Topologies to geometries in protein folding:: Hierarchical and nonhierarchical scenarios

This work presents a method to portray protein folding dynamics at a coarse resolution, based on a pattern-recognition-and-feedback description of the evolution of torsional motions of the backbone chain in the hydrophobic collapse of the protein. The approach permits theory and computation to treat the search of conformation space from picoseconds to the millisecond time scale or longer, the time scales of adiabatic evolution of soft-mode dynamics. The procedure tracks the backbone torsional coordinates modulo the basins of attraction to which they belong in the Ramachandran maps. The state and history of the backbone are represented in a map of local torsional states and hydrophobicity/hydrophilicity matching of the residues comprising the chain, the local topology matrix (LTM). From this map, we infer allowable structural features by recognizing patterns in the LTM as topologically compatible with particular structural forms within a level of frustration tolerance. Each such 3D realization of an LTM leads to a contact map, from which one can infer one or more structures. Introduction of energetic and entropic terms allow elimination of all but the most favored of these structures at each new juncture. The method's predictive power is first established by comparing "final," stable LTMs for natural sequences of intermediate length (N less than or equal to 120) with PDB data. The method is extended further to beta -lactoglobulin (beta -LG, N=162), the quintessential nonhierarchical folder. (C) 2001 American Institute of Physics.