TY - JOUR A1 - Vega, Iliusi A1 - Schütte, Christof A1 - Conrad, Tim T1 - Finding metastable states in real-world time series with recurrence networks JF - Physica A: Statistical Mechanics and its Applications N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1016/j.physa.2015.10.041 VL - 445 SP - 1 EP - 17 ER - TY - JOUR A1 - Conrad, Tim A1 - Genzel, Martin A1 - Cvetkovic, Nada A1 - Wulkow, Niklas A1 - Leichtle, Alexander Benedikt A1 - Vybiral, Jan A1 - Kytyniok, Gitta A1 - Schütte, Christof T1 - Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data JF - BMC Bioinfomatics N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1186/s12859-017-1565-4 VL - 18 IS - 160 ER - TY - JOUR A1 - Rüdrich, S. A1 - Sarich, Marco A1 - Schütte, Christof T1 - Utilizing hitting times for finding metastable sets in non-reversible Markov chains JF - Journal of Comp. Dynamics Y1 - 2017 ER - TY - JOUR A1 - Gupta, Pooja A1 - Gramatke, Annika A1 - Einspanier, Ralf A1 - Schütte, Christof A1 - von Kleist, Max A1 - Sharbati, Jutta T1 - In silico cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements JF - Toxicology in Vitro N2 - 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. KW - Real-time cell analyzer KW - Toxicity KW - Mathematical modeling Y1 - 2017 SN - 1438-0064 VL - 41 SP - 179 EP - 188 ER - TY - JOUR A1 - Klus, Stefan A1 - Gelß, Patrick A1 - Peitz, Sebastian A1 - Schütte, Christof T1 - Tensor-based dynamic mode decomposition JF - Nonlinearity Y1 - 2018 U6 - https://doi.org/10.1088/1361-6544/aabc8f VL - 31 IS - 7 PB - IOP Publishing Ltd & London Mathematical Society ER - TY - JOUR A1 - Weber, Marcus A1 - Fackeldey, Konstantin A1 - Schütte, Christof T1 - Set-Free Markov State Model Building JF - Journal of Chemical Physics Y1 - 2017 U6 - https://doi.org/10.1063/1.4978501 VL - 146 IS - 12 ER - TY - GEN A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Hybrid Models for Chemical Reaction Networks: Multiscale Theory and Application to Gene Regulatory Systems N2 - 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. T3 - ZIB-Report - 17-29 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64264 ER - TY - GEN A1 - Bittracher, Andreas A1 - Koltai, Péter A1 - Klus, Stefan A1 - Banisch, Ralf A1 - Dellnitz, Michael A1 - Schütte, Christof T1 - Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics N2 - We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics. T3 - ZIB-Report - 17-22 KW - metastability KW - slow dynamics KW - effective dynamics KW - transition manifold KW - embedding KW - transfer operator KW - reaction coordinate Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63822 SN - 1438-0064 ER - TY - GEN A1 - Koltai, Péter A1 - Schütte, Christof T1 - A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics N2 - We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one. T3 - ZIB-Report - 17-49 KW - Markov state model KW - non-equilibrium molecular dynamics KW - two timescale master equation KW - non-stationary forcing KW - metastability Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64868 SN - 1438-0064 ER - TY - JOUR A1 - Benn, Andreas A1 - Hiepen, Christian A1 - Osterland, Marc A1 - Schütte, Christof A1 - Zwijsen, An A1 - Knaus, Petra T1 - Role of bone morphogenetic proteins in sprouting angiogenesis: differential BMP receptor-dependent signaling pathways balance stalk vs. tip cell competence JF - FASEB Journal N2 - Before the onset of sprouting angiogenesis, the endothelium is prepatterned for the positioning of tip and stalk cells. Both cell identities are not static, as endothelial cells (ECs) constantly compete for the tip cell position in a dynamic fashion. Here, we show that both bone morphogenetic protein (BMP) 2 and BMP6 are proangiogenic in vitro and ex vivo and that the BMP type I receptors, activin receptor-like kinase (ALK)3 and ALK2, play crucial and distinct roles in this process. BMP2 activates the expression of tip cell–associated genes, such as DLL4 (delta-like ligand 4) and KDR (kinase insert domain receptor), and p38-heat shock protein 27 (HSP27)–dependent cell migration, thereby generating tip cell competence. Whereas BMP6 also triggers collective cell migration via the p38-HSP27 signaling axis, BMP6 induces in addition SMAD1/5 signaling, thereby promoting the expression of stalk cell–associated genes, such as HES1 (hairy and enhancer of split 1) and FLT1 (fms-like tyrosine kinase 1). Specifically, ALK3 is required for sprouting from HUVEC spheroids, whereas ALK2 represses sprout formation. We demonstrate that expression levels and respective complex formation of BMP type I receptors in ECs determine stalk vs. tip cell identity, thus contributing to endothelial plasticity during sprouting angiogenesis. As antiangiogenic monotherapies that target the VEGF or ALK1 pathways have not fulfilled efficacy objectives in clinical trials, the selective targeting of the ALK2/3 pathways may be an attractive new approach. Y1 - 2017 U6 - https://doi.org/10.1096/fj.201700193RR VL - 31 IS - 11 SP - 4720 EP - 4733 ER - 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 - Osterland, Marc A1 - Benn, Andreas A1 - Prohaska, Steffen A1 - Schütte, Christof T1 - Single Cell Tracking in Phase-Contrast Microscopy T2 - EMBL Symposium 