Evaluating conformational free energies: The colony energy and its application to the problem of loop prediction

In this paper, we introduce a method to account for the shape of the potential energy curve in the evaluation of conformational free energies. The method is based on a procedure that generates a set of conformations, each with its own force-field energy, but adds a term to this energy that favors conformations that are close in structure (have a low rmsd) to other conformations. The sum of the force-field energy and rmsd-dependent term is defined here as the "colony energy" of a given conformation, because each conformation that is generated is viewed as representing a colony of points. The use of the colony energy tends to select conformations that are located in broad energy basins. The approach is applied to the ab initio prediction of the conformations of all of the loops in a dataset of 135 nonredundant proteins. By using an rmsd from a native criterion based on the superposition of loop stems, the average rmsd of 5-, 6-, 7-, and 8-residue long loops is 0.85, 0.92, 1.23, and 1.45 Angstrom, respectively. For 8-residue loops, 60 of 61 predictions have an rmsd of less than 3.0 Angstrom. The use of the colony energy is found to improve significantly the results obtained from the potential function alone. (The loop prediction program, "Loopy," can be downloaded at http://trantor.bioc.columbia.edu.)