Denaturation: an example of a catastrophe II. Two-state transitions

In this paper statistical arguments are used within the framework of catastrophe theory to provide a quantitative description of protein transconformation reactions. For a protein-denaturant system, the accessible states (native and denatured) are characterized in terms of approximating Gaussian distributions. The possible transformations between the states of the system upon varying the experimental constraints are studied by assuming that the system is governed by a potential function (in the sense of Thom). The transitions observed to occur are modeled using the theory of singularities of stable mappings. Existing experimental data is used to construct model governing potential functions for proteins undergoing two-state transistions. The examples treated are ribonuclease subject to (T, pH), ichthyocol collagen subject to (T, CaCl₂), and lysozyme subject to (T, pH). Once the potential function has been identified for a given protein-denaturant system it may be used to predict: (i) transition curves for values of the constraints intermediate between those reported in the literature; (ii) transition curves for experiments in which the constraints are varied in an arbitrary manner, e.g., variable pH studies under isothermal conditions; (iii) estimates of difference in thermodynamic potential (i.e., free energy) between the states involved in a transition.