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 -