Dept. of Chemistry
Ohio State University
100 W. 18th Ave.
Columbus, OH 43210
Electrostatic potential map at
the solute/continuum interface
Apparent surface charge, reaction-field solvation models, better known as "polarizable continuum models" (PCMs), represent the most widely-used class of implicit solvent models in quantum chemistry. Given a definition for a solute cavity (e.g., a van der Waals surface) that defines the interface between the solute molecule and the structureless dielectric representation of the solvent, these models provide an approximate solution for Poisson's equation or the linearized Poisson-Boltzmann equation using relatively efficient two-dimensional surface integration, rather than the three-dimensional sampling that is required to solve these differential equations directly. PCMs greatly accelerate conformational or phase-space sampling, since explicit solvent degrees of freedom are absent. Furthermore, as compared to empirical solvation models that are intended only to predict solvation free energies, PCMs are physically-motivated models that are directly interwoven into the system's Hamiltonian, and can thus be used to explore the effects of solvation on a variety of chemical and physical properties. These include solution-phase geometries, vibrational frequencies, electronic excitation energies, and more.
Elimination of explicit solvent molecules also greatly simplifies geometry optimizations and molecular dynamics simulations. This is especially true for excited electronic states. Compared to the ground state, where one can often view geometry optimization and molecular dynamics algorithms as "black boxes", moving about on excited-state potential surfaces is often considerably more complicated, owing to state crossing and near-degeneracies between excited states. We are currently endeavoring to exploit PCMs to explore excited-state potential energy surfaces for macromolecular systems. In addition, the development of higher-accuracy solvation models continues, especially with regard to the non-electrostatic contributions to the solvation energy, such as the dispersion and cavitation energies, and we are beginning to explore these models as alternatives to grid-based three-dimensional Poisson-Boltzmann solvers in biomolecular implicit solvent simulations. The PCMs that we are developing are much more physics-based than other (more empirical) implicit solvent models, and offer an attractive way to enhance conformational sampling in classical MD simulations.
Molecular dynamics simulation of forward|
and reverse proton transfer between two
tautomers of glycine. The solvent is a
continuum model of water.
We have recently revisited the numerical implementation of several widely-used PCMs, and have developed a new technique (the "switching/Gaussian" approach) for discretizing the integral equations that define these models. Our approach guarantees that the solute's potential energy surface is a smooth function of the nuclear coordinates, and also eliminates certain numerical artifacts inherent to some PCM implementations. As such, these PCMs can be used to perform stable ab initio molecular dynamics simulations of chemical reactions, in which chemical bonds are made or broken. In such cases, the cavity shape may change abruptly and dramatically, and a smooth potential surface is essential if one is to obtain stable, energy-conserving molecular dynamics.
Computational scaling of MM/PCM calculations
on single-stranded polyadenine,
on 16 processers.
PCMs are also useful in the context of QM/MM calculations, as a means to avoid costly periodic boundary conditions. Often in QM calculations, the cost of solving the PCM equations is negligible compared to the cost of calculating the wavefunction or molecular orbitals. For QM/MM and molecular mechanics (MM) calculations, however, the size of the solute cavity (and, specifically, the number of grid points necessary to discretize its surface) can become prohibitive. Our PCM implementation is highly efficient and highly parallelized, and can be used even when the solute is a large biological molecule described by an MM force field. (Computational scaling with respect to system size is shown at right.) Because the forces in our MM/PCM models are intrinsically smooth, these methods are ideally suited to molecular dynamics simulations of biological macromolecules in implicit solvent. Work along these lines is underway.
We have recently generalized the "conductor-like screening model" (COSMO), one of the most widely-used PCMs, to solutions of non-zero ionic strength. This new model, which we call the "Debye-Hückel-like screening model" (DESMO), affords an exact, numerically smooth solution of the linearized Poisson-Boltzmann equation. In other words, almost 90 years after the initial development of Debye-Hückel theory, we finally have a numerical technique that generalizes this approach to arbitrary cavity shapes. The molecules in Debye-Hückel theory need not be spherical any more!
A new "p16" Coulomb operator
for GB calculations is 3 times
faster to evaluate than the
traditional "Still" operator.
Finally, we have presented an analytic proof that Generalized Born (GB) models—the most widely-used implicit solvent approaches in biomolecular simulations—are equivalent, under reasonable assumptions, to calculations performed using the conductor-like PCM. This equivalence allows us to use PCMs to generate data sets of exact atomic pairwise-additive interaction energies for large biomolecules, and these data can be used to parameterize new GB models. Based on such tests, we have suggested a new effective Coulomb operator for GB models, which is slightly more accurate than the conventional GB operator introduced long ago by Still and co-workers, but at the same time is less costly to evaluate, by as much as a factor of three.
This material is based upon work supported by the National Science Foundation under Grant Nos. CHE-0748448 and CHE-1300603. Some calculations were performed at the Ohio Supercomputer Center, under Project Nos. PAS0291 and PAS-0003. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding agencies.Last modified November 13, 2015. Proudly powered by Words. By which we mean, hand-written HTML.