Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems

Please always quote using this URN: urn:nbn:de:0297-zib-4247
  • The article surveys the development of novel mathematical concepts and algorithmic approaches based thereon in view of their possible applicability to biomolecular design. Both a first deterministic approach, based on the Frobenius-Perron operator corresponding to the flow of the Hamiltonian dynamics, and later stochastic approaches, based on a spatial Markov operator or on Langevin dynamics, can be subsumed under the unified mathematical roof of the transfer operator approach to effective dynamics of molecular systems. The key idea of constructing specific transfer operators especially taylored for the purpose of conformational dynamics appears as the red line throughout the paper. Different steps of the algorithm are exemplified by a trinucleotide molecular system as a small representative of possible RNA drug molecules.

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Metadaten
Author:Christof Schütte, Wilhelm Huisinga, Peter Deuflhard
Document Type:ZIB-Report
Tag:Ha; Markov chain; Markov process; Transfer operator; biomolecular conformations; canonical ensemble; molecular dynamics; transition prohability
MSC-Classification:47-XX OPERATOR THEORY / 47Bxx Special classes of linear operators / 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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 / 60J25 Continuous-time Markov processes on general state spaces
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 / 60J60 Diffusion processes [See also 58J65]
Date of first Publication:1999/10/18
Series (Serial Number):ZIB-Report (SC-99-36)
Published in:Appeared in: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. B. Fiedler (ed.) Springer 2001, pp. 191-223