Molecular Conformation Dynamics and Computational Drug Design

摘要

We survey recent progress in the mathematical modelling and simulation of essential molecular dynamics. Particular emphasis is put on computational drug design wherein time-scales of milliseconds up to minutes 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{sup}(-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 transfer-operator approach corresponding to some underlying hybrid Monte Carlo process, wherein short-term trajectories enter. The spatial discretization of this operator is a hard problem of its own. In order to avoid the 'curse of dimension', the construction of appropriate spatial boxes requires careful consideration. Once this operator has been discretised a stochastic matrix arises. This matrix is then treated by Perron cluster analysis, a recently developed cluster analysis method involving the numerical solution of an eigenproblem for a cluster of eigenvalues called the Perron cluster. As a biomolecular example we present a rather recent SARS protease inhibitor.