = {The European Physical Journal B}, doi = {10.1140/epjb/s10051-021-00200-0}, language = {en} } @article{BittracherSchuette, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, series = {Physica D: Nonlinear Phenomena}, volume = {416}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2020.132799}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75874}, language = {en} } @article{MollenhauerKlusSchuetteetal., author = {Mollenhauer, Mattes and Klus, Stefan and Sch{\"u}tte, Christof and Koltai, P{\´e}ter}, title = {Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence}, series = {Journal of Machine Learning Research}, volume = {23}, journal = {Journal of Machine Learning Research}, number = {327}, pages = {1 -- 34}, abstract = {We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.}, language = {en} } @book{WinkelmannSchuette, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Stochastic Dynamics in Computational Biology}, series = {Frontiers in Applied Dynamical Systems: Reviews and Tutorials}, volume = {8}, journal = {Frontiers in Applied Dynamical Systems: Reviews and Tutorials}, publisher = {Springer International Publishing}, isbn = {978-3-030-62386-9}, doi = {10.1007/978-3-030-62387-6}, language = {en} } @misc{BittracherSchuette, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78688}, abstract = {Model reduction of large Markov chains is an essential step in a wide array of techniques for understanding complex systems and for efficiently learning structures from high-dimensional data. We present a novel aggregation algorithm for compressing such chains that exploits a specific low-rank structure in the transition matrix which, e.g., is present in metastable systems, among others. It enables the recovery of the aggregates from a vastly undersampled transition matrix which in practical applications may gain a speedup of several orders of mag- nitude over methods that require the full transition matrix. Moreover, we show that the new technique is robust under perturbation of the transition matrix. The practical applicability of the new method is demonstrated by identifying a reduced model for the large-scale traffic flow patterns from real-world taxi trip data.}, language = {en} } @article{ZhangLiSchuette2021, author = {Zhang, Wei and Li, Tiejun and Sch{\"u}tte, Christof}, title = {Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks}, series = {Journal of Computational Physics}, volume = {465}, journal = {Journal of Computational Physics}, doi = {10.1016/j.jcp.2022.111377}, year = {2021}, abstract = {In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.}, language = {en} } @misc{WinkelmannSchuette, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60999}, abstract = {Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.}, language = {en} } @article{WinkelmannZonkerSchuetteetal., author = {Winkelmann, Stefanie and Zonker, Johannes and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading}, series = {Mathematical Biosciences}, volume = {336}, journal = {Mathematical Biosciences}, publisher = {Elsevier}, doi = {10.1016/j.mbs.2021.108619}, abstract = {Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.}, language = {en} } @misc{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Empirical Bayes Methods, Reference Priors, Cross Entropy and the EM Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61230}, abstract = {When estimating a probability density within the empirical Bayes framework, the non-parametric maximum likelihood estimate (NPMLE) usually tends to overfit the data. This issue is usually taken care of by regularization - a penalization term is subtracted from the marginal log-likelihood before the maximization step, so that the estimate favors smooth solutions, resulting in the so-called maximum penalized likelihood estimation (MPLE). The majority of penalizations currently in use are rather arbitrary brute-force solutions, which lack invariance under transformation of the parameters(reparametrization) and measurements. This contradicts the principle that, if the underlying model has several equivalent formulations, the methods of inductive inference should lead to consistent results. Motivated by this principle and using an information-theoretic point of view, we suggest an entropy-based penalization term that guarantees this kind of invariance. The resulting density estimate can be seen as a generalization of reference priors. Using the reference prior as a hyperprior, on the other hand, is argued to be a poor choice for regularization. We also present an insightful connection between the NPMLE, the cross entropy and the principle of minimum discrimination information suggesting another method of inference that contains the doubly-smoothed maximum likelihood estimation as a special case.}, language = {en} } @article{StraubeWinkelmannSchuetteetal., author = {Straube, Arthur and Winkelmann, Stefanie and Sch{\"u}tte, Christof and H{\"o}fling, Felix}, title = {Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles}, series = {J. Phys. Chem. Lett.}, volume = {12}, journal = {J. Phys. Chem. Lett.}, doi = {10.1021/acs.jpclett.1c03016}, pages = {9888 -- 9893}, abstract = {The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.}, language = {en} } @misc{SchuetteKlusHartmann, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88637}, abstract = {One of the main challenges in molecular dynamics is overcoming the "timescale barrier", a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics, and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behavior on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory as well as the algorithmic development from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in MD. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.}, language = {en} } @article{BoltzSirbuStelzeretal., author = {Boltz, Horst-Holger and Sirbu, Alexei and Stelzer, Nina and Lohse, Martin J. and Sch{\"u}tte, Christof and Annibale, Paolo}, title = {Quantitative spectroscopy of single molecule interaction times}, series = {Optic Letters}, volume = {46}, journal = {Optic Letters}, number = {7}, doi = {10.1364/OL.413030}, pages = {1538 -- 1541}, abstract = {Single molecule fluorescence tracking provides information at nanometer-scale and millisecond-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address this aspect by developing a theoretical foundation for a spectroscopy of interaction times, i.e., the inference of interaction from imaging data. A non-trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted, together with the dependence of the exponential term upon the microscopic reaction affinity. Our approach is validated with simulated and experimental datasets.}, language = {en} } @article{BittracherMollenhauerKoltaietal., author = {Bittracher, Andreas and Mollenhauer, Mattes and Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {Optimal Reaction Coordinates: Variational Characterization and Sparse Computation}, series = {Multiscale Modelling \& Simulation}, volume = {21}, journal = {Multiscale Modelling \& Simulation}, number = {2}, doi = {10.1137/21M1448367}, pages = {449 -- 488}, abstract = {Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.}, language = {en} } @article{CardereraPokuttaSchuetteetal., author = {Carderera, Alejandro and Pokutta, Sebastian and Sch{\"u}tte, Christof and Weiser, Martin}, title = {CINDy: Conditional gradient-based Identification of Non-linear Dynamics - Noise-robust recovery}, series = {Journal of Computational and Applied Mathematics}, journal = {Journal of Computational and Applied Mathematics}, abstract = {Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.}, language = {en} } @article{WulkowKoltaiSunkaraetal., author = {Wulkow, Niklas and Koltai, P{\´e}ter and Sunkara, Vikram and Sch{\"u}tte, Christof}, title = {Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory}, series = {J. Stat. Phys.}, journal = {J. Stat. Phys.}, abstract = {We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples.}, language = {en} } @article{WulkowKoltaiSchuette, author = {Wulkow, Niklas and Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading}, series = {Journal of Nonlinear Science}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09673-2}, abstract = {We investigate opinion dynamics based on an agent-based model and are interested in predicting the evolution of the percentages of the entire agent population that share an opinion. Since these opinion percentages can be seen as an aggregated observation of the full system state, the individual opinions of each agent, we view this in the framework of the Mori-Zwanzig projection formalism. More specifically, we show how to estimate a nonlinear autoregressive model (NAR) with memory from data given by a time series of opinion percentages, and discuss its prediction capacities for various specific topologies of the agent interaction network. We demonstrate that the inclusion of memory terms significantly improves the prediction quality on examples with different network topologies.}, language = {en} } @article{ErnstSchuetteSigristetal., author = {Ernst, Ariane and Sch{\"u}tte, Christof and Sigrist, Stephan and Winkelmann, Stefanie}, title = {Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics}, series = {Mathematical Biosciences}, volume = {343}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2021.108760}, abstract = {Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.}, language = {en} } @misc{ErnstSchuetteSigristetal., author = {Ernst, Ariane and Sch{\"u}tte, Christof and Sigrist, Stephan and Winkelmann, Stefanie}, title = {Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics}, issn = {1438-0064}, doi = {10.1016/j.mbs.2021.108760}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82674}, abstract = {Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.}, language = {en} } @article{WeberFackeldeySchuette, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-Free Markov State Model Building}, series = {Journal of Chemical Physics}, volume = {146}, journal = {Journal of Chemical Physics}, number = {12}, doi = {10.1063/1.4978501}, language = {en} } @article{delRazoFroembergStraubeetal., author = {del Razo, Mauricio and Fr{\"o}mberg, Daniela and Straube, Arthur and Sch{\"u}tte, Christof and H{\"o}fling, Felix and Winkelmann, Stefanie}, title = {A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations}, series = {Letters in Mathematical Physics}, volume = {112}, journal = {Letters in Mathematical Physics}, number = {49}, doi = {10.1007/s11005-022-01539-w}, language = {en} } @article{GelssKlusSchusteretal., author = {Gelss, Patrick and Klus, Stefan and Schuster, Ingmar and Sch{\"u}tte, Christof}, title = {Feature space approximation for kernel-based supervised learning}, series = {Knowledge-Based Sytems}, volume = {221}, journal = {Knowledge-Based Sytems}, publisher = {Elsevier}, doi = {https://doi.org/10.1016/j.knosys.2021.106935}, language = {en} } @article{KlusGelssPeitzetal., author = {Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Sch{\"u}tte, Christof}, title = {Tensor-based dynamic mode decomposition}, series = {Nonlinearity}, volume = {31}, journal = {Nonlinearity}, number = {7}, publisher = {IOP Publishing Ltd \& London Mathematical Society}, doi = {10.1088/1361-6544/aabc8f}, language = {en} } @misc{SunkaraRaharinirinaPeppertetal., author = {Sunkara, Vikram and Raharinirina, N. Alexia and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof}, title = {Inferring Gene Regulatory Networks from Single Cell RNA-seq Temporal Snapshot Data Requires Higher Order Moments}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79664}, abstract = {Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver. There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability.