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 - Fackeldey, Konstantin A1 - Röhm, Jonas A1 - Niknejad, Amir A1 - Chewle, Surahit A1 - Weber, Marcus T1 - Analyzing Raman Spectral Data without Separabiliy Assumption JF - Journal of Mathematical Chemistry N2 - Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the Time-Resolved-Raman-Sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix M from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices W and H, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining W and H is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example. Y1 - 2021 U6 - https://doi.org/10.1007/s10910-020-01201-7 VL - 3 IS - 59 SP - 575 EP - 596 PB - Springer 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 - 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 JF - Molecular Simulation 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. 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 μ-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. Y1 - 2020 U6 - https://doi.org/10.1080/08927022.2020.1839660 VL - 46 IS - 18 SP - 1443 EP - 1452 PB - Taylor and Francis ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation JF - Biofabrication N2 - Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics. Y1 - 2020 U6 - https://doi.org/10.1088/1758-5090/aba08f VL - 12 IS - 4 ER - TY - GEN A1 - Weber, Marcus A1 - Durmaz, Vedat A1 - Sabri, Peggy A1 - Reidelbach, Marco T1 - Supplementary simulation data for Science Manuscript ai8636 N2 - The simulation data has been produced by Vedat Durmaz, Peggy Sabri and Marco Reidelbach inside the "Computational Molecular Design" Group headed by Marcus Weber at Zuse-Institut Berlin, Takustr. 7, D-14195 Berlin, Germany. The file contains classical simulation data for different fentanyl derivates in the MOR binding pocket at different pHs. It also includes instruction files for quantum-chemical pKa-value estimations and a description of how we derived the pKa-values from the Gaussian09 log-files. Y1 - 2017 U6 - https://doi.org/10.12752/5.MWB.1.0 N1 - GROMACS trajectories and GAUSSIAN files of MOR and fentanyl derivates ER - TY - GEN A1 - Weber, Marcus T1 - Supplementary: Implications of PCCA+ in Molecular Simulation N2 - Matlab-software and data sets to recapitulate the presented results in M. Weber: Implications of PCCA+ in Molecular Simulation. Computation, 6(1):20, 2018. Y1 - 2018 N1 - This data set includes one folder per published figure. The folders contain all needed resources to recapitulate the presented results. ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Fuerstenau, Daniel A1 - Grabundzija, Ana A1 - Helfmann, Luzie A1 - Park, Martin A1 - Schier, Wolfram A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Weber, Marcus A1 - Wulkow, Niklas A1 - Zonker, Johannes T1 - Mathematical modeling of the spreading of innovations in the ancient world JF - eTopoi. Journal for Ancient Studies Y1 - 2018 U6 - https://doi.org/10.17171/4-7-1 SN - ISSN 2192-2608 VL - 7 ER - TY - JOUR A1 - Weber, Marcus T1 - Implications of PCCA+ in Molecular Simulation JF - Computation N2 - Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., ’bound’ vs. ’unbound’), although the process itself takes place in a continuous space. In this context, the formula chi=XA connects the micro-dynamics of the molecular system to its macro-dynamics. Chi can be understood as a clustering of micro-states of a molecular system into a few macro-states. X is a basis of an invariant subspace of a transfer operator describing the micro-dynamics of the system. The formula claims that there is an unknown linear relation A between these two objects. With the aid of this formula we can understand rebinding effects, the electron flux in pericyclic reactions, and systematic changes of binding rates in kinetic ITC experiments. We can also analyze sequential spectroscopy experiments and rare event systems more easily. This article provides an explanation of the formula and an overview of some of its consequences. Y1 - 2018 U6 - https://doi.org/10.3390/computation6010020 VL - 6 IS - 1 SP - 20 ER - TY - JOUR A1 - Schrade, Katharina A1 - Tröger, Jessica A1 - Eldashan, Adeep A1 - Zühlke, Kerstin A1 - Abdul Azees, Kamal R. A1 - Elkins, Jonathan M. A1 - Neuenschwander, Martin A1 - Oder, Andreas