2015 - Seeing is Believing - Imaging the Processes of Life N2 - 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. Y1 - 2015 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 - THES A1 - Schütte, Christof T1 - Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules N2 - 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. T3 - ZIB-Report - SC-99-18 KW - biochemical conformation KW - almost invariant set KW - Markov chain KW - Hamiltonian system KW - Markov operator KW - quasi-compact operator KW - Perron root KW - Perron- Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4063 ER - TY - GEN A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations N2 - 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. T3 - ZIB-Report - 01-03 KW - almost invariant sets KW - bridge sampling KW - metastability KW - hierarchical annealing KW - hybrid Monte Carlo KW - $n$-pentane molecule KW - ratio of normalizing co Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6296 ER - TY - JOUR A1 - Wulkow, Niklas A1 - Koltai, Péter A1 - Sunkara, Vikram A1 - Schütte, Christof T1 - Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory JF - J. Stat. Phys. N2 - 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. Y1 - 2021 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 - 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 JF - Mathematical Biosciences 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. Y1 - 2022 U6 - https://doi.org/10.1016/j.mbs.2021.108760 VL - 343 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 - JOUR A1 - Peppert, Felix A1 - von Kleist, Max A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks JF - IEEE Transactions on Neural Networks and Learning Systems N2 - Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling. Y1 - 2022 U6 - https://doi.org/10.1109/TNNLS.2021.3072746 VL - 33 IS - 11 SP - 6194 EP - 6205 ER - TY - JOUR A1 - Bittracher, Andreas A1 - Mollenhauer, Mattes A1 - Koltai, Péter A1 - Schütte, Christof T1 - Optimal Reaction Coordinates: Variational Characterization and Sparse Computation JF - Multiscale Modelling & Simulation N2 - Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques. Y1 - 2023 U6 - https://doi.org/10.1137/21M1448367 VL - 21 IS - 2 SP - 449 EP - 488 ER - TY - JOUR A1 - Mollenhauer, Mattes A1 - Klus, Stefan A1 - Schütte, Christof A1 - Koltai, Péter T1 - Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence JF - Journal of Machine Learning Research N2 - We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition. Y1 - 2022 UR - https://jmlr.org/papers/v23/20-442.html VL - 23 IS - 327 SP - 1 EP - 34 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 - Kostré, Margarita A1 - Djurdjevac Conrad, Natasa A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - Exploration of Particle Swarm Optimisation Algorithm with Divergent Parameters JF - Natural Computing Y1 - 2024 ER - TY - JOUR A1 - Regényi, Enikő A1 - Mashreghi, Mir-Farzin A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - Exploring transcription modalities from bimodal, single-cell RNA sequencing data JF - NAR Genomics and Bioinformatics N2 - Abstract There is a growing interest in generating bimodal, single-cell RNA sequencing (RNA-seq) data for studying biological pathways. These data are predominantly utilized in understanding phenotypic trajectories using RNA velocities; however, the shape information encoded in the two-dimensional resolution of such data is not yet exploited. In this paper, we present an elliptical parametrization of two-dimensional RNA-seq data, from which we derived statistics that reveal four different modalities. These modalities can be interpreted as manifestations of the changes in the rates of splicing, transcription or degradation. We performed our analysis on a cell cycle and a colorectal cancer dataset. In both datasets, we found genes that are not picked up by differential gene expression analysis (DGEA), and are consequently unnoticed, yet visibly delineate phenotypes. This indicates that, in addition to DGEA, searching for genes that exhibit the discovered modalities could aid recovering genes that set phenotypes apart. For communities studying biomarkers and cellular phenotyping, the modalities present in bimodal RNA-seq data broaden the search space of genes, and furthermore, allow for incorporating cellular RNA processing into regulatory analyses. Y1 - 2024 U6 - https://doi.org/10.1093/nargab/lqae179 SN - 2631-9268 VL - 6 IS - 4 PB - Oxford University Press (OUP) ER - TY - CHAP A1 - Ribera Borrell, Enric A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Reinforcement Learning with Random Time Horizons T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/borrell25a/borrell25a.pdf VL - 267 SP - 5101 EP - 5123 ER - TY - GEN A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics N2 - Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings. T3 - ZIB-Report - 21-40 KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2021 SN - 1438-0064 ER - TY - JOUR A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning JF - Acta Numerica N2 - One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject. Y1 - 2023 U6 - https://doi.org/10.1017/S0962492923000016 VL - 32 SP - 517 EP - 673 ER -