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 - 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 - 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 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes JF - Multiscale Modeling and Simulation N2 - 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. KW - Markov State Models KW - NESS KW - Non-reversible Markov Processes KW - Mixed-Integer Programming Y1 - 2018 U6 - https://doi.org/10.1137/16M1091162 SN - 1438-0064 VL - 16 IS - 1 SP - 248 EP - 265 ER -