Temperature dependence of three-body hydrophobic interactions: Potential of mean force, enthalpy, entropy, heat capacity, and nonadditivity

Temperature-dependent three-body hydrophobic interactions are investigated by extensive constant-pressure simulations of methane-like nonpolar solutes in TIP4P model water at six temperatures. A multiple-body hydrophobic interaction is considered to be (i) additive, (ii) cooperative, or (iii) anti-cooperative if its potential of mean force (PMF) is (i) equal to, (ii) smaller than, or (iii) larger than the corresponding pairwise sum of two-methane PMFs. We found that three-methane hydrophobic interactions at the desolvation barrier are anti-cooperative at low to intermediate T, and vary from essentially additive to slightly cooperative at high T. Interactions at the contact minimum are slightly anti-cooperative over a wider temperature range. Enthalpy, entropy, and heat capacity are estimated from the computed PMFs. Contrary to the common expectation that burial of solvent-accessible nonpolar surface area always leads to a decrease in heat capacity, the present results show that the change in heat capacity upon three-methane association is significantly positive at the desolvation barrier and slightly positive at the contact minimum. This suggests that the heat capacity signature of a hydrophobic polymer need not vary uniformly nor monotonically with conformational compactness. Ramifications for protein folding are discussed.