First principles prediction of protein folding rates.

Experimental studies have demonstrated that many small, single-domain proteins fold via simple two-state kinetics. We present a first principles approach for predicting these experimentally determined folding rates. Our approach is based on a nucleation-condensation folding mechanism, where the rate-limiting step is a random, diffusive search for the native tertiary topology. To estimate the rates of folding for various proteins via this mechanism, we first determine the probability of randomly sampling a conformation with the native fold topology. Next, we convert these probabilities into folding rates by estimating the rate that a protein samples different topologies during diffusive folding. This topology-sampling rate is calculated using the Einstein diffusion equation in conjunction with an experimentally determined intra-protein diffusion constant. We have applied our prediction method to the 21 topologically distinct small proteins for which two-state rate data is available. For the 18 beta-sheet and mixed alpha-beta native proteins, we predict folding rates within an average factor of 4, even though the experimental rates vary by a factor of approximately 4 x 10(4). Interestingly, the experimental folding rates for the three four-helix bundle proteins are significantly underestimated by this approach, suggesting that proteins with significant helical content may fold by a faster, alternative mechanism. This method can be applied to any protein for which the structure is known and hence can be used to predict the folding rates of many proteins prior to experiment.