TY - JOUR A1 - Möller, Jan A1 - Isbilir, Ali A1 - Sungkaworn, Titiwat A1 - Osberg, Brenda A1 - Karathanasis, Christos A1 - Sunkara, Vikram A1 - Grushevsky, Eugene O A1 - Bock, Andreas A1 - Annibale, Paolo A1 - Heilemann, Mike A1 - Schütte, Christof A1 - Lohse, Martin J. T1 - Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision JF - Nature Chemical Biology Y1 - 2020 U6 - https://doi.org/10.1038/s41589-020-0566-1 VL - 16 SP - 946 EP - 954 ER - TY - JOUR A1 - Bittracher, Andreas A1 - Schütte, Christof T1 - A probabilistic algorithm for aggregating vastly undersampled large Markov chains JF - Physica D: Nonlinear Phenomena Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75874 VL - 416 ER - TY - JOUR A1 - Bittracher, Andreas A1 - Klus, Stefan A1 - Hamzi, Boumediene A1 - Schütte, Christof T1 - Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds JF - Journal of Nonlinear Science N2 - We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches. Y1 - 2021 U6 - https://doi.org/10.1007/s00332-020-09668-z VL - 31 ER - TY - JOUR A1 - Klus, Stefan A1 - Nüske, Feliks A1 - Peitz, Sebastian A1 - Niemann, Jan-Hendrik A1 - Clementi, Cecilia A1 - Schütte, Christof T1 - Data-driven approximation of the Koopman generator: Model reduction, system identification, and control JF - Physica D: Nonlinear Phenomena Y1 - 2020 U6 - https://doi.org/10.1016/j.physd.2020.132416 VL - 406 ER - TY - BOOK A1 - Reuter, Bernhard T1 - Generalisierte Markov-Modellierung N2 - Markov State Models (MSM) sind der Goldstandard zur Modellierung biomolekularer Dynamik, da sie die Identifizierung und Analyse metastabiler Zustände ermöglichen. Die robuste Perron-Cluster-Cluster-Analyse (PCCA+) ist ein verbreiteter Spectral-Clustering-Algorithmus, der für das Clustering hochdimensionaler MSM verwendet wird. Da die PCCA+ auf reversible Prozesse beschränkt ist, wird sie zur Generalisierten PCCA+ (G-PCCA) verallgemeinert, die geeignet ist, nichtreversible Prozesse aufzuklären. Bernhard Reuter untersucht hier mittels G-PCCA die nichtthermischen Auswirkungen von Mikrowellen auf die Proteindynamik. Dazu führt er molekulardynamische Nichtgleichgewichtssimulationen des Amyloid-β-(1–40)-Peptids durch und modelliert diese. Y1 - 2020 SN - 978-3-658-29711-4 U6 - https://doi.org/10.1007/978-3-658-29712-1 PB - Springer Spektrum, Wiesbaden ER - TY - GEN A1 - Bittracher, Andreas A1 - Schütte, Christof ED - Junge, Oliver ED - Schütze, O. ED - Froyland, Gary ED - Ober-Blobaum, S. ED - Padberg-Gehle, E. T1 - A weak characterization of slow variables in stochastic dynamical systems T2 - Advances in Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday Y1 - 2020 SN - 978-3-030-51264-4 U6 - https://doi.org/10.1007/978-3-030-51264-4_6 VL - 304 SP - 132 EP - 150 PB - Springer International ER - TY - GEN A1 - Mollenhauer, Mattes A1 - Schuster, Ingmar A1 - Klus, Stefan A1 - Schütte, Christof ED - Junge, Oliver ED - Schütze, O. ED - Froyland, Gary ED - Ober-Blobaum, S. ED - Padberg-Gehle, K. T1 - Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces T2 - Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday Y1 - 2020 SN - 978-3-030-51264-4 U6 - https://doi.org/10.1007/978-3-030-51264-4_5 VL - 304 SP - 109 EP - 131 PB - Springer International ER - TY - JOUR A1 - Koltai, Péter A1 - Lie, Han Cheng A1 - Plonka, Martin T1 - Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics JF - Nonlinearity N2 - We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron–Frobenius and Koopman operators. Y1 - 2019 U6 - https://doi.org/10.1088/1361-6544/ab1f2a VL - 32 IS - 11 SP - 4232 EP - 4257 ER - TY - JOUR A1 - Klus, Stefan A1 - Husic, Brooke E. A1 - Mollenhauer, Mattes A1 - Noe, Frank T1 - Kernel methods for detecting coherent structures in dynamical data JF - Chaos: An Interdisciplinary Journal of Nonlinear Science Y1 - 2019 U6 - https://doi.org/10.1063/1.5100267 VL - 29 IS - 12 ER - TY - THES A1 - Kostré, Margarita T1 - Hybrid Models and Simulations of Reaction-Diffusion Processes N2 - In this thesis,we are interested in multiscale models for particle-based reaction diffusion (PBRD) simulations,where we focus on coupling particle-based simulations to macroscopic chemical reservoirs. These reservoirs are given by a mean concentration of chemical species that can vary in time and space. We model these reservoirs as reaction-diffusion partial differential equations (PDEs). The goal of this work is to achieve a mathematically consistent coupling between the PBRD simulations and the reaction-diffusion PDEs. Y1 - 2019 ER - TY - GEN A1 - Bittracher, Andreas A1 - Schütte, Christof T1 - A probabilistic algorithm for aggregating vastly undersampled large Markov chains N2 - Model reduction of large Markov chains is an essential step in a wide array of techniques for understanding