Thermal denaturation of a native protein via spinodal decomposition in the framework of first-passage-time analysis

In this paper we present a kinetic model for the thermal unfolding of a native protein. Due to a sufficiently large temperature increase or decrease, the rate with which a cluster of native residues within a protein emits residues becomes larger than the rate of absorption of residues from the unfolded part of the protein in the whole range of cluster sizes up to the size of the whole protein. This leads to the unfolding of the protein in a barrierless way, i.e., as spinodal decomposition. Using the formalism of the first passage time analysis [previously applied also to the problem of protein folding via nucleation by the authors, J. Phys. Chem. B 111, 886 (2007); J. Chem. Phys. 126, 175103 (2007)], one can determine the temperature dependence of the rates of emission and absorption of residues by the cluster. Knowing these rates as functions of temperature and cluster size, one can find the threshold temperatures of cold and hot barrierless denaturation as well as the unfolding times at temperatures lower and higher, respectively, than those threshold values. For a numerical illustration, the method is applied to the thermal unfolding of a model protein consisting of 2500 residues.