SC 99-18 Christof Schuette: Conformational Dynamics: Modelling, Theory, Algorithm, and
Application to Biomolecules
Abstract: The function of many important biomolecules comes from
their
dynamic properties and their ability to switch between
different conformations. In a conformation, the
large
scale geometric structure of the molecule is understood
to be
conserved, whereas on smaller scales the system may well
rotate, oscillate or fluctuate. In a recent article [J.
Comp. Phys., 151,1 (1999)], the present author and
coworkers
demonstrated that (a) conformations can be understood as
almost invariant sets of some Markov chain being defined
via
the Hamiltonian system governing the molecular dynamics
and
that (b) these sets can efficiently be computed via
eigenvectors of the corresponding Markov operator. The
persent manuscript reviews the mathematical modelling
steps
behind the novel concept, includes a rigorous analytical
justification of this approach and especially of the
numerical details of the algorithm, and illustrates its
performance when applied to realistic
molecular systems.
Keywords: biochemical conformation,
almost invariant set,
Markov chain,
Hamiltonian system,
Markov operator,
quasi-compact operator,
Perron root,
Perron-Frobenius operator,
Hybrid Monte Carlo,
ribonucleotide,
coarse graining
MSC: 82C05, 46B09, 60J27, 34E10, 65C05, 65U05