TY - GEN A1 - Weber, Marcus T1 - A Subspace Approach to Molecular Markov State Models via an Infinitesimal Generator N2 - 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. T3 - ZIB-Report - 09-27 KW - Robuste Perron Cluster Analyse KW - Molekülkinetik KW - Übergangsraten KW - Robust Perron cluster analysis KW - molecular kinetics KW - transition rates Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11432 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus T1 - An efficient analysis of rare events in canonical ensemble dynamics N2 - 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. T3 - ZIB-Report - 08-36 KW - Moleküldynamik KW - Kanonische Gesamtheit KW - Metastabilität KW - molecular dynamics KW - canonical ensemble KW - metastability Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10871 SN - 1438-0064 ER - TY - GEN A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Weber, Marcus T1 - Soft Versus Hard Metastable Conformations in Molecular Simulations N2 - 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. T3 - ZIB-Report - 11-27 KW - Proteins, Conformation Space, Meshfree Methods Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13189 ER - TY - THES A1 - Weber, Marcus T1 - A Subspace Approach to Molecular Markov State Models via a New Infinitesimal Generator N2 - 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. KW - Conformation Dynamics KW - Molecular Kinetics KW - Transition Rates KW - Markov State Models Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14025 ER - TY - GEN A1 - Weber, Marcus T1 - The funnel trap paradox N2 - 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”. T3 - ZIB-Report - 12-12 KW - Markov process KW - Robust Perron Cluster Analysis KW - Conformation Dynamics Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14765 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus A1 - Walter, Lionel A1 - Kube, Susanna A1 - Deuflhard, Peter T1 - Stable computation of probability densities for metastable dynamical systems N2 - 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. T3 - ZIB-Report - 06-39 KW - dynamical systems KW - metastability KW - molecular conformations KW - cluster analysis KW - sampling KW - aggregation/disaggregation KW - domain decomposition Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9331 ER - TY - GEN A1 - Weber, Marcus T1 - Clustering by using a simplex structure N2 - 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. T3 - ZIB-Report - 04-03 KW - cluster algorithms KW - Perron cluster analysis KW - stochastic matrices KW - bipartite graphs Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7782 ER - TY - GEN A1 - Weber, Marcus A1 - Rungsarityotin, Wasinee A1 - Schliep, Alexander T1 - Perron Cluster Analysis and Its Connection to Graph Partitioning for Noisy Data N2 - 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. T3 - ZIB-Report - 04-39 KW - Perron cluster analysis KW - spectral graph theory KW - clustering KW - gene expression Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8140 ER - TY - GEN A1 - Weber, Marcus A1 - Kube, Susanna A1 - Riemer, Alexander A1 - Bujotzek, Alexander T1 - Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems N2 - 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. T3 - ZIB-Report - 07-03 KW - dynamical systems KW - stationary distribution KW - rare events KW - metastability KW - cluster analysis Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9467 ER - TY - GEN A1 - Kube, Susanna A1 - Weber, Marcus T1 - Identification of Metastabilities in Monomolecular Conformation Kinetics N2 - 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. T3 - ZIB-Report - 06-01 KW - metastable conformations KW - potential energy surface KW - transition rates KW - eigenvectors KW - clustering Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8956 ER - TY - GEN A1 - Walter, Lionel A1 - Weber, Marcus T1 - ConfJump : a fast biomolecular sampling method which drills tunnels through high mountains N2 - 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. T3 - ZIB-Report - 06-26 KW - Monte Carlo simulation KW - rare events KW - rough potential energy function KW - molecular dynamics Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9204 ER - TY - THES A1 - Weber, Marcus T1 - Meshless Methods in Confirmation Dynamics Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10232 ER - TY - GEN A1 - Weber, Marcus A1 - Becker, Roland A1 - Köppen, Robert A1 - Durmaz, Vedat T1 - Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane N2 - 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. T3 - ZIB-Report - 07-31 KW - Markov process KW - molecular dynamics KW - rate matrix Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10308 SN - 1438-0064 ER - TY - GEN A1 - Tunga, Burcu A1 - Weber, Marcus T1 - Free Energy Calculation Using Mayer Cluster Expansion and Fluctuation Free Integration N2 - 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. T3 - ZIB-Report - 12-35 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16031 