Diffusive searches in high-dimensional spaces and apparent 'two-state' behaviour in protein folding.

We extend a simple model for protein folding as a high-dimensional diffusive search. By solving a steady-state diffusion equation on a hypersphere centred on an absorbing 'native state' we find the general property that the kinetics of such a search will always be nearly single exponential. This explains the common observation of such simple 'two-state' folding kinetics in models that contain considerable intermediate structure. It also suggests that the experimental signature of single-exponential folding kinetics does not imply a simple two-state structure to the folding space.