Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules

Please always quote using this URN: urn:nbn:de:0297-zib-4063
  • 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.

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Metadaten
Author:Christof Schütte
Document Type:Habilitation
Tag:Hamiltonian system; Markov chain; Markov operator; Perron root; Perron-; almost invariant set; biochemical conformation; quasi-compact operator
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Exx Asymptotic theory / 34E10 Perturbations, asymptotics
46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx) / 46Bxx Normed linear spaces and Banach spaces; Banach lattices (For function spaces, see 46Exx) / 46B09 Probabilistic methods in Banach space theory [See also 60Bxx]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J27 Continuous-time Markov processes on discrete state spaces
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
Date of first Publication:1999/06/14
Series (Serial Number):ZIB-Report (SC-99-18)