The ultimate speed limit to protein folding is conformational searching

More than a dozen proteins are known to be ultrafast folders. In addition to being fast, their kinetics is unusual. Like traditional rate processes, fast folding proteins have activation barriers at low temperatures, but unlike traditional processes, they have negative activation energies at high temperatures. We develop a model of ultrafast folders that joins a macroscopic mass-action model with a microscopic energy landscape description; we call it the Thruway Search Model. We find good agreement with experimental rates and equilibria on 13 ultrafast folders. The observed folding rates are found to be proportional to the number of microscopic folding routes: fast-folding proteins have more parallel microscopic routes on energy landscapes. At high temperatures, where traditional barriers are small, the remaining bottleneck is a search through denatured conformations to find thruway routes to the native state. Negative activation arises because increasing temperature expands the denatured ensemble, broadening the search, slowing the folding to the native state. We find that the upper estimate of the free energy barriers are positive but small, as little as 0.5 kT.