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus A1 - Fackeldey, Konstantin T1 - Computing the Minimal Rebinding Effect Included in a Given Kinetics N2 - The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process. On the macro scale this process comprises the Markov property. This Makovian view is spoiled when switching to the atomistic scale of a binding process. We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing ''intermediate'' bound states. This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem. The results form our examples show good agreement with data form laboratory. T3 - ZIB-Report - 13-12 KW - Rebinding KW - Molecular Kinetics KW - Conformation Dynamics Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17796 SN - 1438-0064 ER - TY - GEN A1 - Lie, Han Cheng A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - A square root approximation of transition rates for a Markov State Model N2 - 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. T3 - ZIB-Report - 13-43 KW - Markov State Models KW - Markov chains KW - meshfree methods KW - metastability KW - Voronoi KW - linear programming Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42195 SN - 1438-0064 ER - TY - GEN A1 - Nielsen, Adam A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - On a Generalized Transfer Operator N2 - 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. T3 - ZIB-Report - 13-74 KW - Transfer Operator KW - Pre Kernel KW - Perron Frobenius Generalization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43162 SN - 1438-0064 ER - TY - JOUR A1 - Fackeldey, Konstantin A1 - Koltai, Peter A1 - Nevir, Peter A1 - Rust, Henning A1 - Schild, Axel A1 - Weber, Marcus T1 - From metastable to coherent sets - Time-discretization schemes JF - Chaos: An Interdisciplinary Journal of Nonlinear Science N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1063/1.5058128 VL - 29 SP - 012101 EP - 012101 ER - TY - JOUR A1 - Abbas, Aennes A1 - Schneider, Ilona A1 - Bollmann, Anna A1 - Funke, Jan A1 - Oehlmann, Jörg A1 - Prasse, Carsten A1 - Schulte-Oehlmann, Ulrike A1 - Seitz, Wolfram A1 - Ternes, Thomas A1 - Weber, Marcus A1 - Wesely, Henning A1 - Wagner, Martin T1 - What you extract is what you see: Optimising the preparation of water and wastewater samples for in vitro bioassays JF - Water Research N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1016/j.watres.2018.12.049 VL - 152 SP - 47 EP - 60 ER - TY - JOUR A1 - Reuter, Bernhard A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - Generalized Markov modeling of nonreversible molecular kinetics JF - The Journal of Chemical Physics N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1063/1.5064530 VL - 17 IS - 150 SP - 174103 ER - TY - JOUR A1 - Ernst, Natalia A1 - Fackeldey, Konstantin A1 - Volkamer, Andrea A1 - Opatz, Oliver A1 - Weber, Marcus T1 - Computation of temperature-dependent dissociation rates of metastable protein–ligand complexes JF - Molecular Simulation N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1080/08927022.2019.1610949 VL - 45 IS - 11 SP - 904 EP - 911 ER - TY - JOUR A1 - Villatoro, José A1 - Weber, Marcus A1 - Zühlke, Martin A1 - Lehmann, Andreas A1 - Zechiowski, Karl A1 - Riebe, Daniel A1 - Beitz, Toralf A1 - Löhmannsröben, Hans-Gerd A1 - Kreuzer, Oliver T1 - Structural characterization of synthetic peptides using electronspray ion mobility spectrometry and molecular dynamics simulations JF - International Journal of Mass Spectrometry N2 - 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). Y1 - 2019 U6 - https://doi.org/10.1016/j.ijms.2018.10.036 VL - 436 SP - 108 EP - 117 ER - TY - JOUR A1 - Donati, Luca A1 - Heida, Martin A1 - Keller, Bettina G. A1 - Weber, Marcus T1 - Estimation of the infinitesimal generator by square-root approximation JF - J. Phys.: Condens. Matter N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1088/1361-648X/aadfc8 VL - 30 IS - 42 SP - 425201 EP - 425201 ER - TY - JOUR A1 - Reidelbach, Marco A1 - Weber, Marcus A1 - Imhof, Petra T1 - Prediction of perturbed proton transfer networks JF - PLoS ONE N2 - 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. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1371/journal.pone.0207718 VL - 13 IS - 12 SP - e0207718 EP - e0207718 ER - TY - GEN A1 - Fackeldey, Konstantin A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Spectral Clustering for Non-reversible Markov Chains N2 - Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g. the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We 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. T3 - ZIB-Report - 18-48 KW - spectral clustering KW - Markov chain KW - Schur decomposition KW - non-reversible Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70218 SN - 1438-0064 ER - TY - JOUR A1 - Fackeldey, Konstantin A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Spectral Clustering for Non-Reversible Markov Chains JF - Computational and Applied Mathematics N2 - Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We 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. KW - Spectral clustering KW - Markov chain KW - Non-reversible KW - Schur decomposition KW - GenPCCA Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1007/s40314-018-0697-0 VL - 37 IS - 5 SP - 6376 EP - 6391 ER - TY - JOUR A1 - Lie, Han Cheng A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - A Square Root Approximation of Transition Rates for a Markov State Model JF - SIAM. J. Matrix Anal. Appl. Y1 - 2013 U6 - https://doi.org/10.1137/120899959 VL - 34 IS - 2 SP - 738 EP - 756 ER - TY - JOUR A1 - Scharkoi, Olga A1 - Fackeldey, Konstantin A1 - Merkulow, Igor A1 - Andrae, Karsten A1 - Weber, Marcus A1 - Nehls, Irene T1 - Conformational Analysis of Alternariol on the Quantum Level JF - J. Mol. Model. Y1 - 2013 U6 - https://doi.org/10.1007/s00894-013-1803-2 VL - 19 IS - 6 SP - 2567 EP - 2572 ER - TY - GEN A1 - Bujotzek, Alexander A1 - Schütt, Ole A1 - Nielsen, Adam A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - Efficient Conformational Analysis by Partition-of-Unity Coupling T2 - Math Chem N2 - 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. T3 - ZIB-Report - 13-58 KW - Markov State Models KW - Meshfree KW - Molecular Simulation KW - Partition of Unity Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42570 SN - 1438-0064 ER - TY - GEN A1 - Quer, Jannes A1 - Donati, Luca A1 - Keller, Bettina A1 - Weber, Marcus T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates N2 - 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. T3 - ZIB-Report - 17-09 KW - Adaptive Importance Sampling KW - Molecular Dynamics KW - Metastability KW - Variance Reduction KW - Non Equilibrium Sampling KW - Metadynamics KW - Girsanov Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62075 SN - 1438-0064 ER - TY - JOUR A1 - Spahn, Viola A1 - Del Vecchio, Giovanna A1 - Labuz, Dominika A1 - Rodriguez-Gaztelumendi, Antonio A1 - Massaly, N. A1 - Temp, Julia A1 - Durmaz, Vedat A1 - Sabri, P. A1 - Reidelbach, Marco A1 - Machelska, Halina A1 - Weber, Marcus A1 - Stein, Christoph T1 - A nontoxic pain killer designed by modeling of pathological receptor conformations JF - Science Y1 - 2017 U6 - https://doi.org/10.1126/science.aai8636 VL - 355 IS - 6328 SP - 966 EP - 969 ER - TY - GEN A1 - Weber, Marcus A1 - Fackeldey, Konstantin A1 - Schütte, Christof T1 - Set-free Markov State Building N2 - 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. T3 - ZIB-Report - 17-10 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62167 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus T1 - Eigenvalues of non-reversible Markov chains – A case study N2 - 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. T3 - ZIB-Report - 17-13 KW - non-reversible KW - transition matrix KW - detailed balance Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62191 SN - 1438-0064 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Weber, Marcus A1 - Zhang, Wei T1 - Importance sampling in path space for diffusion processes with slow-fast variables JF - Probability Theory and Related Fields N2 - 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. Y1 - 2017 UR - http://rdcu.be/oA51 U6 - https://doi.org/10.1007/s00440-017-0755-3 N1 - If you are not subscribing to the journal please use the http link below as part of the Springer Nature SharedIt initiative SP - 1 EP - 52 ER - TY - JOUR A1 - Villatoro, José A1 - Zühlke, Martin A1 - Riebe, Daniel A1 - Beitz, Toralf A1 - Weber, Marcus A1 - Riedel, Jens A1 - Löhmannsröben, Hans-Gerd T1 - IR-MALDI ion mobility spectrometry: physical source characterization and application as HPLC detector JF - International Journal for Ion Mobility Spectrometry Y1 - 2016 U6 - https://doi.org/10.1007/s12127-016-0208-1 IS - 19/4 SP - 197 EP - 297 ER - TY - JOUR A1 - Guerler, A. A1 - Moll, Sebastian A1 - Weber, Marcus A1 - Meyer, Holger A1 - Cordes, Frank T1 - Selection and flexible optimization of binding modes from conformation ensembles JF - Biosystems Y1 - 2008 UR - http://www.sciencedirect.com/science/article/pii/S0303264707001670 U6 - https://doi.org/DOI: 10.1016/j.biosystems.2007.11.004 VL - 92 IS - 1 SP - 42 EP - 48 ER - TY - JOUR A1 - Haack, Fiete A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Schmidt, Burkhard A1 - Weber, Marcus T1 - Adaptive Spectral Clustering for Conformation Analysis JF - AIP Conference Proceedings Y1 - 2010 UR - http://link.aip.org/link/?APC/1281/1585/1 U6 - https://doi.org/10.1063/1.3498116 VL - 1281 IS - 1 SP - 1585 EP - 1588 PB - AIP ER - TY - CHAP A1 - Durmaz, Vedat A1 - Fackeldey, Konstantin A1 - Weber, Marcus ED - Mode, Ch. T1 - A rapidly Mixing Monte Carlo Method for the Simulation of Slow Molecular Processes T2 - Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science Y1 - 2011 PB - InTech ER - TY - JOUR A1 - Gürler, A. A1 - Moll, Sebastian A1 - Weber, Marcus A1 - Meyer, Holger A1 - Cordes, Frank T1 - Selection and flexible optimization of binding modes from conformation ensembles JF - Biosystems Y1 - 2007 ER - TY - JOUR A1 - Kube, Susanna A1 - Weber, Marcus T1 - A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations JF - Journal of Chemical Physics Y1 - 2007 U6 - https://doi.org/10.1063/1.2404953 VL - 126 IS - 2 ER - TY - CHAP A1 - Weber, Marcus A1 - Kube, Susanna T1 - Robust Perron Cluster Analysis for Various Applications in Computational Life Science T2 - Computational Life Sciences Y1 - 2005 SP - 57 EP - 66 ER - TY - JOUR A1 - Metzner, Ph. A1 - Weber, Marcus A1 - Schütte, Christof T1 - Observation uncertainty in reversible Markov chains JF - Phys. Rev. E Y1 - 2010 U6 - https://doi.org/10.1103/PhysRevE.82.031114 VL - 82 IS - 3 SP - 031114 PB - American Physical Society ER - TY - JOUR A1 - Klimm, Martina A1 - Bujotzek, Alexander A1 - Weber, Marcus T1 - Direct Reweighting Strategies in Conformation Dynamics JF - MATCH Commun. Math. Comp. Chem. Y1 - 2011 VL - 65(2) SP - 333 EP - 346 ER - TY - CHAP A1 - Kube, Susanna A1 - Weber, Marcus T1 - Computation of equilibrium densities in metastable dynamical systems by domain decomposition T2 - Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 Y1 - 2008 VL - 1048 SP - 339 EP - 342 PB - AIP Conference Proceedings ER - TY - JOUR A1 - Scheibe, Ch. A1 - Bujotzek, Alexander A1 - Dernedde, Jens A1 - Weber, Marcus A1 - Seitz, O. T1 - DNA-programmed spatial screening of carbohydrate-lectin interactions JF - Chem. Sci. Y1 - 2011 VL - 2 SP - 770 EP - 775 ER - TY - JOUR A1 - Siegel, D. A1 - Andrae, Karsten A1 - Proske, Matthias A1 - Kochan, C. A1 - Koch, Matthias A1 - Weber, Marcus A1 - Nehls, Irene T1 - Dynamic covalent hydrazine chemistry as a specific extraction and cleanup technique for the quantification of the Fusarium mycotoxin zearalenone in edible oils JF - Journal of Chromatography A Y1 - 2010 VL - 1217(15) SP - 2206 EP - 15 ER - TY - THES A1 - Weber, Marcus T1 - Meshless Methods in Conformation Dynamics Y1 - 2006 ER - TY - CHAP A1 - Weber, Marcus A1 - Rungsarityotin, Wasinee A1 - Schliep, Alexander ED - Spiliopoulou, Myra ED - Kruse, Rudolf ED - Borgelt, Christian ED - Nürnberger, Andreas ED - Gaul, Wolfgang T1 - An Indicator for the Number of Clusters T2 - From Data and Information Analysis to Knowledge Engineering Y1 - 2006 UR - http://dx.doi.org/10.1007/3-540-31314-1_11 SP - 103 EP - 110 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Weber, Marcus A1 - Andrae, Karsten T1 - A simple method for the estimation of entropy differences JF - MATCH Commun. Math. Comp. Chem. 2010 Y1 - 2010 VL - 63(2) SP - 319 EP - 332 ER - TY - JOUR A1 - Weber, Marcus A1 - Becker, Roland A1 - Köppen, Robert A1 - Durmaz, Vedat T1 - Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane JF - Journal of Molecular Simulation Y1 - 2008 VL - 34 IS - 7 SP - 727 EP - 736 ER - TY - JOUR A1 - Weber, Marcus A1 - Bujotzek, Alexander A1 - Andrae, Karsten A1 - Weinhart, M. A1 - Haag, Rainer T1 - Computational entropy estimation of linear polyether modified surfaces and correlation with protein resistant properties of such surfaces JF - J. Mol. Sim. Y1 - 2011 ER - TY - JOUR A1 - Förster, C. A1 - Brauer, Arnd B. E. A1 - Fürste, J. A1 - Betzel, C. A1 - Weber, Marcus A1 - Cordes, Frank A1 - Erdmann, V. T1 - Visualization of the tRNA(Ser) acceptor step binding site in the seryl-tRNA synthetase JF - BBRC Y1 - 2007 VL - 362 IS - 2 SP - 415 EP - 418 ER - TY - CHAP A1 - Kube, Susanna A1 - Weber, Marcus T1 - Preserving the Markov Property of Reduced Reversible Markov Chains T2 - Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 Y1 - 2008 VL - 1048 SP - 593 EP - 596 ER - TY - JOUR A1 - Weber, Marcus A1 - Kube, Susanna A1 - Walter, Lionel A1 - Deuflhard, Peter T1 - Stable Computation of Probability Densities of Metastable Dynamical Systems JF - SIAM J. Multiscale Model. Simul. Y1 - 2007 VL - 6 IS - 2 SP - 396 EP - 416 ER - TY - JOUR A1 - Köppen, Robert A1 - Riedel, Juliane A1 - Proske, Matthias A1 - Drzymala, Sarah A1 - Rasenko, Tatjana A1 - Durmaz, Vedat A1 - Weber, Marcus A1 - Koch, Matthias T1 - Photochemical trans-/cis-isomerization and quantification of zearalenone in edible oils JF - J. Agric. Food Chem. Y1 - 2012 U6 - https://doi.org/10.1021/jf3037775 VL - 60 SP - 11733 EP - 11740 ER - TY - JOUR A1 - Durmaz, Vedat A1 - Weber, Marcus A1 - Becker, Roland T1 - How to Simulate Affinities for Host-Guest Systems Lacking Binding Mode Information: application to the liquid chromatographic separation of hexabromocyclododecane stereoisomers JF - Journal of Molecular Modeling Y1 - 2012 U6 - https://doi.org/10.1007/s00894-011-1239-5 VL - 18 SP - 2399 EP - 2408 ER - TY - JOUR A1 - Weber, Marcus A1 - Bujotzek, Alexander A1 - Haag, Rainer T1 - Quantifying the rebinding effect in multivalent chemical ligand-receptor systems JF - J. Chem. Phys. Y1 - 2012 VL - 137 IS - 5 SP - 054111 ER - TY - CHAP A1 - Fackeldey, Konstantin A1 - Bujotzek, Alexander A1 - Weber, Marcus T1 - A meshless discretization method for Markov state models applied to explicit water peptide folding simulations T2 - Meshfree Methods for