TY - GEN A1 - Deuflhard, Peter A1 - Schütte, Christof T1 - Molecular Conformation Dynamics and Computational Drug Design N2 - 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. T3 - ZIB-Report - 03-20 KW - conformation dynamics KW - Monte Carlo methods KW - transfer operations KW - Hamiltonian dynamics KW - Smoluchowski dynamics KW - metastable sets KW - Perron cluster an Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7427 ER - TY - CHAP A1 - Schütte, Christof A1 - Huisinga, Wilhelm A1 - Meyn, S. ED - Namachchivaya, N. ED - Lin, Y. T1 - Metastability of Diffusion Processes T2 - Nonlinear Stochastic Dynamics Y1 - 2003 UR - http://publications.imp.fu-berlin.de/127/ VL - 110 SP - 71 EP - 81 PB - Springer ER - TY - JOUR A1 - Huisinga, Wilhelm A1 - Schütte, Christof A1 - Stuart, Andrew T1 - Extracting Macroscopic Stochastic Dynamics JF - Comm. Pure Appl. Math. Y1 - 2003 UR - http://publications.imp.fu-berlin.de/72/ U6 - https://doi.org/10.1002/cpa.10057 VL - 56 IS - 2 SP - 234 EP - 269 ER - TY - CHAP A1 - Schütte, Christof A1 - Huisinga, Wilhelm ED - Ciarlet, P. ED - Le Bris, Claude T1 - Biomolecular Conformations can be Identified as Metastable Sets of Molecular Dynamics T2 - Special Volume Y1 - 2003 UR - http://publications.imp.fu-berlin.de/126/ VL - X SP - 699 EP - 744 PB - Elsevier ER -