Biomedical Engineering Reference
In-Depth Information
a
b
W
K
i
o
i
S
i
π
ij
F
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Fig. 1.2
Molecular surfaces and volumes. (
a
) The solvent accessible surface, in
red
,isdefinedby
tracing the locci of points of a water probe
W
rolling on the boundary of the van der Waals model,
in
blue
.(
b
) Tiling the volume of a restriction with two types of pyramids:
left
, a pyramid topped
with a spherical cap;
right
, a pyramid with flat base
From this a new set of atomic positions and velocities are obtained, applicable
for a short time (“a short time” here being on the order of a fs). This procedure
can be repeated ad infinitum in order to simulate the thermal motions of the
macromolecule.
Such a simulation of a protein in thermal equilibrium allows one to obtain
information regarding the detailed dynamics of the macromolecule as well as
thermodynamic information. The simulation provides a way of approximating the
partition function of the system, which is directly related to the free energy. The
affinity is a natural target for such studies. Many factors are known to contribute
to the free energy change, including desolvation of the two surfaces that will
form the interface, net changes in hydrogen bonding, electrostatic interactions,
and other more detailed contributions. Molecular dynamics simulations can in
principle be used to take all of these effects into account in calculating affinities, but
conformational changes are still particularly difficult to handle due to the relevant
timescales involved.
ΔΔG
◦
values can be targeted if the mutant complexes can be
reasonably assumed to have structures similar to the wild-type protein, so that many
contributions to the free energy change cancel in a first approximation.
Even in calculating affinities from MD simulations, it is often necessary to
call upon geometric surface calculations in order to take into account solvation
energies. One such method is the MM/PBSA method [
29
], a commonly used
“endpoint” thermodynamic approach to affinity calculations [
48
]. This method
calculates the proteins' internal energy contribution to the free-energy change
explicitly, and exploits an implicit solvent approach that relies on the estimation
of the macromolecular surface along with electrostatic terms. An advantage of such
approaches is that solvent entropy is taken into account in large part by the implicit
solvent approaches, relieving the burden of extensive sampling of explicit solvent
in the MD simulations. It might be pointed out that accuracy can be improved by
adding critical waters (e.g., [
8
]) back into the system explicitly [
67
].
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