Biophysical Chemistry 101 – 102 (2002) 295–307 -/02/$ - see front matter  2002 Elsevier Science B.V. All rights reserved. PII: - Ž. - Potential of mean force between two hydrophobic solutes in water  Noel T. Southall , Ken A. Dill * a b, Graduate Group in Biophysics, University of California at San Francisco, San Francisco, CA 94143-1204, USA a Department of Pharmaceutical Chemistry, University of California at San Francisco, 3333 California Street, San Francisco, b CA 94143-1204, USA Received 7 December 2001; accepted 22 February 2002 Abstract We study the potential of mean force between two nonpolar solutes in the Mercedes Benz model of water. Using NPT Monte Carlo simulations, we find that the solute size determines the relative preference of two solute molecules to come into contact (‘contact minimum’) or to be separated by a single layer of water (‘solvent-separated minimum’). Larger solutes more strongly prefer the contacting state, while smaller solutes have more tendency to become solvent- separated, particularly in cold water. The thermal driving forces oscillate with solute separation. Contacts are stabilized by entropy, whereas solvent-separated solute pairing is stabilized by enthalpy. The free energy of interaction for small solutes is well-approximated by scaled-particle theory.  2002 Elsevier Science B.V. All rights reserved. Keywords: Hydrophobic interaction; Potential of mean force; Solvent-separated minimum 1. Introduction An underpinning to many fundamental processes in biology and chemistry is the potential of mean force (PMF) between nonpolar molecules in water. The PMF describes the energetics involved when two molecules in a mutual solvent approach each other and interact. It describes desolvation and  This paper is dedicated to John Schellman, a dear friend and a superb scientist, who has taught us, among many other things, just how subtle the hydrophobic effect can be. *Corresponding author. Tel.: q1-415-476-9964; fax: q1- 415-502-4222. E-mail address: dill@maxwell.ucsf.edu (K.A. Dill). binding. Examples include the binding of a ligand to a protein or the process by which two parts of a protein chain come together as the protein folds. As a simplest model for this process, there have been several studies of the PMFs between two small nonpolar solutes, as when argon associates with argon or methane associates with methane in water w1–11x. Some studies of hydrophobic association in water involve integrals over the PMFs w12x, such as second virial coefficients and related character- izations, which are related to an integrated solute– solute PMF w13–16x, or approximation as two thermodynamic states w17,18x. Work of this type