SC 98-45 Christof Schütte, Alexander Fischer, Wilhelm Huisinga, Peter Deuflhard: A Direct Approach to Conformational Dynamics based on Hybrid
Monte Carlo (Appeared in: Journal of Computational Physics 151, 146-168
(1999)
Abstract: 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(3-5) cytidylyl(3-5) cytidin are given and
interpreted.
Keywords: conformation,
conformational dynamics,
hybrid Monte Carlo,
reweighting,
essential degrees of freedom,
transition probabilities,
Markov operator,
transition operator
MSC: 65U05, 47A75, 47B38, 58F05, 60J20, 65C05