Partial Differential Equations VI Y1 - 2012 VL - 89 SP - 141 EP - 154 PB - Springer ER - TY - JOUR A1 - Fasting, Carlo A1 - Schalley, Christoph A. A1 - Weber, Marcus A1 - Seitz, Oliver A1 - Hecht, Stefan A1 - Koksch, Beate A1 - Dernedde, Jens A1 - Graf, Christina A1 - Knapp, Ernst-Walter A1 - Haag, Rainer T1 - Multivalency as a Chemical Organization and Action Principle JF - Angew. Chem. Int. Ed. Y1 - 2012 VL - 51 IS - 42 SP - 10472 EP - 10498 ER - TY - JOUR A1 - Kube, Susanna A1 - Lasser, Caroline A1 - Weber, Marcus T1 - Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics JF - Journal of Computational Physics Y1 - 2008 U6 - https://doi.org/10.1016/j.jcp.2008.11.016 VL - 228 IS - 6 SP - 1947 EP - 1962 ER - TY - GEN A1 - Kellermann, R. A1 - Weber, Marcus A1 - Bujotzek, Alexander T1 - Vom Dietrich zum Sicherheitsschlüssel – Mathematiker des Matheon simulieren neuen Wirkstoff für die Diabetes-Behandlung Y1 - 2007 IS - 2 PB - DFG-Forschungszentrum Matheon ER - TY - JOUR A1 - Köppen, Robert A1 - Becker, Roland A1 - Weber, Marcus A1 - Durmaz, Vedat A1 - Nehls, Irene T1 - HBCD stereoisimers: Thermal interconversion and enantiospecific trace analysis in biota JF - Organohalogen Compounds Y1 - 2009 VL - 70 SP - 910 EP - 913 ER - TY - JOUR A1 - Bujotzek, Alexander A1 - Weber, Marcus T1 - Efficient Simulation of Ligand-Receptor Binding Processes Using the Conformation Dynamics Approach JF - Journal of Bioinformatics and Computational Biology Y1 - 2009 VL - 7(5) SP - 811 EP - 831 ER - TY - CHAP A1 - Weber, Marcus ED - Dunemann, L. ED - Schmoll, O. T1 - Spurenstoffe im Trinkwasser - Risikoqualifizierung im Rechner? T2 - Schriftenreihe des Vereins für Wasser-, Boden- und Lufthygiene Y1 - 2009 ER - TY - JOUR A1 - Weber, Marcus A1 - Durmaz, Vedat A1 - Becker, Roland A1 - Esslinger, Susanne T1 - Predictive Identification of Pentabromocyclododecane (PBCD) Isomers with high Binding Affinity to hTTR JF - Organohalogen Compounds Y1 - 2009 VL - 71 SP - 247 EP - 252 ER - TY - JOUR A1 - Fackeldey, Konstantin A1 - Klimm, Martina A1 - Weber, Marcus T1 - A Coarse Graining Method for the Dimension Reduction of the State Space of Biomolecules JF - Journal of Mathematical Chemistry Y1 - 2012 VL - 5 IS - 9 SP - 2623 EP - 2635 ER - TY - JOUR A1 - Röblitz, Susanna A1 - Weber, Marcus T1 - Fuzzy Spectral Clustering by PCCA+ JF - Classification and Clustering: Models, Software and Applications Y1 - 2009 UR - http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Report&year=2009&number=26 IS - WIAS Report No. 26 SP - 73 EP - 79 ER - TY - JOUR A1 - Röblitz, Susanna A1 - Weber, Marcus T1 - Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification JF - Advances in Data Analysis and Classification Y1 - 2013 U6 - https://doi.org/10.1007/s11634-013-0134-6 VL - 7 IS - 2 SP - 147 EP - 179 ER - TY - JOUR A1 - Scharkoi, Olga A1 - Esslinger, Susanne A1 - Becker, Roland A1 - Weber, Marcus A1 - Nehls, Irene T1 - Predicting sites of cytochrome P450-mediated hydroxylation applied to CYP3A4 and hexabromocyclododecane JF - Molecular Simulation Y1 - 2014 U6 - https://doi.org/10.1080/08927022.2014.898845 ER - TY - JOUR A1 - Haack, Fiete A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Weber, Marcus A1 - Schmidt, Burkhard T1 - Adaptive spectral clustering with application to tripeptide conformation analysis JF - The Journal of Chemical Physics Y1 - 2013 U6 - https://doi.org/10.1063/1.4830409 VL - 139 SP - 110 EP - 194 ER - TY - CHAP A1 - Igde, Sinaida A1 - Wölk, Hendrik A1 - Röblitz, Susanna A1 - Reidelbach, Marco A1 - Weber, Marcus A1 - Hartmann, Laura T1 - Identifying Multivalent Binding Kinetics of Precision Glycomacromolecules: A Kinetic Study Using kinITC T2 - Münster Symposium on Cooperative Effects 2015 - SFB 858, at Westfälische Wilhelms-Universität Münster, 2015 N2 - 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. Y1 - 2015 ER - TY - JOUR A1 - Quer, Jannes A1 - Donati, Luca A1 - Keller, Bettina A1 - Weber, Marcus T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates JF - SIAM Journal on Scientific Computing N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1137/17m1124772 VL - 40 IS - 2 SP - A653 EP - A670 ER - TY - JOUR A1 - Weber, Marcus T1 - Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung JF - KA Korrespondenz Abwasser, Abfall Y1 - 2018 ER - TY - JOUR A1 - Reuter, Bernhard A1 - Weber, Marcus A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Garcia, Martin E. T1 - Generalized Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on Amyloid β Conformational Dynamics Driven by an Oscillating Electric Field JF - Journal of Chemical Theory and Computation N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1021/acs.jctc.8b00079 VL - 14 IS - 7 SP - 3579 EP - 3594 ER - TY - JOUR A1 - Wagner, Sabine A1 - Zapata, Carlos A1 - Wan, Wei A1 - Gawlitza, Kornelia A1 - Weber, Marcus A1 - Rurack, Knut T1 - Role of Counterions in Molecularly Imprinted Polymers for Anionic Species JF - Langmuir N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1021/acs.langmuir.8b00500 