Sampling protein conformations using segment libraries and a genetic algorithm

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Abstract
We present a new simulation algorithm for minimizing empirical contact potentials for a simplified model of protein structure. The model consists of backbone atoms only (including Cβ) with the φ and ψ dihedral angles as the only degrees of freedom. In addition, φ and ψ are restricted to a finite set of 532 discrete pairs of values, and the secondary structural elements are held fixed in ideal geometries. The potential function consists of a look-up table based on discretized inter-residue atomic distances. The minimization consists of two principal elements: the use of preselected lists of trial moves and the use of a genetic algorithm. The trial moves consist of substitutions of one or two complete loop regions, and the lists are in turn built up using preselected lists of randomly-generated three-residue segments. The genetic algorithm consists of mutation steps (namely, the loop replacements), as well as a hybridization step in which new structures are created by combining parts of two “parents’’ and a selection step in which hybrid structures are introduced into the population. These methods are combined into a Monte Carlo simulated annealing algorithm which has the overall structure of a random walk on a restricted set of preselected conformations. The algorithm is tested using two types of simple model potential. The first uses global information derived from the radius of gyration and the rms deviation to drive the folding, whereas the second is based exclusively on distance-geometry constraints. The hierarchical algorithm significantly outperforms conventional Monte Carlo simulation for a set of test proteins in both cases, with the greatest advantage being for the largest molecule having 193 residues. When tested on a realistic potential function, the method consistently generates structures ranked lower than the crystal structure. The results also show that the improved efficiency of the hierarchical algorithm exceeds that which would be anticipated from tests on either of the two main elements used independently.