Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-851 misc Weber, Marcus; Meyer, Holger ZIBgridfree - Adaptive Conformation Analysis with qualified Support of Transition States and Thermodynamic Weights 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. 2005 urn:nbn:de:0297-zib-8514 ZIB Allgemein OPUS4-679 misc Weber, Marcus; Galliat, Tobias Characterization of Transition States in Conformational Dynamics using Fuzzy Sets Recently, a novel approach for the analysis of molecular dynamics on the basis of a transfer operator has been introduced. Therein conformations are considered to be disjoint metastable clusters within position space of a molecule. These clusters are defined by almost invariant characteristic functions that can be computed via {\em Perron Cluster} analysis. The present paper suggests to replace crisp clusters with {\em fuzzy} clusters, i.e. to replace characteristic functions with membership functions. This allows a more sufficient characterization of transiton states between different confor conformations and therefore leads to a better understanding of molecular dynamics. Fur thermore, an indicator for the uniqueness of metastable fuzzy clusters and a fast algorithm for the computation of these clusters are described. Numerical examples are included. 2002 urn:nbn:de:0297-zib-6791 ZIB Allgemein OPUS4-707 misc Cordes, Frank; Weber, Marcus; Schmidt-Ehrenberg, Johannes Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals 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. 2002 urn:nbn:de:0297-zib-7074 ZIB Allgemein OPUS4-876 misc Kube, Susanna; Weber, Marcus Conformation Kinetics as a Reduced Model for Transition Pathways The complexity of molecular kinetics can be reduced significantly by a restriction to metastable conformations which are almost invariant sets of molecular dynamical systems. With the Robust Perron Cl uster Analysis PCCA+, developed by Weber and Deuflhard, we have a tool available which can be used to identify these conformations from a transition probability matrix. This method can also be applied to the corresponding transition rate matrix which provides important information concerning transition pathways of single molecules. In the present paper, we explain the relationship between these tw o concepts and the extraction of conformation kinetics from transition rates. Moreover, we show how transition rates can be approximated and conclude with numerical examples. 2005 urn:nbn:de:0297-zib-8763 ZIB Allgemein OPUS4-814 misc Weber, Marcus; Rungsarityotin, Wasinee; Schliep, Alexander Perron Cluster Analysis and Its Connection to Graph Partitioning for Noisy Data The problem of clustering data can be formulated as a graph partitioning problem. Spectral methods for obtaining optimal solutions have reveceived a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and, for the first time, establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed using a simple linear map of the eigenvector data. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the min Chi indicator which helps in selecting the number of clusters and confirming the existence of a partition of the data. This gives a non-probabilistic alternative to statistical mixture-models. We close with showing favorable results on the analysis of gene expressi on data for two different cancer types. 2004 urn:nbn:de:0297-zib-8140 ZIB Allgemein OPUS4-726 misc Weber, Marcus Improved Perron Cluster Analysis 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. 2003 urn:nbn:de:0297-zib-7260 ZIB Allgemein OPUS4-741 misc Deuflhard, Peter; Weber, Marcus Robust Perron Cluster Analysis in Conformation Dynamics 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. 2003 urn:nbn:de:0297-zib-7415 ZIB Allgemein OPUS4-778 misc Weber, Marcus Clustering by using a simplex structure In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplicial struture this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplicial structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this kind of approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs. 2003 urn:nbn:de:0297-zib-7782 ZIB Allgemein OPUS4-1143 misc Weber, Marcus A Subspace Approach to Molecular Markov State Models via an Infinitesimal Generator Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern. 2009 urn:nbn:de:0297-zib-11432 Numerical Mathematics OPUS4-1087 misc Weber, Marcus An efficient analysis of rare events in canonical ensemble dynamics For an analysis of a molecular system from a computational statistical thermodynamics point of view, extensive molecular dynamics simulations are very inefficient. During this procedure, at lot of redundant data is generated. Whereas the algorithms spend most of the computing time for a sampling of configurations within the basins of the potential energy landscape of the molecular system, the important information about the long-time behaviour of the molecules is given by transition regions and barriers between the basins, which are sampled rarely only. Thinking of molecular dynamics trajectories, researchers try to figure out which kind of dynamical model is suitable for an efficient simulation. This article suggests to change the point of view from extensive simulation of molecular dynamics trajectories to more efficient sampling strategies of the conformation dynamics approach. 2008 urn:nbn:de:0297-zib-10871 Numerical Mathematics OPUS4-925 misc Meyer, Holger; Moll, Sebastian; Cordes, Frank; Weber, Marcus ConFlow? A new space-based Application for complete Conformational Analysis of Molecules Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort. 2006 urn:nbn:de:0297-zib-9258 ZIB Allgemein OPUS4-929 misc Kube, Susanna; Weber, Marcus Coarse Grained Molecular Kinetics The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods. 2006 urn:nbn:de:0297-zib-9299 ZIB Allgemein OPUS4-960 misc Kube, Susanna; Lasser, Caroline; Weber, Marcus Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy. 2007 urn:nbn:de:0297-zib-9604 Numerical Mathematics OPUS4-933 misc Weber, Marcus; Walter, Lionel; Kube, Susanna; Deuflhard, Peter Stable computation of probability densities for metastable dynamical systems Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples. 2006 urn:nbn:de:0297-zib-9331 ZIB Allgemein OPUS4-895 misc Kube, Susanna; Weber, Marcus Identification of Metastabilities in Monomolecular Conformation Kinetics The identification of metastable conformations of molecules plays an important role in computational drug design. One main difficulty is the fact that the underlying dynamic processes take place in high dimensional spaces. Although the restriction of degrees of freedom to a few dihedral angles significantly reduces the complexity of the problem, the existing algorithms are time-consuming. They are based on the approximation of transition probabilities by an extensive sampling of states according to the Boltzmann distribution. We present a method which can identify metastable conformations without sampling the complete distribution. Our algorithm is based on local transition rates and uses only pointwise information about the potential energy surface. In order to apply the cluster algorithm PCCA+, we compute a few eigenvectors of the rate matrix by the Jacobi-Davidson method. Interpolation techniques are applied to approximate the thermodynamical weights of the clusters. The concluding example illustrates our approach for epigallocatechine, a molecule which can be described by seven dihedral angles. 2005 urn:nbn:de:0297-zib-8956 ZIB Allgemein OPUS4-946 misc Weber, Marcus; Kube, Susanna; Riemer, Alexander; Bujotzek, Alexander Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution. 2006 urn:nbn:de:0297-zib-9467 ZIB Allgemein OPUS4-920 misc Walter, Lionel; Weber, Marcus ConfJump : a fast biomolecular sampling method which drills tunnels through high mountains In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled. 2006 urn:nbn:de:0297-zib-9204 ZIB Allgemein OPUS4-1023 Dissertation Weber, Marcus Meshless Methods in Confirmation Dynamics 2006 urn:nbn:de:0297-zib-10232 Numerical Mathematics OPUS4-1030 misc Weber, Marcus; Becker, Roland; Köppen, Robert; Durmaz, Vedat Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane In this paper, we investigate the interconversion processes of the major flame retardant -- 1,2,5,6,9,10-hexabromocyclododecane (HBCD) -- by the means of statistical thermodynamics based on classical force-fields. Three ideas will be presented. First, the application of classical hybrid Monte-Carlo simulations for quantum mechanical processes will be justified. Second, the problem of insufficient convergence properties of hybrid Monte-Carlo methods for the generation of low temperature canonical ensembles will be solved by an interpolation approach. Furthermore, it will be shown how free energy differences can be used for a rate matrix computation. The results of our numerical simulations will be compared to experimental results. 2007 urn:nbn:de:0297-zib-10308 Numerical Mathematics OPUS4-961 misc Weber, Marcus Conformation-based transition state theory For the treatment of equilibrated molecular systems in a heat bath we propose a transition state theory that is based on conformation dynamics. In general, a set-based discretization of a Markov operator ${\cal P}^\tau$ does not preserve the Markov property. In this article, we propose a discretization method which is based on a Galerkin approach. This discretization method preserves the Markov property of the operator and can be interpreted as a decomposition of the state space into (fuzzy) sets. The conformation-based transition state theory presented here can be seen as a first step in conformation dynamics towards the computation of essential dynamical properties of molecular systems without time-consuming molecular dynamics simulations. 2007 urn:nbn:de:0297-zib-9612 Numerical Mathematics OPUS4-1476 misc Weber, Marcus The funnel trap paradox In this article, an illustrative example is given for the coarse-graining of a Markov process which leads to a shift in the statistical weights of a two-states-system. The example is based on a 2D-funnel trap. The funnel trap is constructed in such a way, that the area inside and outside of the trap is identical. However, observing the flight of the insect as a Markov process, the probability for being "in the trap" is higher. This example can be transferred to several kinds of processes (like receptor-ligandbinding processes in chemistry) and describes the influence of "re-entering events". 2012 urn:nbn:de:0297-zib-14765 Numerical Mathematics OPUS4-1913 Wissenschaftlicher Artikel Abendroth, Frank; Bujotzek, Alexander; Shan, Min; Haag, Rainer; Weber, Marcus; Seitz, Oliver DNA-controlled bivalent presentation of ligands for the estrogen receptor 2011 Angew. Chem. Int. Ed. Numerical Mathematics OPUS4-1402 Habilitation Weber, Marcus A Subspace Approach to Molecular Markov State Models via a New Infinitesimal Generator Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern. 2011 urn:nbn:de:0297-zib-14025 Numerical Mathematics OPUS4-1990 Wissenschaftlicher Artikel Bujotzek, Alexander; Shan, Min; Haag, Rainer; Weber, Marcus Towards a rational spacer design for bivalent inhibition of estrogen receptor 2011 9 J. Comput.