One approach for simulating a small part of a large system (e.g.,
the enzyme active site region of a large protein) uses a solvent boundary
potential (SBP). In SBP simulations, the macromolecular system is separated
into an inner and an outer region. In the outer region, part of the
macromolecule may be included explicitly in a fixed configuration, while the
solvent is represented implicitly as a continuous medium. In the inner
region, the solvent molecules and all or part of the macromolecule are
included explicitly and are allowed to move using molecular or stochastic
dynamics. The SBP aims to “mimic” the average
influence of the surroundings, which are not included explicitly in the
simulation.27 ,28 There are several implementations of the SBP
method in CHARMM. The earliest implementation, called the stochastic
boundary potential (SBOU), uses a soft nonpolar restraining potential to
help maintain a constant solvent density in the inner or
“simulation” region while the molecules in a shell
or buffer region are propagated using Langevin dynamics.27 By virtue of its simplicity, this treatment
remains attractive and it is sufficient for many applications.320 (
link),321 (
link) To improve the treatment of systems with irregular
boundaries in which part of the protein is in the outer region, a refinement
of the method has been developed that first scales the exposed charges to
account for solvent shielding and then corrects for the scaling by
post-processing.307
The Spherical Solvent Boundary Potential (SSBP), which is part of
the Miscellaneous Mean Field Potential (MMFP) module (see Section III F), is
designed to simulate a molecular solute completely surrounded by an
isotropic bulk aqueous phase with a spherical boundary.28 In SSBP the radius of the spherical region is
allowed to fluctuate dynamically and the influence of long-range
electrostatic interactions is incorporated by including the dielectric
reaction field response of the solvent.28 ,29 This approach has
been used to study several systems.322 –325
Because SSBP incorporates the long-range electrostatic reaction field
contribution, the method is particularly useful in free energy calculations
that involve introducing charges.322 –325
Like the SBOU charge-scaling method,307 the Generalized Solvent Boundary Potential (GSBP) is
designed for irregular boundaries when part of the protein is outside the
simulation region.29 However, unlike
SBOU, GSBP includes long-range electrostatic effects and reaction fields. In
the GSBP approach, the influence of the outer region is represented in terms
of a solvent-shielded static field and a reaction field expressed in terms
of a basis set expansion of the charge density in the inner region, with the
basis set coefficients corresponding to generalized electrostatic
multipoles.29 ,326 The solvent-shielded static field from the
outer macromolecular atoms and the reaction field matrix representing the
coupling between the generalized multipoles are both invariant with respect
to the configuration of the explicit atoms in the inner region. They are
calculated only once (with the assumption that the size and shape of inner
region does not change during the simulation) using the finite-difference
Poisson-Boltzmann (PB) equation of the PBEQ module. This formulation is an
accurate and computationally efficient hybrid MD/continuum method for
simulating a small region of a large macromolecular system,326 and is also used in QM/MM approaches.281 (
link),327 (
link)
Brooks B.R., Brooks CL I.I.I., MacKerell AD J.r., Nilsson L., Petrella R.J., Roux B., Won Y., Archontis G., Bartels C., Boresch S., Caflisch A., Caves L., Cui Q., Dinner A.R., Feig M., Fischer S., Gao J., Hodoscek M., Im W., Kuczera K., Lazaridis T., Ma J., Ovchinnikov V., Paci E., Pastor R.W., Post C.B., Pu J.Z., Schaefer M., Tidor B., Venable R.M., Woodcock H.L., Wu X., Yang W., York D.M, & Karplus M. (2009). CHARMM: The Biomolecular Simulation Program. Journal of computational chemistry, 30(10), 1545-1614.