SC 99-25 Christof Schütte, Wilhelm Huisinga: On Conformational Dynamics induced by Langevin Processes
Abstract: The function of many important biomolecules is related to
their
dynamic properties and their ability to switch between
different
conformations, which are understood as almost
invariant
or metastable subsets of the positional state space
of the
system. Recently, the present authors and their coworkers
presented
a novel algorithmic scheme for the direct numerical
determination of
such metastable subsets and the transition probability
between them.
Although being different in most aspects, this
method exploits the same basic idea as DELLNITZ and
JUNGE in their approach to almost invariance in
discrete dynamical systems: the almost invariant sets are
computed
via certain eigenvectors of the Markov operators
associated with the
dynamical behavior.
In the present article we analyze the application of this
approach
to (high-friction) Langevin models describing the
dynamical
behavior of molecular systems coupled to a heat bath. We
will see
that this can be related to theoretical results for
(symmetric)
semigroups of Markov operators going back to DAVIES.
We concentrate on a comparison of our
approach in respect to random perturbations of dynamical
systems.
Keywords: Smoluchowski equation,
Fokker-Planck equation,
semigroup of Markov operators,
canonical ensemble,
small noise,
first exit time,
half time period
MSC: 65U05, 60J25, 60J60, 15A18