-Aided Mol. Des. 25(3) 253 262 Numerical Mathematics OPUS4-2016 Teil eines Buches Deuflhard, Peter; Weber, Marcus Robust Perron Cluster Analysis in Conformation Dynamics Germany Elsevier Journals 2005 23 Lin. Alg. Appl. – Special Issue on Matrices and Mathematical Biology 398 161 184 Numerical Mathematics OPUS4-2207 Wissenschaftlicher Artikel Haack, Fiete; Röblitz, Susanna; Scharkoi, Olga; Schmidt, Burkhard; Weber, Marcus Adaptive Spectral Clustering for Conformation Analysis AIP 2010 3 AIP Conference Proceedings 1281 1 1585 1588 10.1063/1.3498116 Numerical Mathematics OPUS4-2261 Konferenzveröffentlichung Kube, Susanna; Weber, Marcus Computation of equilibrium densities in metastable dynamical systems by domain decomposition AIP Conference Proceedings 2008 3 Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 1048 339 342 Numerical Mathematics OPUS4-2262 Wissenschaftlicher Artikel Kube, Susanna; Weber, Marcus A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations 2007 Journal of Chemical Physics 126 2 10.1063/1.2404953 Numerical Mathematics OPUS4-2289 Wissenschaftlicher Artikel Metzner, Ph.; Weber, Marcus; Schütte, Christof Observation uncertainty in reversible Markov chains American Physical Society 2010 Phys. Rev. E 82 3 031114 10.1103/PhysRevE.82.031114 Numerical Mathematics OPUS4-2192 Wissenschaftlicher Artikel Gürler, A.; Moll, Sebastian; Weber, Marcus; Meyer, Holger; Cordes, Frank Selection and flexible optimization of binding modes from conformation ensembles 2007 Biosystems Numerical Mathematics OPUS4-2194 Wissenschaftlicher Artikel Guerler, A.; Moll, Sebastian; Weber, Marcus; Meyer, Holger; Cordes, Frank Selection and flexible optimization of binding modes from conformation ensembles 2008 6 Biosystems 92 1 42 48 DOI: 10.1016/j.biosystems.2007.11.004 Numerical Mathematics OPUS4-2247 Konferenzveröffentlichung Weber, Marcus; Kube, Susanna Robust Perron Cluster Analysis for Various Applications in Computational Life Science 2005 9 Computational Life Sciences 57 66 Numerical Mathematics OPUS4-2255 Wissenschaftlicher Artikel Klimm, Martina; Bujotzek, Alexander; Weber, Marcus Direct Reweighting Strategies in Conformation Dynamics 2011 13 MATCH Commun. Math. Comp. Chem. 65(2) 333 346 Numerical Mathematics OPUS4-2645 Wissenschaftlicher Artikel Durmaz, Vedat; Weber, Marcus; Becker, Roland How to Simulate Affinities for Host-Guest Systems Lacking Binding Mode Information: application to the liquid chromatographic separation of hexabromocyclododecane stereoisomers 2012 9 Journal of Molecular Modeling 18 2399 2408 10.1007/s00894-011-1239-5 Numerical Mathematics OPUS4-2646 Wissenschaftlicher Artikel Weber, Marcus; Bujotzek, Alexander; Haag, Rainer Quantifying the rebinding effect in multivalent chemical ligand-receptor systems 2012 J. Chem. Phys. 137 5 054111 Numerical Mathematics OPUS4-2649 Wissenschaftlicher Artikel Fasting, Carlo; Schalley, Christoph A.; Weber, Marcus; Seitz, Oliver; Hecht, Stefan; Koksch, Beate; Dernedde, Jens; Graf, Christina; Knapp, Ernst-Walter; Haag, Rainer Multivalency as a Chemical Organization and Action Principle 2012 26 Angew. Chem. Int. Ed. 51 42 10472 10498 Numerical Mathematics OPUS4-2644 Wissenschaftlicher Artikel Köppen, Robert; Riedel, Juliane; Proske, Matthias; Drzymala, Sarah; Rasenko, Tatjana; Durmaz, Vedat; Weber, Marcus; Koch, Matthias Photochemical trans-/cis-isomerization and quantification of zearalenone in edible oils 2012 7 J. Agric. Food Chem. 60 11733 11740 10.1021/jf3037775 Numerical Mathematics OPUS4-2619 Wissenschaftlicher Artikel Kube, Susanna; Lasser, Caroline; Weber, Marcus Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics 2008 15 Journal of Computational Physics 228 6 1947 1962 10.1016/j.jcp.2008.11.016 Numerical Mathematics OPUS4-2627 misc Kellermann, R.; Weber, Marcus; Bujotzek, Alexander Vom Dietrich zum Sicherheitsschlüssel - Mathematiker des Matheon simulieren neuen Wirkstoff für die Diabetes-Behandlung DFG-Forschungszentrum Matheon 2007 2 Numerical Mathematics OPUS4-2628 Wissenschaftlicher Artikel Köppen, Robert; Becker, Roland; Weber, Marcus; Durmaz, Vedat; Nehls, Irene HBCD stereoisimers: Thermal interconversion and enantiospecific trace analysis in biota 2009 3 Organohalogen Compounds 70 910 913 Numerical Mathematics OPUS4-2629 Wissenschaftlicher Artikel Bujotzek, Alexander; Weber, Marcus Efficient Simulation of Ligand-Receptor Binding Processes Using the Conformation Dynamics Approach 2009 20 Journal of Bioinformatics and Computational Biology 7(5) 811 831 Numerical Mathematics OPUS4-2630 Teil eines Buches Weber, Marcus Dunemann, L.; Schmoll, O. Spurenstoffe im Trinkwasser - Risikoqualifizierung im Rechner? 2009 Schriftenreihe des Vereins für Wasser-, Boden- und Lufthygiene Numerical Mathematics OPUS4-2631 Wissenschaftlicher Artikel Weber, Marcus; Durmaz, Vedat; Becker, Roland; Esslinger, Susanne Predictive Identification of Pentabromocyclododecane (PBCD) Isomers with high Binding Affinity to hTTR 2009 5 Organohalogen Compounds 71 247 252 Numerical Mathematics OPUS4-5141 Wissenschaftlicher Artikel Schütte, Christof; Nielsen, Adam; Weber, Marcus Markov State Models and Molecular Alchemy 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. 2015 9 Molecular Physics 113 1 69 78 10.1080/00268976.2014.944597 Numerical Mathematics OPUS4-5164 misc Stein, Christoph; Weber, Marcus; Zöllner, Christian; Scharkoi, Olga Fentanyl derivatives as pH-dependent opioid receptor agonists 2013 European Patent Application, Bulletin 2013/08 Numerical Mathematics OPUS4-5165 misc Stein, Christoph; Weber, Marcus; Scharkoi, Olga; Deuflhard, Peter Method and system for identifying compounds that bind and preferably activate a target opioid receptor in a pH-dependent manner 2013 European Patent Application, Bulletin 2013/28 Numerical Mathematics OPUS4-4671 misc Schütte, Christof; Nielsen, Adam; Weber, Marcus Markov State Models and Molecular Alchemy 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. 2014 urn:nbn:de:0297-zib-46718 10.1080/00268976.2014.944597 Numerical Mathematics OPUS4-4650 Wissenschaftlicher Artikel Shan, Min; Carlson, Kathryn E.; Bujotzek, Alexander; Wellner, Anja; Gust, Ronald; Weber, Marcus; Katzenellenbogen, John A.; Haag, Rainer Nonsteroidal Bivalent Estrogen Ligands - An Application of the Bivalent Concept to the Estrogen Receptor 2013 8 ACS Chem. Biol. 8 4 707 715 Numerical Mathematics OPUS4-4652 Wissenschaftlicher Artikel Weber, Marcus Adaptive Spectral Clustering in Molecular Simulation. In: Studies in Classification, Data Analysis, and Knowledge Organization 2013 10 XIV: Classification and Data Mining, A. Giusti, G. Ritter, M. Vichi (Eds.), Springer Series 147 157 Numerical Mathematics OPUS4-4655 Wissenschaftlicher Artikel Shan, Min; Bujotzek, Alexander; Abendroth, Frank; Seitz, Oliver; Weber, Marcus; Haag, Rainer Conformational Analysis of Bivalent Estrogen Receptor-Ligands: From Intramolecular to Intermolecular Binding 2011 11 ChemBioChem, 12(17) 2587 2598 10.1002/cbic.201100529 Numerical Mathematics OPUS4-4639 Wissenschaftlicher Artikel Scharkoi, Olga; Esslinger, Susanne; Becker, Roland; Weber, Marcus; Nehls, Irene Predicting sites of cytochrome P450-mediated hydroxylation applied to CYP3A4 and hexabromocyclododecane 2014 Molecular Simulation 10.1080/08927022.2014.898845 Numerical Mathematics OPUS4-4647 Wissenschaftlicher Artikel Scharkoi, O.; Esslinger, Susanne; Becker, Roland; Weber, Marcus; Nehls, Irene Phase I oxidation of alpha- and gamma-hexabromocyclododecane by cytochrome P450 enzymes: simulation of the stereoisomerism of hydroxylated metabolites 2011 3 Organohalogen Compounds 73 730 733 Numerical Mathematics OPUS4-4648 Wissenschaftlicher Artikel Durmaz, Vedat; Schmidt, Sebastian; Sabri, Peggy; Piechotta, Christian; Weber, Marcus A hands-off linear interaction energy approach to binding mode and affinity estimation of estrogens 2013 7 Journal of Chemical Information and Modeling 53 10 2681 2688 Numerical Mathematics OPUS4-4649 Wissenschaftlicher Artikel Tyagi, Rahul; Malhotra, Shashwat; Thünemann, Andreas F.; Sedighi, Amir; Weber, Marcus; Schäfer, Andreas; Haag, Rainer Investigations of Host-Guest Interactions with Shape-persistent Nonionic Dendritic Micelles 2013 10 J. Phys. Chem. C 117 23 12307 12317 Numerical Mathematics OPUS4-5428 Wissenschaftlicher Artikel Weber, Marcus; Zoschke, Christian; Sedighi, Amir; Fleige, Emanuel; Haag, Rainer; Schäfer-Korting, Monika Free Energy Simulations of Drug loading for Core-Multishell Nanotransporters 2014 J Nanomed Nanotechnol 5 5 234 10.4172/2157-7439.1000234 Numerical Mathematics OPUS4-5794 Wissenschaftlicher Artikel Djurdjevac Conrad, Natasa; Weber, Marcus; Schütte, Christof Finding dominant structures of nonreversible Markov processes 2016 21 Multiscale Modeling and Simulation 14 4 1319 1340 10.1137/15M1032272 Numerical Mathematics OPUS4-6034 Konferenzveröffentlichung Igde, Sinaida; Wölk, Hendrik; Röblitz, Susanna; Reidelbach, Marco; Weber, Marcus; Hartmann, Laura Identifying Multivalent Binding Kinetics of Precision Glycomacromolecules: A Kinetic Study Using kinITC Multivalent sugar/protein interactions are well-known to proceed through different binding modes 1-5 which in turn can be described by their binding kinetics 3-5. This study provides additional insight into the association and dissociation reaction rates of complex multivalent sugar/protein interactions. Binding kinetics of recently introduced multivalent precision glycomacromolecules 6-8 to Concanavalin A (Con A) were studied by " kinetic Isothermal Titration Calorimetry " (kinITC) 9-11. The effect of multivalency is evaluated by comparing rate constants of glycomacromolecules obtaining the same and different valency of mannose ligands and by variation of the overall backbone properties, such as hydrophilic/ hydrophoboc. In addition, binding kinetics were studied using different conformations of Con A (homodimer vs.-tetramer) and thus a different protein valency. Our results show that precision glycomacromolecule/Con A binding proceeds non-cooperatively. Further, association and dissociation rates are mainly described by intermolecular complex formation. Together with the so-called functional valency, we can discriminate between " bound " and " unbound " states for macroscopic on-and off-rates, even for such complex glycooligomer/protein systems. By comparing e.g. a mono-to a divalent glycomacromolecule for their binding to dimeric Con A, we see a lower dissociation rate for the latter. As both bind monovalently to Con A, this is a strong indication for a statistical rebinding event. Further, there is a strong dependence of multivalent binding kinetics on the ligand density of glycomacromolecules as well as the Con A conformation and thus the overall on-and off-rates. 