}, language = {en} } @article{RaharinirinaPeppertvonKleistetal., author = {Raharinirina, Alexia N. and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Inferring gene regulatory networks from single-cell RNA-seq temporal snapshot data requires higher-order moments}, series = {Patterns}, volume = {2}, journal = {Patterns}, number = {9}, doi = {10.1016/j.patter.2021.100332}, abstract = {Single-cell RNA sequencing (scRNA-seq) has become ubiquitous in biology. Recently, there has been a push for using scRNA-seq snapshot data to infer the underlying gene regulatory networks (GRNs) steering cellular function. To date, this aspiration remains unrealized due to technical and computational challenges. In this work we focus on the latter, which is under-represented in the literature. We took a systemic approach by subdividing the GRN inference into three fundamental components: data pre-processing, feature extraction, and inference. We observed that the regulatory signature is captured in the statistical moments of scRNA-seq data and requires computationally intensive minimization solvers to extract it. Furthermore, current data pre-processing might not conserve these statistical moments. Although our moment-based approach is a didactic tool for understanding the different compartments of GRN inference, this line of thinking—finding computationally feasible multi-dimensional statistics of data—is imperative for designing GRN inference methods.}, language = {en} } @article{PeppertvonKleistSchuetteetal., author = {Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks}, series = {IEEE Transactions on Neural Networks and Learning Systems}, volume = {33}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, number = {11}, doi = {10.1109/TNNLS.2021.3072746}, pages = {6194 -- 6205}, abstract = {Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling.}, language = {en} } @article{SchulzePeppertSchuetteetal., author = {Schulze, Kenrick and Peppert, Felix and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Chimeric U-Net-Modifying the standard U-Net towards Explainability}, series = {bioRxiv}, journal = {bioRxiv}, doi = {10.1101/2022.12.01.518699}, language = {en} } @article{ShaoBjaanaesHellandetal., author = {Shao, Borong and Bjaanaes, Maria and Helland, Aslaug and Sch{\"u}tte, Christof and Conrad, Tim}, title = {EMT network-based feature selection improves prognosis prediction in lung adenocarcinoma}, series = {PLOS ONE}, volume = {14}, journal = {PLOS ONE}, number = {1}, doi = {10.1371/journal.pone.0204186}, abstract = {Various feature selection algorithms have been proposed to identify cancer prognostic biomarkers. In recent years, however, their reproducibility is criticized. The performance of feature selection algorithms is shown to be affected by the datasets, underlying networks and evaluation metrics. One of the causes is the curse of dimensionality, which makes it hard to select the features that generalize well on independent data. Even the integration of biological networks does not mitigate this issue because the networks are large and many of their components are not relevant for the phenotype of interest. With the availability of multi-omics data, integrative approaches are being developed to build more robust predictive models. In this scenario, the higher data dimensions create greater challenges. We proposed a phenotype relevant network-based feature selection (PRNFS) framework and demonstrated its advantages in lung cancer prognosis prediction. We constructed cancer prognosis relevant networks based on epithelial mesenchymal transition (EMT) and integrated them with different types of omics data for feature selection. With less than 2.5\% of the total dimensionality, we obtained EMT prognostic signatures that achieved remarkable prediction performance (average AUC values above 0.8), very significant sample stratifications, and meaningful biological interpretations. In addition to finding EMT signatures from different omics data levels, we combined these single-omics signatures into multi-omics signatures, which improved sample stratifications significantly. Both single- and multi-omics EMT signatures were tested on independent multi-omics lung cancer datasets and significant sample stratifications were obtained.}, language = {en} } @article{WulkowTelgmannHungenbergetal., author = {Wulkow, Niklas and Telgmann, Regina and Hungenberg, Klaus-Dieter and Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples}, series = {Macromolecular Theory and Simulations}, volume = {30}, journal = {Macromolecular Theory and Simulations}, doi = {10.1002/mats.202100017}, abstract = {Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.}, language = {en} } @article{ConradGenzelCvetkovicetal., author = {Conrad, Tim and Genzel, Martin and Cvetkovic, Nada and Wulkow, Niklas and Vybiral, Jan and Kutyniok, Gitta and Sch{\"u}tte, Christof}, title = {Sparse Proteomics Analysis - a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data}, series = {BMC Bioinformatics}, volume = {18}, journal = {BMC Bioinformatics}, number = {160}, doi = {10.1186/s12859-017-1565-4}, pages = {1 -- 20}, abstract = {Motivation: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested how MS spectra dier between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust to noise and outliers, and the identied feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based on the theory of Compressed Sensing that allows to identify a minimal discriminating set of features from mass spectrometry data-sets. We show how our method performs on artificial and real-world data-sets.}, language = {en} } @article{ConradGenzelCvetkovicetal., author = {Conrad, Tim and Genzel, Martin and Cvetkovic, Nada and Wulkow, Niklas and Leichtle, Alexander Benedikt and Vybiral, Jan and Kytyniok, Gitta and Sch{\"u}tte, Christof}, title = {Sparse Proteomics Analysis - a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data}, series = {BMC Bioinfomatics}, volume = {18}, journal = {BMC Bioinfomatics}, number = {160}, doi = {10.1186/s12859-017-1565-4}, abstract = {Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA),based on thet heory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets.}, language = {en} } @article{VegaSchuetteConrad, author = {Vega, Iliusi and Sch{\"u}tte, Christof and Conrad, Tim}, title = {Finding metastable states in real-world time series with recurrence networks}, series = {Physica A: Statistical Mechanics and its Applications}, volume = {445}, journal = {Physica A: Statistical Mechanics and its Applications}, doi = {10.1016/j.physa.2015.10.041}, pages = {1 -- 17}, abstract = {In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with a complex time series example. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points.}, language = {en} } @misc{SchuetteConrad, author = {Sch{\"u}tte, Christof and Conrad, Tim}, title = {Showcase 3: Information-based medicine}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {66 -- 67}, language = {en} } @misc{VegaSchuetteConrad, author = {Vega, Iliusi and Sch{\"u}tte, Christof and Conrad, Tim}, title = {SAIMeR: Self-adapted method for the identification of metastable states in real-world time series}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50130}, abstract = {In the framework of time series analysis with recurrence networks, we introduce SAIMeR, a heuristic self-adapted method that determines the elusive recurrence threshold and identifies metastable states in complex time series. To identify metastable states as well as the transitions between them, we use graph theory concepts and a fuzzy partitioning clustering algorithm. We illustrate SAIMeR by applying it to three real-world time series and show that it is able to identify metastable states in real-world data with noise and missing data points. Finally, we suggest a way to choose the embedding parameters used to construct the state space in which this method is performed, based on the analysis of how the values of these parameters affect two recurrence quantitative measurements: recurrence rate and entropy.}, language = {en} } @article{ZhangKlusConradetal., author = {Zhang, Wei and Klus, Stefan and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Learning chemical reaction networks from trajectory data}, series = {SIAM Journal on Applied Dynamical Systems (SIADS)}, volume = {18}, journal = {SIAM Journal on Applied Dynamical Systems (SIADS)}, number = {4}, doi = {10.1137/19M1265880}, pages = {2000 -- 2046}, abstract = {We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.}, language = {en} } @article{WulkowConradDjurdjevacConradetal., author = {Wulkow, Hanna and Conrad, Tim and Djurdjevac Conrad, Natasa and M{\"u}ller, Sebastian A. and Nagel, Kai and Sch{\"u}tte, Christof}, title = {Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts}, series = {PLOS One}, volume = {16}, journal = {PLOS One}, number = {4}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0249676}, language = {en} } @article{HelfmannHeitzigKoltaietal., author = {Helfmann, Luzie and Heitzig, Jobst and Koltai, P{\´e}ter and Kurths, J{\"u}rgen and Sch{\"u}tte, Christof}, title = {Statistical analysis of tipping pathways in agent-based models}, series = {Eur. Phys. J. Spec. Top.}, volume = {230}, journal = {Eur. Phys. J. Spec. Top.}, doi = {10.1140/epjs/s11734-021-00191-0}, pages = {3249 -- 3271}, abstract = {Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.}, language = {en} } @article{HorenkoLorenzSchuetteetal.2005, author = {Horenko, Illia and Lorenz, S. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Adaptive Approach for Non-Linear Sensitivity Analysis of Reaction Kinetics}, series = {J. Comp. Chem.}, volume = {26}, journal = {J. Comp. Chem.}, number = {9}, doi = {10.1002/jcc.20234}, pages = {941 -- 948}, year = {2005}, language = {en} } @article{MeerbachSchuetteFischer2005, author = {Meerbach, E. and Sch{\"u}tte, Christof and Fischer, Alexander}, title = {Eigenvalue Bounds on Restrictions of Reversible Nearly Uncoupled Markov Chains}, series = {Lin. Alg. Appl.}, volume = {398}, journal = {Lin. Alg. Appl.}, doi = {10.1016/j.laa.2004.10.018}, pages = {141 -- 160}, year = {2005}, language = {en} } @article{AntonySchmidtSchuette2005, author = {Antony, Jens and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Nonadiabatic Effects on Peptide Vibrational Dynamics Induced by Conformational Changes}, series = {J. Chem. Phys.}, volume = {122}, journal = {J. Chem. Phys.}, number = {1}, doi = {10.1063/1.1829057}, pages = {014309}, year = {2005}, language = {en} } @article{HorenkoDittmerSchuette2005, author = {Horenko, Illia and Dittmer, E. and Sch{\"u}tte, Christof}, title = {Reduced Stochastic Models for Complex Molecular Systems}, series = {Comp. Vis. Sci.}, volume = {9}, journal = {Comp. Vis. Sci.}, number = {2}, doi = {10.1007/s00791-006-0021-1}, pages = {89 -- 102}, year = {2005}, language = {en} } @article{DellnitzNeumannSchuette2005, author = {Dellnitz, M. and Neumann, M. and Sch{\"u}tte, Christof}, title = {Special Issue on Matrices and Mathematical Biology}, series = {Lin. Alg. Appl.}, volume = {398}, journal = {Lin. Alg. Appl.}, doi = {10.1016/j.laa.2004.12.006}, pages = {1 -- 245}, year = {2005}, language = {en} } @inproceedings{HorenkoSchmidtEhrenbergSchuette2006, author = {Horenko, Illia and Schmidt-Ehrenberg, Johannes and Sch{\"u}tte, Christof}, title = {Set-oriented dimension reduction: Localizing principal component analysis via hidden Markov models}, series = {Computational Life Sciences II: Second International Symposium CompLife 2006, Cambridge (UK), Sept. 2006}, volume = {4216}, booktitle = {Computational Life Sciences II: Second International Symposium CompLife 2006, Cambridge (UK), Sept. 2006}, editor = {Berthold, Michael R. and Glen, Robert C. and Fischer, Ingrid}, publisher = {Springer}, doi = {10.1007/11875741_8}, pages = {74 -- 85}, year = {2006}, language = {en} } @incollection{MeerbachSchuetteHorenkoetal.2007, author = {Meerbach, E. and Sch{\"u}tte, Christof and Horenko, Illia and Schmidt, Burkhard}, title = {Metastable Conformational Structure and Dynamics}, series = {Analysis and Control of Ultrafast Photoinduced Reactions}, volume = {87}, booktitle = {Analysis and Control of Ultrafast Photoinduced Reactions}, editor = {K{\"u}hn, O. and W{\"o}ste, L.