A1 - Elkewedi, Mohamed A1 - Jaksch, Sarah A1 - Andrae, Karsten A1 - Li, Jinliang A1 - Fernandes, Jaoa A1 - Müller, Paul Markus A1 - Grunwald, Stephan A1 - Marino, Stephen F. A1 - Vukicevic, Tanja A1 - Eichhorst, Jenny A1 - Wiesner, Burkhard A1 - Weber, Marcus A1 - Kapiloff, Michael A1 - Rocks, Oliver A1 - Daumke, Oliver A1 - Wieland, Thomas A1 - Knapp, Stefan A1 - von Kries, Jens Peter A1 - Klussmann, Enno T1 - An AKAP-Lbc-RhoA interaction inhibitor promotes the translocation of aquaporin-2 to the plasma membrane of renal collecting duct principal cells JF - PLOS ONE N2 - Stimulation of renal collecting duct principal cells with antidiuretic hormone (arginine-vasopressin, AVP) results in inhibition of the small GTPase RhoA and the enrichment of the water channel aquaporin-2 (AQP2) in the plasma membrane. The membrane insertion facilitates water reabsorption from primary urine and fine-tuning of body water homeostasis. Rho guanine nucleotide exchange factors (GEFs) interact with RhoA, catalyze the exchange of GDP for GTP and thereby activate the GTPase. However, GEFs involved in the control of AQP2 in renal principal cells are unknown. The A-kinase anchoring protein, AKAP-Lbc, possesses GEF activity, specifically activates RhoA, and is expressed in primary renal inner medullary collecting duct principal (IMCD) cells. Through screening of 18,431 small molecules and synthesis of a focused library around one of the hits, we identified an inhibitor of the interaction of AKAP-Lbc and RhoA. This molecule, Scaff10-8, bound to RhoA, inhibited the AKAP-Lbc-mediated RhoA activation but did not interfere with RhoA activation through other GEFs or activities of other members of the Rho family of small GTPases, Rac1 and Cdc42. Scaff10-8 promoted the redistribution of AQP2 from intracellular vesicles to the periphery of IMCD cells. Thus, our data demonstrate an involvement of AKAP-Lbc-mediated RhoA activation in the control of AQP2 trafficking. Y1 - 2018 U6 - https://doi.org/10.1371/journal.pone.0191423 VL - 13 IS - 1 SP - e0191423 EP - e0191423 ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis JF - BioRxiv N2 - Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies. Y1 - 2019 U6 - https://doi.org/10.1101/725317 ER - TY - JOUR A1 - Lang, Annemarie A1 - Fischer, Lisa A1 - Weber, Marie-Christin A1 - Gaber, Timo A1 - Ehrig, Rainald A1 - Röblitz, Susanna A1 - Buttgereit, Frank T1 - Combining in vitro simulation and in silico modelling towards a sophisticated human osteoarthritis model JF - Osteoarthritis and Cartilage N2 - Our project aimed at building an in silico model based on our recently developed in vitro osteoarthritis (OA) model seeking for refinement of the model to enhance validity and translatability towards the more sophisticated simulation of OA. In detail, the previously 3D in vitro model is based on 3D chondrogenic constructs generated solely from human bone marrow derived mesenchymal stromal cells (hMSCs). Besides studying the normal state of the model over 3 weeks, the in vitro model was treated with interleukin-1β (IL-1β) and tumor necrosis factor alpha (TNFα) to mimic an OA-like environment. Y1 - 2019 U6 - https://doi.org/10.1016/j.joca.2019.02.277 VL - 27 SP - S183 ER - TY - JOUR A1 - Chewle, Surahit A1 - Emmerling, Franziska A1 - Weber, Marcus T1 - Effect of choice of solvent on crystallization pathway of Paracetamol: An experimental and theoretical case study JF - Crystals N2 - The choice of solvents influences crystalline solid formed during the crystallization of active pharmaceutical ingredients (API). The underlying effects are not always well understood because of the complexity of the systems. Theoretical models are often insufficient to describe this phenomenon. In this study, the crystallization behavior of the model drug paracetamol in different solvents was studied based on experimental and molecular dynamics data. The crystallization process was followed in situ using time-resolved Raman spectroscopy. Molecular dynamics with simulated annealing algorithm was used for an atomistic understanding of the underlying processes. The experimental and theoretical data indicate that paracetamol molecules adopt a particular geometry in a given solvent predefining the crystallization of certain polymorphs. Y1 - 