Percolation-like phase transitions in network models of protein dynamics

In broad terms, percolation theory describes the conditions under which clusters of nodes are fully connected in a random network. A percolation phase transition occurs when, as edges are added to a network, its largest connected cluster abruptly jumps from insignificance to complete dominance. In this article, we apply percolation theory to meticulously constructed networks of protein folding dynamics called Markov state models. As rare fluctuations are systematically repressed (or reintroduced), we observe percolation-like phase transitions in protein folding networks: whole sets of conformational states switch from nearly complete isolation to complete connectivity in a rapid fashion. We analyze the general and critical properties of these phase transitions in seven protein systems and discuss how closely dynamics on protein folding landscapes relate to percolation on random lattices.