A fast method to sample real protein conformational space

A fast computer program, FOLDTRAJ, to generate plausible random protein structures is reported. All-atom proteins are made directly in continuous three-dimensional space starting from primary sequence with an N to C directed build-up method. The method uses a novel pipelined residue addition approach in which the leading edge of the protein is constructed three residues at a time for optimal protein geometry, including the placement of cis proline. Build-up methods represent a classic N-body problem, expected to scale as N(2). When proteins become more collapsed, build-up methods are susceptible to backtracking problems which can scale exponentially with the number of residues required to back out of a trapped walk. We have provided solutions to both these problems, using a multiway binary tree that makes the N-body problem of bump-checking scale as NlogN, and speeding up backtracking by varying the number of tries before backtracking based on available conformational space. FOLDTRAJ is independent of energy potentials, other than that implicit in the geometrical properties derived by statistical studies of known structures, and in atomic Van der Waals radii. WHAT-CHECK shows that the program generates chirally and physically valid proteins with all bond lengths, angles and dihedrals within allowable tolerances. Random structures built using sequences from PDB files 1SEM, 2HPR, and 1RTP typically have 5-15% alpha-helical content (according to DSSP) and on the order of 20% beta-strand/extended content. Ensembles of random structures are compared with polymer theory and with experimentally determined fluorescence resonance energy transfer distances. Reasonably sized structure ensembles do sample most of the conformational space available to proteins. The method is also capable of protein reconstruction using Calpha--Calpha direction vectors, and it compares favorably with methods that reconstruct protein backbones based on alpha-carbon coordinates, having an average backbone and Cbeta root mean square deviation of 0.63 A for nine different protein folds. Proteins 2000;39:112-131.