2020 U6 - https://doi.org/10.3390/cryst10121107 VL - 10 IS - 12 SP - 1107 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Jöster, Annika A1 - Schütte, Christof A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting N2 - Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples. Y1 - 2026 ER - TY - GEN A1 - Weber, Tobias A1 - Sager, Sebastian A1 - Gleixner, Ambros T1 - Solving Quadratic Programs to High Precision using Scaled Iterative Refinement N2 - Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and Mészáros benchmark library. T3 - ZIB-Report - 18-04 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68152 SN - 1438-0064 ER - TY - JOUR A1 - Weber, Tobias A1 - Sager, Sebastian A1 - Gleixner, Ambros T1 - Solving Quadratic Programs to High Precision using Scaled Iterative Refinement JF - Mathematical Programming Computation N2 - Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and Mészáros benchmark library. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-019-00154-6 VL - 11 SP - 421 EP - 455 PB - Springer Berlin Heidelberg ER - TY - GEN A1 - Cordes, Frank A1 - Weber, Marcus A1 - Schmidt-Ehrenberg, Johannes T1 - Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals N2 - Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol. T3 - ZIB-Report - 02-40 KW - metastability KW - Perron-Cluster Cluster Analysis KW - curse of dimension KW - Hybrid Monte Carlo KW - significant dihedrals Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7074 ER - TY - GEN A1 - Weber, Marcus T1 - Improved Perron Cluster Analysis N2 - The problem of clustering data can often be transformed into the problem of finding a hidden block diagonal structure in a stochastic matrix. Deuflhard et al. have proposed an algorithm that state s the number $k$ of clusters and uses the sign structure of $k$ eigenvectors of the stochastic matrix to solve the cluster problem. Recently Weber and Galliat discovered that this system of eigenvectors can easily be transformed into a system of $k$ membership functions or soft characteristic functions describing the clusters. In this article we explain the corresponding cluster algorithm and point out the underlying theory. By means of numerical examples we explain how the grade of membership can be interpreted. T3 - ZIB-Report - 03-04 KW - cluster analysis KW - stochastic matrices KW - almost invariant sets Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7260 ER - TY - GEN A1 - Deuflhard, Peter A1 - Weber, Marcus T1 - Robust Perron Cluster Analysis in Conformation Dynamics N2 - The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included. T3 - ZIB-Report - 03-19 KW - Markov chains KW - cluster algorithms KW - Perron cluster analysis KW - conformation dynamics Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7415 ER - TY - GEN A1 - Weber, Marcus A1 - Meyer, Holger T1 - ZIBgridfree - Adaptive Conformation Analysis with qualified Support of Transition States and Thermodynamic Weights N2 - This paper introduces a new algorithm of conformational analysis based on mesh-free methods as described in [M. Weber. Mehless methods in Conformation Dynamics.(2005)]. The adaptive decomposition of the conformational space by softly limiting functions avoids trapping effects and allows adaptive refinement strategies. These properties of the algorithm makes ZIBgridfree particularly suitable for the complete exploration of high-dimensional conformational space. The adaptive control of the algorithm benefits from the tight integration of molecular simulation and conformational analysis. An emphasized part of the analysis is the Robust Perron Cluster Analysis (PCCA+) based on the work of Peter Deuflhard and Marcus Weber. PCCA+ supports an almost-characteristic cluster definition with an outstanding mapping of transition states. The outcome is expressed by the metastable sets of conformations, their thermodynamic weights and flexibility. T3 - ZIB-Report - 05-17 KW - Molecular Dynamics KW - Meshfree Methods KW - Conformation Analysis KW - Quality Functions Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8514 ER - TY - JOUR A1 - Abendroth, Frank A1 - Bujotzek, Alexander A1 - Shan, Min A1 - Haag, Rainer A1 - Weber, Marcus A1 - Seitz, Oliver T1 - DNA-controlled bivalent presentation of ligands for the estrogen receptor JF - Angew. Chem. Int. Ed. Y1 - 2011 ER - TY - JOUR A1 - Bujotzek, Alexander A1 - Shan, Min A1 - Haag, Rainer A1 - Weber, Marcus T1 - Towards a rational spacer design for bivalent inhibition of estrogen receptor JF - J. Comput.