Alpha Complexes in Protein Structure Prediction

Abstract

Reducing the computational effort and increasing the accuracy of potential energy functions is of utmost importance in modeling biological systems, for instance in protein structure prediction, docking or design. Evaluating interactions between nonbonded atoms is the bottleneck of such computations. It is shown that local properties of α-complexes (subcomplexes of Delaunay tessellations) make it possible to identify nonbonded pairs of atoms whose contributions to the potential energy are not marginal and cannot be disregarded. Computational experiments indicate that using the local properties of α-complexes, the relative error (when compared to the potential energy contributions of all nonbonded pairs of atom) is well within 2%. Furthermore, the computational effort (assuming that α-complexes are given) is comparable to even the simplest and therefore also fastest cutoff approaches. The determination of α-complexes from scratch for every configuration encountered during the search for the native structure would make this approach hopelessly slow. However, it is argued that kinetic α-complexes can be used to reduce the computational effort of determining the potential energy when "moving" from one configuration to a neighboring one. As a consequence, relatively expensive (initial) construction of an α-complex is expected to be compensated by subsequent fast kinetic updates during the search process. Computational results presented in this paper are limited. However, they suggest that the applicability of αcomplexes and kinetic α-complexes in protein related problems (e.g., protein structure prediction and proteinligand docking) deserves furhter investigation.