To gain insight into the free energy changes accompanying protein hydrophobic core formation, we have used computer simulations to study the formation of small clusters of nonpolar solutes in water. A barrier to association is observed at the largest solute separation that does not allow substantial solvent penetration. The barrier reflects an effective increase in the size of the cavity occupied by the expanded but water-excluding cluster relative to both the close-packed cluster and the fully solvated separated solutes; a similar effect may contribute to the barrier to protein foldinghnfolding. Importantly for the simulation of protein folding without explicit solvent, we find that the interactions between nonpolar solutes of varying size and number can be approximated by a linear function of the molecular surface, but not the solvent-accessible surface of the solutes. Comparison of the free energy of cluster formation to that of dimer formation suggests that the assumption of pair additivity implicit in current protein database derived potentials may be in error. Keywords: hydrophobic interaction; potential of mean force; protein foldingThe hydrophobic interaction is extremely important in the folding and stabilization of proteins (Kauzmann, 1959;Dill, 1990), but is relatively poorly understood. In spite of this poor understanding, computer modeling of protein folding has developed substantially over the past IO years. One approach is to simulate protein folding in the presence of explicitly modeled water molecules, which, depending upon the accuracy of the water model, should at least in part reproduce the hydrophobic interaction. Molecular dynamics simulations with an explicit solvent model have provided valuable insights into possible foldinghnfolding trajectories (Daggett & Levitt, 1994;Karplus & Sali, 1995). However, because of the complexity of the processes being simulated and the absence of an obvious reaction coordinate, most studies have focused on qualitative features of the trajectories and not sought to calculate free energy changes (the study of Brooks and Boczko [I9951 is an exception). A second approach avoids the complexity and high computational demands of simulations with hundreds of explicit water molecules by deriving effective potentials from the distribution of amino acid residues in known protein structures (reviewed in Jones & Thornton, 1996). Although not modeled explicitly, the hydrophobic interaction dominates such "knowledge-based' potentials. These relationships are not true interaction potentials in a rigorous sense, but they have been extremely useful in a wide variety of applications, including protein fold recognition (Jones &

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