Chemistry Reference
In-Depth Information
applications to large-scale systems.
58,129,134
We reiterate here that continuum
electrostatic methods can yield insights into solvation phenomena, but care
should be taken in applying these methods because they do not account for
ion correlations, finite ion sizes, and specific interactions between ions and
solvent, all of which can be important for detailed free energy studies. (MG
methods have been developed to go beyond the mean-field PB level of theory
while still maintaining the grid representation.
135
) In this section we describe
some of the recent progress in real-space electrostatic calculations. After dis-
cussion of continuum dielectric approaches, applications of MG methods used
to compute electrostatic forces in molecular-level simulations will be pre-
sented, along with some alternative views of electrostatic calculations.
In the 1990s, several groups developed FD-MG solvers for the nonlinear
PB equation.
58,142-148,216
As noted above, a significant nonlinearity arises due
to the exponential terms for the equilibrium charge densities, and these non-
linearities can lead to numerical difficulties. This earlier work has been sum-
marized, along with some of the potential pitfalls in PB calculations, by
Coalson and Beck,
142
Beck,
58
and Baker.
134
Once a solution is obtained, the
output of a PB calculation consists of the potential over the domain, from
which the continuous charge distributions of the mobile ions can be computed.
In addition, the potential yields an approximation for the free energy of the ion
''gas,'' so potentials of mean force (PMFs) can be computed for interactions
between large biological molecules.
Significant effort has been directed at deriving more accurate, efficient,
and parallel solutions of the PB equation.
217-221
Those efforts have included
adaptive FE approaches that automatically refine the mesh based on a poste-
riori error estimates from a coarse-level calculation. A discretize-solve-
estimate-refine procedure is repeated until a solution of nearly uniform quality
is obtained over the whole domain. Holst, Baker, and Wang
220
found this FE
algorithm to outperform standard uniform-mesh discretization in terms of
overall accuracy and efficiency. In a second study, Baker, Holst and
Wang
221
tested the algorithm on challenging electrostatics problem in biophy-
sics, namely a 36-mer DNA structure and three proteins.
Baker et al.
218
subsequently extended the adaptive focusing method to
FD representations and developed a massively parallel version of their code.
The algorithm obtains linear-scaling complexity due to the use of multiscale
techniques. They applied the method to examination of electrostatic effects
in extremely large biological nanosystems including a million-atom microtu-
bule and the ribosome. Examination of the electrostatic potential profile for
the microtubule structure identified potential drug binding sites. Similarly,
the studies of the ribosome revealed interesting electrostatic effects near the
active site. The potential utility of this efficient PB solver in dynamics simula-
tions of large structures was noted.
In work simulating flexible polyelectrolyte structures with free energies
determined by solution of the PB equation, Tsonchev et al.
148
modeled the