VL - 34 IS - 23 SP - 6963 EP - 6975 ER - TY - JOUR A1 - Spahn, Viola A1 - Del Vecchio, Giovanna A1 - Rodriguez-Gaztelumendi, Antonio A1 - Temp, Julia A1 - Labuz, Dominika A1 - Kloner, Michael A1 - Reidelbach, Marco A1 - Machelska, Halina A1 - Weber, Marcus A1 - Stein, Christoph T1 - Opioid receptor signaling, analgesic and side effects induced by a computationally designed pH-dependent agonist JF - Scientific Reports N2 - Novel pain killers without adverse effects are urgently needed. Y1 - 2018 VL - 8 SP - 8965 PB - Springer Nature ER - TY - JOUR A1 - Erlekam, Franziska A1 - Igde, Sinaida A1 - Röblitz, Susanna A1 - Hartmann, Laura A1 - Weber, Marcus T1 - Modeling of Multivalent Ligand-Receptor Binding Measured by kinITC JF - Computation N2 - 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. Y1 - 2019 U6 - https://doi.org/10.3390/computation7030046 VL - 7 IS - 3 SP - 46 ER - TY - JOUR A1 - Weber, Marcus T1 - Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung JF - KA Korrespondenz Abwasser, Abfall Y1 - 2019 VL - 7 SP - 551 EP - 557 ER - TY - JOUR A1 - Venkatareddy, Narendra Lagumaddepalli A1 - Wilke, Patrick A1 - Ernst, Natalia A1 - Horch, Justus A1 - Weber, Marcus A1 - Dallmann, Andre A1 - Börner, Hans G. T1 - Mussel-glue inspired adhesives: A study on the relevance of L-Dopa and the function of the sequence at nanomaterial-peptide interfaces JF - Advanced Materials Interfaces N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1002/admi.201900501 VL - 6 IS - 13 SP - 1900501 ER - TY - JOUR A1 - Del Vecchio, Giovanna A1 - Labuz, Dominika A1 - Temp, Julia A1 - Seitz, Viola A1 - Kloner, Michael A1 - Negrete, Roger A1 - Rodriguez-Gaztelumendi, Antonio A1 - Weber, Marcus A1 - Machelska, Halina A1 - Stein, Christoph T1 - pKa of opioid ligands as a discriminating factor for side effects JF - Scientific Reports N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1038/s41598-019-55886-1 VL - 9 SP - 19344 ER - TY - JOUR A1 - Villatoro, José A1 - Zühlke, Martin A1 - Riebe, Daniel A1 - Beitz, Toralf A1 - Weber, Marcus A1 - Löhmannsröben, Hans-Gerd T1 - Sub-ambient pressure IR-MALDI ion mobility spectrometer for the determination of low and high field mobilities JF - Analytical and Bioanalytical Chemistry N2 - 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. Y1 - 2020 U6 - https://doi.org/10.1007/s00216-020-02735-0 VL - 412 SP - 5247 EP - 5260 ER - TY - JOUR A1 - Weber, Marcus A1 - Weitere Autoren, ED - Reichardt, Christine T1 - DIN SPEC 2343: Übertragung von sprachbasierten Daten zwischen Künstlichen Intelligenzen - Festlegung von Parametern und Formaten JF - Beuth Verlag N2 - Dieses Dokument legt Parameter und Formate für die Übertragung sprachbasierter Daten zwischen verschiedenen KI-Ökosystemen fest. Y1 - 2020 ER - TY - JOUR A1 - Rabben, Robert Julian A1 - Ray, Sourav A1 - Weber, Marcus T1 - ISOKANN: Invariant subspaces of Koopman operators learned by a neural network JF - The Journal of Chemical Physics N2 - The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network. Y1 - 2020 U6 - https://doi.org/10.1063/5.0015132 VL - 153 IS - 11 SP - 114109 ER - TY - GEN A1 - Ray, Sourav A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Weber, Marcus T1 - How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs N2 - Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a $\mu$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction. T3 - ZIB-Report - 20-18 KW - Opioid, Ligand-Receptor Interaction, Binding Kinetics, Molecular Dynamics, Metadynamics, SQRA Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78437 SN - 1438-0064 ER - TY - JOUR A1 - Fackeldey, Konstantin A1 - Röhm, Jonas A1 - Niknejad, Amir A1 - Chewle, Surahit A1 - Weber, Marcus T1 - Analyzing Raman Spectral Data without Separabiliy Assumption JF - Journal of Mathematical Chemistry N2 - Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the Time-Resolved-Raman-Sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix M from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices W and H, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining W and H is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example. Y1 - 2021 U6 - https://doi.org/10.1007/s10910-020-01201-7 VL - 3 IS - 59 SP - 575 EP - 596 PB - Springer ER - TY - JOUR A1 - Röhl, Susanne A1 - Weber, Marcus A1 - Fackeldey, Konstantin T1 - Computing the minimal rebinding effect for non-reversible processes JF - Multiscale Modeling and Simulation N2 - The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1137/20M1334966 VL - 19 IS - 1 SP - 460 EP - 477 ER - TY - JOUR A1 - Ray, Sourav A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Weber, Marcus T1 - How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs JF - Molecular Simulation N2 - Molecular simulations of ligand–receptor interactions are a computational challenge, especially when their association- (‘on’-rate) and dissociation- (‘off’-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab. Y1 - 2020 U6 - https://doi.org/10.1080/08927022.2020.1839660 VL - 46 IS - 18 SP - 1443 EP - 1452 PB - Taylor and Francis ER - TY - GEN A1 - Weber, Marcus A1 - Durmaz, Vedat A1 - Sabri, Peggy A1 - Reidelbach, Marco T1 - Supplementary simulation data for Science Manuscript ai8636 N2 - The simulation data has been produced by Vedat Durmaz, Peggy Sabri and Marco Reidelbach inside the "Computational Molecular Design" Group headed by Marcus Weber at Zuse-Institut Berlin, Takustr. 