Calculating excess chemical potentials using dynamic simulations in the fourth dimension

A general method for computing excess chemical potentials is presented. The excess chemical potential of a solute or ligand molecule is estimated from the potential of mean-force (PMF) calculated along a nonphysical fourth sp atial dimension, w, into which the molecule is gradually inserted or from w hich it is gradually abstracted. According to this "4D-PMF" (four dimension al) scheme, the free energy difference between two limiting states defines the excess chemical potential: At w = +/-infinity, the molecule is not inte racting with the rest of the system, whereas at w=0, it is fully interactin g. Use of a fourth dimension avoids the numerical instability in the equati ons of motion encountered upon growing or shrinking solute atoms in convent ional free energy perturbation simulations performed in three dimensions, w hile benefiting from the efficient sampling of configurational space afford ed by PMF calculations. The applicability and usefulness of the method are illustrated with calculations of the hydration free energy of simple Lennar d-Jones (LJ) solutes, a water molecule, and camphor, using molecular dynami cs simulations and umbrella sampling. Physical insight into the nature of t he PMF profiles is gained from a continuum treatment of short- and long-ran ge interactions. The short-range barrier for dissolution of a LJ solute in the added dimension provides an apparent surface tension of the solute. An approximation to the long-range behavior of the PMF profiles is made in ter ms of a continuum treatment of LJ dispersion and electrostatic interactions . Such an analysis saves the need for configurational sampling in the long- range limit of the fourth dimension. The 4D-PMF method of calculating exces s chemical potentials should be useful for neutral solute and ligand molecu les with a wide range of sizes, shapes, and polarities. (C) 1999 American I nstitute of Physics. [S0021-9606(99)51231-2].