@misc{FischerCordesSchuette1997, 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}, year = {1997}, 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{HuisingaBestCordesetal.1998, 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}, year = {1998}, 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} } @article{ZimperDjurdjevacHartmannetal.2025, author = {Zimper, Sebastian and Djurdjevac, Ana and Hartmann, Carsten and Sch{\"u}tte, Christof and Conrad, Natasa Djurdjevac}, title = {Mean-field optimal control with stochastic leaders}, arxiv = {http://arxiv.org/abs/2512.19201}, year = {2025}, abstract = {We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small number of leaders (influencers) can steer the behaviour of a large population of followers. In this context, we study a partial mean-field limit where the number of followers tends to infinity, while the number of leaders stays constant. The partial mean-field limit dynamics is then given by a McKean-Vlasov stochastic differential equation (SDE) for the followers, coupled to a controlled It{\^o}-SDE governing the dynamics of the lead agents. For a given cost functional that the lead agents seek to minimise, we show that the unique optimal control of the finite agent system convergences to the optimal control of the limiting system. This establishes that the low-dimensional control of the partial (mean-field) system provides an effective approximation for controlling the high-dimensional finite agent system. In addition, we propose a stochastic gradient descent algorithm that can efficiently approximate the mean-field control. Our theoretical results are illustrated on opinion dynamics model with lead agents, where the control objective is to drive the followers to reach consensus in finite time.}, language = {en} } @article{HartmannJoesterSchuetteetal.2026, author = {Hartmann, Carsten and J{\"o}ster, Annika and Sch{\"u}tte, Christof and Sikorski, Alexander and Weber, Marcus}, title = {Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting}, arxiv = {http://arxiv.org/abs/2601.01489}, year = {2026}, abstract = {Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples.}, language = {en} } @misc{DeuflhardSchuette2003, 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}, year = {2003}, 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} } @phdthesis{Schuette1994, 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}, year = {1994}, 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{SchuetteHuisinga1999, 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}, year = {1999}, 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} } @misc{Schuette1999, 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}, year = {1999}, 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{SchuetteHuisingaDeuflhard1999, 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}, year = {1999}, 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{DeuflhardHuisingaFischeretal.1998, 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}, year = {1998}, 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.1998, 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}, year = {1998}, 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} } @misc{WangHartmannSchuette2013, 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}, year = {2013}, 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} } @inproceedings{DeuflhardSchuette2004, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, 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} } @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}, volume = {4}, booktitle = {Computational molecular dynamics}, editor = {Deuflhard, Peter}, publisher = {Berlin: Springer.}, pages = {98 -- 115}, year = {1998}, 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}, volume = {315}, journal = {Lin. Alg. Appl.}, pages = {39 -- 59}, year = {2000}, 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}, volume = {4216}, journal = {Computational Life Sciences II}, publisher = {Springer}, pages = {98 -- 115}, year = {2006}, language = {en} } @misc{WillenbockelSchuette2015, 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}, year = {2015}, 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} } @article{BanischDjurdjevacConradSchuette2015, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof}, title = {Reactive flows and unproductive cycles for random walks on complex networks}, journal = {The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387}, doi = {10.1140/epjst/e2015-02417-8}, year = {2015}, language = {en} } @misc{DjurdjevacConradWeberSchuette2015, 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}, year = {2015}, 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{GelssMateraSchuette2015, 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}, year = {2015}, 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} } @misc{EncisoSchuetteDelleSite2015, 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}, year = {2015}, 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} } @misc{SchuetteSarich2015, 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}, year = {2015}, 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{BanischDjurdjevacConradSchuette2015, 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}, year = {2015}, 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{ZhangWangHartmannetal.2014, 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}, volume = {36}, journal = {Siam Journal on Scientific Computing}, number = {6}, doi = {10.1137/14096493X}, pages = {A2654 -- A2672}, year = {2014}, language = {en} } @misc{DjurdjevacConradBanischSchuette2014, 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}, year = {2014}, 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{WangSchuetteCiccottietal.2014, 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}, volume = {10}, journal = {Journal of Chemical Theory and Computation}, number = {4}, doi = {10.1021/ct400993e}, pages = {1376 -- 1386}, year = {2014}, 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{WinkelmannSchuettevonKleist2014, 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}, volume = {12}, journal = {Communications in Mathematical Sciences}, number = {5}, doi = {10.4310/CMS.2014.v12.n5.a4}, pages = {859 -- 877}, year = {2014}, 