Self-organization and mismatch tolerance in protein folding: General theory and an application

Abstract

The folding of a protein is a process both expeditious and robust. The analysis of this process presented here uses a coarse, discretized representation of the evolving form of the backbone chain, based on its torsional states. This coarse description consists of discretizing the torsional coordinates modulo the Ramachandran basins in the local softmode dynamics. Whenever the representation exhibits “contact patterns” that correspond to topological compatibilities with particular structural forms, secondary and then tertiary, the elements constituting the pattern are effectively entrained by a reduction of their rates of exploration of their discretized configuration space. The properties “expeditious and robust” imply that the folding protein must have some tolerance to both torsional “frustrated” and side-chain contact mismatches which may occur during the folding process. The energy-entropy consequences of the staircase or funnel topography of the potential surface should allow the folding protein to correct these mismatches, eventually. This tolerance lends itself to an iterative pattern-recognition-and-feedback description of the folding process that reflects mismatched local torsional states and hydrophobic/polar contacts. The predictive potential of our algorithm is tested by application to the folding of bovine pancreatic trypsin inhibitor (BPTI), a protein whose ability to form its active structure is contingent upon its frustration tolerance.