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Denaturation: an example of a catastrophe.

We show that a "phase diagram" for the conformational states of proteins can be constructed using the mathematical theory of singularities of functions developed recently by René Thom. For proteins subjected to the disruptive influences of temperature and/or concentration of denaturing agent, this theory can be used as a predictive tool to account for the shape, sense, and changes in the curves that result when the optical rotatory dispersion is plotted as a function of these two constraints. The mathematical model is found to be in accord with known experimental data on collagen, lysozyme, and ribonuclease.