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{SarichSchuette2014, author = {Sarich, Marco and Sch{\"u}tte, Christof}, title = {Markov Model Theory}, 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}, year = {2014}, 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} } @misc{SarichSchuette2014, 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}, year = {2014}, 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{DjurdjevacConradBanischSchuette2015, author = {Djurdjevac Conrad, Natasa and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Modularity of Directed Networks: Cycle Decomposition Approach}, journal = {Journal of Computational Dynamics 2 (2015) pp. 1-24}, doi = {10.3934/jcd.2015.2.1}, year = {2015}, 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{EncisoSchuetteDelleSite2013, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {A pH-dependent coarse-grained model for peptides}, volume = {9}, journal = {Soft Matter}, number = {26}, doi = {10.1039/C3SM27893J}, pages = {6118 -- 6127}, year = {2013}, 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{WinkelmannSchuettevonKleist2013, 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}, volume = {2}, journal = {International Journal of Biomathematics and Biostatistics}, number = {1}, year = {2013}, 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{SchuetteNielsenWeber2015, author = {Sch{\"u}tte, Christof and Nielsen, Adam and Weber, Marcus}, title = {Markov State Models and Molecular Alchemy}, volume = {113}, journal = {Molecular Physics}, number = {1}, doi = {10.1080/00268976.2014.944597}, pages = {69 -- 78}, year = {2015}, 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.2014, 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}, volume = {141}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.4886807}, pages = {034102}, year = {2014}, language = {en} } @misc{WangSchuette2014, 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}, year = {2014}, 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{GulSchuetteBernhard2015, 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}, year = {2015}, 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} } @book{OPUS4-5339, title = {Molecular Dynamics Simulation}, journal = {Entropy (special issue)}, editor = {Ciccotti, Giovanni and Ferrario, Mauro and Sch{\"u}tte, Christof}, publisher = {Multidisciplinary Digital Publishing Institute (MDPI)}, year = {2014}, language = {en} } @article{KlusSchuette2016, author = {Klus, Stefan and Sch{\"u}tte, Christof}, title = {Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {2}, doi = {10.3934/jcd.2016007}, pages = {139 -- 161}, year = {2016}, 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{HartmannSchuetteZhang2016, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Model reduction algorithms for optimal control and importance sampling of diffusions}, volume = {29}, journal = {Nonlinearity}, number = {8}, doi = {10.1088/0951-7715/29/8/2298}, pages = {2298 -- 2326}, year = {2016}, 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{KlusKoltaiSchuette2016, author = {Klus, Stefan and Koltai, Peter and Sch{\"u}tte, Christof}, title = {On the numerical approximation of the Perron-Frobenius and Koopman operator}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2016003}, pages = {51 -- 77}, year = {2016}, 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{HuttaryGoubergritsSchuetteetal.2017, 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}, volume = {87}, journal = {Computers in Biology and Medicine}, doi = {10.1016/j.compbiomed.2017.05.021}, pages = {104 -- 123}, year = {2017}, language = {en} } @misc{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 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}, 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 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.2018, 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}, volume = {28}, journal = {Journal of Nonlinear Science}, number = {3}, doi = {10.1007/s00332-017-9437-7}, pages = {985 -- 1010}, year = {2018}, language = {en} } @article{KoltaiCiccottiSchuette2016, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On Markov state models for non-equilibrium molecular dynamics}, volume = {145}, journal = {The Journal of Chemical Physics}, number = {174103}, doi = {10.1063/1.4966157}, year = {2016}, language = {en} } @article{GelssMateraSchuette2016, 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}, volume = {314}, journal = {Journal of Computational Physics}, doi = {10.1016/j.jcp.2016.03.025}, pages = {489 -- 502}, year = {2016}, 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} } @article{VegaSchuetteConrad2016, author = {Vega, Iliusi and Sch{\"u}tte, Christof and Conrad, Tim}, title = {Finding metastable states in real-world time series with recurrence networks}, volume = {445}, journal = {Physica A: Statistical Mechanics and its Applications}, doi = {10.1016/j.physa.2015.10.041}, pages = {1 -- 17}, year = {2016}, 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} } @article{ConradGenzelCvetkovicetal.2017, 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}, volume = {18}, journal = {BMC Bioinfomatics}, number = {160}, doi = {10.1186/s12859-017-1565-4}, year = {2017}, 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{RuedrichSarichSchuette2017, 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}, journal = {Journal of Comp. Dynamics}, year = {2017}, 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}, 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{KlusGelssPeitzetal.2018, author = {Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Sch{\"u}tte, Christof}, title = {Tensor-based dynamic mode decomposition}, volume = {31}, journal = {Nonlinearity}, number = {7}, publisher = {IOP Publishing Ltd \& London Mathematical Society}, doi = {10.1088/1361-6544/aabc8f}, year = {2018}, language = {en} } @article{WeberFackeldeySchuette2017, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-Free Markov State Model Building}, volume = {146}, journal = {Journal of Chemical Physics}, number = {12}, doi = {10.1063/1.4978501}, year = {2017}, language = {en} } @misc{WinkelmannSchuette2017, 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}, year = {2017}, 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} }