Recent molecular-dynamics simulations have demonstrated that the use of an empirical hydrophobic potential displaying two minima, i.e., one for hydrophobes in close contact and one for hydrophobes separated by a hydration layer, leads to a marked improvement in protein structure prediction. This potential is supported by experimental data and simulations, but its physical origin and mathematical formulation have not been derived as yet. Here we show that water-mediated attraction (the "wetting regime") between two hydrophobic molecules originates in the interaction between the dipoles induced at the surface of the hydrophobes by the surrounding structured water. As an example, we derive the effective hydrophobic potential that describes the interaction between two methane molecules, a classical model of a double-well energy function. We found an excellent agreement with published results from all-atom, explicit solvent molecular-dynamics simulations of this interaction. The approach presented here provides the theoretical basis for implementing an adequate representation of the wetting regime of the hydrophobic interactions in force fields used for structure prediction. The results are useful for modeling both protein folding and binding.
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