Stochastic Models of Complex Systems
In many situations of physical interest one would like to concentrate
on slow dynamics occuring on a long time scale and neglect any
rapid motions which play little role in large global changes in the system.
We are currently examining the use of generalized Langevin equations constructed by eliminating fast degrees of freedom
to describe the long time structural changes in biomolecular systems.
This approach can be implemented in a biomolecular system by modeling
flexible regions of a generic protein
as hinges and more robust secondary structures, such as helices, quasi-harmonically.
By eliminating short-wavelength modes of the secondary structural
elements, one can obtain generalized Langevin equations for the
angular motions and other slowly varying modes of the system.
A natural question is therefore to what extent can the dynamics be
simplified by making simple approximations for the memory kernel?
Initial analysis of a harmonic rotor has been conducted
to explore this issue.
These studies indicate that memory effects are extremely important in the dynamics of the rotor,
which suggests that simple stochastic dynamical methods, such as
Brownian MD, may be inappropriate for simulations of in vacuo biomolecules.
Of course, the nature of the dynamics in
solution is often qualitatively different than that in vacuo,
and interactions with the solvent can lead to rapid loss of memory
depending on the strength and time scale of system-bath interactions.
We are currently attempting to extend our analysis of the
harmonic rotor to include solvent interactions. The major challenge
that must be addressed is how one can utilize stochastic models when
there is a clear lack of separation of time
scale between the system-bath interactions and the motions of the
system. Similar problems exist in many models of polymer dynamics,
such as the Rouse or Rouse-Zimm models which attempt to incorporate
the effect of the solvent in an approximate fashion.
A number of fundamental questions concerning the effects
and appropriateness of eliminating fast variables are targeted. These include:
What slow modes of the secondary structural elements of the protein couple significantly
to the hinge dynamics? What is the nature of the ``noise'' and memory in the angular
dynamics? Does a hydrodynamic-like mode-coupling theory of the memory functions
make sense? These issues should help clarify the feasibility of constructing simple analytical
models of protein dynamics.
Created by Jeremy Schofield
Last modified: Tu Dec 3 17:53:20 EST 2001