}, publisher = {Springer}, address = {Berlin}, doi = {10.1007/978-3-540-68038-3_9}, pages = {796 -- 806}, year = {2007}, language = {en} } @inproceedings{DellnitzMoloMetzneretal.2006, author = {Dellnitz, M. and Molo, M. and Metzner, Ph. and Preis, R. and Sch{\"u}tte, Christof}, title = {Graph Algorithms for Dynamical Systems}, series = {Analysis, Modeling and Simulation of Multiscale Problems}, booktitle = {Analysis, Modeling and Simulation of Multiscale Problems}, editor = {Mielke, A.}, publisher = {Springer}, doi = {10.1007/3-540-35657-6_23}, pages = {619 -- 645}, year = {2006}, language = {en} } @inproceedings{MeerbachDittmerHorenkoetal.2006, author = {Meerbach, E. and Dittmer, E. and Horenko, Illia and Sch{\"u}tte, Christof}, title = {Multiscale Modelling in Molecular Dynamics}, series = {Computer Simulations in Condensed Matter}, volume = {703}, booktitle = {Computer Simulations in Condensed Matter}, editor = {Ferrario, Mauro and Ciccotti, Giovanni and Binder, Kurt}, publisher = {Springer}, pages = {475 -- 497}, year = {2006}, language = {en} } @article{ConradLeichtleHagehuelsmannetal.2006, author = {Conrad, Tim and Leichtle, Alexander Benedikt and Hageh{\"u}lsmann, Andre and Diederichs, Elmar and Baumann, Sven and Thiery, Joachim and Sch{\"u}tte, Christof}, title = {Beating the Noise}, series = {Lecture Notes in Computer Science}, volume = {4216}, journal = {Lecture Notes in Computer Science}, publisher = {Springer}, pages = {119 -- 128}, year = {2006}, language = {en} } @article{HorenkoDittmerFischeretal.2006, author = {Horenko, Illia and Dittmer, E. and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Automated Model Reduction for Complex Systems exhibiting Metastability}, series = {Mult. Mod. Sim.}, volume = {5}, journal = {Mult. Mod. Sim.}, number = {3}, doi = {10.1137/050623310}, pages = {802 -- 827}, year = {2006}, language = {en} } @article{MetznerSchuetteVandenEijnden2006, author = {Metzner, Ph. and Sch{\"u}tte, Christof and Vanden-Eijnden, E.}, title = {Illustration of Transition Path Theory on a Collection of Simple Examples}, series = {J. Chem. Phys.}, volume = {125}, journal = {J. Chem. Phys.}, number = {8}, doi = {10.1063/1.2335447}, pages = {084110}, year = {2006}, language = {en} } @inproceedings{WalterSchuette2006, author = {Walter, J. and Sch{\"u}tte, Christof}, title = {Conditional Averaging for Diffusive Fast-Slow Systems}, series = {Analysis, Modeling and Simulation of Multiscale Problems}, booktitle = {Analysis, Modeling and Simulation of Multiscale Problems}, editor = {Mielke, A.}, publisher = {Springer}, doi = {10.1007/3-540-35657-6_24}, pages = {647 -- 682}, year = {2006}, language = {en} } @inproceedings{SchuetteHuisinga2000, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Biomolecular Conformations as Metastable Sets of Markov Chains}, series = {Proceedings of the 38th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinoins/USA}, booktitle = {Proceedings of the 38th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinoins/USA}, editor = {Sreenivas, R. and Jones, D.}, publisher = {University of Illinois at Urbana-Champaign}, pages = {1106 -- 1115}, year = {2000}, language = {en} } @incollection{GraefeSchuetteNordmeier2009, author = {Gr{\"a}fe, Ch. and Sch{\"u}tte, Christof and Nordmeier, V.}, title = {"Learner as creator" - Sch{\"u}lerInnen generieren eigene Lernspiele}, series = {Didaktik der Physik - Bochum 2009}, booktitle = {Didaktik der Physik - Bochum 2009}, publisher = {Lehmanns Media}, address = {Berlin}, year = {2009}, language = {en} } @article{RathYousefKatzensteinetal., author = {Rath, Barbara and Yousef, Kaveh and Katzenstein, D. and Shafer, R. and Sch{\"u}tte, Christof and von Kleist, Max and Merigan, T.}, title = {HIV-1 Evolution in Response to Triple Reverse Transcriptase Inhibitor Induced Selective Pressure in vitro}, series = {PLoS ONE}, volume = {8}, journal = {PLoS ONE}, number = {4}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0061102}, pages = {e61102}, language = {en} } @article{AicheReinertSchuetteetal.2012, author = {Aiche, Stephan and Reinert, Knut and Sch{\"u}tte, Christof and Hildebrand, Diana and Schl{\"u}ter, Hartmut and Conrad, Tim}, title = {Inferring Proteolytic Processes from Mass Spectrometry Time Series Data Using Degradation Graphs}, series = {PLoS ONE}, volume = {7}, journal = {PLoS ONE}, number = {7}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0040656}, pages = {e40656}, year = {2012}, language = {en} } @article{WangSchuetteSite2012, author = {Wang, Han and Sch{\"u}tte, Christof and Site, Luigi Delle}, title = {Adaptive Resolution Simulation (AdResS): A Smooth Thermodynamic and Structural Transition from Atomistic to Coarse Grained Resolution and Vice Versa in a Grand Canonical Fashion.}, series = {J. Chem. Theo. Comp.}, volume = {8}, journal = {J. Chem. Theo. Comp.}, number = {8}, doi = {10.1021/ct3003354}, pages = {2878 -- 2887}, year = {2012}, language = {en} } @article{WeissPaulusSteinhilberetal.2012, author = {Weiss, Maximilian and Paulus, Florian and Steinhilber, D. and Nikitin, Anatoly and Haag, Rainer and Sch{\"u}tte, Christof}, title = {Estimating Kinetic Parameters for the Spontaneous Polymerization of Glycidol at Elevated Temperatures}, series = {MACROMOLECULAR THEORY and SIMULATIONS}, volume = {21}, journal = {MACROMOLECULAR THEORY and SIMULATIONS}, number = {7}, doi = {10.1002/mats.201200003}, pages = {470 -- 481}, year = {2012}, language = {en} } @article{MenzLatorreSchuetteetal.2012, author = {Menz, Stephan and Latorre, J. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Hybrid Stochastic--Deterministic Solution of the Chemical Master Equation}, series = {SIAM Interdisciplinary Journal Multiscale Modeling and Simulation (MMS)}, volume = {10}, journal = {SIAM Interdisciplinary Journal Multiscale Modeling and Simulation (MMS)}, number = {4}, doi = {10.1137/110825716}, pages = {1232 -- 1262}, year = {2012}, language = {en} } @article{WangSchuetteZhang2012, author = {Wang, Han and Sch{\"u}tte, Christof and Zhang, P.}, title = {Error Estimate of Short-Range Force Calculation in the Inhomogeneous Molecular Systems}, series = {Phys. Rev. E}, volume = {86}, journal = {Phys. Rev. E}, number = {02}, doi = {10.1103/PhysRevE.86.026704}, pages = {026704}, year = {2012}, language = {en} } @article{DjurdjevacConradSarichSchuette2012, author = {Djurdjevac Conrad, Natasa and Sarich, Marco and Sch{\"u}tte, Christof}, title = {Estimating the eigenvalue error of Markov State Models}, series = {Multiscale Modeling \& Simulation}, volume = {10}, journal = {Multiscale Modeling \& Simulation}, number = {1}, doi = {10.1137/100798910}, pages = {61 -- 81}, year = {2012}, language = {en} } @article{DuwalSchuettevonKleist2012, author = {Duwal, Sulav and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Pharmacokinetics and Pharmacodynamics of the Reverse Transcriptase Inhibitor Tenofovir \& Prophylactic Efficacy against HIV-1 Infection.}, series = {PLoS One}, volume = {7}, journal = {PLoS One}, number = {7}, doi = {10.1371/journal.pone.0040382}, pages = {e40382}, year = {2012}, language = {en} } @article{DjurdjevacConradBrucknerConradetal.2012, author = {Djurdjevac Conrad, Natasa and Bruckner, Stefanie and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Random Walks on Complex Modular Networks}, series = {Journal of Numerical Analysis, Industrial and Applied Mathematics}, volume = {6}, journal = {Journal of Numerical Analysis, Industrial and Applied Mathematics}, number = {1-2}, publisher = {European Society of Computational Methods in Sciences and Engineering}, pages = {29 -- 50}, year = {2012}, language = {en} } @article{WangZhangSchuette2012, author = {Wang, Han and Zhang, P. and Sch{\"u}tte, Christof}, title = {On the Numerical Accuracy of Ewald, Smooth Particle Mesh Ewald, and Staggered Mesh Ewald Methods for Correlated Molecular Systems}, series = {J. Chem. Theo. Comp.}, volume = {8}, journal = {J. Chem. Theo. Comp.}, number = {9}, doi = {10.1021/ct300343y}, pages = {3243 -- 3256}, year = {2012}, language = {en} } @article{EncisoSchuetteSite2012, author = {Enciso, Marta and Sch{\"u}tte, Christof and Site, Luigi Delle}, title = {A pH-dependent coarse-grained model of peptides}, series = {Soft Matter}, volume = {9}, journal = {Soft Matter}, number = {26}, doi = {10.1039/C3SM27893J}, pages = {6118 -- 6127}, year = {2012}, language = {en} } @article{MarsalekFrigatoVandeVondeleetal.2010, author = {Marsalek, Ondrej and Frigato, Tomaso and VandeVondele, Joost and Bradforth, Stephen E. and Schmidt, Burkhard and Sch{\"u}tte, Christof and Jungwirth, Pavel}, title = {Hydrogen Forms in Water by Proton Transfer to a Distorted Electron}, series = {J. Phys. Chem. B}, volume = {114}, journal = {J. Phys. Chem. B}, number = {2}, doi = {10.1021/jp908986z}, pages = {915 -- 920}, year = {2010}, language = {en} } @article{SchuetteWulkow1992, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of Raman Spectroscopy.}, series = {preprint}, journal = {preprint}, year = {1992}, language = {en} } @article{FiedlerLeichtleKaseetal.2009, author = {Fiedler, Georg Martin and Leichtle, Alexander Benedikt and Kase, Julia and Baumann, Sven and Ceglarek, Uta and Felix, Klaus and Conrad, Tim and Witzigmann, Helmut and Weimann, Arved and Sch{\"u}tte, Christof and Hauss, Johann and B{\"u}chler, Markus and Thiery, Joachim}, title = {Serum Peptidome Profiling Revealed Platelet Factor 4 as a Potential Discriminating Peptide Associated With Pancreatic Cancer}, series = {Clinical Cancer Research}, volume = {15}, journal = {Clinical Cancer Research}, number = {11}, publisher = {American Association for Cancer Research,}, doi = {10.1158/1078-0432.CCR-08-2701}, pages = {3812 -- 3819}, year = {2009}, language = {en} } @article{NoeSchuetteVandenEijndenetal.2009, author = {No{\´e}, Frank and Sch{\"u}tte, Christof and Vanden-Eijnden, E. and Reich, L. and Weikl, T.}, title = {Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations}, series = {Proc. Natl. Acad. Sci. USA}, volume = {106}, journal = {Proc. Natl. Acad. Sci. USA}, number = {45}, doi = {10.1073/pnas.0905466106}, pages = {19011 -- 19016}, year = {2009}, language = {en} } @article{FrigatoVandeVondeleSchmidtetal.2008, author = {Frigato, Tomaso and VandeVondele, Joost and Schmidt, Burkhard and Sch{\"u}tte, Christof and Jungwirth, Pavel}, title = {Ab Initio Molecular Dynamics Simulation of a Medium-Sized Water Cluster Anion}, series = {J. Phys. Chem. A}, volume = {112}, journal = {J. Phys. Chem. A}, number = {27}, doi = {10.1021/jp711545s}, pages = {6125 -- 6133}, year = {2008}, language = {en} } @article{HorenkoKleinDolaptchievetal.2008, author = {Horenko, Illia and Klein, Rupert and Dolaptchiev, S. and Sch{\"u}tte, Christof}, title = {Automated Generation of Reduced Stochastic Weather Models I}, series = {Mult. Mod. Sim.}, volume = {6}, journal = {Mult. Mod. Sim.}, number = {4}, doi = {10.1137/060670535}, pages = {1125 -- 1145}, year = {2008}, language = {en} } @incollection{BernhardZoukraSchuette2010, author = {Bernhard, Stefan and Zoukra, Kristine Al and Sch{\"u}tte, Christof}, title = {From non-invasive hemodynamic measurements towards patient-specific cardiovascular diagnosis}, series = {Quality Assurance in Healthcare Service Delivery, Nursing and Personalized Medicine}, booktitle = {Quality Assurance in Healthcare Service Delivery, Nursing and Personalized Medicine}, editor = {Daskalaki, A. and Lazakidou, A.}, publisher = {Hershey, PA: Medical Information Science Reference}, year = {2010}, language = {en} } @article{GraefeNordmeierSchuette2009, author = {Gr{\"a}fe, Ch. and Nordmeier, V. and Sch{\"u}tte, Christof}, title = {Computerspiel zum Thema Molek{\"u}ldynamik f{\"u}r Sch{\"u}ler der 7.-10. Klasse, Experimentelles Protyping zur Entwicklung eines Lernspiels}, series = {Jahrestagung 2008 der GDCP (Gesellschaft f{\"u}r Didaktik der Chemie und Physik)}, volume = {1}, journal = {Jahrestagung 2008 der GDCP (Gesellschaft f{\"u}r Didaktik der Chemie und Physik)}, publisher = {LIT VERLAG Dr. W. Hopf}, pages = {77 -- 79}, year = {2009}, language = {en} } @article{SchuetteWulkow2010, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {A Hybrid Galerkin-Monte-Carlo Approach to Higher-Dimensional Population Balances in Polymerization Kinetics}, series = {Macromol. React. Eng.}, volume = {4}, journal = {Macromol. React. Eng.