Molecular Conformation Dynamics and Computational Drug Design

Please always quote using this URN: urn:nbn:de:0297-zib-7427
  • The paper surveys recent progress in the mathematical modelling and simulation of essential molecular dynamics. Particular emphasis is put on computational drug design wherein time scales of $msec$ up to $min$ play the dominant role. Classical long-term molecular dynamics computations, however, would run into ill-conditioned initial value problems already after time spans of only $psec=10^{-12} sec$. Therefore, in order to obtain results for times of pharmaceutical interest, a combined deterministic-stochastic model is needed. The concept advocated in this paper is the direct identification of metastable conformations together with their life times and their transition patterns. It can be interpreted as a {\em transfer operator} approach corresponding to some underlying hybrid Monte Carlo process, wherein short-term trajectories enter. Once this operator has been discretized, which is a hard problem of its own, a stochastic matrix arises. This matrix is then treated by {\em Perron cluster analysis}, a recently developed cluster analysis method involving the numerical solution of an eigenproblem for a Perron cluster of eigenvalues. In order to avoid the 'curse of dimension', the construction of appropriate boxes for the spatial discretization of the Markov operator requires careful consideration. As a biomolecular example we present a rather recent SARS protease inhibitor.

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Metadaten
Author:Peter Deuflhard, Christof Schütte
Document Type:ZIB-Report
Tag:Hamiltonian dynamics; Monte Carlo methods; Perron cluster an; Smoluchowski dynamics; conformation dynamics; metastable sets; transfer operations
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C40 Computational Markov chains
65-XX NUMERICAL ANALYSIS / 65Pxx Numerical problems in dynamical systems [See also 37Mxx] / 65P10 Hamiltonian systems including symplectic integrators
Date of first Publication:2003/07/02
Series (Serial Number):ZIB-Report (03-20)
Published in:Appeared in: J. M. Hill, R. Moore (eds.) Applied Mathematics Entering the 21st Century. Proc. ICIAM 2003, Sydney, Australia, 2004, pp. 91-119 (2004)