Statistical mechanics of kinetic proofreading in protein folding in vivo

The statistical energy landscape picture of protein folding has led to the understanding that the energy landscape must have guiding forces leading to a protein folding funnel in order to avoid the Levinthal paradox in vitro. Since folding in vivo often requires the action of chaperone molecules and ATP hydrolysis, we must ask whether folding in a system maintained away from equilibrium can avoid the Levinthal paradox in other ways. We describe a model of the action of chaperone molecules in protein folding in vivo on the basis of a repetitive cycle of binding and unbinding, allowing the possibility of kinetic proofreading. We also study models in which chaperone binding is locally biased, depending on the similarity of the conformation to the native one. We show that while kinetic proofreading can modestly facilitate folding, it is insufficient by itself to overcome the Levinthal paradox. On the other hand, such kinetic proofreading with biasing can provide the nonequilibrium analog of a folding funnel and greatly enhance folding yields and speed up folding.