Molecular simulation study of cooperativity in hydrophobic association

To investigate the cooperativity of hydrophobic interactions, the potential of mean force of two- and three-molecule methane clusters in water was det ermined by molecular dynamics simulations using two methods: umbrella-sampl ing with the weighted histogram analysis method and thermodynamic integrati on. Two water models, TIP3P and TIP4P, were used, while each methane molecu le was modeled as a united atom. It was found that the three-body potential of mean force is net additive, i.e.. it cannot be calculated as a sum of t wo-body contributions, but requires an additional three-body cooperative te rm. The cooperative term, which amounts to only about 10% of the total hydr ophobic association free energy, was found to increase the strength of hydr ophobic association; this finding differs from the results of earlier Monte Carlo studies with the free energy perturbation method of Rank and Baker ( 1997). As in the work of Rank and Baker, the solvent contribution to the po tential of mean force was found to be well approximated by the molecular su rface of two methane molecules, Moreover, we also found that the cooperativ e term is well represented by the difference between the molecular surface of the three-methane cluster and those of all thr ee pairs of methane molec ules. In addition, it was found that, while there is a cooperative contribu tion to the hydrophobic association free energy albeit a small one, the err ors associated with the use of pairwise potentials are comparable to or lar ger than this contribution.