@article{MoellerIsbilirSungkawornetal.2020, author = {M{\"o}ller, Jan and Isbilir, Ali and Sungkaworn, Titiwat and Osberg, Brenda and Karathanasis, Christos and Sunkara, Vikram and Grushevsky, Eugene O and Bock, Andreas and Annibale, Paolo and Heilemann, Mike and Sch{\"u}tte, Christof and Lohse, Martin J.}, title = {Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, year = {2020}, language = {en} } @article{BittracherSchuette2021, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, volume = {416}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2020.132799}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75874}, year = {2021}, language = {en} } @article{BittracherKlusHamzietal.2021, author = {Bittracher, Andreas and Klus, Stefan and Hamzi, Boumediene and Sch{\"u}tte, Christof}, title = {Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09668-z}, year = {2021}, abstract = {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.}, language = {en} } @article{KlusNueskePeitzetal.2020, author = {Klus, Stefan and N{\"u}ske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Sch{\"u}tte, Christof}, title = {Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume = {406}, journal = {Physica D: Nonlinear Phenomena}, doi = {10.1016/j.physd.2020.132416}, year = {2020}, language = {en} } @book{Reuter2020, author = {Reuter, Bernhard}, title = {Generalisierte Markov-Modellierung}, publisher = {Springer Spektrum, Wiesbaden}, isbn = {978-3-658-29711-4}, doi = {10.1007/978-3-658-29712-1}, year = {2020}, abstract = {Markov State Models (MSM) sind der Goldstandard zur Modellierung biomolekularer Dynamik, da sie die Identifizierung und Analyse metastabiler Zust{\"a}nde erm{\"o}glichen. Die robuste Perron-Cluster-Cluster-Analyse (PCCA+) ist ein verbreiteter Spectral-Clustering-Algorithmus, der f{\"u}r das Clustering hochdimensionaler MSM verwendet wird. Da die PCCA+ auf reversible Prozesse beschr{\"a}nkt ist, wird sie zur Generalisierten PCCA+ (G-PCCA) verallgemeinert, die geeignet ist, nichtreversible Prozesse aufzukl{\"a}ren. Bernhard Reuter untersucht hier mittels G-PCCA die nichtthermischen Auswirkungen von Mikrowellen auf die Proteindynamik. Dazu f{\"u}hrt er molekulardynamische Nichtgleichgewichtssimulationen des Amyloid-β-(1-40)-Peptids durch und modelliert diese.}, language = {de} } @misc{BittracherSchuette2020, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A weak characterization of slow variables in stochastic dynamical systems}, volume = {304}, journal = {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}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, E.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_6}, pages = {132 -- 150}, year = {2020}, language = {en} } @misc{MollenhauerSchusterKlusetal.2020, author = {Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces}, volume = {304}, journal = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, K.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_5}, pages = {109 -- 131}, year = {2020}, language = {en} } @article{KoltaiLiePlonka2019, author = {Koltai, P{\´e}ter and Lie, Han Cheng and Plonka, Martin}, title = {Fr{\´e}chet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic dynamics}, volume = {32}, journal = {Nonlinearity}, number = {11}, doi = {10.1088/1361-6544/ab1f2a}, pages = {4232 -- 4257}, year = {2019}, abstract = {We prove the Fr{\´e}chet 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.}, language = {en} } @article{KlusHusicMollenhaueretal.2019, author = {Klus, Stefan and Husic, Brooke E. and Mollenhauer, Mattes and Noe, Frank}, title = {Kernel methods for detecting coherent structures in dynamical data}, volume = {29}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {12}, doi = {10.1063/1.5100267}, year = {2019}, language = {en} } @misc{Kostre2019, type = {Master Thesis}, author = {Kostr{\´e}, Margarita}, title = {Hybrid Models and Simulations of Reaction-Diffusion Processes}, school = {Zuse Institute Berlin (ZIB)}, pages = {77}, year = {2019}, abstract = {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.