Kinetics of protein folding

The master equation that describes the kinetics of protein folding is introduced to treat general problems and solved for different models and for native proteins. The solutions are obtained by a Laplace transformation, analytically for simple problems or numerically for general ones. The solutions are presented for the two-state model and for three different foldable models as well as for two native proteins. Taken together, all of the results show that native proteins fold fast cooperatively. The global energy minimum can be reached after a sufficiently long folding time regardless of the initial state. A protein folds to its native conformation regardless of the existence of local energy minima. The numerical solutions for the two native proteins also show that the conformation of a protein molecule can transform from non-native states to the native state even if it originates in different conformational families. A protein molecule adopts a set of conformations, when the folding reaches the equilibrium distribution, in which the global minimum has the largest probability. This is the basis for simulating the folding of a native protein by searching for the global energy minimum on its potential energy hyper-surface.