7, D-14195 Berlin, Germany. The file contains classical simulation data for different fentanyl derivates in the MOR binding pocket at different pHs. It also includes instruction files for quantum-chemical pKa-value estimations and a description of how we derived the pKa-values from the Gaussian09 log-files. Y1 - 2017 U6 - https://doi.org/10.12752/5.MWB.1.0 N1 - GROMACS trajectories and GAUSSIAN files of MOR and fentanyl derivates ER - TY - GEN A1 - Weber, Marcus T1 - Supplementary: Implications of PCCA+ in Molecular Simulation N2 - Matlab-software and data sets to recapitulate the presented results in M. Weber: Implications of PCCA+ in Molecular Simulation. Computation, 6(1):20, 2018. Y1 - 2018 N1 - This data set includes one folder per published figure. The folders contain all needed resources to recapitulate the presented results. ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Fuerstenau, Daniel A1 - Grabundzija, Ana A1 - Helfmann, Luzie A1 - Park, Martin A1 - Schier, Wolfram A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Weber, Marcus A1 - Wulkow, Niklas A1 - Zonker, Johannes T1 - Mathematical modeling of the spreading of innovations in the ancient world JF - eTopoi. Journal for Ancient Studies Y1 - 2018 U6 - https://doi.org/10.17171/4-7-1 SN - ISSN 2192-2608 VL - 7 ER - TY - JOUR A1 - Weber, Marcus T1 - Implications of PCCA+ in Molecular Simulation JF - Computation N2 - Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., ’bound’ vs. ’unbound’), although the process itself takes place in a continuous space. In this context, the formula chi=XA connects the micro-dynamics of the molecular system to its macro-dynamics. Chi can be understood as a clustering of micro-states of a molecular system into a few macro-states. X is a basis of an invariant subspace of a transfer operator describing the micro-dynamics of the system. The formula claims that there is an unknown linear relation A between these two objects. With the aid of this formula we can understand rebinding effects, the electron flux in pericyclic reactions, and systematic changes of binding rates in kinetic ITC experiments. We can also analyze sequential spectroscopy experiments and rare event systems more easily. This article provides an explanation of the formula and an overview of some of its consequences. Y1 - 2018 U6 - https://doi.org/10.3390/computation6010020 VL - 6 IS - 1 SP - 20 ER - TY - JOUR A1 - Schrade, Katharina A1 - Tröger, Jessica A1 - Eldashan, Adeep A1 - Zühlke, Kerstin A1 - Abdul Azees, Kamal R. A1 - Elkins, Jonathan M. A1 - Neuenschwander, Martin A1 - Oder, Andreas A1 - Elkewedi, Mohamed A1 - Jaksch, Sarah A1 - Andrae, Karsten A1 - Li, Jinliang A1 - Fernandes, Jaoa A1 - Müller, Paul Markus A1 - Grunwald, Stephan A1 - Marino, Stephen F. A1 - Vukicevic, Tanja A1 - Eichhorst, Jenny A1 - Wiesner, Burkhard A1 - Weber, Marcus A1 - Kapiloff, Michael A1 - Rocks, Oliver A1 - Daumke, Oliver A1 - Wieland, Thomas A1 - Knapp, Stefan A1 - von Kries, Jens Peter A1 - Klussmann, Enno T1 - An AKAP-Lbc-RhoA interaction inhibitor promotes the translocation of aquaporin-2 to the plasma membrane of renal collecting duct principal cells JF - PLOS ONE N2 - Stimulation of renal collecting duct principal cells with antidiuretic hormone (arginine-vasopressin, AVP) results in inhibition of the small GTPase RhoA and the enrichment of the water channel aquaporin-2 (AQP2) in the plasma membrane. The membrane insertion facilitates water reabsorption from primary urine and fine-tuning of body water homeostasis. Rho guanine nucleotide exchange factors (GEFs) interact with RhoA, catalyze the exchange of GDP for GTP and thereby activate the GTPase. However, GEFs involved in the control of AQP2 in renal principal cells are unknown. The A-kinase anchoring protein, AKAP-Lbc, possesses GEF activity, specifically activates RhoA, and is expressed in primary renal inner medullary collecting duct principal (IMCD) cells. Through screening of 18,431 small molecules and synthesis of a focused library around one of the hits, we identified an inhibitor of the interaction of AKAP-Lbc and RhoA. This molecule, Scaff10-8, bound to RhoA, inhibited the AKAP-Lbc-mediated RhoA activation but did not interfere with RhoA activation through other GEFs or activities of other members of the Rho family of small GTPases, Rac1 and Cdc42. Scaff10-8 promoted the redistribution of AQP2 from intracellular vesicles to the periphery of IMCD cells. Thus, our data demonstrate an involvement of AKAP-Lbc-mediated RhoA activation in the control of