2015 Münster Symposium on Cooperative Effects 2015 - SFB 858, at Westfälische Wilhelms-Universität Münster, 2015 Numerical Mathematics OPUS4-6053 Wissenschaftlicher Artikel Villatoro, José; Zühlke, Martin; Riebe, Daniel; Beitz, Toralf; Weber, Marcus; Riedel, Jens; Löhmannsröben, Hans-Gerd IR-MALDI ion mobility spectrometry: physical source characterization and application as HPLC detector 2016 100 International Journal for Ion Mobility Spectrometry 19/4 197 297 10.1007/s12127-016-0208-1 Numerical Mathematics OPUS4-4985 misc Schütte, Christof; Deuflhard, Peter; Noé, Frank; Weber, Marcus Deuflhard, Peter; Grötschel, Martin; Hömberg, Dietmar; Horst, Ulrich; Kramer, Jürg; Mehrmann, Volker; Polthier, Konrad; Schmidt, Frank; Schütte, Christof; Skutella, Martin; Sprekels, Jürgen Design of functional molecules European Mathematical Society 2014 16 MATHEON-Mathematics for Key Technologies 1 49 65 Numerical Mathematics OPUS4-6646 Wissenschaftlicher Artikel Igde, Sinaida; Röblitz, Susanna; Müller, Anne; Kolbe, Katharina; Boden, Sophia; Fessele, Claudia; Lindhorst, Thisbe; Weber, Marcus; Hartmann, Laura Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH 2017 Marcomolecular Bioscience 17 12 1700198 10.1002/mabi.201700198 Numerical Mathematics OPUS4-6710 Wissenschaftlicher Artikel Weber, Marcus Implications of PCCA+ in Molecular Simulation 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. 2018 Computation 6 1 20 10.3390/computation6010020 Numerical Mathematics OPUS4-6713 misc Weber, Marcus; Durmaz, Vedat; Sabri, Peggy; Reidelbach, Marco Supplementary simulation data for Science Manuscript ai8636 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. 2017 10.12752/5.MWB.1.0 Computational Molecular Design OPUS4-6663 Wissenschaftlicher Artikel Schrade, Katharina; Tröger, Jessica; Eldashan, Adeep; Zühlke, Kerstin; Abdul Azees, Kamal R.; Elkins, Jonathan M.; Neuenschwander, Martin; Oder, Andreas; Elkewedi, Mohamed; Jaksch, Sarah; Andrae, Karsten; Li, Jinliang; Fernandes, Jaoa; Müller, Paul Markus; Grunwald, Stephan; Marino, Stephen F.; Vukicevic, Tanja; Eichhorst, Jenny; Wiesner, Burkhard; Weber, Marcus; Kapiloff, Michael; Rocks, Oliver; Daumke, Oliver; Wieland, Thomas; Knapp, Stefan; von Kries, Jens Peter; Klussmann, Enno An AKAP-Lbc-RhoA interaction inhibitor promotes the translocation of aquaporin-2 to the plasma membrane of renal collecting duct principal cells 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. 2018 30 PLOS ONE 13 1 e0191423 e0191423 10.1371/journal.pone.0191423 Numerical Mathematics OPUS4-6714 misc Weber, Marcus Supplementary: Implications of PCCA+ in Molecular Simulation Matlab-software and data sets to recapitulate the presented results in M. Weber: Implications of PCCA+ in Molecular Simulation. Computation, 6(1):20, 2018. 2018 Numerical Mathematics OPUS4-6214 Wissenschaftlicher Artikel Spahn, Viola; Del Vecchio, Giovanna; Labuz, Dominika; Rodriguez-Gaztelumendi, Antonio; Massaly, N.; Temp, Julia; Durmaz, Vedat; Sabri, P.; Reidelbach, Marco; Machelska, Halina; Weber, Marcus; Stein, Christoph A nontoxic pain killer designed by modeling of pathological receptor conformations 2017 3 Science 355 6328 966 969 10.1126/science.aai8636 Numerical Mathematics OPUS4-6219 misc Weber, Marcus Eigenvalues of non-reversible Markov chains - A case study Finite reversible Markov chains are characterized by a transition matrix P that has real eigenvalues and pi-orthogonal eigenvectors, where pi is the stationary distribution of P. This means, that a transition matrix with complex eigenvalues corresponds to a non-reversible Markov chain. This observation leads to the question, whether the imaginary part of that eigendecomposition corresponds to or indicates the "pattern" of the nonreversibility. This article shows that the direct relation between imaginary parts of eigendecompositions and the non-reversibility of a transition matrix is not given. It is proposed to apply the Schur decomposition of P instead of the eigendecomposition in order to characterize its nonreversibility. 2017 urn:nbn:de:0297-zib-62191 Numerical Mathematics OPUS4-2407 Wissenschaftlicher Artikel Siegel, D.; Andrae, Karsten; Proske, Matthias; Kochan, C.; Koch, Matthias; Weber, Marcus; Nehls, Irene Dynamic covalent hydrazine chemistry as a specific extraction and cleanup technique for the quantification of the Fusarium mycotoxin zearalenone in edible oils 2010 -2191 Journal of Chromatography A 1217(15) 2206 15 Numerical Mathematics OPUS4-2397 Wissenschaftlicher Artikel Scheibe, Ch.; Bujotzek, Alexander; Dernedde, Jens; Weber, Marcus; Seitz, O. DNA-programmed spatial screening of carbohydrate-lectin interactions 2011 5 Chem. Sci. 2 770 775 Numerical Mathematics OPUS4-2443 Teil eines Buches Weber, Marcus; Rungsarityotin, Wasinee; Schliep, Alexander Spiliopoulou, Myra; Kruse, Rudolf; Borgelt, Christian; Nürnberger, Andreas; Gaul, Wolfgang An Indicator for the Number of Clusters Springer Berlin Heidelberg 2006 7 From Data and Information Analysis to Knowledge Engineering 103 110 Numerical Mathematics OPUS4-2447 Wissenschaftlicher Artikel Weber, Marcus; Andrae, Karsten A simple method for the estimation of entropy differences 2010 13 MATCH Commun. Math. Comp. Chem. 2010 63(2) 319 332 Numerical Mathematics OPUS4-2448 Wissenschaftlicher Artikel Weber, Marcus; Becker, Roland; Köppen, Robert; Durmaz, Vedat Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane 2008 9 Journal of Molecular Simulation 34 7 727 736 Numerical Mathematics OPUS4-2450 Wissenschaftlicher Artikel Weber, Marcus; Bujotzek, Alexander; Andrae, Karsten; Weinhart, M.; Haag, Rainer Computational entropy estimation of linear polyether modified surfaces and correlation with protein resistant properties of such surfaces 2011 J. Mol. Sim. Numerical Mathematics OPUS4-2451 Wissenschaftlicher Artikel Förster, C.; Brauer, Arnd B. E.; Fürste, J.; Betzel, C.; Weber, Marcus; Cordes, Frank; Erdmann, V. Visualization of the tRNA(Ser) acceptor step binding site in the seryl-tRNA synthetase 2007 3 BBRC 362 2 415 418 Numerical Mathematics OPUS4-2452 Konferenzveröffentlichung Kube, Susanna; Weber, Marcus Preserving the Markov Property of Reduced Reversible Markov Chains 2008 3 Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 1048 593 596 Numerical Mathematics OPUS4-2439 Dissertation Weber, Marcus Meshless Methods in Conformation Dynamics 2006 Numerical Mathematics OPUS4-2455 Wissenschaftlicher Artikel Weber, Marcus; Kube, Susanna; Walter, Lionel; Deuflhard, Peter Stable Computation of Probability Densities of Metastable Dynamical Systems 2007 20 SIAM J. Multiscale Model. Simul. 6 2 396 416 Numerical Mathematics OPUS4-5879 misc Bojarovski, Stefan; Hege, Hans-Christian; Lie, Han Cheng; Weber, Marcus Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects. The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function. The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models. 2015 Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany Numerical Mathematics OPUS4-5882 Wissenschaftlicher Artikel Krebek, von, Larissa K. S.; Achazi, Andreas J.; Solleder, Marthe; Weber, Marcus; Paulus, Beate; Schalley, Christoph A. Allosteric and Chelate Cooperativity in Divalent Crown Ether-Ammonium Complexes with Strong Binding Enhancements 2016 9 Chem. Eur. J. 22 43 15475 15484 10.1002/chem.201603098 Numerical Mathematics OPUS4-5573 misc Djurdjevac Conrad, Natasa; Weber, Marcus; Schütte, Christof Finding dominant structures of nonreversible Markov processes 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. 2015 urn:nbn:de:0297-zib-55739 10.1137/15M1032272 Numerical Mathematics OPUS4-5592 Wissenschaftlicher Artikel Abendroth, Frank; Solleder, Marthe; Welker, Pia; Licha, Kai; Weber, Marcus; Seitz, Oliver; Mangoldt, Dorothea High affinity flourescence labelled ligands for the estrogen receptor 2015 9 Eur. J. Org. Chem. 2015 10 2157 2166 Numerical Mathematics OPUS4-5593 Wissenschaftlicher Artikel Koschek, ; Durmaz, Vedat; Krylova, ; Wieczorek, ; Gupta, Pooja; Richter, ; Bujotzek, Alexander; Fischer, ; Haag, Rainer; Freund, ; Weber, Marcus; Rademann, Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands 2015 10 Beilstein J. Org. Chem. 11 837 847 Numerical Mathematics OPUS4-5594 Wissenschaftlicher Artikel Durmaz, Vedat; Weber, Marcus; Meyer, ; Mückter, Computergestützte Simulationen zur Abschätzung gesundheitlicher Risiken durch anthropogene Spurenstoffe der Wassermatrix 2015 3 KA Korrespondenz Abwasser, Abfall 3/15 264 267 Numerical Mathematics OPUS4-4583 Wissenschaftlicher Artikel Röblitz, Susanna; Weber, Marcus Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification 2013 32 Advances in Data Analysis and Classification 7 2 147 179 10.1007/s11634-013-0134-6 Numerical Mathematics OPUS4-5329 misc Nielsen, Adam; Weber, Marcus Computing the nearest reversible Markov chain 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. 2014 urn:nbn:de:0297-zib-53292 Numerical Mathematics OPUS4-5330 Wissenschaftlicher Artikel Nielsen, Adam; Weber, Marcus Computing the nearest reversible Markov chain 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. 2015 16 Numerical Linear Algebra with Applications 22 3 483 499 10.1002/nla.1967 Numerical Mathematics OPUS4-5233 misc Deuflhard, Peter; Weber, Marcus Deuflhard, Peter; Grötschel, Martin; Hömberg, Dietmar; Horst, Ulrich; Kramer, Jürg; Mehrmann, Volker; Polthier, Konrad; Schmidt, Frank; Skutella, Martin; Sprekels, Jürgen Mathematics without pain European Mathematical Society 2014 2 MATHEON-Mathematics for Key Technologies 1 26 28 10.4171/137 Numerical Mathematics OPUS4-4614 Wissenschaftlicher Artikel Röblitz, Susanna; Weber, Marcus Fuzzy Spectral Clustering by PCCA+ 2009 6 Classification and Clustering: Models, Software and Applications WIAS Report No. 26 73 79 Numerical Mathematics OPUS4-7563 Wissenschaftlicher Artikel Erlekam, Franziska; Igde, Sinaida; Röblitz, Susanna; Hartmann, Laura; Weber, Marcus Modeling of Multivalent Ligand-Receptor Binding Measured by kinITC In addition to the conventional Isothermal Titration Calorimetry (ITC), kinetic ITC (kinITC) not only gains thermodynamic information, but also kinetic data from a biochemical binding process. Moreover, kinITC gives insights into reactions consisting of two separate kinetic steps, such as protein folding or sequential binding processes. The ITC method alone cannot deliver kinetic parameters, especially not for multivalent bindings. This paper describes how to solve the problem using kinITC and an invariant subspace projection. The algorithm is tested for multivalent systems with different valencies. 