}, number = {9-10}, doi = {10.1002/mren.200900073}, pages = {562 -- 577}, year = {2010}, language = {en} } @inproceedings{DjurdjevacConradSarichSchuette2010, author = {Djurdjevac Conrad, Natasa and Sarich, Marco and Sch{\"u}tte, Christof}, title = {On Markov State Models for Metastable Processes}, series = {Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010}, booktitle = {Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010}, year = {2010}, language = {en} } @article{SchuetteJahnke2009, author = {Sch{\"u}tte, Christof and Jahnke, Tobias}, title = {Towards Effective Dynamics in Complex Systems by Markov Kernel Approximation}, series = {Mathematical Modelling and Numerical Analysis (ESAIM)}, volume = {43}, journal = {Mathematical Modelling and Numerical Analysis (ESAIM)}, number = {4}, publisher = {EDP Sciences}, doi = {10.1051/m2an/2009027}, pages = {721 -- 742}, year = {2009}, language = {en} } @article{HorenkoSchuette2010, author = {Horenko, Illia and Sch{\"u}tte, Christof}, title = {On metastable conformational analysis of non-equilibrium biomolecular time series}, series = {Multiscale Modeling \& Simulation}, volume = {8}, journal = {Multiscale Modeling \& Simulation}, number = {2}, doi = {10.1137/080744347}, pages = {701 -- 716}, year = {2010}, language = {en} } @article{MetznerNoeSchuette2009, author = {Metzner, Ph. and No{\´e}, Frank and Sch{\"u}tte, Christof}, title = {Estimating the Sampling Error}, series = {Phys. Rev. E}, volume = {80}, journal = {Phys. Rev. E}, number = {2}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.80.021106}, pages = {021106}, year = {2009}, language = {en} } @article{SarichNoeSchuette2010, author = {Sarich, Marco and No{\´e}, Frank and Sch{\"u}tte, Christof}, title = {On the Approximation Quality of Markov State Models}, series = {Multiscale Model. Simul.}, volume = {8}, journal = {Multiscale Model. Simul.}, number = {4}, doi = {10.1137/090764049}, pages = {1154 -- 1177}, year = {2010}, language = {en} } @article{PlockHammerschmidtBurgeretal., author = {Plock, Matthias and Hammerschmidt, Martin and Burger, Sven and Schneider, Philipp-Immanuel and Sch{\"u}tte, Christof}, title = {Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions}, series = {Metrologia}, volume = {60}, journal = {Metrologia}, doi = {10.1088/1681-7575/ace4cd}, pages = {054001}, abstract = {In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.}, language = {en} } @article{DjurdjevacConradFuerstenauGrabundzijaetal., author = {Djurdjevac Conrad, Natasa and Fuerstenau, Daniel and Grabundzija, Ana and Helfmann, Luzie and Park, Martin and Schier, Wolfram and Sch{\"u}tt, Brigitta and Sch{\"u}tte, Christof and Weber, Marcus and Wulkow, Niklas and Zonker, Johannes}, title = {Mathematical modeling of the spreading of innovations in the ancient world}, series = {eTopoi. Journal for Ancient Studies}, volume = {7}, journal = {eTopoi. Journal for Ancient Studies}, issn = {ISSN 2192-2608}, doi = {10.17171/4-7-1}, language = {en} } @article{FrankvonKleistKunzetal.2011, author = {Frank, M. and von Kleist, Max and Kunz, A. and Harms, G. and Sch{\"u}tte, Christof and Kloft, Ch.}, title = {Quantifying the impact of nevirapine-based prophylaxis strategies to prevent mother-to-child transmission of HIV-1}, series = {Antimicrob. Agents Chemother.}, volume = {55}, journal = {Antimicrob. Agents Chemother.}, number = {12}, pages = {5529 -- 5540}, year = {2011}, language = {en} } @incollection{BernhardZoukraSchuette2011, author = {Bernhard, Stefan and Zoukra, Kristine Al and Sch{\"u}tte, Christof}, title = {Statistical parameter estimation and signal classification in cardiovascular diagnosis}, series = {Modelling in Medicine and Biology}, volume = {IX}, booktitle = {Modelling in Medicine and Biology}, number = {15}, editor = {Knets, I. and Brebbia, C. and Miftahof, R. and Kasyanov, V. and Popov, V.}, publisher = {WIT Press}, address = {Southampton \& Boston}, year = {2011}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Huisinga, Wilhelm and Sch{\"u}tte, Christof}, title = {HIV Quasispecies Dynamics during Pro-active Treatment Switching}, series = {Plos One}, volume = {6}, journal = {Plos One}, number = {3}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0018204}, pages = {e18204}, year = {2011}, language = {en} } @article{PrinzWuSarichetal.2011, author = {Prinz, J.-H. and Wu, Hao and Sarich, Marco and Keller, B. and Fischbach, M. and Held, M. and Chodera, J. and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Markov models of molecular kinetics}, series = {J. Chem. Phys.}, volume = {134}, journal = {J. Chem. Phys.}, doi = {10.1063/1.3565032}, pages = {174105}, year = {2011}, language = {en} } @article{SchuetteNoeLuetal.2011, author = {Sch{\"u}tte, Christof and No{\´e}, Frank and Lu, Jianfeng and Sarich, Marco and Vanden-Eijnden, E.}, title = {Markov State Models Based on Milestoning}, series = {J. Chem. Phys.}, volume = {134}, journal = {J. Chem. Phys.}, number = {20}, doi = {10.1063/1.3590108}, pages = {204105}, year = {2011}, language = {en} } @article{vonKleistMetznerMarquetetal.2012, author = {von Kleist, Max and Metzner, Ph. and Marquet, R. and Sch{\"u}tte, Christof}, title = {Polymerase Inhibition by Nucleoside Analogs}, series = {Plos Computational Biology}, volume = {8}, journal = {Plos Computational Biology}, number = {1}, doi = {10.1371/journal.pcbi.1002359}, pages = {e1002359}, year = {2012}, language = {en} } @article{MetznerSchuetteVandenEijnden2009, author = {Metzner, Ph. and Sch{\"u}tte, Christof and Vanden-Eijnden, E.}, title = {Transition Path Theory for Markov Jump Processes}, series = {Mult. Mod. Sim.}, volume = {7}, journal = {Mult. Mod. Sim.}, number = {3}, doi = {10.1137/070699500}, pages = {1192 -- 1219}, year = {2009}, language = {en} } @article{MeerbachLatorreSchuette2012, author = {Meerbach, E. and Latorre, J. and Sch{\"u}tte, Christof}, title = {Sequential Change Point Detection in Molecular Dynamics Trajectories}, series = {Multicale Model. Sim.}, volume = {10}, journal = {Multicale Model. Sim.}, number = {4}, doi = {10.1137/110850621}, pages = {1263 -- 1291}, year = {2012}, language = {en} } @article{WinkelmannSchuettevonKleist2012, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation}, series = {Communications in Mathematical Sciences}, volume = {12}, journal = {Communications in Mathematical Sciences}, number = {859}, year = {2012}, language = {en} } @article{NettesheimBornemannSchmidtetal.1996, author = {Nettesheim, Peter and Bornemann, Folkmar A. and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {An Explicit and Symplectic Integrator for Quantum-Classical Molecular Dynamics}, series = {Chem. Phys. Lett.}, volume = {256}, journal = {Chem. Phys. Lett.}, number = {6}, doi = {10.1016/0009-2614(96)00471-X}, pages = {581 -- 588}, year = {1996}, language = {en} } @article{ManzParamonovPolaseketal.1994, author = {Manz, J{\"o}rn and Paramonov, G. and Polasek, M. and Sch{\"u}tte, Christof}, title = {Overtone State-Selective Isomerization by a Series of Picosecond Infrared Laser Pulses - Model Simulations for Be2H3D}, series = {Isr. J. Chem.}, volume = {34}, journal = {Isr. J. Chem.}, number = {1}, pages = {115 -- 125}, year = {1994}, language = {en} } @article{BornemannNettesheimSchuette1996, author = {Bornemann, Folkmar A. and Nettesheim, Peter and Sch{\"u}tte, Christof}, title = {Quantum-classical molecular dynamics as an approximation to full quantum dynamics}, series = {J. Chem. Phys.}, volume = {105}, journal = {J. Chem. Phys.}, number = {3}, doi = {10.1063/1.471952}, pages = {1074 -- 1083}, year = {1996}, language = {en} } @article{Schuette1993, author = {Sch{\"u}tte, Christof}, title = {A Quasiresonant Smoothing Algorithm for the Fast Analysis of Selective Vibrational Excitation}, series = {Impact of Computing in Sci. Eng.}, volume = {5}, journal = {Impact of Computing in Sci. Eng.}, number = {3}, doi = {10.1006/icse.1993.1008}, pages = {176 -- 200}, year = {1993}, language = {en} } @article{NettesheimHuisingaSchuette1996, author = {Nettesheim, Peter and Huisinga, Wilhelm and Sch{\"u}tte, Christof}, title = {Chebyshev-Approximation for Wavepacket-Dynamics}, series = {preprint}, journal = {preprint}, year = {1996}, language = {en} } @article{SchuetteZumbuschBrinkmann1995, author = {Sch{\"u}tte, Christof and Zumbusch, Gerhard and Brinkmann, Ralf}, title = {Dynamics of Erbium-doped Waveguide Lasers}, series = {preprint}, journal = {preprint}, year = {1995}, language = {en} } @article{SchuetteDinand1995, author = {Sch{\"u}tte, Christof and Dinand, Manfred}, title = {Theoretical Modeling of Relaxation Oscillations in Er-Doped Wave-Guide Lasers}, series = {J. Lightw. Techn.}, volume = {13}, journal = {J. Lightw. Techn.}, number = {1}, pages = {14 -- 23}, year = {1995}, language = {en} } @misc{Schuette1995, author = {Sch{\"u}tte, Christof}, title = {Smoothed Molecular Dynamics for Thermally Embedded Systems}, year = {1995}, language = {en} } @inproceedings{NettesheimSchuette1999, author = {Nettesheim, Peter and Sch{\"u}tte, Christof}, title = {Numerical Integrators for Quantum-Classical Molecular Dynamics}, series = {Computational Molecular Dynamics}, volume = {4}, booktitle = {Computational Molecular Dynamics}, editor = {Deuflhard, Peter and Hermans, J. and Leimkuhler, Benedict and Marks, A. and Reich, Sebastian and Skeel, R.}, publisher = {Springer}, pages = {396 -- 411}, year = {1999}, language = {en} } @article{FischerCordesSchuette1998, author = {Fischer, Alexander and Cordes, Frank and Sch{\"u}tte, Christof}, title = {Hybrid Monte Carlo with adaptive temperature in mixed-canonical ensemble}, series = {J. Comp. Chem.}, volume = {19}, journal = {J. Comp. Chem.}, number = {15}, doi = {10.1002/(SICI)1096-987X(19981130)19:15<1689::AID-JCC2>3.0.CO;2-J}, pages = {1689 -- 1697}, year = {1998}, language = {en} } @inproceedings{SchuetteNettesheim1999, author = {Sch{\"u}tte, Christof and Nettesheim, Peter}, title = {Nonadiabatic Effects in Quantum-Classical Molecular Dynamics}, series = {Scientific Computing in Chemical Engineering II}, booktitle = {Scientific Computing in Chemical Engineering II}, editor = {Keil, F. and Mackens, W. and Voss, H. and Werther, J.}, publisher = {Springer}, pages = {42 -- 56}, year = {1999}, language = {en} } @article{BornemannSchuette1999, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {On the Singular Limit of the Quantum-Classical Molecular Dynamics Model}, series = {J. Appl. Math.}, volume = {59}, journal = {J. Appl. Math.}, number = {4}, doi = {10.1137/S0036139997318834}, pages = {1208 -- 1224}, year = {1999}, language = {en} } @article{BornemannSchuette1998, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {A mathematical investigation of the Car-Parrinello Method}, series = {Num. Math.}, volume = {78}, journal = {Num. Math.}, number = {3}, doi = {10.1007/s002110050316}, pages = {359 -- 376}, year = {1998}, language = {en} } @article{SchuetteBornemann1997, author = {Sch{\"u}tte, Christof and Bornemann, Folkmar A.}, title = {Homogenization Approach to Smoothed Molecular Dynamics}, series = {Nonlinear Analysis}, volume = {30}, journal = {Nonlinear Analysis}, number = {3}, doi = {10.1016/S0362-546X(97)00216-2}, pages = {1805 -- 1814}, year = {1997}, language = {en} } @article{BornemannSchuette1997, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {Homogenization of Hamiltonian Systems with a Strong Constraining Potential}, series = {Physica D}, volume = {102}, journal = {Physica D}, number = {1-2}, doi = {10.1016/S0167-2789(96)00245-X}, pages = {57 -- 77}, year = {1997}, language = {en} } @phdthesis{Schuette1999, author = {Sch{\"u}tte, Christof}, title = {Partial Wigner transforms and the quantum-classical Liouville equation}, year = {1999}, language = {en} } @inproceedings{SchuetteBornemann1999, author = {Sch{\"u}tte, Christof and Bornemann, Folkmar A.}, title = {Approximation Properties and Limits of the Quantum-Classical Molecular Dynamics Model}, series = {Computational Molecular Dynamics}, volume = {4}, booktitle = {Computational Molecular Dynamics}, editor = {Deuflhard, Peter and Hermans, J. and Leimkuhler, Benedict and Marks, A. and Reich, Sebastian and Skeel, R.