Molecular Simulation and Systems Biology - Systems Biology: Networks, Models, and Applications - page 72

but it also can be used to generate a sample set of the configurations
that a system might take subject to conditions of fixed density and
energy. If one wants to model conditions where the molecular system
is in contact with a heat bath of some specified temperature, or one
where it is in a container subject to some external pressure, one can
use MC or variations of standard MD where the motion of the
molecules is modified in a way to reflect the effect of the heat bath
and/or pressure on the system. It must be remembered, however, that
such variations in the MD algorithm necessarily affect the dynamics
of the molecules under study.
In addition to MD, Monte Carlo techniques are often employed
to simulate molecular systems in contact with a heat bath or under
conditions of some externally applied pressure. In Metropolis MC
(see box on page 73), one produces a large set of configurations for the
system by the generation of a Markov chain. With this procedure, one
makes various types of random moves of molecules in the system to
produce a trial state. The trial state is either accepted or rejected. If the
trial state is rejected, the state from which the trial state was obtained
is retained. This process is then repeated many times. The acceptance/
rejection criterion depends on the temperature as well as on the types
of moves that are being performed, and it is carefully designed such
that if one averages properties over all of the states produced, one gets
a result that is characteristic of the particular thermodynamic condition
being studied. With MC techniques the system evolves in a way that
attempts to sample new configurations with the appropriate thermal
weighting; the succession of configurations does not represent any real
“time evolution” of the system.
The third type of information that can be derived from simulations
relates to the kinetics or dynamical motion of the system. Molecular
dynamics is the method required for these types of studies since it
describes the behavior of molecules that are subject only to the forces
on them from their molecular interactions. Questions that require an
understanding of kinetics include “How quickly do proteins fold?”
Biological processes occur on a variety of time scales, and the length
of the simulation required to study them depends on the particular
phenomena under study. In order to have adequate statistical confi-
dence in kinetic results, enough effort must be expended to observe
not just one but dozens or hundreds of the events of interest. Because
of this, there are still many interesting and important biological
processes that are currently beyond the reach of meaningful simulation.
Force Fields
Typically, a force field expresses the energy as a sum of expressions of
different types: one type to describe contributions from chemical bond
stretching, one for angle bending, one for twisting, or torsional, motion