ABSTRACT
It is widely accepted that electrostatics plays a pivotal role in
biological processes. This is because of its long-range influence, its
effects on the aqueous solvent, and the highly specific patterns it
can engender during biomolecular recognition. Electrostatics also
affects the structure and the dynamical behavior of biomolecules
and often dominates intermolecular and intramolecular interactions
despite the screening exerted by the solvent and the electrolytes
[Sheinerman et al. (2000); Radic et al. (1997)]. Together with the direct Coulombic interaction, the so-called reaction field, that is,
the response of the system to the electric field generated by the
charge present on the solute molecule, is probably the conceptually
simplest and most used model of electrostatic effects adopted in
biomolecular simulations. The long-range nature of electrostatics
makes these calculations very time-consuming, as in principle,
they scale as the square of the charged interacting centers. The
computational burden is particularly heavy in atomistic simulations,
such as in molecular dynamics, when all the degrees of freedom
(DOFs) are treated explicitly. In this kind of simulations, the time
evolution of every DOF is calculated for systems at the thermody-
namic equilibrium so as to derive an estimate of interesting physical
quantities. The computation may have to progress for a long time
in order to achieve a good level of accuracy and the electrostatic
contribution often represents the major computational bottleneck.
To face this issue, several algorithmic solutions have been devised,
the Particle Mesh Ewald being probably the most widely adopted
[Darden et al. (1993)]. On the other side, alternative models try to make an a priori average of some DOFs, so as to reduce the overall computational cost. This is the case of so-called implicit solvent models, where the DOFs of the solvent, possibly including those of a dissolved salt, are averaged out under some simplifying
assumptions. The reason behind this approach is that one is usually
not interested in studying the evolution of the individual solvent
DOFs but rather to consider the effects of the solvent on the
behavior of the solute. In this framework, the Poisson-Boltzmann
equation (PBE) proved to be extremely useful in providing a tool that
estimates reaction field and electrostatic interaction energy. Here, a
basic derivation of the PBE is described as well as the grid-based
numerical approach adopted by one widely used PBE solver, the
DelPhi software [Honig and Nicholls (1995); Rocchia et al. (2001)].
