Scaling approach to the folding kinetics of large proteins

We study a nucleation-growth model of protein folding and extend it to describe larger proteins with multiple folding units. The model is of one of an extremely simple type in which amino acids are allowed just two states-either folded (frozen) or unfolded. Its energetics are heterogeneous and Gō-like, the energy being defined in terms of the number of atom-to-atom contacts that would occur between frozen amino acids in the native crystal structure of the protein. Each collective state of the amino acids is intended to represent a small free energy microensemble consisting of the possible configurations of unfolded loops, open segments, and free ends constrained by the cross-links that form between folded parts of the molecule. We approximate protein free energy landscapes by an infinite subset of these microensemble topologies in which loops and open unfolded segments can be viewed roughly as independent objects for the purpose of calculating their entropy, and we develop a means to implement this approximation in Monte Carlo simulations. We show that this approach describes transition state structures (values) more accurately and identifies folding intermediates that were unavailable to previous versions of the model that restricted the number of loops and nuclei.