2019 Computation 7 3 46 10.3390/computation7030046 Numerical Mathematics OPUS4-7564 Wissenschaftlicher Artikel Weber, Marcus Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung 2019 6 KA Korrespondenz Abwasser, Abfall 7 551 557 Numerical Mathematics OPUS4-7565 Wissenschaftlicher Artikel Venkatareddy, Narendra Lagumaddepalli; Wilke, Patrick; Ernst, Natalia; Horch, Justus; Weber, Marcus; Dallmann, Andre; Börner, Hans G. Mussel-glue inspired adhesives: A study on the relevance of L-Dopa and the function of the sequence at nanomaterial-peptide interfaces Mussel glue-proteins undergo structural transitions at material interfaces to optimize adhesive surface contacts. Those intriguing structure responses are mimicked by a mussel-glue mimetic peptide (HSY*SGWSPY*RSG (Y* = l-Dopa)) that was previously selected by phage-display to adhere to Al2O3 after enzymatic activation. Molecular level insights into the full-length adhesion domain at Al2O3 surfaces are provided by a divergent-convergent analysis, combining nuclear Overhauser enhancement based 2D NOESY and saturation transfer difference NMR analysis of submotifs along with molecular dynamics simulations of the full-length peptide. The peptide is divided into two submotifs, each containing one Dopa "anchor" (Motif-1 and 2). The analysis proves Motif-1 to constitute a dynamic Al2O3 binder and adopting an "M"-structure with multiple surface contacts. Motif-2 binds stronger by two surface contacts, forming a compact "C"-structure. Taking these datasets as constraints enables to predict the structure and propose a binding process model of the full-length peptide adhering to Al2O3. 2019 Advanced Materials Interfaces 6 13 1900501 10.1002/admi.201900501 Numerical Mathematics OPUS4-7571 Wissenschaftlicher Artikel Del Vecchio, Giovanna; Labuz, Dominika; Temp, Julia; Seitz, Viola; Kloner, Michael; Negrete, Roger; Rodriguez-Gaztelumendi, Antonio; Weber, Marcus; Machelska, Halina; Stein, Christoph pKa of opioid ligands as a discriminating factor for side effects The non-selective activation of central and peripheral opioid receptors is a major shortcoming of currently available opioids. Targeting peripheral opioid receptors is a promising strategy to preclude side effects. Recently, we showed that fentanyl-derived μ-opioid receptor (MOR) agonists with reduced acid dissociation constants (pKa) due to introducing single fluorine atoms produced injury-restricted antinociception in rat models of inflammatory, postoperative and neuropathic pain. Here, we report that a new double-fluorinated compound (FF6) and fentanyl show similar pKa, MOR affinity and [35S]-GTPγS binding at low and physiological pH values. In vivo, FF6 produced antinociception in injured and non-injured tissue, and induced sedation and constipation. The comparison of several fentanyl derivatives revealed a correlation between pKa values and pH-dependent MOR activation, antinociception and side effects. An opioid ligand's pKa value may be used as discriminating factor to design safer analgesics. 2019 Scientific Reports 9 19344 10.1038/s41598-019-55886-1 Numerical Mathematics OPUS4-7959 Wissenschaftlicher Artikel Villatoro, José; Zühlke, Martin; Riebe, Daniel; Beitz, Toralf; Weber, Marcus; Löhmannsröben, Hans-Gerd Sub-ambient pressure IR-MALDI ion mobility spectrometer for the determination of low and high field mobilities A new ion mobility (IM) spectrometer, enabling mobility measurements in the pressure range between 5 and 500 mbar and in the reduced field strength range E/N of 5-90 Td, was developed and characterized. Reduced mobility (K0) values were studied under low E/N (constant value) as well as high E/N (deviation from low field K0) for a series of molecular ions in nitrogen. Infrared matrix-assisted laser desorption ionization (IR-MALDI) was used in two configurations: a source working at atmospheric pressure (AP) and, for the first time, an IR-MALDI source working with a liquid (aqueous) matrix at sub-ambient/reduced pressure (RP). The influence of RP on IR-MALDI was examined and new insights into the dispersion process were gained. This enabled the optimization of the IM spectrometer for best analytical performance. While ion desolvation is less efficient at RP, the transport of ions is more efficient, leading to intensity enhancement and an increased number of oligomer ions. When deciding between AP and RP IR-MALDI, a trade-off between intensity and resolving power has to be considered. Here, the low field mobility of peptide ions was first measured and compared with reference values from ESI-IM spectrometry (at AP) as well as collision cross sections obtained from molecular dynamics simulations. The second application was the determination of the reduced mobility of various substituted ammonium ions as a function of E/N in nitrogen. The mobility is constant up to a threshold at high E/N. Beyond this threshold, mobility increases were observed. This behavior can be explained by the loss of hydrated water molecules. 2020 13 Analytical and Bioanalytical Chemistry 412 5247 5260 10.1007/s00216-020-02735-0 Numerical Mathematics OPUS4-8013 Wissenschaftlicher Artikel Sikorski, Alexander; Weber, Marcus; Schütte, Christof The Augmented Jump Chain Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated. Wiley-VCH 2021 Advanced Theory and Simulations 4 4 10.1002/adts.202000274 Numerical Mathematics OPUS4-7163 Wissenschaftlicher Artikel Reidelbach, Marco; Weber, Marcus; Imhof, Petra Prediction of perturbed proton transfer networks The transfer of protons through proton translocating channels is a complex process, for which direct samplings of different protonation states and side chain conformations in a transition network calculation provide an efficient, bias-free description. In principle, a new transition network calculation is required for every unsampled change in the system of interest, e.g. an unsampled protonation state change, which is associated with significant computational costs. Transition networks void of or including an unsampled change are termed unperturbed or perturbed, respectively. Here, we present a prediction method, which is based on an extensive coarse-graining of the underlying transition networks to speed up the calculations. It uses the minimum spanning tree and a corresponding sensitivity analysis of an unperturbed transition network as initial guess and refinement parameter for the determination of an unknown, perturbed transition network. Thereby, the minimum spanning tree defines a sub-network connecting all nodes without cycles and minimal edge weight sum, while the sensitivity analysis analyzes the stability of the minimum spanning tree towards individual edge weight reductions. Using the prediction method, we are able to reduce the calculation costs in a model system by up to 80%, while important network properties are maintained in most predictions. 2018 23 PLoS ONE 13 12 e0207718 e0207718 https://doi.org/10.1371/journal.pone.0207718 Numerical Mathematics OPUS4-7164 Wissenschaftlicher Artikel Villatoro, José; Weber, Marcus; Zühlke, Martin; Lehmann, Andreas; Zechiowski, Karl; Riebe, Daniel; Beitz, Toralf; Löhmannsröben, Hans-Gerd; Kreuzer, Oliver Structural characterization of synthetic peptides using electronspray ion mobility spectrometry and molecular dynamics simulations Electrospray ionization-ion mobility spectrometry was employed for the determination of collision cross sections (CCS) of 25 synthetically produced peptides in the mass range between 540-3310 Da. The experimental measurement of the CCS is complemented by their calculation applying two different methods. One prediction method is the intrinsic size parameter (ISP) method developed by the Clemmer group. The second new method is based on the evaluation of molecular dynamics (MD) simulation trajectories as a whole, resulting in a single, averaged collision cross-section value for a given peptide in the gas phase. A high temperature MD simulation is run in order to scan through the whole conformational space. The lower temperature conformational distribution is obtained through thermodynamic reweighting. In the first part, various correlations, e.g. CCS vs. mass and inverse mobility vs. m/z correlations, are presented. Differences in CCS between peptides are also discussed in terms of their respective mass and m/z differences, as well as their respective structures. In the second part, measured and calculated CCS are compared. The agreement between the prediction results and the experimental values is in the same range for both calculation methods. While the calculation effort of the ISP method is much lower, the MD method comprises several tools providing deeper insights into the conformations of peptides. Advantages and limitations of both methods are discussed. Based on the separation of two pairs of linear and cyclic peptides of virtually the same mass, the influence of the structure on the cross sections is discussed. The shift in cross section differences and peak shape after transition from the linear to the cyclic peptide can be well understood by applying different MD tools, e.g. the root-mean-square deviation (RMSD) and the root mean square fluctuation (RMSF). 2019 9 International Journal of Mass Spectrometry 436 108 117 10.1016/j.ijms.2018.10.036 Numerical Mathematics OPUS4-7176 Wissenschaftlicher Artikel Abbas, Aennes; Schneider, Ilona; Bollmann, Anna; Funke, Jan; Oehlmann, Jörg; Prasse, Carsten; Schulte-Oehlmann, Ulrike; Seitz, Wolfram; Ternes, Thomas; Weber, Marcus; Wesely, Henning; Wagner, Martin What you extract is what you see: Optimising the preparation of water and wastewater samples for in vitro bioassays The assessment of water quality is crucial for safeguarding drinking water resources and ecosystem integrity. To this end, sample preparation and extraction is critically important, especially when investigating emerging contaminants and the toxicity of water samples. As extraction methods are rarely optimised for bioassays but rather adopted from chemical analysis, this may result in a misrepresentation of the actual toxicity. In this study, surface water, groundwater, hospital and municipal wastewater were used to characterise the impacts of common sample preparation techniques (acidification, filtration and solid phase extraction (SPE)) on the outcomes of eleven in vitro bioassays. The latter covered endocrine activity (reporter gene assays for estrogen, androgen, aryl-hydrocarbon, retinoic acid, retinoid X, vitamin D, thyroid receptor), mutagenicity (Ames fluctuation test), genotoxicity (umu test) and cytotoxicity. Water samples extracted using different SPE sorbents (Oasis HLB, Supelco ENVI-Carb+, Telos C18/ENV) at acidic and neutral pH were compared for their performance in recovering biological effects. Acidification, commonly used for stabilisation, significantly altered the endocrine activity and toxicity of most (waste)water samples. Sample filtration did not affect the majority of endpoints but in certain cases affected the (anti-)estrogenic and dioxin-like activities. SPE extracts (10.4 × final concentration), including WWTP effluents, induced significant endocrine effects that were not detected in aqueous samples (0.63 × final concentration), such as estrogenic, (anti-)androgenic and dioxin-like activities. When ranking the SPE methods using multivariate Pareto optimisation an extraction with Telos C18/ENV at pH 7 was most effective in recovering toxicity. At the same time, these extracts were highly cytotoxic masking the endpoint under investigation. Compared to that, extraction at pH 2.5 enriched less cytotoxicity. In summary, our study demonstrates that sample preparation and extraction critically affect the outcome of bioassays when assessing the toxicity of water samples. Depending on the water matrix and the bioassay, these methods need to be optimised to accurately assess water quality. 