How the folding rate constant of simple, single-domain proteins depends on the number of native contacts

Experiments have shown that the folding rate constants of two dozen structurally unrelated, small, single-domain proteins can be expressed in terms of one quantity (the contact order) that depends exclusively on the topology of the folded state. Such dependence is unique in chemical kinetics. Here we investigate its physical origin and derive the approximate formula ln(k) = ln(N) + a + bN, were N is the number of contacts in the folded state, and a and b are constants whose physical meaning is understood. This formula fits well the experimentally determined folding rate constants of the 24 proteins, with single values for a and b.