Efficient protein folding implies a microscopic funnel-like multidimensional free-energy landscape. Macroscopically, conformational entropy reduction can manifest itself as part of an empirical barrier in the traditional view of folding, but experiments show that such barriers can also entail significant unfavorable enthalpy changes. This observation raises the puzzling possibility, irrespective of conformational entropy, that individual microscopic folding trajectories may encounter large uphill moves and thus the multidimensional free-energy landscape may not be funnel-like. Here, we investigate how nanoscale hydrophobic interactions might underpin this salient enthalpic effect in biomolecular assembly by computer simulations of the association of two preformed polyalanine or polyleucine helices in water. We observe a high, positive enthalpic signature at room temperature when the helix separation is less than a single layer of water molecules. Remarkably, this unfavorable enthalpy change, with a parallel increase in void volume, is largely compensated for by a concomitant increase in solvent entropy, netting only a small or nonexistent microscopic free-energy barrier. Thus, our findings suggest that high enthalpic folding barriers can be consistent with a funnel picture of folding and are mainly a desolvation phenomenon indicative of a cooperative mechanism of simultaneous formation of multiple side-chain contacts at the rate-limiting step.

The combined effect of pressure and temperature on hydrophobic hydration of a nonpolar methanelike solute is investigated by extensive simulations in the TIP4P model of water. Using test-particle insertion techniques, free energies of hydration under a range of pressures from 1 to 3000 atm are computed at eight temperatures ranging from 278.15 to 368.15 K. Corresponding enthalpy, entropy, and heat capacity accompanying the hydration process are estimated from the temperature dependence of the free energies. Partial molar and excess volumes calculated using pressure derivatives of the simulated free energies are consistent with those determined by direct volume simulations; but direct volume determination offers more reliable estimates for compressibility. At 298.15 K, partial molar and excess isothermal compressibilities of methane are negative at 1 atm. Partial molar and excess adiabatic (isentropic) compressibilities are estimated to be also negative under the same conditions. But partial molar and excess isothermal compressibilities are positive at high pressures, with a crossover from negative to positive compressibility at approximately 100-1000 atm. This trend is consistent with experiments on aliphatic amino acids and pressure-unfolded states of proteins. For the range of pressures simulated, hydration heat capacity exhibits little pressure dependence, also in apparent agreement with experiment. When pressure is raised at constant room temperature, hydration free energy increases while its entropic component remains essentially constant. Thus, the increasing unfavorability of hydration under raised pressure is seen as largely an enthalpic effect. Ramifications of the findings of the authors for biopolymer conformational transitions are discussed.

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.

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