Theory for the rate of contact formation in a polymer chain with local conformational transitions

Abstract

I derive an expression for the rate of contact formation between two residues in a polymer chain when both residues undergo native to non-native conformational transitions. A contact can only form when the two residues are brought into contact by interresidue diffusion and are in the native conformations at the same time. The entropy of the chain connecting the two residues are accounted for by the potential of mean force for the interresidue distance. Both the equilibrium probabilities of the native conformations and the time scales of the transitions between the native and non-native conformations are important in determining the contact formation rate. For protein residues, transitions between native and non-native conformations occur in the picoseconds time scale. In comparison, the average time for traversing the distance of a few Å by interresidue diffusion is in the nanoseconds time scale. This separation of time scales between residue conformational transitions and interresidue diffusion ensures that the rate of contact formation is much higher than what is expected from the equilibrium probability for both residues to be in the native conformations.