The MSC Fast Solvation Model (FSM) for Predicting Solvation Energies

Mario Blanco, Changmoon Park, and William A. Goddard III

Materials Process and Simulation Center

California Institute of Technology

Abstract

The solvation of a molecule can have a dramatic effect on energetics and structure of the molecule. Thus, accurate predictions of solvation effects is critical for problems ranging from protein folding, to chemical equilibrium in aqueous solutions, to drug bioavailability, and to the environmental fate of chemicals. Consequently, there has been great interest in predicting the solvation energy of molecules (proteins, drugs, etc) in various media. A general approach was developed by Barry Honig (implemented in the DelPhi and Grasp software), where the Poisson-Boltzmann (PB) equation was solved to obtain the reaction field in the solvent resulting from the electrostatic charge distribution of the solute and the interaction of the solute with this reaction field was used to calculate the electrostatic component of the solvation energy. The other components to solvation involve the van der Waals (vdW) and hydrogen bonding (HB) terms, which were generally combined into an area dependent cavity term. In order to calculate the structure of the solute in solution one must determine the forces due to solvation. To do this the PBF software (in Jaguar) was developed. Using the charge density from quantum mechanical calculations (from Hartree Fock, LMP2, or density functional theory), accurate calculations of the electrostatic terms are made. Again, the vdW and HB terms were included with a cavity term empirically fitted to data for hydrocarbons in water. Using a database of 120 compounds, it was shown that this leads to an RMS error of ~0.5 kcal/mol. Unfortunately, PBF is too slow to be practical for MD calculations. Thus the Surface Generalized Born method (Clark Still), which simplifies the Poisson-Boltzmann calculation, was implemented in the IMPACT and MPSim MD codes. This also includes an approximate cavity term. However, while faster than PBF, SGB is still too slow to do every MD or Monte Carlo step.

In order to develop a method sufficiently fast to use every step of an MD or MC calculation, we developed the MSC Fast Solvation Model (FSM) for predicting solvation energies. FSM uses the solvent-exposed van der Waal's surface area (AI) of individual atoms in the molecule to estimate the free energy of solvation. Thus for each atom I there is a surface tension (energy per unit area exposed to solvent), s I, and the total solvation energy is given by

Solvation energy = S I s I AI

Here s I includes the effect of electrostatic, van der Waals, and hydrogen bonding interations with the solvent. Here we assume that s I depends only on the chemical character of the atom, using the classification scheme of the DREIDING FF. For the 120 molecules tested with PBF, we find that MFS leads to an accuracy of 0.8 kcal/mol. For the Burroughs-Wellcome database of 375 saturated and unsaturated hydrocarbons, alcohols, amines, ketones, acids, aldehydes, nitrogenated, chlorinated, fluorinated, phosphorous and sulfur containing compounds, we obtain an RMS error of 1.0 kcal/mol.