Contribution of secondary structure to the heat capacity and enthalpy distribution of the unfolded state in proteins.

We have recently shown that one can construct the enthalpy distribution for protein molecules from experimental knowledge of the temperature dependence of the heat capacity. For many proteins the enthalpy distribution evaluated at the midpoint of the denaturation transition (corresponding to the maximum in the heat capacity vs temperature curve) is broad and biphasic, indicating two different populations of molecules (native and unfolded) with distinctly different enthalpies. At temperatures above the denaturation point, the heat capacity for the unfolded state in many proteins is quite large and using the analysis just mentioned, we obtain a gaussian-like enthalpy distribution that is very broad. A large value of the heat capacity indicates that there are structural changes going on in the unfolded state above the transition temperature. In the present paper we investigate the origin of this large heat capacity by considering the presence of changing amounts of secondary structure (specifically, alpha-helix) in the unfolded state. For this purpose we use the empirical estimates of the Zimm-Bragg sigma and s factors for all of the native amino acids in water as determined by Scheraga and co-workers. Using myoglobin as an example, we calculate probability profiles and distribution functions for the total number of helix states in the specific-sequence molecule. Given the partition function for the specific-sequence molecule, we can then calculate a set of enthalpy moments for the molecule from which we obtain a good estimate of the enthalpy distribution in the unfolded state. This distribution turns out to be quite narrow when compared with the distribution obtained from the raw heat capacity data. We conclude that there must be other major structural changes (backbone and solvent) that are not accounted for by the inclusion of alpha-helix in the unfolded state.