2019 13 Water Research 152 47 60 10.1016/j.watres.2018.12.049 Numerical Mathematics OPUS4-6897 Wissenschaftlicher Artikel Wagner, Sabine; Zapata, Carlos; Wan, Wei; Gawlitza, Kornelia; Weber, Marcus; Rurack, Knut Role of Counterions in Molecularly Imprinted Polymers for Anionic Species Small-molecule oxoanions are often imprinted noncovalently as carboxylates into molecularly imprinted polymers (MIPs), requiring the use of an organic counterion. Popular species are either pentamethylpiperidine (PMP) as a protonatable cation or tetraalkylammonium (TXA) ions as permanent cations. The present work explores the influence of the TXA as a function of their alkyl chain length, from methyl to octyl, using UV/vis absorption, fluorescence titrations, and HPLC as well as MD simulations. Protected phenylalanines (Z-L/D-Phe) served as templates/analytes. While the influence of the counterion on the complex stability constants and anion-induced spectral changes shows a monotonous trend with increasing alkyl chain length at the prepolymerization stage, the cross-imprinting/rebinding studies showed a unique pattern that suggested the presence of adaptive cavities in the MIP matrix, related to the concept of induced fit of enzyme-substrate interaction. Larger cavities formed in the presence of larger counterions can take up pairs of Z-x-Phe and smaller TXA, eventually escaping spectroscopic detection. Correlation of the experimental data with the MD simulations revealed that counterion mobility, the relative distances between the three partners, and the hydrogen bond lifetimes are more decisive for the response features observed than actual distances between interacting atoms in a complex or the orientation of binding moieties. TBA has been found to yield the highest imprinting factor, also showing a unique dual behavior regarding the interaction with template and fluorescent monomer. Finally, interesting differences between both enantiomers have been observed in both theory and experiment, suggesting true control of enantioselectivity. The contribution concludes with suggestions for translating the findings into actual MIP development. 2018 12 Langmuir 34 23 6963 6975 10.1021/acs.langmuir.8b00500 Numerical Mathematics OPUS4-6898 Wissenschaftlicher Artikel Spahn, Viola; Del Vecchio, Giovanna; Rodriguez-Gaztelumendi, Antonio; Temp, Julia; Labuz, Dominika; Kloner, Michael; Reidelbach, Marco; Machelska, Halina; Weber, Marcus; Stein, Christoph Opioid receptor signaling, analgesic and side effects induced by a computationally designed pH-dependent agonist Novel pain killers without adverse effects are urgently needed. Springer Nature 2018 Scientific Reports 8 8965 Numerical Mathematics OPUS4-6899 Wissenschaftlicher Artikel Weber, Marcus Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung 2018 KA Korrespondenz Abwasser, Abfall Numerical Mathematics OPUS4-8802 Wissenschaftlicher Artikel Sechi, Renata; Fackeldey, Konstantin; Chewle, Surahit; Weber, Marcus SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension "measured times" versus "measured wavenumbers" and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components' fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra. 2022 Algorithms 15 9 297 10.3390/a15090297 Modeling and Simulation of Complex Processes OPUS4-8516 Wissenschaftlicher Artikel Bauer, Wolfgang; Weber, Marcus; Diehl-Wiesenecker, Eva; Galtung, Noa; Prpic, Monika; Somasundaram, Rajan; Tauber, Rudolf; Schwenk, Jochen; Micke, Patrick; Kappert, Kai Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection 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. 2021 Viruses 13 12 2456 10.3390/v13122456 Computational Molecular Design OPUS4-7960 Wissenschaftlicher Artikel Weber, Marcus; Weitere Autoren, Reichardt, Christine DIN SPEC 2343: Übertragung von sprachbasierten Daten zwischen Künstlichen Intelligenzen - Festlegung von Parametern und Formaten Dieses Dokument legt Parameter und Formate für die Übertragung sprachbasierter Daten zwischen verschiedenen KI-Ökosystemen fest. 2020 Beuth Verlag Numerical Mathematics OPUS4-8871 misc Reidelbach, Marco; Weber, Marcus MaRDI - The mathematical Research Data Initiative 2022 Aktionstag Forschungsdaten 10.5281/zenodo.7397588 Modeling and Simulation of Complex Processes OPUS4-6207 misc Quer, Jannes; Donati, Luca; Keller, Bettina; Weber, Marcus An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities. 2017 urn:nbn:de:0297-zib-62075 Numerical Mathematics OPUS4-5662 misc Weber, Marcus; Quer, Jannes Estimating exit rates in rare event dynamical systems via extrapolation In this article we present a new idea for approximating exit rates for diffusion processes living in a craggy landscape. We are especially interested in the exit rates of a process living in a metastable regions. Due to the fact that Monte Carlo simulations perform quite poor and are very computational expensive in this setting we create several similar situations with a smoothed potential. For this we introduce a new parameter $\lambda \in [0,1]$ ($\lambda = 1$ very smoothed potential, $\lambda=0$ original potential) into the potential which controls the influence the smoothing. We then sample the exit rate for different parameters $\lambda$ the exit rate from a given region. Due to the fact that $\lambda$ is connected to the exit rate we can use this dependency to approximate the real exit rate. The method can be seen as something between hyperdynamics and temperature accelerated MC. 2015 urn:nbn:de:0297-zib-56622 Numerical Mathematics OPUS4-1603 misc Tunga, Burcu; Weber, Marcus Free Energy Calculation Using Mayer Cluster Expansion and Fluctuation Free Integration This work aims to develop a new algorithm to calculate the free energy of water molecules by using a deterministic way. For this purpose, we assume a closed system confined to a physical volume, having water molecules in gas phase. To calculate the free energy of this sytem we utilized Mayer cluster expansion and the fluctuation free integration method. 2012 urn:nbn:de:0297-zib-16031 Numerical Mathematics OPUS4-8837 Wissenschaftlicher Artikel Donati, Luca; Weber, Marcus; Keller, Bettina G. A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential U(x) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) to reweight transition probabilities; the second method was originally developed to discretize the Fokker-Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses. AIP Publishing 2022 21 Journal of Mathematical Physics 63 12 123306-1 123306-21 10.1063/5.0127227 Modeling and Simulation of Complex Processes OPUS4-8956 Wissenschaftlicher Artikel Fernandes, Rita; Chaowdhary, Suvrat; Saleh, Noureldin; Mikula, Natalia; Kanevche, Katerina; Berlepsch, Hans; Hosogi, Naoki; Heberle, Joachim; Weber, Marcus; Böttcher, Christoph; Koksch, Beate Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures A conjugated Cy5 dye-peptide system reveals the formation of two novel and structurally distinct supramolecular assemblies with photo-physical characteristics of H-type dimers or tetramers, respectively. The molecular ultrastructures are triggered by the complementary interplay of mutual chromophore coupling and pH induced changes in the peptide charge pattern. 2022 Angewandte Chemie 61 48 e202208647 Modeling and Simulation of Complex Processes OPUS4-8545 Wissenschaftlicher Artikel Heida, Martin; Sikorski, Alexander; Weber, Marcus Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $d \geq 2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity. 2022 SIAM Journal on Numerical Analysis 10.20347/WIAS.PREPRINT.2913 Computational Molecular Design OPUS4-8105 Wissenschaftlicher Artikel Chewle, Surahit; Emmerling, Franziska; Weber, Marcus Effect of choice of solvent on crystallization pathway of Paracetamol: An experimental and theoretical case study 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. 2020 Crystals 10 12 1107 10.3390/cryst10121107 Numerical Mathematics OPUS4-7065 Wissenschaftlicher Artikel Donati, Luca; Heida, Martin; Keller, Bettina G.; Weber, Marcus Estimation of the infinitesimal generator by square-root approximation In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system. 2018 0 J. Phys.: Condens. Matter 30 42 425201 425201 10.1088/1361-648X/aadfc8 Numerical Mathematics OPUS4-9069 Wissenschaftlicher Artikel Donati, Luca; Weber, Marcus; Keller, Bettina G. Markov models from the square root approximation of the Fokker-Planck equation: calculating the grid-dependent flux Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker-Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker-Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to $\mathcal{O}\left(1{0}^{6}\right)$ states can be obtained within seconds on a single high-performance compute server if regular grids are used. 2021 Journal of Physics: Condensed Matter 33 11 115902 10.1088/1361-648X/abd5f7 Modeling and Simulation of Complex Processes OPUS4-8823 Wissenschaftlicher Artikel Donati, Luca; Weber, Marcus Assessing transition rates as functions of environmental variables We present a method to estimate the transition rates of molecular systems under different environmental conditions which cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios", governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then we use the Square Root Approximation (SqRA) method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis (PCCA+) method to coarse-grain the kinetic model. This permits to efficiently estimate the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work we formalize the theoretical framework of the procedure and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies which take into account how the cellular environment influences biochemical processes. AIP Publishing 2022 14 The Journal of Chemical Physics 157 22 224103-1 224103-14 10.1063/5.0109555 Modeling and Simulation of Complex Processes OPUS4-8925 misc Ternes, Thomas; Bauer, Karl-Heinz; Brauer, Frank; Drewes, Jürgen; Jewell, Kevin; Joss, Adriano; Oehlmann, Jörg; Radtke, Michael; Schulte-Oehlmann, Ulrike; Schwartz, Thomas; Seel, Peter; Völker, Jeanette; Weber, Lilo; Weber, Marcus Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kläranlagen Der DWA-Themenband beschreibt ein Konzept zur weitergehenden Abwasserbehandlung für die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfahrensoptionen als auch für die Bewertung großtechnischer Anlagen. Emissionsseitig basiert das Konzept auf bereits regulatorisch definierten Parametern wie anorganischen Stickstoff-Verbindungen oder Phosphat sowie auf neuen noch nicht in der Abwasserverordnung regulierten Parametern. Die immissionsseitige Betrachtung erfolgt auf Basis der rechtlich durch die Europäische Wasserrahmenrichtlinie und andere Anforderungen bindenden Instrumente. Hierfür werden spezifische Vorgehensweisen vorgeschlagen. Anhand zweier ausgewählter Praxisbeispiele wird deutlich, dass es zur Bewertung der Verfahrensoptionen an einem Standort dienlich ist, ausgewählte Reduktionen bzw. Entfernungen von Stoffen, Organismen und Effekten zu bestimmen. DWA 2023 DWA-Themen T1/2023 Computational Molecular Design OPUS4-6035 misc Witzig, Jakob; Beckenbach, Isabel; Eifler, Leon; Fackeldey, Konstantin; Gleixner, Ambros; Grever, Andreas; Weber, Marcus Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. 