@article{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}, volume = {143}, journal = {Journal of Chemical Physics}, number = {24}, doi = {https://doi.org/10.1063/1.4935707}, year = {2015}, language = {en} } @misc{WillenbockelSchuette2016, 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}, year = {2016}, 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} } @article{SchuetteSarich2015, author = {Sch{\"u}tte, Christof and Sarich, Marco}, title = {A Critical Appraisal of Markov State Models}, volume = {224}, journal = {The European Physical Journal Special Topics}, number = {12}, doi = {10.1140/epjst/e2015-02421-0}, pages = {2445 -- 2462}, 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{HartmannBanischSarichetal.2013, 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}, year = {2013}, 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{SarichBanischHartmannetal.2013, 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}, year = {2013}, 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} } @misc{SchuetteNielsenWeber2014, 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}, year = {2014}, 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{OsterlandBennProhaskaetal.2015, author = {Osterland, Marc and Benn, Andreas and Prohaska, Steffen and Sch{\"u}tte, Christof}, title = {Single Cell Tracking in Phase-Contrast Microscopy}, journal = {EMBL Symposium 2015 - Seeing is Believing - Imaging the Processes of Life}, year = {2015}, 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} } @misc{KoltaiCiccottiSchuette2016, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On metastability and Markov state models for non-stationary molecular dynamics}, 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}, year = {2016}, 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} } @article{DjurdjevacConradWeberSchuette2016, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, year = {2016}, language = {en} } @misc{GuptaRoeblitzKrauseetal.2013, 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}, journal = {Computational Models in biology and medicine, 2013, Dresden, Germany}, year = {2013}, language = {en} } @inproceedings{GuptaKrauseRikeitetal.2014, 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}, booktitle = {10th International BMP conference, 2014, Berlin, Germany}, year = {2014}, language = {en} } @article{GulSchuetteBernhard2016, author = {Gul, Raheem and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries}, journal = {Applied Mathematical Modelling}, doi = {10.1016/j.apm.2016.03.041}, year = {2016}, language = {en} } @misc{BittracherBanischSchuette2017, 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}, year = {2017}, 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} } @phdthesis{Schuette1999, 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}, year = {1999}, 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.2001, 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}, year = {2001}, 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} } @article{WulkowKoltaiSunkaraetal.2021, 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}, journal = {J. Stat. Phys.}, arxiv = {http://arxiv.org/abs/2112.06742}, year = {2021}, 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} } @misc{ErnstSchuetteSigristetal.2021, 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}, year = {2021}, 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{ErnstSchuetteSigristetal.2022, 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}, volume = {343}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2021.108760}, year = {2022}, 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{ThiesSunkaraRayetal.2023, 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}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, year = {2023}, 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} } @misc{RayThiesSunkaraetal.2021, 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}, year = {2021}, 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} } @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}, volume = {83}, journal = {SIAM Journal on Applied Mathematics}, number = {2}, arxiv = {http://arxiv.org/abs/2201.02613}, 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} }