TY - THES A1 - Schütte, Christof T1 - Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules N2 - The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric structure of the molecule is understood to be conserved, whereas on smaller scales the system may well rotate, oscillate or fluctuate. In a recent article [J. Comp. Phys., 151,1 (1999)], the present author and coworkers demonstrated that (a) conformations can be understood as almost invariant sets of some Markov chain being defined via the Hamiltonian system governing the molecular dynamics and that (b) these sets can efficiently be computed via eigenvectors of the corresponding Markov operator. The persent manuscript reviews the mathematical modelling steps behind the novel concept, includes a rigorous analytical justification of this approach and especially of the numerical details of the algorithm, and illustrates its performance when applied to realistic molecular systems. T3 - ZIB-Report - SC-99-18 KW - biochemical conformation KW - almost invariant set KW - Markov chain KW - Hamiltonian system KW - Markov operator KW - quasi-compact operator KW - Perron root KW - Perron- Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4063 ER - TY - GEN A1 - Hartmann, Carsten A1 - Richter, Lorenz A1 - Schütte, Christof A1 - Zhang, Wei T1 - Variational characterization of free energy: Theory and algorithms N2 - The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated. T3 - ZIB-Report - 17-52 KW - Importance sampling KW - Donsker-Varadhan principle KW - thermodynamic free energy KW - nonequilibrium molecular dynamics KW - stochastic approximation KW - cross-entropy method Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65045 SN - 1438-0064 ER - TY - GEN A1 - Wang, Han A1 - Schütte, Christof T1 - Building Markov State Models for Periodically Driven Non-Equilibrium Systems N2 - Recent years have seen an increased interest in non-equilibrium molecular dynamics (NEMD) simulations, especially for molecular systems with periodic forcing by external fields, e.g., in the context of studying effects of electromagnetic radiation on the human body tissue. Lately, an NEMD methods with local thermostating has been proposed that allows for studying non-equilibrium processes in a statistically reliable and thermodynamically consistent way. In this article, we demonstrate how to construct Markov State Models (MSMs) for such NEMD simulations. MSM building has been well-established for systems in equilibrium where MSMs with just a few (macro-)states allow for accurate reproduction of the essential kinetics of the molecular system under consideration. Non-equilibrium MSMs have been lacking so far. The article presents how to construct such MSMs and illustrates their validity and usefulness for the case of conformation dynamics of alanine dipeptide in an external electric field. T3 - ZIB-Report - 14-46 KW - Non-equilibrium KW - Markov states model KW - Alanine dipeptide KW - Electric field KW - Floquet theory Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53167 SN - 1438-0064 N1 - To appear in: Journal of Chemical Theory and Computation ER -