}, publisher = {Springer}, pages = {380 -- 395}, year = {1999}, language = {en} } @article{HuisingaBestRoitzschetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Roitzsch, Rainer and Sch{\"u}tte, Christof and Cordes, Frank}, title = {From Simulation Data to Conformational Ensembles}, series = {J. Comp. Chem.}, volume = {20}, journal = {J. Comp. Chem.}, number = {16}, doi = {10.1002/(SICI)1096-987X(199912)20:16<1760::AID-JCC8>3.0.CO;2-2}, pages = {1760 -- 1774}, year = {1999}, language = {en} } @inproceedings{SchuetteHuisinga2000, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {On Conformational Dynamics induced by Langevin Processes}, series = {Equadiff 99}, volume = {2}, booktitle = {Equadiff 99}, editor = {Fiedler, B. and Grger, K. and Sprekels, J{\"u}rgen}, publisher = {World Scientific}, doi = {10.1142/9789812792617_0234}, pages = {1247 -- 1262}, year = {2000}, language = {en} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo}, series = {J. Comp. Phys}, volume = {151}, journal = {J. Comp. Phys}, number = {1}, doi = {10.1006/jcph.1999.6231}, pages = {146 -- 168}, year = {1999}, language = {en} } @inproceedings{SchuetteCordes2000, author = {Sch{\"u}tte, Christof and Cordes, Frank}, title = {On Dynamical Transitions between Conformational Ensembles}, series = {Molecular Dynamics on Parallel Computers}, booktitle = {Molecular Dynamics on Parallel Computers}, editor = {Esser, R. and Grassberger, P. and Grotendorst, J. and Lewerenz, M.}, publisher = {World Scientific}, doi = {10.1142/9789812793768_0002}, pages = {32 -- 45}, year = {2000}, language = {en} } @article{FischerCordesSchuette1999, author = {Fischer, Alexander and Cordes, Frank and Sch{\"u}tte, Christof}, title = {Hybrid Monte Carlo with adaptive temperature choice}, series = {Comp. Phys. Comm.}, volume = {121}, journal = {Comp. Phys. Comm.}, doi = {10.1016/S0010-4655(99)00274-X}, pages = {37 -- 39}, year = {1999}, language = {en} } @article{BornemannSchuette1999, author = {Bornemann, Folkmar A. and Sch{\"u}tte, Christof}, title = {Adaptive Accuracy Control for Car-Parrinello Simulations}, series = {Num. Math.}, volume = {83}, journal = {Num. Math.}, number = {2}, doi = {10.1007/s002110050445}, pages = {179 -- 186}, year = {1999}, language = {en} } @article{Schuette1999, author = {Sch{\"u}tte, Christof}, title = {Conformational Dynamics}, series = {preprint}, journal = {preprint}, year = {1999}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, series = {Computational Methods for Macromolecules}, volume = {24}, booktitle = {Computational Methods for Macromolecules}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, series = {Lin. Alg. Appl.}, volume = {315}, journal = {Lin. Alg. Appl.}, number = {1-3}, doi = {10.1016/S0024-3795(00)00095-1}, pages = {39 -- 59}, year = {2000}, language = {en} } @inproceedings{SchuetteHuisingaDeuflhard2001, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems}, series = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, editor = {Fiedler, B.}, publisher = {Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @article{HorenkoSalzmannSchmidtetal.2002, author = {Horenko, Illia and Salzmann, Ch. and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Quantum-Classical Liouville Approach to Molecular Dynamics}, series = {J. Chem. Phys.}, volume = {117}, journal = {J. Chem. Phys.}, number = {24}, doi = {10.1063/1.1522712}, pages = {11075 -- 11088}, year = {2002}, language = {en} } @inproceedings{SchuetteHuisingaMeyn2003, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Meyn, S.}, title = {Metastability of Diffusion Processes}, series = {Nonlinear Stochastic Dynamics}, volume = {110}, booktitle = {Nonlinear Stochastic Dynamics}, editor = {Namachchivaya, N. and Lin, Y.}, publisher = {Springer}, pages = {71 -- 81}, year = {2003}, language = {en} } @article{HorenkoSchmidtSchuette2002, author = {Horenko, Illia and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Multidimensional Classical Liouville Dynamics with Quantum Initial Conditions}, series = {J. Chem. Phys.}, volume = {117}, journal = {J. Chem. Phys.}, number = {10}, doi = {10.1063/1.1498467}, pages = {4643 -- 4650}, year = {2002}, language = {en} } @article{HorenkoSchmidtSchuette2001, author = {Horenko, Illia and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {A Theoretical Model for Molecules Interacting with Intense Laser Pulses}, series = {J. Chem. Phys.}, volume = {115}, journal = {J. Chem. Phys.}, number = {13}, doi = {10.1063/1.1398577}, pages = {5733 -- 5743}, year = {2001}, language = {en} } @article{HuisingaSchuetteStuart2003, author = {Huisinga, Wilhelm and Sch{\"u}tte, Christof and Stuart, Andrew}, title = {Extracting Macroscopic Stochastic Dynamics}, series = {Comm. Pure Appl. Math.}, volume = {56}, journal = {Comm. Pure Appl. Math.}, number = {2}, doi = {10.1002/cpa.10057}, pages = {234 -- 269}, year = {2003}, language = {en} } @inproceedings{SchuetteForsterMeerbachetal.2005, author = {Sch{\"u}tte, Christof and Forster, R. and Meerbach, E. and Fischer, Alexander}, title = {Uncoupling-Coupling Techniques for Metastable Dynamical Systems}, series = {Domain Decomposition Methods in Science and Engineering}, volume = {40}, booktitle = {Domain Decomposition Methods in Science and Engineering}, editor = {Kornhuber, Ralf and Hoppe, Ronald H. W. and P{\~A}\copyrightriaux, J. and Pironneau, O. and Widlund, Olof and Xu, J.}, publisher = {Springer}, pages = {115 -- 129}, year = {2005}, language = {en} } @inproceedings{DeuflhardSchuette2004, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, series = {Applied Mathematics Entering the 21st Century}, volume = {116}, booktitle = {Applied Mathematics Entering the 21st Century}, editor = {Hill, James and Moore, Ross}, publisher = {SIAM}, pages = {91 -- 119}, year = {2004}, language = {en} } @inproceedings{SchuetteHuisinga2003, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Biomolecular Conformations can be Identified as Metastable Sets of Molecular Dynamics}, series = {Special Volume}, volume = {X}, booktitle = {Special Volume}, editor = {Ciarlet, P. and Le Bris, Claude}, publisher = {Elsevier}, pages = {699 -- 744}, year = {2003}, language = {en} } @article{HorenkoWeiserSchmidtetal.2004, author = {Horenko, Illia and Weiser, Martin and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Fully Adaptive Propagation of the Quantum-Classical Liouville Equation}, series = {J. Chem. Phys.}, volume = {120}, journal = {J. Chem. Phys.}, number = {19}, doi = {10.1063/1.1691015}, pages = {8913 -- 8923}, year = {2004}, language = {en} } @article{HuisingaMeynSchuette2004, author = {Huisinga, Wilhelm and Meyn, S. and Sch{\"u}tte, Christof}, title = {Phase Transitions and Metastability in Markovian and Molecular Systems}, series = {Ann. Appl. Prob.}, volume = {14}, journal = {Ann. Appl. Prob.}, number = {1}, doi = {10.1214/aoap/1075828057}, pages = {419 -- 458}, year = {2004}, language = {en} } @article{PreisDellnitzHesseletal.2004, author = {Preis, R. and Dellnitz, M. and Hessel, M. and Sch{\"u}tte, Christof and Meerbach, E.}, title = {Dominant Paths Between Almost Invariant Sets of Dynamical Systems}, series = {preprint}, journal = {preprint}, year = {2004}, language = {en} } @article{WalterSchuettePavliotisetal.2004, author = {Walter, J. and Sch{\"u}tte, Christof and Pavliotis, G. and Stuart, Andrew}, title = {Averaging of Stochastic Differential Equations}, series = {preprint}, journal = {preprint}, year = {2004}, language = {en} } @inproceedings{HeldMeerbachHinderlichetal.2007, author = {Held, M. and Meerbach, E. and Hinderlich, S. and Reutter, W. and Sch{\"u}tte, Christof}, title = {Conformational Studies of UDP-GlcNAc in Environments of Increasing Complexity}, series = {From Computational Biophysics to Systems Biology}, volume = {36}, booktitle = {From Computational Biophysics to Systems Biology}, editor = {Hansmann, U. and Meinke, J. and Mohanty, S. and Zimmermann, O.}, publisher = {John von Neumann Institut for Computing}, pages = {145 -- 148}, year = {2007}, language = {en} } @article{FischerWaldhausenHorenkoetal.2007, author = {Fischer, Alexander and Waldhausen, S. and Horenko, Illia and Meerbach, E. and Sch{\"u}tte, Christof}, title = {Identification of Biomolecular Conformations from Incomplete Torsion Angle Observations by Hidden Markov Models}, series = {J. Comp. Chem.}, volume = {28}, journal = {J. Comp. Chem.}, number = {15}, doi = {10.1002/jcc.20692}, pages = {2453 -- 2464}, year = {2007}, language = {en} } @article{MetznerHorenkoSchuette2007, author = {Metzner, Ph. and Horenko, Illia and Sch{\"u}tte, Christof}, title = {Generator Estimation of Markov Jump Processes Based on Incomplete Observations Nonequidistant in Time}, series = {Phys. Rev. E}, volume = {76}, journal = {Phys. Rev. E}, number = {06}, doi = {10.1103/PhysRevE.76.066702}, pages = {066702}, year = {2007}, language = {en} } @article{LorenzDiederichsTelgmannetal.2007, author = {Lorenz, S. and Diederichs, Elmar and Telgmann, R. and Sch{\"u}tte, Christof}, title = {Discrimination of Dynamical System Models for Biological and Chemical Processes}, series = {J. Comp. Chem.}, volume = {28}, journal = {J. Comp. Chem.}, number = {8}, doi = {10.1002/jcc.20674}, pages = {1384 -- 1399}, year = {2007}, language = {en} } @article{MetznerDittmerJahnkeetal.2007, author = {Metzner, Ph. and Dittmer, E. and Jahnke, Tobias and Sch{\"u}tte, Christof}, title = {Generator Estimation of Markov Jump Processes}, series = {J. Comp. Phys.}, volume = {227}, journal = {J. Comp. Phys.}, number = {1}, doi = {10.1016/j.jcp.2007.07.032}, pages = {353 -- 375}, year = {2007}, language = {en} } @article{NoeHorenkoSchuetteetal.2007, author = {No{\´e}, Frank and Horenko, Illia and Sch{\"u}tte, Christof and Smith, J.}, title = {Hierarchical Analysis of Conformational Dynamics in Biomolecules}, series = {J. Chem. Phys.}, volume = {126}, journal = {J. Chem. Phys.}, number = {15}, doi = {10.1063/1.2714539}, pages = {155102}, year = {2007}, language = {en} } @article{HorenkoDittmerLankasetal.2008, author = {Horenko, Illia and Dittmer, E. and Lankas, F. and Maddocks, J. and Metzner, Ph. and Sch{\"u}tte, Christof}, title = {Macroscopic Dynamics of Complex Metastable Systems}, series = {J. Appl. Dyn. Syst.}, volume = {7}, journal = {J. Appl. Dyn. Syst.}, number = {2}, doi = {10.1137/050630064}, pages = {532 -- 560}, year = {2008}, language = {en} } @article{HorenkoSchuette2008, author = {Horenko, Illia and Sch{\"u}tte, Christof}, title = {Likelihood-Based Estimation of Multidimensional Langevin Models and its Application to Biomolecular Dynamics}, series = {Mult. Mod. Sim.}, volume = {7}, journal = {Mult. Mod. Sim.}, number = {2}, doi = {10.1137/070687451}, pages = {731 -- 773}, year = {2008}, language = {en} } @article{NoeSmithSchuette2007, author = {No{\´e}, Frank and Smith, J. and Sch{\"u}tte, Christof}, title = {A network-based approach to biomolecular dynamics}, series = {From Computational Biophysics to Systems Biology (CBSB07). Editors}, volume = {NIC Series 36}, journal = {From Computational Biophysics to Systems Biology (CBSB07). Editors}, publisher = {John von Neumann Institute for Computing, J{\"u}lich}, year = {2007}, language = {en} } @article{DiederichsJuditskiSpokoinyetal.2008, author = {Diederichs, Elmar and Juditski, A. and Spokoiny, V. and Sch{\"u}tte, Christof}, title = {Sparse Non-Gaussian Component Analysis}, series = {IEEE Transactions on Information Theory, submitted}, journal = {IEEE Transactions on Information Theory, submitted}, year = {2008}, language = {en} } @incollection{GraefeSchuetteNordmeier2008, author = {Gr{\"a}fe, Ch. and Sch{\"u}tte, Christof and Nordmeier, V.}, title = {Spielend lernen - ein Online-Computerspiel zur Molek{\"u}ldynamik}, series = {Didaktik der Physik ?}, booktitle = {Didaktik der Physik ?