Computing the transition state populations in simple protein models

Abstract

We describe the master equation method for computing the kinetics of protein folding. We illustrate the method using a simple Go model. Presently most models of two-state fast-folding protein folding kinetics invoke the classical idea of a transition state to explain why there is a single exponential decay in time. However, if proteins fold via funnel-shaped energy landscapes, as predicted by many theoretical studies, then it raises the question of what is the transition state. Is it a specific structure, or a small ensemble of structures, as is expected from classical transition state theory? Or is it more like the denatured states of proteins, a very broad ensemble? The answer that is usually obtained depends on the assumptions made about the transition state. The present method is a rigorous way to find transition states, without assumptions or approximations, even for very nonclassical shapes of energy landscapes. We illustrate the method here, showing how the transition states in two-state protein folding can be very broad ensembles.