2016 urn:nbn:de:0297-zib-60353 10.1137/16M1091162 Numerical Mathematics OPUS4-6029 Wissenschaftlicher Artikel Witzig, Jakob; Beckenbach, Isabel; Eifler, Leon; Fackeldey, Konstantin; Gleixner, Ambros; Grever, Andreas; Weber, Marcus Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. 2018 17 Multiscale Modeling and Simulation 16 1 248 265 10.1137/16M1091162 Numerical Mathematics OPUS4-8928 Wissenschaftlicher Artikel Sikorski, Alexander; Ribera Borrell, Enric; Weber, Marcus Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude. 2024 Journal of Mathematical Physics https://doi.org/10.1063/5.0140764 Modeling and Simulation of Complex Processes OPUS4-6595 Wissenschaftlicher Artikel Quer, Jannes; Donati, Luca; Keller, Bettina; Weber, Marcus An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities. 2018 18 SIAM Journal on Scientific Computing 40 2 A653 A670 10.1137/17m1124772 Numerical Mathematics OPUS4-7898 Wissenschaftlicher Artikel Röhl, Susanne; Weber, Marcus; Fackeldey, Konstantin Computing the minimal rebinding effect for non-reversible processes 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. 2021 18 Multiscale Modeling and Simulation 19 1 460 477 https://doi.org/10.1137/20M1334966 Numerical Mathematics OPUS4-5550 misc Weber, Marcus; Fackeldey, Konstantin G-PCCA: Spectral Clustering for Non-reversible Markov Chains 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. 2015 urn:nbn:de:0297-zib-55505 Numerical Mathematics OPUS4-7314 Wissenschaftlicher Artikel Reuter, Bernhard; Fackeldey, Konstantin; Weber, Marcus Generalized Markov modeling of nonreversible molecular kinetics Markov state models are to date the gold standard for modeling molecular kinetics since they enable the identification and analysis of metastable states and related kinetics in a very instructive manner. The state-of-the-art Markov state modeling methods and tools are very well developed for the modeling of reversible processes in closed equilibrium systems. On the contrary, they are largely not well suited to deal with nonreversible or even nonautonomous processes of nonequilibrium systems. Thus, we generalized the common Robust Perron Cluster Cluster Analysis (PCCA+) method to enable straightforward modeling of nonequilibrium systems as well. The resulting Generalized PCCA (G-PCCA) method readily handles equilibrium as well as nonequilibrium data by utilizing real Schur vectors instead of eigenvectors. This is implemented in the G-PCCA algorithm that enables the semiautomatic coarse graining of molecular kinetics. G-PCCA is not limited to the detection of metastable states but also enables the identification and modeling of cyclic processes. This is demonstrated by three typical examples of nonreversible systems. 2019 The Journal of Chemical Physics 17 150 174103 10.1063/1.5064530 Numerical Mathematics OPUS4-2647 Konferenzveröffentlichung Fackeldey, Konstantin; Bujotzek, Alexander; Weber, Marcus A meshless discretization method for Markov state models applied to explicit water peptide folding simulations Springer 2012 13 Meshfree Methods for Partial Differential Equations VI 89 141 154 Numerical Mathematics OPUS4-4257 misc Bujotzek, Alexander; Schütt, Ole; Nielsen, Adam; Fackeldey, Konstantin; Weber, Marcus Efficient Conformational Analysis by Partition-of-Unity Coupling Obtaining a sufficient sampling of conformational space is a common problem in molecular simulation. We present the implementation of an umbrella-like adaptive sampling approach based on function-based meshless discretization of conformational space that is compatible with state of the art molecular dynamics code and that integrates an eigenvector-based clustering approach for conformational analysis and the computation of inter-conformational transition rates. The approach is applied to three example systems, namely n-pentane, alanine dipeptide, and a small synthetic host-guest system, the latter two including explicitly modeled solvent. 2013 Math Chem urn:nbn:de:0297-zib-42570 Numerical Mathematics OPUS4-7021 misc Fackeldey, Konstantin; Sikorski, Alexander; Weber, Marcus Spectral Clustering for Non-reversible Markov Chains 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 also extend this spectral clustering method 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 do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e. Generalized PCCA), since it includes the case of non reversible processes. We also apply the method to real world eye tracking data. 2018 urn:nbn:de:0297-zib-70218 Numerical Mathematics OPUS4-6262 Wissenschaftlicher Artikel Weber, Marcus; Fackeldey, Konstantin; Schütte, Christof Set-Free Markov State Model Building 2017 Journal of Chemical Physics 146 12 10.1063/1.4978501 Numerical Mathematics OPUS4-1318 misc Fackeldey, Konstantin; Röblitz, Susanna; Scharkoi, Olga; Weber, Marcus Soft Versus Hard Metastable Conformations in Molecular Simulations Particle methods have become indispensible in conformation dynamics to compute transition rates in protein folding, binding processes and molecular design, to mention a few. Conformation dynamics requires at a decomposition of a molecule's position space into metastable conformations. In this paper, we show how this decomposition can be obtained via the design of either ``soft'' or ``hard'' molecular conformations. We show, that the soft approach results in a larger metastabilitiy of the decomposition and is thus more advantegous. This is illustrated by a simulation of Alanine Dipeptide. 2011 urn:nbn:de:0297-zib-13189 Numerical Mathematics OPUS4-4660 Wissenschaftlicher Artikel Weber, Marcus; Fackeldey, Konstantin Local Refinements in Classical Molecular Dynamics Simulations 2014 J. Phys. Conf. Ser. 490 012016 Numerical Mathematics OPUS4-7040 Wissenschaftlicher Artikel Fackeldey, Konstantin; Sikorski, Alexander; Weber, Marcus Spectral Clustering for Non-Reversible Markov Chains 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 also extend this spectral clustering method 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 do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e., generalized PCCA), since it includes the case of non-reversible processes. We also apply the method to real-world eye-tracking data. 2018 15 Computational and Applied Mathematics 37 5 6376 6391 https://doi.org/10.1007/s40314-018-0697-0 Numerical Mathematics OPUS4-7315 Wissenschaftlicher Artikel Ernst, Natalia; Fackeldey, Konstantin; Volkamer, Andrea; Opatz, Oliver; Weber, Marcus Computation of temperature-dependent dissociation rates of metastable protein-ligand complexes Molecular simulations are often used to analyse the stability of protein-ligand complexes. The stability can be characterised by exit rates or using the exit time approach, i.e. by computing the expected holding time of the complex before its dissociation. However determining exit rates by straightforward molecular dynamics methods can be challenging for stochastic processes in which the exit event occurs very rarely. Finding a low variance procedure for collecting rare event statistics is still an open problem. In this work we discuss a novel method for computing exit rates which uses results of Robust Perron Cluster Analysis (PCCA+). This clustering method gives the possibility to define a fuzzy set by a membership function, which provides additional information of the kind 'the process is being about to leave the set'. Thus, the derived approach is not based on the exit event occurrence and, therefore, is also applicable in case of rare events. The novel method can be used to analyse the temperature effect of protein-ligand systems through the differences in exit rates, and, thus, open up new drug design strategies and therapeutic applications. 2019 7 Molecular Simulation 45 11 904 911 10.1080/08927022.2019.1610949 Numerical Mathematics OPUS4-7893 Wissenschaftlicher Artikel Fackeldey, Konstantin; Röhm, Jonas; Niknejad, Amir; Chewle, Surahit; Weber, Marcus Analyzing Raman Spectral Data without Separabiliy Assumption 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. Springer 2021 21 Journal of Mathematical Chemistry 3 59 575 596 10.1007/s10910-020-01201-7 Numerical Mathematics OPUS4-7223 Wissenschaftlicher Artikel Fackeldey, Konstantin; Koltai, Peter; Nevir, Peter; Rust, Henning; Schild, Axel; Weber, Marcus From metastable to coherent sets - Time-discretization schemes In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application. 2019 11 Chaos: An Interdisciplinary Journal of Nonlinear Science 29 012101 012101 10.1063/1.5058128 Numerical Mathematics OPUS4-8752 Wissenschaftlicher Artikel Erlekam, Franziska; Zumbansen, Maximilian; Weber, Marcus Parameter estimation on multivalent ITC data sets The Wiseman fitting can be used to extract binding parameters from ITC data sets, such as heat of binding, number of binding sites, and the overall dissociation rate. The classical Wiseman fitting assumes a direct binding process and neglects the possibility of intermediate binding steps. In principle, it only provides thermodynamic information and not the kinetics of the process. In this article we show that a concentration dependent dissociation constant could possibly stem from intermediate binding steps. The mathematical form of this dependency can be exploited with the aid of the Robust Perron Cluster Cluster Analysis method. Our proposed extension of the Wiseman fitting rationalizes the concentration dependency, and can probably also be used to determine the kinetic parameters of intermediate binding steps of a multivalent binding process. The novelty of this paper is to assume that the binding rate varies per titration step due to the change of the ligand concentration and to use this information in the Wiseman fitting. We do not claim to produce the most accurate values of the binding parameters, we rather present a novel method of how to approach multivalent bindings from a different angle. 2022 Scientific Reports 12 13402 10.1038/s41598-022-17188-x Mathematics for Life and Materials Science OPUS4-5173 Wissenschaftlicher Artikel Weber, Marcus; Fackeldey, Konstantin Computing the Minimal Rebinding Effect Included in a Given Kinetics 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. 2014 16 Multiscale Model. Simul. 