complex systems and for efficiently learning structures from high-dimensional data. We present a novel aggregation algorithm for compressing such chains that exploits a specific low-rank structure in the transition matrix which, e.g., is present in metastable systems, among others. It enables the recovery of the aggregates from a vastly undersampled transition matrix which in practical applications may gain a speedup of several orders of mag- nitude over methods that require the full transition matrix. Moreover, we show that the new technique is robust under perturbation of the transition matrix. The practical applicability of the new method is demonstrated by identifying a reduced model for the large-scale traffic flow patterns from real-world taxi trip data. T3 - ZIB-Report - 20-21 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78688 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/7587 SN - 1438-0064 ER - TY - JOUR A1 - Boltz, Horst-Holger A1 - Sirbu, Alexei A1 - Stelzer, Nina A1 - Lohse, Martin J. A1 - Schütte, Christof A1 - Annibale, Paolo T1 - Quantitative spectroscopy of single molecule interaction times JF - Optic Letters N2 - Single molecule fluorescence tracking provides information at nanometer-scale and millisecond-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address this aspect by developing a theoretical foundation for a spectroscopy of interaction times, i.e., the inference of interaction from imaging data. A non-trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted, together with the dependence of the exponential term upon the microscopic reaction affinity. Our approach is validated with simulated and experimental datasets. Y1 - 2021 U6 - https://doi.org/10.1364/OL.413030 VL - 46 IS - 7 SP - 1538 EP - 1541 ER - TY - JOUR A1 - Rabben, Robert Julian A1 - Ray, Sourav A1 - Weber, Marcus T1 - ISOKANN: Invariant subspaces of Koopman operators learned by a neural network JF - The Journal of Chemical Physics N2 - The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network. Y1 - 2020 U6 - https://doi.org/10.1063/5.0015132 VL - 153 IS - 11 SP - 114109 ER - TY - GEN A1 - Ray, Sourav A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Weber, Marcus T1 - How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs N2 - Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a $\mu$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction. T3 - ZIB-Report - 20-18 KW - Opioid, Ligand-Receptor Interaction, Binding Kinetics, Molecular Dynamics, Metadynamics, SQRA Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78437 SN - 1438-0064 ER - TY - JOUR A1 - Röhl, Susanne A1 - Weber, Marcus A1 - Fackeldey, Konstantin T1 - Computing the minimal rebinding effect for non-reversible processes JF - Multiscale Modeling and Simulation N2 - The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1137/20M1334966 VL - 19 IS - 1 SP - 460 EP - 477 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 - Kameda, Takeru A1 - Saha, Daniel K. A1 - Ray, Sourav A1 - Togashi, Yuichi A1 - Asano, Katsura T1 - Protocol for calculating binding free energy of RNA:RNA interactions through molecular dynamics simulations using adaptive biasing force technique JF - STAR Protocols Y1 - 2024 U6 - https://doi.org/10.1016/j.xpro.2024.103223 VL - 5 IS - 3 PB - Elsevier BV ER - TY - JOUR A1 - Bauer, Wolfgang A1 - Weber, Marcus A1 - Diehl-Wiesenecker, Eva A1 - Galtung, Noa A1 - Prpic, Monika A1 - Somasundaram, Rajan A1 - Tauber, Rudolf A1 - Schwenk, Jochen A1 - Micke, Patrick A1 - Kappert, Kai T1 - Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection JF - Viruses N2 - We evaluated how plasma proteomic signatures in patients with suspected COVID-19 can unravel the pathophysiology, and determine kinetics and clinical outcome of the infection. We identified distinct plasma proteins linked to the presence and course of COVID-19. These plasma proteomic findings may translate to a protein fingerprint, helping to assist clinical management decisions. Y1 - 2021 U6 - https://doi.org/10.3390/v13122456 VL - 13 IS - 12 SP - 2456 ER - TY - BOOK A1 - Ternes, Thomas A1 - Bauer, Karl-Heinz A1 - Brauer, Frank A1 - Drewes, Jörg A1 - Joss, Adriano A1 - Hiller, Georg A1 - Jewell, Kevin A1 - Oehlmann, Jörg A1 - Radke, Michael A1 - Schulte-Oehlmann, Ulrike A1 - Schwartz, Thomas A1 - Seel, Peter A1 - Völker, Jeanette A1 - Weber, Lilo A1 - Weber, Marcus ED - Wilhelm, Christian T1 - Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kläranlagen N2 - Das vorliegende Statuspapier beschreibt ein Konzept zur weitergehenden Abwasserbehandlung für die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfah- rensoptionen als auch für die Bewertung großtechnischer Anlagen. Y1 - 2023 SN - 978-3-96862-563-8 VL - T1/2023 PB - DWA / GDCh ER -