-Aided Mol. Des. Y1 - 2011 VL - 25(3) SP - 253 EP - 262 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Weber, Marcus T1 - Robust Perron Cluster Analysis in Conformation Dynamics T2 - Lin. Alg. Appl. – Special Issue on Matrices and Mathematical Biology Y1 - 2005 VL - 398 SP - 161 EP - 184 PB - Elsevier Journals CY - Germany ER - TY - JOUR A1 - Rigort, Alexander A1 - Günther, David A1 - Hegerl, Reiner A1 - Baum, Daniel A1 - Weber, Britta A1 - Prohaska, Steffen A1 - Medalia, Ohad A1 - Baumeister, Wolfgang A1 - Hege, Hans-Christian T1 - Automated segmentation of electron tomograms for a quantitative description of actin filament networks JF - Journal of Structural Biology Y1 - 2012 U6 - https://doi.org/10.1016/j.jsb.2011.08.012 VL - 177 SP - 135 EP - 144 ER - TY - JOUR A1 - Weber, Britta A1 - Greenan, Garrett A1 - Prohaska, Steffen A1 - Baum, Daniel A1 - Hege, Hans-Christian A1 - Müller-Reichert, Thomas A1 - Hyman, Anthony A1 - Verbavatz, Jean-Marc T1 - Automated tracing of microtubules in electron tomograms of plastic embedded samples of Caenorhabditis elegans embryos JF - Journal of Structural Biology Y1 - 2012 UR - http://www.sciencedirect.com/science/article/pii/S1047847711003509 U6 - https://doi.org/10.1016/j.jsb.2011.12.004 VL - 178 IS - 2 SP - 129 EP - 138 ER - TY - JOUR A1 - Torsney-Weir, Thomas A1 - Saad, Ahmed A1 - Möller, Torsten A1 - Hege, Hans-Christian A1 - Weber, Britta A1 - Verbavatz, Jean-Marc T1 - Tuner: Principled Parameter Finding for Image Segmentation Algorithms Using Visual Response Surface Exploration JF - IEEE Trans. Vis. Comput. Graph. Y1 - 2011 VL - 17 IS - 12 SP - 1892 EP - 1901 ER - TY - JOUR A1 - Pöthkow, Kai A1 - Weber, Britta A1 - Hege, Hans-Christian T1 - Probabilistic Marching Cubes JF - Computer Graphics Forum Y1 - 2011 U6 - https://doi.org/10.1111/j.1467-8659.2011.01942.x VL - 30 IS - 3 SP - 931 EP - 940 ER - TY - CHAP A1 - Weber, Britta A1 - Möller, Marit A1 - Verbavatz, Jean-Marc A1 - Baum, Daniel A1 - Hege, Hans-Christian A1 - Prohaska, Steffen T1 - Fast Tracing of Microtubule Centerlines in Electron Tomograms T2 - BioVis 2011 Abstracts, 1st IEEE Symposium on Biological Data Visualization Y1 - 2011 ER - TY - JOUR A1 - Goubergrits, Leonid A1 - Weber, Sarah A1 - Petz, Christoph A1 - Spuler, Andreas A1 - Pöthke, Jens A1 - Berthe, André A1 - Hege, Hans-Christian T1 - Wall-PIV as a Near Wall Flow Validation Tool for CFD JF - Journal of Visualization Y1 - 2009 VL - 12 IS - 3 SP - 241 EP - 250 ER - TY - CHAP A1 - Dercksen, Vincent J. A1 - Weber, Britta A1 - Günther, David A1 - Oberlaender, Marcel A1 - Prohaska, Steffen A1 - Hege, Hans-Christian T1 - Automatic alignment of stacks of filament data T2 - Proc. IEEE International Symposium on Biomedical Imaging Y1 - 2009 SP - 971 EP - 974 PB - IEEE press CY - Boston, USA ER - TY - JOUR A1 - Sahner, Jan A1 - Weber, Britta A1 - Lamecker, Hans A1 - Prohaska, Steffen T1 - Extraction of feature Lines on surface meshes based on discrete Morse theory JF - Computer Graphics Forum Y1 - 2008 U6 - https://doi.org/10.1111/j.1467-8659.2008.01202.x VL - 27 IS - 3 SP - 735 EP - 742 CY - Eindhoven, Netherlands ER - TY - JOUR A1 - Koschek, A1 - Durmaz, Vedat A1 - Krylova, A1 - Wieczorek, A1 - Gupta, Pooja A1 - Richter, A1 - Bujotzek, Alexander A1 - Fischer, A1 - Haag, Rainer A1 - Freund, A1 - Weber, Marcus A1 - Rademann, T1 - Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands JF - Beilstein J. Org. Chem. Y1 - 2015 VL - 11 SP - 837 EP - 847 ER - TY - JOUR A1 - Durmaz, Vedat A1 - Weber, Marcus A1 - Meyer, A1 - Mückter, T1 - Computergestützte Simulationen zur Abschätzung gesundheitlicher Risiken durch anthropogene Spurenstoffe der Wassermatrix JF - KA Korrespondenz Abwasser, Abfall Y1 - 2015 VL - 3/15 SP - 264 EP - 267 ER - TY - GEN A1 - Weber, Marcus A1 - Fackeldey, Konstantin T1 - G-PCCA: Spectral Clustering for Non-reversible Markov Chains N2 - Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We extend this spectral clustering method also to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension, non-reversible Markov