12 1 318 334 10.1137/13091124X Numerical Mathematics OPUS4-4658 Wissenschaftlicher Artikel Bujotzek, Alexander; Schütt, Ole; Nielsen, Adam; Fackeldey, Konstantin; Weber, Marcus ZIBgridfree: Efficient Conformational Analysis by Partition-of-Unity Coupling 2014 23 Journal of Mathematical Chemistry 52 3 781 804 10.1007/s10910-013-0265-1 Numerical Mathematics OPUS4-2815 Wissenschaftlicher Artikel Lie, Han Cheng; Fackeldey, Konstantin; Weber, Marcus A Square Root Approximation of Transition Rates for a Markov State Model 2013 18 SIAM. J. Matrix Anal. Appl. 34 2 738 756 10.1137/120899959 Numerical Mathematics OPUS4-4640 Wissenschaftlicher Artikel Haack, Fiete; Fackeldey, Konstantin; Röblitz, Susanna; Scharkoi, Olga; Weber, Marcus; Schmidt, Burkhard Adaptive spectral clustering with application to tripeptide conformation analysis 2013 84 The Journal of Chemical Physics 139 110 194 10.1063/1.4830409 Numerical Mathematics OPUS4-2637 Wissenschaftlicher Artikel Fackeldey, Konstantin; Klimm, Martina; Weber, Marcus A Coarse Graining Method for the Dimension Reduction of the State Space of Biomolecules 2012 12 Journal of Mathematical Chemistry 5 9 2623 2635 Numerical Mathematics OPUS4-1779 misc Weber, Marcus; Fackeldey, Konstantin Computing the Minimal Rebinding Effect Included in a Given Kinetics 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. 2013 urn:nbn:de:0297-zib-17796 10.1137/13091124X Numerical Mathematics OPUS4-6392 Wissenschaftlicher Artikel Fackeldey, Konstantin; Niknejad, Amir; Weber, Marcus Finding Metastabilities in Reversible Markov Chains based on Incomplete Sampling: Case of Molecular Simulation 2017 8 Special Matrices 5/1 73 81 10.1515/spma-2017-0006 Numerical Mathematics OPUS4-8864 Wissenschaftlicher Artikel Raharinirina, N. Alexia; Fackeldey, Konstantin; Weber, Marcus Qualitative Euclidean embedding of Disjoint Sets of Points We consider two disjoint sets of points with a distance metric, or a proximity function, associated with each set. If each set can be separately embedded into separate Euclidean spaces, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function (might require scaling). 2022 Modeling and Simulation of Complex Processes OPUS4-8257 misc Raharinirina, N. Alexia; Weber, Marcus; Birk, Ralph; Fackeldey, Konstantin; Klasse, Sarah M.; Richter, Tonio Sebastian Different Tools and Results for Correspondence Analysis This is a list of codes generated from ancient egyptian texts. The codes are used for a correspondence analysis (CA). Codes and CA software are available from the linked webpage. 2021 10.12752/8257 Numerical Mathematics OPUS4-9101 Buch (Monographie) Ternes, Thomas; Bauer, Karl-Heinz; Brauer, Frank; Drewes, Jörg; Joss, Adriano; Hiller, Georg; Jewell, Kevin; Oehlmann, Jörg; Radke, Michael; Schulte-Oehlmann, Ulrike; Schwartz, Thomas; Seel, Peter; Völker, Jeanette; Weber, Lilo; Weber, Marcus Wilhelm, Christian Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kläranlagen 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. DWA / GDCh 2023 T1/2023 978-3-96862-563-8 Modeling and Simulation of Complex Processes OPUS4-8711 Wissenschaftlicher Artikel Benner, Peter; Burger, Michael; Göddeke, Dominik; Görgen, Christiane; Himpe, Christian; Heiland, Jan; Koprucki, Thomas; Ohlberger, Mario; Rave, Stephan; Reidelbach, Marco; Saak, Jens; Schöbel, Anita; Tabelow, Karsten; Weber, Marcus Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative) 2022 3 GAMM Rundbrief 1 40 43 Modeling and Simulation of Complex Processes OPUS4-8382 Wissenschaftlicher Artikel Sechi, Renata; Weber, Marcus; Heyne, Karsten MSM building and projection for the analysis of time-resolved spectra Understanding the kinetics between the components of time-resolved spectra is a crucial step in the study of photo-activatedprocesses. However, modeling the kinetics requires usually some a priori knowledge about the system. In our approach, webuild a Markov State Model (MSM) from the spectral data, and obtain a Koopman transition matrix K(t). With genPCCA,an invariant subspace projection, we project the process into its metastable components. The result of the application of gen-PCCA is a transition matrix Kc(t), from which we can read the transition probability between the metastable components of the reaction. We discuss the application of this analysis method to the transient absorption spectrum of brominated Al-corrole 2021 Proceedings in Applied Mathematics and Mechanics 21 e202100102 https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100102 https://doi.org/10.1002/pamm.202100102 Computational Molecular Design OPUS4-8015 Wissenschaftlicher Artikel Sechi, Renata; Sikorski, Alexander; Weber, Marcus Estimation of the Koopman Generator by Newton's Extrapolation This article addresses the problem of estimating the Koopman generator of a Markov process. The direct computation of the infinitesimal generator is not easy because of the discretization of the state space, in particular because of the trade-off inherent in the choice of the best lag time to study the process. Short lag times implies a strong discretization of the state space and a consequent loss of Markovianity. Large lag times bypass events on fast timescales. We propose a method to approximate the generator with the computation of the Newton polynomial extrapolation. This technique is a multistep approach which uses as its input Koopman transfer operators evaluated for a series of lag times. Thus, the estimated infinitesimal generator combines information from different time resolutions and does not bias only fast- or slow-decaying dynamics. We show that the multi-scale Newton method can improve the estimation of the generator in comparison to the computation using finite difference or matrix logarithm methods. SIAM 2021 16 Multiscale Modeling and Simulation 19 2 758 774 10.1137/20M1333006 Numerical Mathematics OPUS4-6709 Wissenschaftlicher Artikel Djurdjevac Conrad, Natasa; Fuerstenau, Daniel; Grabundzija, Ana; Helfmann, Luzie; Park, Martin; Schier, Wolfram; Schütt, Brigitta; Schütte, Christof; Weber, Marcus; Wulkow, Niklas; Zonker, Johannes Mathematical modeling of the spreading of innovations in the ancient world 2018 eTopoi. Journal for Ancient Studies 7 10.17171/4-7-1 Numerical Mathematics OPUS4-9228 Wissenschaftlicher Artikel Chewle, Surahit; Weber, Marcus; Emmerling, Franziska Revealing Kinetics of Paracetamol Crystallization Using Time-Resolved Raman Spectroscopy, Orthogonal Time-Lapse Photography, and Non-Negative Matrix Factorization (OSANO) Crystallization is a complex phenomenon with far-reaching implications for the production and formulation of active pharmaceutical ingredients. Understanding this process is critical for achieving control over key physicochemical properties that can affect, for example, the bioavailability and stability of a drug. In this study, we were able to reveal intricate and diverse dynamics of the formation of metastable intermediates of paracetamol crystallization varying with the choice of solvent. We demonstrate the efficacy of our novel approach utilizing an objective function-based non-negative matrix factorization technique for the analysis of time-resolved Raman spectroscopy data, in conjunction with time-lapse photography. Furthermore, we emphasize the crucial importance of integrating Raman spectroscopy with supplementary experimental instrumentation for the mathematical analysis of the obtained spectra. Crystal Growth & Design American Chemical Society 2023 9 Crystal Growth & Design 23 9 6737 6746 10.1021/acs.cgd.3c00617 Modeling and Simulation of Complex Processes OPUS4-4316 misc Nielsen, Adam; Fackeldey, Konstantin; Weber, Marcus On a Generalized Transfer Operator We introduce a generalized operator for arbitrary stochastic processes by using a pre-kernel, which is a generalization of the Markov kernel. For deterministic processes, such an operator is already known as the Frobenius-Perron operator, which is defined for a large class of measures. For Markov processes, there exists transfer operators being only well defined for stationary measures in $L^2$. Our novel generalized transfer operator is well defined for arbitrary stochastic processes, in particular also for deterministic ones. We can show that this operator is acting on $L^1$. For stationary measures, this operator is also an endomorphism of $L^2$ and, therefore, allows for a mathematical analysis in Hilbert spaces. 2013 urn:nbn:de:0297-zib-43162 Numerical Mathematics OPUS4-2116 Teil eines Buches Durmaz, Vedat; Fackeldey, Konstantin; Weber, Marcus Mode, Ch. A rapidly Mixing Monte Carlo Method for the Simulation of Slow Molecular Processes InTech 2011 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science Numerical Mathematics OPUS4-8507 Wissenschaftlicher Artikel Fackeldey, Konstantin; Gorgulla, Christoph; Weber, Marcus Neue Medikamente dank Supercomputern Die aktuelle Pandemie verdeutlicht, wie wichtig es ist, rasch geeignete Arzneimittel zu finden. In Computer­simulationen gelingt das erheblich schneller als im Labor. Gegen das Coronavirus ließen sich auf diese Weise bereits Wirkstoffkandidaten identifizieren. 2021 6 Spektrum der Wissenschaft 11 40 46 Numerical Mathematics OPUS4-4219 misc Lie, Han Cheng; Fackeldey, Konstantin; Weber, Marcus A square root approximation of transition rates for a Markov State Model Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular configuration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in configuration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional configuration space provides proof of concept and an example for which we compare the performance of different discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, finding discretizations of higher-dimensional configuration spaces in which metastable sets can be identified remains a challenge. 2013 urn:nbn:de:0297-zib-42195 10.1137/120899959 Numerical Mathematics OPUS4-6607 misc Fackeldey, Konstantin; Koltai, Péter; Névir, Peter; Rust, Henning; Schild, Axel; Weber, Marcus From Metastable to Coherent Sets - time-discretization schemes Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application. 2017 urn:nbn:de:0297-zib-66074 Numerical Mathematics OPUS4-6922 Wissenschaftlicher Artikel Reuter, Bernhard; Weber, Marcus; Fackeldey, Konstantin; Röblitz, Susanna; Garcia, Martin E. Generalized Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on Amyloid β Conformational Dynamics Driven by an Oscillating Electric Field Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems. To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid β (1−40) peptide, periodically driven by an oscillating electric field. 2018 15 Journal of Chemical Theory and Computation 14 7 3579 3594 10.1021/acs.jctc.8b00079 Numerical Mathematics OPUS4-6216 misc Weber, Marcus; Fackeldey, Konstantin; Schütte, Christof Set-free Markov State Building Molecular dynamics (MD) simulations face challenging problems since the timescales of interest often are much longer than what is possible to simulate and even if sufficiently long simulation are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant timescales accessible via coarse grained representations that also allows for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM. 2017 urn:nbn:de:0297-zib-62167 10.1063/1.4978501 Numerical Mathematics OPUS4-4653 Wissenschaftlicher Artikel Fackeldey, Konstantin; Röblitz, Susanna; Scharkoi, O.; Weber, Marcus Soft Versus Hard Metastable Conformations in Molecular Simulations 2011 10 Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.) 