}, publisher = {Lehmanns Media}, address = {Berlin}, year = {2008}, language = {en} } @article{HorenkoSchuette2008, author = {Horenko, Illia and Sch{\"u}tte, Christof}, title = {Dimension Reduction for Time Series with Hidden Phase Transitions and Economic Applications}, series = {Adv. Data Anal. Class., submitted}, journal = {Adv. Data Anal. Class., submitted}, year = {2008}, language = {en} } @article{MeerbachSchuette2008, author = {Meerbach, E. and Sch{\"u}tte, Christof}, title = {Sequential Change Point Detection in Molecular Dynamics Trajectories}, series = {Journal of Multivariate Analysis, submitted}, journal = {Journal of Multivariate Analysis, submitted}, year = {2008}, language = {en} } @article{RiberaBorrellQuerRichteretal., author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, series = {SIAM Journal on Scientific Computing (SISC)}, journal = {SIAM Journal on Scientific Computing (SISC)}, doi = {10.1137/22M1503464}, pages = {S298 -- S323}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @article{HelfmannRiberaBorrellSchuetteetal., author = {Helfmann, Luzie and Ribera Borrell, Enric and Sch{\"u}tte, Christof and Koltai, Peter}, title = {Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics}, series = {Journal of Nonlinear Science}, volume = {30}, journal = {Journal of Nonlinear Science}, doi = {https://doi.org/10.1007/s00332-020-09652-7}, pages = {3321 -- 3366}, language = {en} } @inproceedings{ChaukairSchuetteSunkara, author = {Chaukair, Mustafa and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Activation Space of ReLU Equipped Deep Neural Networks}, series = {Procedia Computer Science}, volume = {222}, booktitle = {Procedia Computer Science}, doi = {10.1016/j.procs.2023.08.200}, pages = {624 -- 635}, abstract = {Modern Deep Neural Networks are getting wider and deeper in their architecture design. However, with an increasing number of parameters the decision mechanisms becomes more opaque. Therefore, there is a need for understanding the structures arising in the hidden layers of deep neural networks. In this work, we present a new mathematical framework for describing the canonical polyhedral decomposition in the input space, and in addition, we introduce the notions of collapsing- and preserving patches, pertinent to understanding the forward map and the activation space they induce. The activation space can be seen as the output of a layer and, in the particular case of ReLU activations, we prove that this output has the structure of a polyhedral complex.}, language = {en} } @misc{RiberaBorrellQuerRichteretal., author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, issn = {1438-0064}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @misc{WeberFackeldeySchuette, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-free Markov State Building}, issn = {1438-0064}, doi = {10.1063/1.4978501}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62167}, abstract = {Molecular dynamics (MD) simulations face challenging problems since the timescales of interest often are much longer than what is possible to simulate and even if sufficiently long simulation are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant timescales accessible via coarse grained representations that also allows for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.}, language = {en} } @article{GelssMateraSchuette, author = {Gelß, Patrick and Matera, Sebastian and Sch{\"u}tte, Christof}, title = {Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model}, series = {Journal of Computational Physics}, volume = {314}, journal = {Journal of Computational Physics}, doi = {10.1016/j.jcp.2016.03.025}, pages = {489 -- 502}, abstract = {In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased}, language = {en} } @misc{HartmannBanischSarichetal., author = {Hartmann, Carsten and Banisch, Ralf and Sarich, Marco and Badowski, Thomas and Sch{\"u}tte, Christof}, title = {Characterization of Rare Events in Molecular Dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42410}, abstract = {A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski's equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.}, language = {en} } @misc{GelssMateraSchuette, author = {Gelß, Patrick and Matera, Sebastian and Sch{\"u}tte, Christof}, title = {Solving the master equation without kinetic Monte Carlo: tensor train approximations for a CO oxidation model}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55743}, abstract = {In multiscale models of heterogeneous catalysis, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. This usually is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO_2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.}, language = {en} } @article{GelssKlusEisertetal., author = {Gelß, Patrick and Klus, Stefan and Eisert, Jens and Sch{\"u}tte, Christof}, title = {Multidimensional Approximation of Nonlinear Dynamical Systems}, series = {Journal of Computational and Nonlinear Dynamics}, volume = {14}, journal = {Journal of Computational and Nonlinear Dynamics}, number = {6}, doi = {10.1115/1.4043148}, abstract = {A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.}, language = {en} } @misc{ZhangHartmannSchuette, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective Dynamics Along Given Reaction Coordinates, and Reaction Rate Theory}, issn = {1438-0064}, doi = {10.1039/C6FD00147E}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59706}, abstract = {In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: We first show that if we start with an ergodic diffusion processes whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Zwanzig-Mori, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the "equation-free" approach and the "heterogeneous multiscale method" can be seen as special cases of our approach.}, language = {en} } @misc{HartmannRichterSchuetteetal., author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: Theory and algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65045}, abstract = {The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.}, language = {en} } @misc{ZhangWangHartmannetal., author = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Applications of the cross-entropy method to importance sampling and optimal control of diffusions}, issn = {1438-0064}, doi = {10.1137/14096493X}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49720}, abstract = {We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.}, language = {en} } @article{SchuetteKlusHartmann, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, series = {Acta Numerica}, volume = {32}, journal = {Acta Numerica}, doi = {10.1017/S0962492923000016}, pages = {517 -- 673}, abstract = {One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.}, language = {en} } @misc{SarichBanischHartmannetal., author = {Sarich, Marco and Banisch, Ralf and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Markov State Models for Rare Events in Molecular Dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42420}, abstract = {Rare but important transition events between long lived states are a key feature of many molecular systems. In many cases the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible even on the most powerful computers because of the immensely long simulation timescales needed. Recently a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs), has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore we introduce a novel approach to using MSMs for the efficient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls.}, language = {en} } @article{LatorreMetznerHartmannetal.2011, author = {Latorre, J. and Metzner, Ph. and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Structure-preserving numerical discretization of reversible diffusions}, series = {Commun. Math. Sci.}, volume = {9}, journal = {Commun. Math. Sci.}, number = {4}, pages = {1051 -- 1072}, year = {2011}, language = {en} } @article{ZhangHartmannSchuette, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective dynamics along given reaction coordinates, and reaction rate theory}, series = {Faraday Discussions}, journal = {Faraday Discussions}, number = {195}, doi = {10.1039/C6FD00147E}, pages = {365 -- 394}, language = {en} } @misc{WangHartmannSchuette, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Linear response theory and optimal control for a molecular system under nonequilibrium conditions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18944}, abstract = {In this paper, we propose a straightforward generalization of linear response theory to systems in nonequilibrium that are subject to nonequilibrium driving. We briefly revisit the standard linear response result for equilibrium systems, where we consider Langevin dynamics as a special case, and then give an alternative derivation using a change-of-measure argument that does not rely on any stationarity or reversibility assumption. This procedure moreover easily enables us to calculate the second order correction to the linear response formula (which may or may not be useful in practice). Furthermore, we outline how the novel nonequilibirum linear response formula can be used to compute optimal controls of molecular systems for cases in which one wants to steer the system to maximize a certain target expectation value. We illustrate our approach with simple numerical examples.}, language = {en} } @article{HartmannSchuetteZhang2018, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms}, series = {Journal of Statistical Physics}, volume = {175}, journal = {Journal of Statistical Physics}, number = {6}, doi = {10.1007/s10955-019-02286-4}, pages = {1214 -- 1261}, year = {2018}, abstract = {In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.}, language = {en} } @article{WangHartmannSchuetteetal.2013, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof and Site, Luigi Delle}, title = {Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique}, series = {Phys. Rev. X}, volume = {3}, journal = {Phys. Rev. X}, doi = {10.1103/PhysRevX.3.011018}, pages = {011018}, year = {2013}, language = {en} } @article{HorenkoHartmannSchuetteetal.2007, author = {Horenko, Illia and Hartmann, Carsten and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Data-based Parameter Estimation of Generalized Multidimensional Langevin Processes}, series = {Phys. Rev. E}, volume = {76}, journal = {Phys. Rev. E}, number = {01}, doi = {10.1103/PhysRevE.76.016706}, pages = {016706}, year = {2007}, language = {en} } @article{HartmannSchuetteKalibaevaetal.2009, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Kalibaeva, G. and Pierro, M. and Ciccotti, Giovanni}, title = {Fast Simulation of Polymer Chains}, series = {J. Chem. Phys.}, volume = {130}, journal = {J. Chem. Phys.}, doi = {10.1063/1.3110603}, pages = {144101}, year = {2009}, language = {en} } @article{HartmannSchuette2012, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Efficient rare event simulation by optimal nonequilibrium forcing}, series = {J. Stat. Mech. Theor. Exp.}, volume = {2012}, journal = {J. Stat. Mech. Theor. Exp.}, doi = {10.1088/1742-5468/2012/11/P11004}, pages = {P11004}, year = {2012}, language = {en} } @article{HartmannSchuetteCiccotti2010, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Ciccotti, Giovanni}, title = {On the linear response of mechanical systems with constraints}, series = {J. Chem. Phys.}, volume = {132}, journal = {J. Chem. Phys.}, number = {11}, doi = {10.1063/1.3354126}, pages = {111103}, year = {2010}, language = {en} } @article{HartmannVulcanovSchuette2010, author = {Hartmann, Carsten and Vulcanov, V.-M. and Sch{\"u}tte, Christof}, title = {Balanced Truncation of Second Order Systems}, series = {Multiscale Model. Simul.}, volume = {8}, journal = {Multiscale Model. Simul.}, number = {4}, doi = {10.1137/080732717}, pages = {1348 -- 1367}, year = {2010}, language = {en} } @article{HartmannSchuette2005, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Geometric Approach to Constrained Molecular Dynamics and Free Energy}, series = {Comm. Math. Sci.}, volume = {3}, journal = {Comm. Math. Sci.}, number = {1}, pages = {1 -- 20}, year = {2005}, language = {en} } @article{SchuetteNoeMeerbachetal.2009, author = {Sch{\"u}tte, Christof and No{\´e}, Frank and Meerbach, E. and Metzner, Ph. and Hartmann, Carsten}, title = {Conformation Dynamics}, series = {Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.),}, journal = {Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.),}, publisher = {EMS publishing house}, doi = {10.4171/056-1/15}, pages = {297 -- 335}, year = {2009}, language = {en} } @article{SchuetteWalterHartmannetal.2004, author = {Sch{\"u}tte, Christof and Walter, J. and Hartmann, Carsten and Huisinga, Wilhelm}, title = {An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations}, series = {Multiscale Model. Simul.