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Biomolecular conformations can be identified as metastable sets of molecular dynamics. (English) Zbl 1066.81658

Le Bris, Claude (ed.), Special volume: Computational chemistry. Amsterdam: North-Holland (ISBN 0-444-51248-9/hbk). Handb. Numer. Anal. 10, 699-744 (2003).
From the introduction: The article is organized as follows: First we sharpen and conceptually complement the two characterizations of metastability (Section 2), then we shortly summarize the different dynamical models designed to describe different aspects of the dynamical and statistical properties of molecules (Section 3). This is followed by the presentation of the mathematical framework of the transfer operator approach to metastability (Sections 4 and 5). Within this framework we reformulate the two concepts of metastability and justify in detail the key idea of the transfer operator approach. Moreover, it is shown that the framework allows to incorporate almost all different dynamical models available. In Section 6 the theoretical level is left and the issues of practical realization are discussed: The concept of Galerkin discretization of transfer operators is studied which leads to the question of whether a discretization of the eigenvalue problem in huge dimensional state spaces will be possible without risking the increase of numerical effort beyond any tolerable amount. It is illustrated how this problem can be circumvented. Sections 7 and 8 conclude the article by demonstrating the application of the approach. In Section 7 the entire concept is illustrated by means of a simple but completely comprehensible test system whereas Section 8 is devoted to the application to a small oligonucleotide.
For the entire collection see [Zbl 1052.81001].

MSC:

81V55 Molecular physics
92C40 Biochemistry, molecular biology

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