Free energy distributions in proteins

Protein molecules in solution have a broad distribution of enthalpy states. A good approximation to the distribution function for enthalpy states can be calculated, using the maximum-entropy method, from the moments of the di stribution that, in turn, are obtained from the experimental temperature de pendence of the heat capacity. In the present paper, we show that the entha lpy probability distribution can then be formulated in terms of a free ener gy function that gives the free energy of the protein corresponding to a pa rticular value of the enthalpy. By the location of the minima in this funct ion, the free energy distribution graphically indicates the most probable v alues of the enthalpy for the protein. We find that the behavior of the fre e energy functions for proteins falls somewhere between two different cases ; a two-state like function with two minima, the relative levels of the two states changing with temperature; and, a single-minimum function where the position of the minimum shifts to higher enthalpy values as the temperatur e is increased. We show that the temperature dependence of the free energy function can be expressed in terms of a central free energy distribution fo r a given, fixed temperature (which is most conveniently chosen as the temp erature of the maximum in the heat capacity). The nature of this central fr ee energy function for a given protein thus yields all of the thermodynamic behavior of that protein over the temperature range of the denaturation pr ocess. (C) 2001 Wiley-Liss, Inc.