}, volume = {2}, journal = {Multiscale Model. Simul.}, number = {3}, doi = {10.1137/030600308}, pages = {501 -- 526}, year = {2004}, language = {en} } @article{SchuetteWinkelmannHartmann2012, author = {Sch{\"u}tte, Christof and Winkelmann, Stefanie and Hartmann, Carsten}, title = {Optimal control of molecular dynamics using Markov state models}, series = {Math. Program. (Series B)}, volume = {134}, journal = {Math. Program. (Series B)}, number = {1}, doi = {10.1007/s10107-012-0547-6}, pages = {259 -- 282}, year = {2012}, language = {en} } @article{HartmannSchuette2008, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Balancing of partially-observed stochastic differential equations}, series = {47th IEEE Conference on Decision and Control}, journal = {47th IEEE Conference on Decision and Control}, doi = {10.1109/CDC.2008.4739161}, pages = {4867 -- 4872}, year = {2008}, language = {en} } @article{LatorreHartmannSchuette2010, author = {Latorre, J. and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Free energy computation by controlled Langevin processes}, series = {Procedia Computer Science}, volume = {1}, journal = {Procedia Computer Science}, number = {1}, doi = {10.1016/j.procs.2010.04.179}, pages = {1591 -- 1600}, year = {2010}, language = {en} } @article{SchaeferBungHartmannSchmidtetal.2011, author = {Sch{\"a}fer-Bung, B. and Hartmann, Carsten and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Dimension reduction by balanced truncation}, series = {J. Chem. Phys.}, volume = {135}, journal = {J. Chem. Phys.}, number = {1}, pages = {014112}, year = {2011}, language = {en} } @article{HartmannSchuette2007, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Comment on Two Distinct Notions of Free Energy}, series = {Physica D}, volume = {228}, journal = {Physica D}, number = {1}, doi = {10.1016/j.physd.2007.02.006}, pages = {59 -- 63}, year = {2007}, language = {en} } @article{HartmannSchuette2005, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Constrained Hybrid Monte-Carlo Algorithm and the Problem of Calculating the Free Energy in Several Variables}, series = {Z. Angew. Math. Mech.}, volume = {85}, journal = {Z. Angew. Math. Mech.}, number = {10}, doi = {10.1002/zamm.200410218}, pages = {700 -- 710}, year = {2005}, language = {en} } @article{HartmannSchuetteWeberetal., author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Weber, Marcus and Zhang, Wei}, title = {Importance sampling in path space for diffusion processes with slow-fast variables}, series = {Probability Theory and Related Fields}, journal = {Probability Theory and Related Fields}, doi = {10.1007/s00440-017-0755-3}, pages = {1 -- 52}, abstract = {Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton-Jacobi-Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.}, language = {en} } @article{HartmannSchuetteZhang, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Model reduction algorithms for optimal control and importance sampling of diffusions}, series = {Nonlinearity}, volume = {29}, journal = {Nonlinearity}, number = {8}, doi = {10.1088/0951-7715/29/8/2298}, pages = {2298 -- 2326}, abstract = {We propose numerical algorithms for solving optimal control and importance sampling problems based on simplified models. The algorithms combine model reduction techniques for multiscale diffusions and stochastic optimization tools, with the aim of reducing the original, possibly high-dimensional problem to a lower dimensional representation of the dynamics, in which only a few relevant degrees of freedom are controlled or biased. Specifically, we study situations in which either a reaction coordinate onto which the dynamics can be projected is known, or situations in which the dynamics shows strongly localized behavior in the small noise regime. No explicit assumptions about small parameters or scale separation have to be made. We illustrate the approach with simple, but paradigmatic numerical examples.}, language = {en} } @article{ZhangWangHartmannetal., author = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Applications of the cross-entropy method to importance sampling and optimal control of diffusions}, series = {Siam Journal on Scientific Computing}, volume = {36}, journal = {Siam Journal on Scientific Computing}, number = {6}, doi = {10.1137/14096493X}, pages = {A2654 -- A2672}, language = {en} } @article{HartmannBanischSarichetal., author = {Hartmann, Carsten and Banisch, Ralf and Sarich, Marco and Badowski, Thomas and Sch{\"u}tte, Christof}, title = {Characterization of Rare Events in Molecular Dynamics}, series = {Entropy (Special Issue)}, volume = {16}, journal = {Entropy (Special Issue)}, number = {1}, doi = {10.3390/e16010350}, pages = {350 -- 376}, language = {en} } @article{WangHartmannSchuette, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Linear response theory and optimal control for a molecular system under nonequilibrium conditions}, series = {Molecular Physics}, volume = {111}, journal = {Molecular Physics}, doi = {10.1080/00268976.2013.844370}, pages = {3555 -- 3564}, language = {en} } @article{SarichBanischHartmannetal., author = {Sarich, Marco and Banisch, Ralf and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Markov State Models for Rare Events in Molecular Dynamics}, series = {Entropy (Special Issue)}, volume = {16}, journal = {Entropy (Special Issue)}, number = {1}, doi = {10.3390/e16010258}, pages = {258 -- 286}, language = {en} } @article{HartmannRichterSchuetteetal., author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, series = {Entropy}, volume = {19}, journal = {Entropy}, number = {11}, doi = {10.3390/e19110626}, pages = {626}, language = {en} } @article{ErnstUngerSchuetteetal., author = {Ernst, Ariane and Unger, Nathalie and Sch{\"u}tte, Christof and Walter, Alexander and Winkelmann, Stefanie}, title = {Rate-limiting recovery processes in neurotransmission under sustained stimulation}, series = {Mathematical Biosciences}, volume = {362}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2023.109023}, abstract = {At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution.}, language = {de} } @article{MontefuscoSchuetteWinkelmann2023, author = {Montefusco, Alberto and Sch{\"u}tte, Christof and Winkelmann, Stefanie}, title = {A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures}, series = {SIAM Journal on Applied Mathematics}, volume = {83}, journal = {SIAM Journal on Applied Mathematics}, number = {2}, doi = {10.1137/22M1488831}, pages = {837 -- 861}, year = {2023}, abstract = {The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257-2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.}, language = {en} } @article{HelfmannConradLorenzSpreenetal., author = {Helfmann, Luzie and Conrad, Natasa Djurdjevac and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Modelling opinion dynamics under the impact of influencer and media strategies}, series = {Scientific Reports}, volume = {13}, journal = {Scientific Reports}, doi = {10.1038/s41598-023-46187-9}, pages = {19375}, abstract = {Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation.}, language = {en} } @misc{HelfmannDjurdjevacConradLorenzSpreenetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies}, doi = {10.12752/9267}, abstract = {This repository contains the Julia code accompanying the paper "Modelling opinion dynamics under the impact of influencer and media strategies", Scientific Reports, Vol.13, p. 19375, 2023.}, language = {en} } @misc{KostreSunkaraSchuetteetal., author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Nataša}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86764}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{KostreSunkaraSchuetteetal.2022, author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, series = {Applied Network Science}, volume = {7}, journal = {Applied Network Science}, publisher = {Springer Nature}, doi = {10.1007/s41109-022-00492-w}, pages = {18}, year = {2022}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{DjurdjevacConradChemnitzKostreetal., author = {Djurdjevac Conrad, Natasa and Chemnitz, Robin and Kostre, Margarita and Schweigart, Fleur and Fless, Friederike and Sch{\"u}tte, Christof and Ducke, Benjamin}, title = {A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia}, language = {en} } @article{ZhangSchuette, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {4}, doi = {10.1002/pamm.202300189}, abstract = {High-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.}, language = {en} } @misc{BittracherKoltaiKlusetal., author = {Bittracher, Andreas and Koltai, P{\´e}ter and Klus, Stefan and Banisch, Ralf and Dellnitz, Michael and Sch{\"u}tte, Christof}, title = {Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63822}, abstract = {We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.}, language = {en} } @article{GaskinConradPavliotisetal., author = {Gaskin, Thomas and Conrad, Tim and Pavliotis, Grigorios A. and Sch{\"u}tte, Christof}, title = {Neural parameter calibration and uncertainty quantification for epidemic forecasting}, series = {PLOS ONE}, journal = {PLOS ONE}, abstract = {The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.}, language = {en} } @article{SeckerFackeldeyWeberetal., author = {Secker, Christopher and Fackeldey, Konstantin and Weber, Marcus and Ray, Sourav and Gorgulla, Christoph and Sch{\"u}tte, Christof}, title = {Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists}, series = {Journal of Cheminformatics}, volume = {15}, journal = {Journal of Cheminformatics}, doi = {10.1186/s13321-023-00746-4}, abstract = {Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale.}, language = {en} } @article{ThiesSunkaraRayetal., author = {Thies, Arne and Sunkara, Vikram and Ray, Sourav and Wulkow, Hanna and Celik, M. {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, series = {Scientific Reports}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, abstract = {We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @article{RaySunkaraSchuetteetal.2020, author = {Ray, Sourav and Sunkara, Vikram and Sch{\"u}tte, Christof and Weber, Marcus}, title = {How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs}, series = {Molecular Simulation}, volume = {46}, journal = {Molecular Simulation}, number = {18}, publisher = {Taylor and Francis}, doi = {10.1080/08927022.2020.1839660}, pages = {1443 -- 1452}, year = {2020}, abstract = {Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- ('on'-rate) and dissociation- ('off'-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab.}, language = {en} } @misc{RayThiesSunkaraetal., author = {Ray, Sourav and Thies, Arne and Sunkara, Vikram and Wulkow, Hanna and Celik, {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82797}, abstract = {Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @misc{RaySunkaraSchuetteetal., author = {Ray, Sourav and Sunkara, Vikram and Sch{\"u}tte, Christof and Weber, Marcus}, title = {How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs}, issn = {1438-0064}, doi = {10.1080/08927022.2020.1839660}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78437}, abstract = {Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a \$\mu\$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.}, language = {en} } @misc{WangSchuette, author = {Wang, Han and Sch{\"u}tte, Christof}, title = {Building Markov State Models for Periodically Driven Non-Equilibrium Systems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53167}, abstract = {Recent years have seen an increased interest in non-equilibrium molecular dynamics (NEMD) simulations, especially for molecular systems with periodic forcing by external fields, e.g., in the context of studying effects of electromagnetic radiation on the human body tissue. Lately, an NEMD methods with local thermostating has been proposed that allows for studying non-equilibrium processes in a statistically reliable and thermodynamically consistent way. In this article, we demonstrate how to construct Markov State Models (MSMs) for such NEMD simulations. MSM building has been well-established for systems in equilibrium where MSMs with just a few (macro-)states allow for accurate reproduction of the essential kinetics of the molecular system under consideration. Non-equilibrium MSMs have been lacking so far. The article presents how to construct such MSMs and illustrates their validity and usefulness for the case of conformation dynamics of alanine dipeptide in an external electric field.