Molecular simulation study of cooperativity in hydrophobic association: clusters of four hydrophobic particles.

The multibody contribution to the potential of mean force (PMF) of hydrophobic association of four methane molecules in water was investigated by means of umbrella-sampling molecular dynamics. Two systems were considered: (i). a trigonal pyramid with three methane molecules at contact distance forming a fixed base, the fourth molecule being placed on the top with variable distance from the base; and (ii). a regular uniformly expanding tetrahedron. Methane-methane distances as far as 12.5 A, i.e. beyond the second solvent-separated minimum of the PMF, were considered to address the baseline problem. In contrast to the small effect in the three-body case studied previously (Protein Sci 9 (2000) 1235), the multibody contribution was found to amount to approximately 0.2 kcal/mol per methane-methane pair, or approximately 25% of the depth of the contact minimum in the PMF. The main effect of the multibody contribution to the PMF is a reduction of the height of the barrier between the contact and solvent separated minima and a narrowing of the region of its maximum, while the region of the contact minimum is affected only weakly. The reduction of the barrier is due to four-body contributions. The cooperative contributions to the PMF agree very well with those computed from the molecular surface of the systems under consideration, which further supports earlier observations that the molecular surface can be used with good accuracy to describe the energetics of hydrophobic association.