Routes are trees: the parsing perspective on protein folding

An important puzzle in structural biology is the question of how proteins are able to fold so quickly into their unique native structures. There is much evidence that protein folding is hierarchic. In that case, folding routes are not linear, but have a tree structure. Trees are commonly used to represent the grammatical structure of natural language sentences, and chart parsing algorithms efficiently search the space of all possible trees for a given input string. Here we show that one such method, the CKY algorithm, can be useful both for providing novel insight into the physical protein folding process, and for computational protein structure prediction. As proof of concept, we apply this algorithm to the HP lattice model of proteins. Our algorithm identifies all direct folding route trees to the native state and allows us to construct a simple model of the folding process. Despite its simplicity, our model provides an account for the fact that folding rates depend only on the topology of the native state but not on sequence composition.