AQP2 trafficking. Y1 - 2018 U6 - https://doi.org/10.1371/journal.pone.0191423 VL - 13 IS - 1 SP - e0191423 EP - e0191423 ER - TY - JOUR A1 - Chewle, Surahit A1 - Emmerling, Franziska A1 - Weber, Marcus T1 - Effect of choice of solvent on crystallization pathway of Paracetamol: An experimental and theoretical case study JF - Crystals N2 - The choice of solvents influences crystalline solid formed during the crystallization of active pharmaceutical ingredients (API). The underlying effects are not always well understood because of the complexity of the systems. Theoretical models are often insufficient to describe this phenomenon. In this study, the crystallization behavior of the model drug paracetamol in different solvents was studied based on experimental and molecular dynamics data. The crystallization process was followed in situ using time-resolved Raman spectroscopy. Molecular dynamics with simulated annealing algorithm was used for an atomistic understanding of the underlying processes. The experimental and theoretical data indicate that paracetamol molecules adopt a particular geometry in a given solvent predefining the crystallization of certain polymorphs. Y1 - 2020 U6 - https://doi.org/10.3390/cryst10121107 VL - 10 IS - 12 SP - 1107 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Jöster, Annika A1 - Schütte, Christof A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting N2 - Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples. Y1 - 2026 ER - TY - GEN A1 - Cordes, Frank A1 - Weber, Marcus A1 - Schmidt-Ehrenberg, Johannes T1 - Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals N2 - Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol. T3 - ZIB-Report - 02-40 KW - metastability KW - Perron-Cluster Cluster Analysis KW - curse of dimension KW - Hybrid Monte Carlo KW - significant dihedrals Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7074 ER - TY - GEN A1 - Weber, Marcus T1 - Improved Perron Cluster Analysis N2 - The problem of clustering data can often be transformed into the problem of finding a hidden block diagonal structure in a stochastic matrix. Deuflhard et al. have proposed an algorithm that state s the number $k$ of clusters and uses the sign structure of $k$ eigenvectors of the stochastic matrix to solve the cluster problem. Recently Weber and Galliat discovered that this system of eigenvectors can easily be transformed into a system of $k$ membership functions or soft characteristic functions describing the clusters. In this article we explain the corresponding cluster algorithm and point out the underlying theory. By means of numerical examples we explain how the grade of membership can be interpreted. T3 - ZIB-Report - 03-04 KW - cluster analysis KW - stochastic matrices KW - almost invariant sets Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7260 ER - TY - GEN A1 - Deuflhard, Peter A1 - Weber, Marcus T1 - Robust Perron Cluster Analysis in Conformation Dynamics N2 - The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included. T3 - ZIB-Report - 03-19 KW - Markov chains KW - cluster algorithms KW - Perron cluster analysis KW - conformation dynamics Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7415 ER - TY - GEN A1 - Weber, Marcus A1 - Meyer, Holger T1 - ZIBgridfree - Adaptive Conformation Analysis with qualified Support of Transition States and Thermodynamic Weights N2 - This paper introduces a new algorithm of conformational analysis based on mesh-free methods as described in [M. Weber. Mehless methods in Conformation Dynamics.(2005)]. The adaptive decomposition of the conformational space by softly limiting functions avoids trapping effects and allows adaptive refinement strategies. These properties of the algorithm makes ZIBgridfree particularly suitable for the complete exploration of high-dimensional conformational space. The adaptive control of the algorithm benefits from the tight integration of molecular simulation and conformational analysis. An emphasized part of the analysis is the Robust Perron Cluster Analysis (PCCA+) based on the work of Peter Deuflhard and Marcus Weber. PCCA+ supports an almost-characteristic cluster definition with an outstanding mapping of transition states. The outcome is expressed by the metastable sets of conformations, their thermodynamic weights and flexibility. T3 - ZIB-Report - 05-17 KW - Molecular Dynamics KW - Meshfree Methods KW - Conformation Analysis KW - Quality Functions Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8514 ER - TY - JOUR A1 - Abendroth, Frank A1 - Bujotzek, Alexander A1 - Shan, Min A1 - Haag, Rainer A1 - Weber, Marcus A1 - Seitz, Oliver T1 - DNA-controlled bivalent presentation of ligands for the estrogen receptor JF - Angew. Chem. Int. Ed. Y1 - 2011 ER - TY - JOUR A1 - Bujotzek, Alexander A1 - Shan, Min A1 - Haag, Rainer A1 - Weber, Marcus T1 - Towards a rational spacer design for bivalent inhibition of estrogen receptor JF - J. Comput.-Aided Mol. Des. Y1 - 2011 VL - 25(3) SP - 253 EP - 262 ER -