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A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo

Please always quote using this URN: urn:nbn:de:0297-zib-3889
  • Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of $T$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted.

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Author:Christof Schütte, Alexander Fischer, Wilhelm Huisinga, Peter Deuflhard
Document Type:ZIB-Report
Tag:Markov operator; conformation; conformational dynamics; essential degrees of freedom; hybrid Monte Carlo; reweighting; transition probabilities
MSC-Classification:47-XX OPERATOR THEORY / 47Axx General theory of linear operators / 47A75 Eigenvalue problems [See also 47J10, 49R05]
47-XX OPERATOR THEORY / 47Bxx Special classes of linear operators / 47B38 Operators on function spaces (general)
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 / 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
Date of first Publication:1999/01/04
Series (Serial Number):ZIB-Report (SC-98-45)
Published in:Appeared in: Journal of Computational Physics 151, 146-168 (1999)
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