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Accurate
molecular dynamics simulations remain a major challenge in computational
biology, since they involve thousands of degrees of freedom in the molecule
of interest in addition to the need to account for the water environment.
Computer simulations that include a large number of water molecules remain
the state of the art in this field. They are however inefficient, since
a large fraction of the computing time is spent calculating a detailed
trajectory of the solvent molecules, even though it is primarily the solute
behavior that is of interest. It is therefore desirable to develop different
approaches in which the effect of the solvent is taken into account implicitly.
Such treatment would make it possible to perform simulations covering
much longer time intervals, and including much larger molecular systems.
For some tasks such as energy refinement, energy minimization may be preferable
to molecular dynamics as less noise is introduced into the system and
less sampling is needed to remove this noise. Since explicit water molecules
can only be used with molecular dynamics (a stationary water molecule
is ice), implicit solvent models could be very useful for energy refinement.
Implicit solvent potentials have been developed that approximate well
the effect of the solvent on the molecule. Such an implicit potential
is the sum of two terms, one describing electrostatic interactions and
the other non-polar contributions. While the former can be formulated
as a pair potential and thus easily incorporated into molecular dynamics,
the situation is less simple with the latter. Non-polar interactions can
be described using the accessible surface area (ASA) of each atom, a quantity
that changes in complex ways during folding and other molecular motions.
We are working on incorporating the suite of programs for computing alpha-shapes
developed by Edelsbrunner within Encad, the molecular dynamics system
developed by Levitt. The surface areas of all atoms of a protein can be
computed based on alpha-complex associated with the alpha-shape of the
molecule. We have shown that the derivatives of these surface area terms
with respect to atomic position can be computed using the same combinatorial
structures, with minimal cost both in terms of memory and CPU. One step
of a molecular dynamics simulation in vacuo of a 90-residue proteins requires
approximately 40 ms on a 600 Mhz Pentium III computer; the same simulation
performed with explicit water simulations requires 240 ms. An implicit
solvent simulation should therefore position itself between these two
figures.
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