Protein folding on rugged energy landscapes: Conformational diffusion on fractal networks

We perform simulations of model proteins to study folding on rugged energy landscapes. We construct "first-passage" networks as the system transitions from unfolded to native states. The nodes and bonds in these networks correspond to basins and transitions between them in the energy landscape. We find power-law relations between the folding time and the number of nodes and bonds. We show that these scalings are determined by the fractal properties of first-passage networks. Thus, we have identified a possible mechanism-the small fractal dimension of first passage networks-which can give rise to reliable folding in proteins with rugged energy landscapes.