chains can be analyzed. Furthermore, the chains need not have a positive stationary distribution. And additionally to metastabilities, dominant cycles and sinks can be identified, too. T3 - ZIB-Report - 15-35 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55505 ER - TY - GEN A1 - Djurdjevac Conrad, Natasa A1 - Weber, Marcus A1 - Schütte, Christof T1 - Finding dominant structures of nonreversible Markov processes N2 - Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments. T3 - ZIB-Report - 15-40 KW - nonreversible Markov processes KW - metastable sets KW - cycle decomposition KW - Schur decomposition Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55739 SN - 1438-0064 ER - TY - JOUR A1 - Abendroth, Frank A1 - Solleder, Marthe A1 - Welker, Pia A1 - Licha, Kai A1 - Weber, Marcus A1 - Seitz, Oliver A1 - Mangoldt, Dorothea T1 - High affinity flourescence labelled ligands for the estrogen receptor JF - Eur. J. Org. Chem. Y1 - 2015 VL - 2015 IS - 10 SP - 2157 EP - 2166 ER - TY - JOUR A1 - Weber, Marcus A1 - Zoschke, Christian A1 - Sedighi, Amir A1 - Fleige, Emanuel A1 - Haag, Rainer A1 - Schäfer-Korting, Monika T1 - Free Energy Simulations of Drug loading for Core-Multishell Nanotransporters JF - J Nanomed Nanotechnol Y1 - 2014 U6 - https://doi.org/10.4172/2157-7439.1000234 VL - 5 IS - 5 SP - 234 ER - TY - GEN A1 - Stein, Christoph A1 - Weber, Marcus A1 - Zöllner, Christian A1 - Scharkoi, Olga T1 - Fentanyl derivatives as pH-dependent opioid receptor agonists T2 - European Patent Application, Bulletin 2013/08 Y1 - 2013 ER - TY - GEN A1 - Stein, Christoph A1 - Weber, Marcus A1 - Scharkoi, Olga A1 - Deuflhard, Peter T1 - Method and system for identifying compounds that bind and preferably activate a target opioid receptor in a pH-dependent manner T2 - European Patent Application, Bulletin 2013/28 Y1 - 2013 ER - TY - JOUR 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 JF - Siam Journal on Scientific Computing Y1 - 2014 U6 - https://doi.org/10.1137/14096493X VL - 36 IS - 6 SP - A2654 EP - A2672 ER - TY - JOUR A1 - Andrae, Karsten A1 - Merkel, Stefan A1 - Durmaz, Vedat A1 - Fackeldey, Konstantin A1 - Köppen, Robert A1 - Weber, Marcus A1 - Koch, Matthias T1 - Investigation of the Ergopeptide Epimerization Process JF - Computation N2 - Ergopeptides, like ergocornine and a-ergocryptine, exist in an S- and in an R-configuration. Kinetic experiments imply that certain configurations are preferred depending on the solvent. The experimental methods are explained in this article. Furthermore, computational methods are used to understand this configurational preference. Standard quantum chemical methods can predict the favored configurations by using minimum energy calculations on the potential energy landscape. However, the explicit role of the solvent is not revealed by this type of methods. In order to better understand its influence, classical mechanical molecular simulations are applied. It appears from our research that “folding” the ergopeptide molecules into an intermediate state (between the S- and the R-configuration) is mechanically hindered for the preferred configurations. Y1 - 2014 U6 - https://doi.org/10.3390/computation2030102 VL - 2 IS - 3 SP - 102 EP - 111 ER - TY - GEN A1 - Deuflhard, Peter 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 - Skutella, Martin ED - Sprekels, Jürgen T1 - Mathematics without pain T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 U6 - https://doi.org/10.4171/137 VL - 1 SP - 26 EP - 28 PB - European Mathematical Society ER - TY - JOUR A1 - Weber, Britta A1 - Tranfield, Erin M. A1 - Höög, Johanna L. A1 - Baum, Daniel A1 - Antony, Claude A1 - Hyman, Tony A1 - Verbavatz, Jean-Marc A1 - Prohaska, Steffen T1 - Automated stitching of microtubule centerlines across serial electron tomograms JF - PLoS ONE Y1 - 2014 U6 - https://doi.org/10.1371/journal.pone.0113222 SP - e113222 ER - TY - GEN A1 - Redemann, Stefanie A1 - Weber, Britta A1 - Möller, Marit A1 - Verbavatz, Jean-Marc A1 - Hyman, Anthony A1 - Baum, Daniel A1 - Prohaska, Steffen A1 - Müller-Reichert, Thomas T1 - The Segmentation of Microtubules in Electron Tomograms Using Amira T2 - Mitosis: Methods and Protocols Y1 - 2014 U6 - https://doi.org/10.1007/978-1-4939-0329-0_12 SP - 261 EP - 278 PB - Springer ER - TY - JOUR