TY - JOUR A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems JF - The Journal of Chemical Physics N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1063/1.4986560 VL - 147 IS - 11 SP - 114115-1 EP - 114115-18 ER - TY - GEN A1 - Vega, Iliusi A1 - Schütte, Christof A1 - Conrad, Tim T1 - SAIMeR: Self-adapted method for the identification of metastable states in real-world time series N2 - 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. T3 - ZIB-Report - 14-16 KW - time series analysis KW - application in statistical physics KW - recurrence quantification analysis KW - threshold KW - metastability KW - non-linear dynamics Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50130 SN - 1438-0064 ER - TY - GEN A1 - Bockmayr, Alexander A1 - Siebert, Heike A1 - Röblitz, Susanna A1 - Schütte, Christof A1 - Deuflhard, Peter ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutela, Martin ED - Sprekels, Jürgen T1 - Advanced mathematical modeling in systems biology T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 29 EP - 44 PB - European Mathematical Society ER - TY - GEN A1 - Agarwal, Animesh A1 - Wang, Han A1 - Schütte, Christof A1 - Delle Site, Luigi T1 - Chemical potential of liquids and mixtures via Adaptive Resolution Simulation N2 - 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. T3 - ZIB-Report - 14-25 KW - Coarse graining KW - adaptive resolution KW - molecular dynamics KW - chemical potential Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50972 SN - 1438-0064 ER - TY - GEN A1 - Banisch, Ralf A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Module Detection in Directed Real-World Networks N2 - 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. T3 - ZIB-Report - 14-13 KW - Module identification and classification KW - cycle decomposition KW - communication KW - directed networks Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-49849 SN - 1438-0064 ER - TY - GEN A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Noé, Frank A1 - Weber, Marcus ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - Design of functional molecules T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 49 EP - 65 PB - European Mathematical Society ER - TY - GEN A1 - Deuflhard, Peter A1 - Schütte, Christof ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - Life Sciences T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 1 EP - 5 PB - European Mathematical Society ER - TY - GEN A1 - Schütte, Christof A1 - Conrad, Tim ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Skutella, Martin ED - Sprekels, Jürgen T1 - Showcase 3: Information-based medicine T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 66 EP - 67 PB - European Mathematical Society ER - TY - GEN A1 - Zhang, Wei A1 - Wang, Han A1 - Hartmann, Carsten A1 - Weber, Marcus A1 - Schütte, Christof T1 - Applications of the cross-entropy method to importance sampling and optimal control of diffusions N2 - 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. T3 - ZIB-Report - 14-10 KW - important sampling KW - optimal control KW - cross-entropy method KW - rare events KW - change of measure Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-49720 SN - 1438-0064 ER - TY - GEN A1 - Klebanov, Ilja A1 - Sikorski, Alexander A1 - Schütte, Christof A1 - Röblitz, Susanna T1 - Prior estimation and Bayesian inference from large cohort data sets N2 - 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. T3 - ZIB-Report - 16-09 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57475 SN - 1438-0064 ER - TY - JOUR A1 - Kryven, Ivan A1 - Röblitz, Susanna A1 - Schütte, Christof T1 - Solution of the chemical master equation by radial basis functions approximation with interface tracking JF - BMC Systems Biology N2 - 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 Y1 - 2015 U6 - https://doi.org/10.1186/s12918-015-0210-y VL - 9 IS - 67 SP - 1 EP - 12 ER - TY - JOUR A1 - Enciso, Marta A1 - Schütte, Christof A1 - Delle Site, Luigi T1 - Influence of pH and sequence in peptide aggregation via molecular simulation JF - Journal of Chemical Physics Y1 - 2015 U6 - https://doi.org/https://doi.org/10.1063/1.4935707 VL - 143 IS - 24 ER - TY - GEN A1 - Willenbockel, Christian Tobias A1 - Schütte, Christof T1 - Variational Bayesian Inference and Model Selection for the Stochastic Block Model with Irrelevant Vertices N2 - 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. T3 - ZIB-Report - 16-01 KW - Clustering KW - Variational Bayes EM KW - Model Selection, KW - Stochastic Block Model KW - Networks KW - unsupervised classification KW - Noise Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57003 SN - 1438-0064 ER - TY - JOUR A1 - Schütte, Christof A1 - Sarich, Marco T1 - A Critical Appraisal of Markov State Models JF - The European Physical Journal Special Topics N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1140/epjst/e2015-02421-0 VL - 224 IS - 12 SP - 2445 EP - 2462 ER - TY - GEN A1 - Hartmann, Carsten A1 - Banisch, Ralf A1 - Sarich, Marco A1 - Badowski, Thomas A1 - Schütte, Christof T1 - Characterization of Rare Events in Molecular Dynamics N2 - 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. T3 - ZIB-Report - 13-51 KW - rare events KW - moleculare dynamics KW - optimal pathways KW - stochastic control KW - dynamic programming KW - change of measure KW - cumulant generating function Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42410 SN - 1438-0064 ER - TY - GEN A1 - Sarich, Marco A1 - Banisch, Ralf A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - Markov State Models for Rare Events in Molecular Dynamics N2 - 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. T3 - ZIB-Report - 13-52 KW - rare events KW - Markov state models KW - long timescales KW - optimal control Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42420 SN - 1438-0064 ER - TY - GEN A1 - Schütte, Christof A1 - Nielsen, Adam A1 - Weber, Marcus T1 - Markov State Models and Molecular Alchemy N2 - 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. T3 - ZIB-Report - 14-05 KW - Girsanov Theorem KW - Stochastic Differential Equation KW - Importance Sampling Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-46718 SN - 1438-0064 ER - TY - GEN A1 - Koltai, Peter A1 - Ciccotti, Giovanni A1 - Schütte, Christof T1 - On metastability and Markov state models for non-stationary molecular dynamics BT - 2016 Editor's Choice of The Journal of Chemical Physics T2 - The Journal of Chemical Physics N2 - 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. T3 - ZIB-Report - 16-11 KW - coherent set, KW - Markov state model KW - non-equilibrium molecular dynamics KW - metastability Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57869 SN - 1438-0064 VL - 174103 ET - 145 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Weber, Marcus A1 - Schütte, Christof T1 - Finding dominant structures of nonreversible Markov processes JF - Multiscale Modeling and Simulation Y1 - 2016 U6 - https://doi.org/10.1137/15M1032272 VL - 14 IS - 4 SP - 1319 EP - 1340 ER - TY - GEN A1 - Gupta, Pooja A1 - Röblitz, Susanna A1 - Krause, Carola A1 - Knaus, Petra A1 - Schütte, Christof T1 - Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density T2 - Computational Models in biology and medicine, 2013, Dresden, Germany Y1 - 2013 ER - TY - CHAP A1 - Gupta, Pooja A1 - Krause, Carola A1 - Rikeit, Paul A1 - Röblitz, Susanna A1 - Knaus, Petra A1 - Schütte, Christof T1 - Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density T2 - 10th International BMP conference, 2014, Berlin, Germany Y1 - 2014 ER - TY - JOUR A1 - Gul, Raheem A1 - Schütte, Christof A1 - Bernhard, Stefan T1 - Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries JF - Applied Mathematical Modelling Y1 - 2016 U6 - https://doi.org/10.1016/j.apm.2016.03.041 ER - TY - GEN A1 - Bittracher, Andreas A1 - Banisch, Ralf A1 - Schütte, Christof T1 - Data-driven Computation of Molecular Reaction Coordinates N2 - 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. T3 - ZIB-Report - 17-77 KW - reaction coordinate KW - coarse graining KW - transition manifold KW - transfer operator KW - Galerkin method KW - meshfree basis KW - data-driven Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66179 SN - 1438-0064 ER - TY - GEN A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics N2 - 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. T3 - ZIB-Report - 21-15 KW - linear reaction networks KW - cross-correlation KW - neurotransmission Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82674 SN - 1438-0064 ER - TY - JOUR A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Ray, Sourav A1 - Wulkow, Hanna A1 - Celik, M. Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design JF - Scientific Reports N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-27699-w VL - 13 IS - 607 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - 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. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Winkelmann, Stefanie T1 - A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures JF - SIAM Journal on Applied Mathematics N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1137/22M1488831 VL - 83 IS - 2 SP - 837 EP - 861 ER - TY - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies N2 - 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. Y1 - 2023 U6 - https://doi.org/10.12752/9267 ER - TY - JOUR A1 - Wehlitz, Nathalie A1 - Sadeghi, Mohsen A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Pavliotis, Grigorios A. A1 - Winkelmann, Stefanie T1 - Approximating particle-based clustering dynamics by stochastic PDEs JF - SIAM Journal on Applied Dynamical Systems N2 - This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number. Y1 - 2025 U6 - https://doi.org/10.1137/24M1676661 VL - 24 IS - 2 SP - 1231 EP - 1250 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Helfmann, Luzie A1 - Okunola, Toluwani A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Partial mean-field model for neurotransmission dynamics JF - Mathematical Biosciences N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1016/j.mbs.2024.109143 VL - 369 ER - TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Klus, Stefan A1 - Conrad, Natasa Djurdjevac A1 - Schütte, Christof T1 - Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems JF - Physica D: Nonlinear Phenomena N2 - 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. Y1 - 2024 U6 - https://doi.org/https://doi.org/10.1016/j.physd.2024.134052 VL - 460 SP - 134052 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Chemnitz, Robin A1 - Kostre, Margarita A1 - Schweigart, Fleur A1 - Fless, Friederike A1 - Schütte, Christof A1 - Ducke, Benjamin T1 - A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia JF - PLoS ONE N2 - Romanisation is a multi-faceted historical phenomenon with profound and lasting cultural impact on the ancient world. In the modern-day territory of Tunisia, this is