899 909 Numerical Mathematics OPUS4-6395 Wissenschaftlicher Artikel Fackeldey, Konstantin; Weber, Marcus GenPCCA -- Markov State Models for Non-Equilibrium Steady States 2017 10 Big data clustering: Data preprocessing, variable selection, and dimension reduction. WIAS Report No. 29 70 80 10.20347/WIAS.REPORT.29 Numerical Mathematics OPUS4-5172 Wissenschaftlicher Artikel Andrae, Karsten; Merkel, Stefan; Durmaz, Vedat; Fackeldey, Konstantin; Köppen, Robert; Weber, Marcus; Koch, Matthias Investigation of the Ergopeptide Epimerization Process 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. 2014 9 Computation 2 3 102 111 10.3390/computation2030102 Numerical Mathematics OPUS4-4645 Wissenschaftlicher Artikel Andrae, Karsten; Durmaz, Vedat; Fackeldey, Konstantin; Scharkoi, Olga; Weber, Marcus Medizin aus dem Computer Springer 2013 -4 Der Anaesthesist 62 7 561 557 10.1007/s00101-013-2202-x Numerical Mathematics OPUS4-2816 Wissenschaftlicher Artikel Scharkoi, Olga; Fackeldey, Konstantin; Merkulow, Igor; Andrae, Karsten; Weber, Marcus; Nehls, Irene Conformational Analysis of Alternariol on the Quantum Level 2013 5 J. Mol. Model. 19 6 2567 2572 10.1007/s00894-013-1803-2 Numerical Mathematics OPUS4-4972 misc Zhang, Wei; Wang, Han; Hartmann, Carsten; Weber, Marcus; Schütte, Christof Applications of the cross-entropy method to importance sampling and optimal control of diffusions 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. 2014 urn:nbn:de:0297-zib-49720 10.1137/14096493X Numerical Mathematics OPUS4-6177 Wissenschaftlicher Artikel Hartmann, Carsten; Schütte, Christof; Weber, Marcus; Zhang, Wei Importance sampling in path space for diffusion processes with slow-fast variables Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton-Jacobi-Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example. 2017 51 Probability Theory and Related Fields 1 52 10.1007/s00440-017-0755-3 Numerical Mathematics OPUS4-5167 Wissenschaftlicher Artikel Zhang, Wei; Wang, Han; Hartmann, Carsten; Weber, Marcus; Schütte, Christof Applications of the cross-entropy method to importance sampling and optimal control of diffusions 2014 NaN Siam Journal on Scientific Computing 36 6 A2654 A2672 10.1137/14096493X Numerical Mathematics OPUS4-8869 Wissenschaftlicher Artikel Boege, Tobias; Fritze, René; Görgen, Christiane; Hanselmann, Jeroen; Iglezakis, Dorothea; Kastner, Lars; Koprucki, Thomas; Krause, Tabea; Lehrenfeld, Christoph; Polla, Silvia; Reidelbach, Marco; Riedel, Christian; Saak, Jens; Schembera, Björn; Tabelow, Karsten; Weber, Marcus Research-Data Management Planning in the German Mathematical Community In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians' research processes and discuss their usage all along the data life cycle. 2023 7 Eur. Math. Soc. Mag. 130 40 47 10.4171/mag/152 Modeling and Simulation of Complex Processes OPUS4-8586 Wissenschaftlicher Artikel Birk, Ralph; Raharinirina, N. Alexia; Fackeldey, Konstantin; Richter, Tonio Sebastian; Weber, Marcus Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts In this paper, we explore the relationship patterns between Ancient Egyptian texts of the corpus ``Synodal decrees'', which are originating between 243 and 185 BCE, during the Ptolemaic period. Particularly, we are interested in analyzing the grammatical features of the different texts. Conventional data analysis methods such as correspondence Analysis are very useful to explore the patterns of statistical interdependence between categories of variables. However, it is based on a PCA-like dimension-reduction method and turned out to be unsuitable for our dataset due to the high dimensionality of our data representations. Additionally, the similarity between pairs of texts and pairs of grammatical features is observed through the distance between their representation, but the degree of association between a particular grammatical feature and a text is not. Here, we applied a qualitative Euclidean embedding method that provides a new Euclidean representation of the categories of variables. This new representation of the categories is constructed in such a way that all the patterns of statistical interdependence, similarity, and association, are seen through the Euclidean distance between them. Nevertheless, the PCA-like dimension-reduction method also performed poorly on our new representation. Therefore, we obtained a two-dimensional visualization using non-linear methods such UMAP or t-SNE. Although these dimension-reduction methods reduced the interpretability of interpoint distances, we were still able to identify important similarity patterns between the Synodal text as well as their association patterns with the grammatical features. 2021 Modeling and Simulation of Complex Processes OPUS4-9158 Wissenschaftlicher Artikel Donati, Luca; Weber, Marcus Efficient Estimation of Transition Rates as Functions of pH Extracting the kinetic properties of a system whose dynamics depend on the pH of the environment with which it exchanges energy and atoms requires sampling the Grand Canonical Ensemble. As an alternative, we present a novel strategy that requires simulating only the most recurrent Canonical Ensembles that compose the Grand Canonical Ensemble. The simulations are used to estimate the Gran Canonical distribution for a specific pH value by reweighting and to construct the transition rate matrix by discretizing the Fokker-Planck equation by Square Root Approximation and robust Perron Cluster Cluster Analysis. As an application, we have studied the tripeptide Ala-Asp-Ala. 2023 Proceedings in Applied Mathematics & Mechanics 23 10.1002/pamm.202300264 Modeling and Simulation of Complex Processes OPUS4-9066 Wissenschaftlicher Artikel Donati, Luca; Fackeldey, Konstantin; Weber, Marcus Augmented ant colony algorithm for virtual drug discovery Docking is a fundamental problem in computational biology and drug discovery that seeks to predict a ligand's binding mode and affinity to a target protein. However, the large search space size and the complexity of the underlying physical interactions make docking a challenging task. Here, we review a docking method, based on the ant colony optimization algorithm, that ranks a set of candidate ligands by solving a minimization problem for each ligand individually. In addition, we propose an augmented version that takes into account all energy functions collectively, allowing only one minimization problem to be solved. The results show that our modification outperforms in accuracy and efficiency. 2024 18 Journal of Mathematical Chemistry 62 367 385 10.1007/s10910-023-01549-6 Modeling and Simulation of Complex Processes OPUS4-9452 Wissenschaftlicher Artikel Donati, Luca; Schütte, Christof; Weber, Marcus The Kramers turnover in terms of a macro-state projection on phase space We analyze how Langevin dynamics is affected by the friction coefficient using an invariant subspace projection of the associated Koopman operator. This provides the friction-dependent metastable macro-states of the dynamical system as well as the transition rates in the entire phase space. We used the algorithm ISOKANN for a wide range of friction coefficient values and reproduced results consistent with the Kramers turnover. 2024 Submitted to Molecular Physics 10.48550/arXiv.2402.00211 Modeling and Simulation of Complex Processes OPUS4-9027 Wissenschaftlicher Artikel Secker, Christopher; Fackeldey, Konstantin; Weber, Marcus; Ray, Sourav; Gorgulla, Christoph; Schütte, Christof Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale. 2023 Journal of Cheminformatics 15 10.1186/s13321-023-00746-4 Numerical Mathematics OPUS4-8274 Wissenschaftlicher Artikel Thies, Arne; Sunkara, Vikram; Ray, Sourav; Wulkow, Hanna; Celik, M. Özgür; Yergöz, Fatih; Schütte, Christof; Stein, Christoph; Weber, Marcus; Winkelmann, Stefanie Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design 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. 2023 Scientific Reports 13 607 10.1038/s41598-023-27699-w Numerical Mathematics OPUS4-7939 Wissenschaftlicher Artikel Ray, Sourav; Sunkara, Vikram; Schütte, Christof; Weber, Marcus How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs 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. Taylor and Francis 2020 9 Molecular Simulation 46 18 1443 1452 10.1080/08927022.2020.1839660 Numerical Mathematics OPUS4-8886 Wissenschaftlicher Artikel Ray, Sourav; Fackeldey, Konstantin; Stein, Christoph; Weber, Marcus Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane In our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the 𝜇-opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the 𝜇-opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe's parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane. 2023 12 Biophysica 3 2 263 275 10.3390/biophysica3020017 Modeling and Simulation of Complex Processes OPUS4-7961 Wissenschaftlicher Artikel Rabben, Robert Julian; Ray, Sourav; Weber, Marcus ISOKANN: Invariant subspaces of Koopman operators learned by a neural network 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. 2020 The Journal of Chemical Physics 153 11 114109 10.1063/5.0015132 Numerical Mathematics OPUS4-8279 misc Ray, Sourav; Thies, Arne; Sunkara, Vikram; Wulkow, Hanna; Celik, Özgür; Yergöz, Fatih; Schütte, Christof; Stein, Christoph; Weber, Marcus; Winkelmann, Stefanie Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design 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. 2021 urn:nbn:de:0297-zib-82797 Numerical Mathematics OPUS4-7843 misc Ray, Sourav; Sunkara, Vikram; Schütte, Christof; Weber, Marcus How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs 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. 2020 urn:nbn:de:0297-zib-78437 10.1080/08927022.2020.1839660 Modeling and Simulation of Complex Processes OPUS4-9555 Wissenschaftlicher Artikel Sikorski, Alexander; Rabben, Robert Julian; Chewle, Surahit; Weber, Marcus Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations produce useful trajectories, obtaining macroscopic information directly from microstate data presents significant challenges. This paper addresses this gap by introducing the concept of membership functions being the macrostates themselves. We derive equations for the holding times of these macrostates and demonstrate their consistency with the classical definition. Furthermore, we discuss the application of the ISOKANN method for learning these quantities from simulation data. In addition, we present a novel method for extracting transition paths based on the ISOKANN results and demonstrate its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this approach we provide a new perspective on analyzing the macroscopic behaviour of Markov systems. 2024 Modeling and Simulation of Complex Processes OPUS4-9553 Wissenschaftlicher Artikel Sikorski, Alexander; Niknejad, Amir; Weber, Marcus; Donati, Luca Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA. 2024 Journal of Chemical Physics https://doi.org/10.1063/5.0187792 Modeling and Simulation of Complex Processes