}, language = {en} } @misc{BittracherSchuette2020, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78688}, year = {2020}, abstract = {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.}, language = {en} } @article{BoltzSirbuStelzeretal.2021, author = {Boltz, Horst-Holger and Sirbu, Alexei and Stelzer, Nina and Lohse, Martin J. and Sch{\"u}tte, Christof and Annibale, Paolo}, title = {Quantitative spectroscopy of single molecule interaction times}, volume = {46}, journal = {Optic Letters}, number = {7}, doi = {10.1364/OL.413030}, pages = {1538 -- 1541}, year = {2021}, abstract = {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.}, language = {en} } @article{RabbenRayWeber2020, author = {Rabben, Robert Julian and Ray, Sourav and Weber, Marcus}, title = {ISOKANN: Invariant subspaces of Koopman operators learned by a neural network}, volume = {153}, journal = {The Journal of Chemical Physics}, number = {11}, doi = {10.1063/5.0015132}, pages = {114109}, year = {2020}, abstract = {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.}, language = {en} } @misc{RaySunkaraSchuetteetal.2020, author = {Ray, Sourav and Sunkara, Vikram and Sch{\"u}tte, Christof and Weber, Marcus}, title = {How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs}, issn = {1438-0064}, doi = {10.1080/08927022.2020.1839660}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78437}, year = {2020}, abstract = {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.}, language = {en} } @article{RoehlWeberFackeldey2021, author = {R{\"o}hl, Susanne and Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the minimal rebinding effect for non-reversible processes}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {1}, arxiv = {http://arxiv.org/abs/2007.08403}, doi = {https://doi.org/10.1137/20M1334966}, pages = {460 -- 477}, year = {2021}, abstract = {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.}, language = {en} } @article{ThiesSunkaraRayetal.2023, author = {Thies, Arne and Sunkara, Vikram and Ray, Sourav and Wulkow, Hanna and Celik, M. {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, year = {2023}, abstract = {We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @misc{RayThiesSunkaraetal.2021, author = {Ray, Sourav and Thies, Arne and Sunkara, Vikram and Wulkow, Hanna and Celik, {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82797}, year = {2021}, abstract = {Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @article{KamedaSahaRayetal.2024, author = {Kameda, Takeru and Saha, Daniel K. and Ray, Sourav and Togashi, Yuichi and Asano, Katsura}, title = {Protocol for calculating binding free energy of RNA:RNA interactions through molecular dynamics simulations using adaptive biasing force technique}, volume = {5}, journal = {STAR Protocols}, number = {3}, publisher = {Elsevier BV}, doi = {10.1016/j.xpro.2024.103223}, year = {2024}, language = {en} } @article{BauerWeberDiehlWieseneckeretal.2021, author = {Bauer, Wolfgang and Weber, Marcus and Diehl-Wiesenecker, Eva and Galtung, Noa and Prpic, Monika and Somasundaram, Rajan and Tauber, Rudolf and Schwenk, Jochen and Micke, Patrick and Kappert, Kai}, title = {Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection}, volume = {13}, journal = {Viruses}, number = {12}, doi = {10.3390/v13122456}, pages = {2456}, year = {2021}, abstract = {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.}, language = {en} } @book{TernesBauerBraueretal.2023, author = {Ternes, Thomas and Bauer, Karl-Heinz and Brauer, Frank and Drewes, J{\"o}rg and Joss, Adriano and Hiller, Georg and Jewell, Kevin and Oehlmann, J{\"o}rg and Radke, Michael and Schulte-Oehlmann, Ulrike and Schwartz, Thomas and Seel, Peter and V{\"o}lker, Jeanette and Weber, Lilo and Weber, Marcus}, title = {Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kl{\"a}ranlagen}, volume = {T1/2023}, editor = {Wilhelm, Christian}, publisher = {DWA / GDCh}, isbn = {978-3-96862-563-8}, year = {2023}, abstract = {Das vorliegende Statuspapier beschreibt ein Konzept zur weitergehenden Abwasserbehandlung f{\"u}r die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfah- rensoptionen als auch f{\"u}r die Bewertung großtechnischer Anlagen.}, language = {de} }