Enthalpy distributions in proteins

Experimental data on the temperature dependence of the heat capacity of proteins can be used to calculate approximate enthalpy distributions for these molecules using the maximum-entropy method. C(p) (T) data is first used to calculate a set of moments of the enthalpy distribution, and these are then used to estimate the enthalpy distribution. If one knows the temperature expansion of the heat capacity through the (n - 2)th power of DeltaT (measured from the expansion center), then this is enough information to calculate the nth moment of the enthalpy distribution. Using four or more moments is in turn enough information to resolve bimodal behavior in the distribution. If the enthalpy distribution of a protein exhibits two distinct peaks, then this is direct experimental confirmation of a two-state mechanism of denaturation, the two peaks corresponding to the enthalpy of the native and unfolded species respectively. If the heat capacity of a protein exhibits a maximum at the denaturation temperature, then there is the possibility that the enthalpy distribution will be bimodal, but the presence of a maximum in the heat capacity is not a sufficient condition for this kind of behavior. We construct a phase diagram in terms of the appropriate variables to indicate when a maximum in the heat capacity will also give rise to bimodal behavior in the enthalpy distribution. We illustrate the phase diagram using literature data for a set of proteins.