}, language = {en} } @misc{KoltaiSchuette, author = {Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64868}, abstract = {We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.}, language = {en} } @article{NiemannWinkelmannWolfetal., author = {Niemann, Jan-Hendrik and Winkelmann, Stefanie and Wolf, Sarah and Sch{\"u}tte, Christof}, title = {Agent-based modeling: Population limits and large timescales}, series = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {31}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {3}, issn = {1438-0064}, doi = {10.1063/5.0031373}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77309}, abstract = {Modeling, simulation and analysis of interacting agent systems is a broad field of research, with existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (ODEs and SDEs, respectively) for medium to large populations. By means of an appropriately adapted transfer operator approach we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations. This approach has the potential to drastically reduce computational effort for the analysis of ABMs.}, language = {en} } @article{NiemannKlusSchuette, author = {Niemann, Jan-Hendrik and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Data-driven model reduction of agent-based systems using the Koopman generator}, series = {PLOS ONE}, volume = {16}, journal = {PLOS ONE}, number = {5}, doi = {10.1371/journal.pone.0250970}, abstract = {The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation or real-world data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.}, language = {en} } @misc{NiemannSchuetteKlus, author = {Niemann, Jan-Hendrik and Sch{\"u}tte, Christof and Klus, Stefan}, title = {Simulation data: Data-driven model reduction of agent-based systems using the Koopman generator}, series = {PLOS ONE}, volume = {16}, journal = {PLOS ONE}, number = {5}, doi = {http://doi.org/10.5281/zenodo.4522119}, language = {en} } @article{KlusNueskePeitzetal., author = {Klus, Stefan and N{\"u}ske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Sch{\"u}tte, Christof}, title = {Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, series = {Physica D: Nonlinear Phenomena}, volume = {406}, journal = {Physica D: Nonlinear Phenomena}, doi = {10.1016/j.physd.2020.132416}, language = {en} } @article{NiemannKlusConradetal., author = {Niemann, Jan-Hendrik and Klus, Stefan and Conrad, Natasa Djurdjevac and Sch{\"u}tte, Christof}, title = {Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems}, series = {Physica D: Nonlinear Phenomena}, volume = {460}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2024.134052}, pages = {134052}, abstract = {Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend on potentially nonlinear control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.}, language = {en} } @article{SherrattSrivastavaAinslieetal., author = {Sherratt, Katharine and Srivastava, Ajitesh and Ainslie, Kylie and Singh, David E. and Cublier, Aymar and Marinescu, Maria Cristina and Carretero, Jesus and Garcia, Alberto Cascajo and Franco, Nicolas and Willem, Lander and Abrams, Steven and Faes, Christel and Beutels, Philippe and Hens, Niel and M{\"u}ller, Sebastian and Charlton, Billy and Ewert, Ricardo and Paltra, Sydney and Rakow, Christian and Rehmann, Jakob and Conrad, Tim O.F. and Sch{\"u}tte, Christof and Nagel, Kai and Abbott, Sam and Grah, Rok and Niehus, Rene and Prasse, Bastian and Sandmann, Frank and Funk, Sebastian}, title = {Characterising information gains and losses when collecting multiple epidemic model outputs}, series = {Epidemics}, journal = {Epidemics}, publisher = {Elsevier BV}, issn = {1755-4365}, doi = {10.1016/j.epidem.2024.100765}, abstract = {Collaborative comparisons and combinations of epidemic models are used as policy-relevant evidence during epidemic outbreaks. In the process of collecting multiple model projections, such collaborations may gain or lose relevant information. Typically, modellers contribute a probabilistic summary at each time-step. We compared this to directly collecting simulated trajectories. We aimed to explore information on key epidemic quantities; ensemble uncertainty; and performance against data, investigating potential to continuously gain information from a single cross-sectional collection of model results. Methods We compared July 2022 projections from the European COVID-19 Scenario Modelling Hub. Five modelling teams projected incidence in Belgium, the Netherlands, and Spain. We compared projections by incidence, peaks, and cumulative totals. We created a probabilistic ensemble drawn from all trajectories, and compared to ensembles from a median across each model's quantiles, or a linear opinion pool. We measured the predictive accuracy of individual trajectories against observations, using this in a weighted ensemble. We repeated this sequentially against increasing weeks of observed data. We evaluated these ensembles to reflect performance with varying observed data. Results. By collecting modelled trajectories, we showed policy-relevant epidemic characteristics. Trajectories contained a right-skewed distribution well represented by an ensemble of trajectories or a linear opinion pool, but not models' quantile intervals. Ensembles weighted by performance typically retained the range of plausible incidence over time, and in some cases narrowed this by excluding some epidemic shapes. Conclusions. We observed several information gains from collecting modelled trajectories rather than quantile distributions, including potential for continuously updated information from a single model collection. The value of information gains and losses may vary with each collaborative effort's aims, depending on the needs of projection users. Understanding the differing information potential of methods to collect model projections can support the accuracy, sustainability, and communication of collaborative infectious disease modelling efforts. Data availability All code and data available on Github: https://github.com/covid19-forecast-hub-europe/aggregation-info-loss}, language = {en} } @article{MontefuscoHelfmannOkunolaetal., author = {Montefusco, Alberto and Helfmann, Luzie and Okunola, Toluwani and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Partial mean-field model for neurotransmission dynamics}, series = {Mathematical Biosciences}, volume = {369}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2024.109143}, abstract = {This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.}, language = {en} } @article{ZhangSchuette2024, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {On finding optimal collective variables for complex systems by minimizing the deviation between effective and full dynamics}, year = {2024}, abstract = {This paper is concerned with collective variables, or reaction coordinates, that map a discrete-in-time Markov process X_n in R^d to a (much) smaller dimension k≪d. We define the effective dynamics under a given collective variable map ξ as the best Markovian representation of X_n under ξ. The novelty of the paper is that it gives strict criteria for selecting optimal collective variables via the properties of the effective dynamics. In particular, we show that the transition density of the effective dynamics of the optimal collective variable solves a relative entropy minimization problem from certain family of densities to the transition density of X_n. We also show that many transfer operator-based data-driven numerical approaches essentially learn quantities of the effective dynamics. Furthermore, we obtain various error estimates for the effective dynamics in approximating dominant timescales / eigenvalues and transition rates of the original process X_n and how optimal collective variables minimize these errors. Our results contribute to the development of theoretical tools for the understanding of complex dynamical systems, e.g. molecular kinetics, on large timescales. These results shed light on the relations among existing data-driven numerical approaches for identifying good collective variables, and they also motivate the development of new methods.}, language = {en} } @article{DonatiSchuetteWeber, author = {Donati, Luca and Sch{\"u}tte, Christof and Weber, Marcus}, title = {The Kramers turnover in terms of a macro-state projection on phase space}, series = {Molecular Physics}, journal = {Molecular Physics}, doi = {10.48550/arXiv.2402.00211}, abstract = {We have investigated how Langevin dynamics is affected by the friction coefficient using the novel algorithm ISOKANN, which combines the transfer operator approach with modern machine learning techniques. ISOKANN describes the dynamics in terms of an invariant subspace projection of the Koopman operator defined in the entire state space, avoiding approximations due to dimensionality reduction and discretization. Our results are consistent with the Kramers turnover and show that in the low and moderate friction regimes, metastable macro-states and transition rates are defined in phase space, not only in position space.}, language = {en} } @misc{BanischDjurdjevacConradSchuette, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof}, title = {Reactive flows and unproductive cycles for random walks on complex networks}, issn = {1438-0064}, doi = {10.1140/epjst/e2015-02417-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54239}, abstract = {We present a comprehensive theory for analysis and understanding of transition events between an initial set A and a target set B for general ergodic finite-state space Markov chains or jump processes, including random walks on networks as they occur, e.g., in Markov State Modelling in molecular dynamics. The theory allows us to decompose the probability flow generated by transition events between the sets A and B into the productive part that directly flows from A to B through reaction pathways and the unproductive part that runs in loops and is supported on cycles of the underlying network. It applies to random walks on directed networks and nonreversible Markov processes and can be seen as an extension of Transition Path Theory. Information on reaction pathways and unproductive cycles results from the stochastic cycle decomposition of the underlying network which also allows to compute their corresponding weight, thus characterizing completely which structure is used how often in transition events. The new theory is illustrated by an application to a Markov State Model resulting from weakly damped Langevin dynamics where the unproductive cycles are associated with periodic orbits of the underlying Hamiltonian dynamics.}, language = {en} } @article{DjurdjevacConradBanischSchuette, author = {Djurdjevac Conrad, Natasa and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Modularity of Directed Networks: Cycle Decomposition Approach}, series = {Journal of Computational Dynamics 2 (2015) pp. 1-24}, journal = {Journal of Computational Dynamics 2 (2015) pp. 1-24}, doi = {10.3934/jcd.2015.2.1}, abstract = {The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.}, language = {en} } @article{SarichDjurdjevacConradBruckneretal.2014, author = {Sarich, Marco and Djurdjevac Conrad, Natasa and Bruckner, Sharon and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Modularity revisited: A novel dynamics-based concept for decomposing complex networks}, series = {Journal of Computational Dynamics}, volume = {1}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2014.1.191}, pages = {191 -- 212}, year = {2014}, language = {en} }