A1 - Schütte, Christof A1 - Nielsen, Adam A1 - Weber, Marcus T1 - Markov State Models and Molecular Alchemy JF - Molecular Physics 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 experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent 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 properties 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 energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed. KW - MSM KW - Reweighting KW - Girsanov Y1 - 2015 U6 - https://doi.org/10.1080/00268976.2014.944597 VL - 113 IS - 1 SP - 69 EP - 78 ER - TY - JOUR A1 - Weber, Marcus A1 - Fackeldey, Konstantin T1 - Computing the Minimal Rebinding Effect Included in a Given Kinetics JF - Multiscale Model. Simul. N2 - The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process. On the macro scale this process comprises the Markov property. This Makovian view is spoiled when switching to the atomistic scale of a binding process. We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing ''intermediate'' bound states. This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem. The results form our examples show good agreement with data form laboratory. Y1 - 2014 U6 - https://doi.org/10.1137/13091124X VL - 12 IS - 1 SP - 318 EP - 334 ER - TY - GEN A1 - Weber, Britta A1 - Tranfield, Erin M. A1 - Höög, Johanna L. A1 - Baum, Daniel A1 - Antony, Claude A1 - Hyman, Tony A1 - Verbavatz, Jean-Marc A1 - Prohaska, Steffen T1 - Automated stitching of microtubule centerlines across serial electron tomograms N2 - Tracing microtubule centerlines in serial section electron tomography requires microtubules to be stitched across sections, that is lines from different sections need to be aligned, endpoints need to be matched at section boundaries to establish a correspondence between neighboring sections, and corresponding lines need to be connected across multiple sections. We present computational methods for these tasks: 1) An initial alignment is computed using a distance compatibility graph. 2) A fine alignment is then computed with a probabilistic variant of the iterative closest points algorithm, which we extended to handle the orientation of lines by introducing a periodic random variable to the probabilistic formulation. 3) Endpoint correspondence is established by formulating a matching problem in terms of a Markov random field and computing the best matching with belief propagation. Belief propagation is not generally guaranteed to converge to a minimum. We show how convergence can be achieved, nonetheless, with minimal manual input. In addition to stitching microtubule centerlines, the correspondence is also applied to transform and merge the electron tomograms. We applied the proposed methods to samples from the mitotic spindle in C. elegans, the meiotic spindle in X. laevis, and sub-pellicular microtubule arrays in T. brucei. The methods were able to stitch microtubules across section boundaries in good agreement with experts’ opinions for the spindle samples. Results, however, were not satisfactory for the microtubule arrays. For certain experiments, such as an analysis of the spindle, the proposed methods can replace manual expert tracing and thus enable the analysis of microtubules over long distances with reasonable manual effort. T3 - ZIB-Report - 14-41 KW - electron tomography KW - microtubules KW - serial sectioning KW - image analysis KW - geometry reconstruction KW - image and geometry alignment KW - point correspondence Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-52958 SN - 1438-0064 ER - TY - GEN A1 - Nielsen, Adam A1 - Weber, Marcus T1 - Computing the nearest reversible Markov chain N2 - Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem. T3 - ZIB-Report - 14-48 KW - Reversible Markov Chain KW - Convex Optimization KW - MSM Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53292 SN - 1438-0064 ER - TY - JOUR A1 - Nielsen, Adam A1 - Weber, Marcus T1 - Computing the nearest reversible Markov chain JF - Numerical Linear Algebra with Applications N2 - Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem. KW - Reversible Markov Chain KW - Convex Optimization KW - MSM Y1 - 2015 U6 - https://doi.org/10.1002/nla.1967 VL - 22 IS - 3 SP - 483 EP - 499 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 -