SC 99-36 Christof Schütte, Wilhelm Huisinga, Peter Deuflhard: Transfer Operator Approach to Conformational Dynamics in
Biomolecular Systems
Abstract: 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.
Keywords: Transfer operator,
Markov process,
Markov chain,
molecular dynamics,
biomolecular conformations,
canonical ensemble,
transition prohability,
Hamiltonian dynamics,
Langevin dynamics,
nearly degenerate eigenvalues,
Perron cluster
MSC: 65U05, 60J25, 60J60, 47B15