Empirical protein partition functions.

In the present paper, we outline how to construct the partition function for a protein using empirical heat capacity data. The procedure is based on the calculation of a set of energy moments from the temperature dependence of the heat capacity. Given a set of energy moments, one can then use the maximum-entropy method to calculate an approximate energy distribution for the protein; the more energy moments one has, the better the approximation. The energy distribution can then be used to calculate the probability that the molecule is in a given energy level, which, using standard statistical mechanics, gives the degeneracy of the particular energy level. The degeneracy as a function of energy is the central ingredient in the construction of the partition function. Given the partition function, one can calculate all of the thermodynamic functions of the protein (free energy, energy, entropy, heat capacity, and energy probability distribution) as a function of temperature. The three-dimensional plot of the probability that the protein has a given energy at a given temperature tells one graphically (without imposing the assumption) whether or not it is a good approximation to divide the terms in the partition function into two or more groups, reflecting, for example, the presence of distinct native and denatured species.