Relation between the convergence temperatures Th* and Ts* in protein unfolding.

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Abstract
A challenge in understanding the thermodynamics of protein unfolding is to explain the 1979 puzzle posed by Privalov. Why do values of the specific enthalpy and specific entropy of unfolding both converge to common values at approximately the same temperature (Th* approximately equal to Ts*) when extrapolated linearly versus temperature? In 1986, a liquid hydrocarbon model gave an explanation for convergence of the specific entropies at Ts*: it happens because the contribution of the hydrophobic effect to the entropy of unfolding goes to zero at Ts*. The reason for convergence of the specific enthalpies at Th* and for the equality Th* approximately equal to Ts* has remained, however, a matter for speculation; recently, some explanations have been given that are based on models for polar interactions in protein folding. We show here that the relation Th* approximately equal to Ts* can be derived straightforwardly without making any assumptions either about polar interactions or about splitting the hydrophobic interaction into two terms--one for the "hydrophobic hydration" and the other for the residual effect, as suggested recently. Thus, the liquid hydrocarbon model explains both halves of Privalov's puzzle. A similar conclusion has been reached independently by A. Doig and D. H. Williams (personal communication). It has been proposed recently that a correction should be made for the relative sizes of a hydrocarbon solute and water when computing the thermodynamic properties of the hydrophobic interaction from a solvent transfer experiment. This correction affects the temperature at which the entropy of transfer equals zero, and it is important to evaluate its effect on the convergence temperature Ts*. We show that making the size correction does not change the conclusion, reached earlier, that the liquid hydrocarbon model explains the convergence of the specific entropies of protein unfolding.