Biophysical models of protein denaturation. I. An improvement of the model of two states.

The model of two states (native and denatured), frequently used for the description of protein denaturation, has been complemented by relations defining, on theoretical grounds, the temperature dependence of the relevant thermodynamic functions. In essence, this was achieved by assuming that the temperature dependence of Gibbs free energies of the native protein and of denaturation can be approximated, within the interval (0 degree C, 100 degrees C), by second-order partial sums of Taylor series. The improved model operates with four parameters: the temperature of denaturation, the heat capacities of the native and denatured protein at the temperature of denaturation, and the entropy of denaturation at that temperature. A theoretical treatment is included of the temperature dependence of total heat capacity, the variable recorded in the form of continuous thermograms by means of differential scanning calorimetry. Our model correctly reproduces experimental thermograms of proteins and provides for the biophysical interpretation of a number of their geometric components. Fitting procedures were complemented by a newly devised method for estimating starting values of model parameters from calorimetric data. The phenomenon of cold denaturation was also reproduced quantitatively by our model, which supplies explicit proof of the exothermal nature of this phenomenon. Finally, the relationship between temperature profiles of thermodynamic functions describing denaturation has been defined by sequences of profile magnitudes at points where the profiles intersect the temperature axis and/or cross each other. Model-derived sequences of profile magnitudes, representative of cross-point temperatures and of intervals in between, together constitute a general characteristics of denaturation, uninfluenced by differences in thermodynamic stability between protein species.