particularly manifest during the first four centuries AD, under the reign of the Roman Empire. We derive a reduced, operational concept of Romanisation as a cultural diffusion process that is observable in the archaeological remains of the Roman era settlement system. We then introduce a novel mathematical model that computes spatio-temporal approximations for the Romanisation of the settlement system. The model is based on the concept of temporal road activation and makes minimal assumptions regarding input data quality. The results of our study contribute to the understanding of the time dynamics of the region’s road network, under the influence of Romanisation. Our model can be applied in similar archaeological research scenarios, to generate spatio-temporal backbones for the analysis of otherwise intractably complex social processes. Y1 - 2024 U6 - https://doi.org/10.1371/journal.pone.0309752 VL - 19 IS - 9 ER - TY - JOUR A1 - Winkelmann, Stefanie A1 - Zonker, Johannes A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading JF - Mathematical Biosciences N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1016/j.mbs.2021.108619 VL - 336 PB - Elsevier ER - TY - JOUR A1 - del Razo, Mauricio A1 - Frömberg, Daniela A1 - Straube, Arthur A1 - Schütte, Christof A1 - Höfling, Felix A1 - Winkelmann, Stefanie T1 - A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations JF - Letters in Mathematical Physics Y1 - 2022 U6 - https://doi.org/10.1007/s11005-022-01539-w VL - 112 IS - 49 ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Schütte, Christof A1 - Höfling, Felix T1 - Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles JF - J. Phys. Chem. Lett. N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1021/acs.jpclett.1c03016 VL - 12 SP - 9888 EP - 9893 ER - TY - JOUR A1 - Helfmann, Luzie A1 - Conrad, Natasa Djurdjevac A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Modelling opinion dynamics under the impact of influencer and media strategies JF - Scientific Reports N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-46187-9 VL - 13 SP - 19375 ER - TY - JOUR A1 - Ernst, Ariane A1 - Unger, Nathalie A1 - Schütte, Christof A1 - Walter, Alexander A1 - Winkelmann, Stefanie T1 - Rate-limiting recovery processes in neurotransmission under sustained stimulation JF - Mathematical Biosciences N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1016/j.mbs.2023.109023 VL - 362 ER - TY - JOUR A1 - Secker, Christopher A1 - Fackeldey, Konstantin A1 - Weber, Marcus A1 - Ray, Sourav A1 - Gorgulla, Christoph A1 - Schütte, Christof T1 - Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists JF - Journal of Cheminformatics N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1186/s13321-023-00746-4 VL - 15 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - 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. Y1 - 2021 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Schütte, Christof T1 - The Augmented Jump Chain JF - Advanced Theory and Simulations N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1002/adts.202000274 VL - 4 IS - 4 PB - Wiley-VCH ER - TY - JOUR A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia JF - Applied Network Science N2 - 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. KW - mesoscale spreading process KW - network inference KW - time-evolving network KW - romanization spreading KW - scarce data Y1 - 2022 U6 - https://doi.org/10.1007/s41109-022-00492-w VL - 7 PB - Springer Nature ER - TY - GEN A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Nataša T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia N2 - 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. T3 - ZIB-Report - 22-10 KW - mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86764 SN - 1438-0064 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - 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 framework, the new framework 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. Y1 - 2025 U6 - https://doi.org/10.1016/j.cam.2025.116675 VL - 470 ER - TY - GEN A1 - Zhang, Wei A1 - Schütte, Christof T1 - Reliable approximation of long relaxation timescales in molecular dynamics N2 - 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. T3 - ZIB-Report - 17-19 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63718 SN - 1438-0064 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Zhang, Wei T1 - Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms JF - Journal of Statistical Physics N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-019-02286-4 VL - 175 IS - 6 SP - 1214 EP - 1261 ER - TY - JOUR A1 - Zhang, Wei A1 - Li, Tiejun A1 - Schütte, Christof T1 - Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks JF - Journal of Computational Physics N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1016/j.jcp.2022.111377 VL - 465 ER - TY - JOUR A1 - Zhang, Wei A1 - Klus, Stefan A1 - Conrad, Tim A1 - Schütte, Christof T1 - Learning chemical reaction networks from trajectory data JF - SIAM Journal on Applied Dynamical Systems (SIADS) N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1137/19M1265880 VL - 18 IS - 4 SP - 2000 EP - 2046 ER - TY - JOUR A1 - Akhyar, Fatima-Zahrae A1 - Zhang, Wei A1 - Stoltz, Gabriel A1 - Schütte, Christof T1 - Generative modeling of conditional probability distributions on the level-sets of collective variables N2 - Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $\xi: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k