TY - JOUR A1 - Nielsen, Adam T1 - The Monte Carlo Computation Error of Transition Probabilities JF - Statistics & Probability Letters N2 - In many applications one is interested to compute transition probabilities of a Markov chain. This can be achieved by using Monte Carlo methods with local or global sampling points. In this article, we analyze the error by the difference in the $L^2$ norm between the true transition probabilities and the approximation achieved through a Monte Carlo method. We give a formula for the error for Markov chains with locally computed sampling points. Further, in the case of reversible Markov chains, we will deduce a formula for the error when sampling points are computed globally. We will see that in both cases the error itself can be approximated with Monte Carlo methods. As a consequence of the result, we will derive surprising properties of reversible Markov chains. Y1 - 2016 U6 - https://doi.org/10.1016/j.spl.2016.06.011 VL - 118 SP - 163 EP - 170 PB - Elsevier 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 - THES A1 - Breitbach, Paula T1 - Molecular Binding Kinetics of CYP P450 by Using the Infinitesimal Generator Approach Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69076 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 - THES A1 - Bender, Wilhelm T1 - On a Novel Approach for Global Optimization of Non-Convex Problems N2 - In this work new approaches for global optimization are developed. We move from theoretical connections in complexity theory to very practical results in protein-ligand docking. In regard to the efficiency of the suggested optimizer, continuity methods are motivated, that yield an improved optimization method. Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77074 ER - TY - BOOK A1 - Reuter, Bernhard T1 - Generalisierte Markov-Modellierung N2 - Markov State Models (MSM) sind der Goldstandard zur Modellierung biomolekularer Dynamik, da sie die Identifizierung und Analyse metastabiler Zustände ermöglichen. Die robuste Perron-Cluster-Cluster-Analyse (PCCA+) ist ein verbreiteter Spectral-Clustering-Algorithmus, der für das Clustering hochdimensionaler MSM verwendet wird. Da die PCCA+ auf reversible Prozesse beschränkt ist, wird sie zur Generalisierten PCCA+ (G-PCCA) verallgemeinert, die geeignet ist, nichtreversible Prozesse aufzuklären. Bernhard Reuter untersucht hier mittels G-PCCA die nichtthermischen Auswirkungen von Mikrowellen auf die Proteindynamik. Dazu führt er molekulardynamische Nichtgleichgewichtssimulationen des Amyloid-β-(1–40)-Peptids durch und modelliert diese. Y1 - 2020 SN - 978-3-658-29711-4 U6 - https://doi.org/10.1007/978-3-658-29712-1 PB - Springer Spektrum, Wiesbaden ER - TY - THES A1 - Wulkow, Niklas T1 - Modelling the Spread of Innovations by a Markov Process in a Bayesian Framework Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66869 ER - TY - THES A1 - Durmaz, Vedat T1 - Atomistic Binding Free Energy Estimations for Biological Host–Guest Systems N2 - Accurate quantifications of protein–ligand binding affinities by means of in silico methods increasingly gain importance in various scientific branches including toxicology and pharmacology. In silico techniques not only are generally less demanding than laboratory experiments regarding time as well as cost, in particular, if binding assays or synthesis protocols need to be developed in advance. At times, they also provide the only access to risk assessments on novel chemical compounds arising from biotic or abiotic degradation of anthropogenic substances. However, despite the continuous technological and algorithmic progress over the past decades, binding free energy estimations through molecular dynamics simulations still pose an enormous computational challenge owed to the mathematical complexity of solvated macromolecular systems often consisting of hundreds of thousands of atoms. The goals of this thesis can roughly be divided into two categories dealing with different aspects of host–guest binding quantification. On the one side algorithmic strategies for a comprehensive exploration and decomposition of conformational space in conjunction with an automated selection of representative molecular geometries and binding poses have been elaborated providing initial structures for free energy calculations. In light of the dreaded trapping problem typically associated with molecular dynamics simulations, the focus was laid on a particularly systematic generation of representatives covering a broad range of physically accessible molecular conformations and interaction modes. On the other side and ensuing from these input geometries, binding affinity models based on the linear interaction energy (LIE) method have been developed for a couple of (bio)molecular systems. The applications included a successful prediction of the liquid-chromatographic elution order as well as retention times of highly similar hexabromocyclododecane (HBCD) stereoisomers, a novel empirical LIE–QSAR hybrid binding affinity model related to the human estrogen receptor α (ERα), and, finally, the (eco)toxicological prioritization of transformation products originating from the antibiotic sulfamethoxazole with respect to their binding affinities to the bacterial enzyme dihydropteroate synthase. Altogether, a fully automated approach to binding mode and affinity estimation has been presented that is content with an arbitrary geometry of a small molecule under observation and a spatial vector specifying the binding site of a potential target molecule. According to our studies, it is superior to conventional docking and thermodynamic average methods and primarily suggesting binding free energy calculation on the basis of several heavily distinct complex geometries. Both chromatographic retention times of HBCD and binding affinities to ERα yielded squared coefficients of correlation with experimental results significantly higher than 0.8. Approximately 85 % (100 %) of predicted receptor–ligand binding modes deviated less than 1.53 Å (2.05 Å) from available crystallographic structures. KW - molecular modelling KW - molecular dynamics KW - molecular simulation KW - binding affinity KW - prediction KW - free energy KW - receptor ligand KW - retention time KW - liquid chromatography Y1 - 2016 UR - http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000103765 PB - FU Dissertationen Online 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 - 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 - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Djurdjevac, Ana A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - From interacting agents to density-based modeling with stochastic PDEs N2 - Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. T3 - ZIB-Report - 19-21 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73456 SN - 1438-0064 ER -