Protein docking using spherical polar Fourier correlations

We present a new computational method of docking pairs of proteins by using spherical polar Fourier correlations to accelerate the search for candidate low‐energy conformations. Interaction energies are estimated using a hydrophobic excluded volume model derived from the notion of “overlapping surface skins,” augmented by a rigorous but “soft” model of electrostatic complementarity. This approach has several advantages over former three‐dimensional grid‐based fast Fourier transform (FFT) docking correlation methods even though there is no analogue to the FFT in a spherical polar representation. For example, a complete search over all six rigid‐body degrees of freedom can be performed by rotating and translating only the initial expansion coefficients, many infeasible orientations may be eliminated rapidly using only low‐resolution terms, and the correlations are easily localized around known binding epitopes when this knowledge is available. Typical execution times on a single processor workstation range from 2 hours for a global search (5 × 108 trial orientations) to a few minutes for a local search (over 6 × 107 orientations). The method is illustrated with several domain dimer and enzyme–inhibitor complexes and 20 large antibody–antigen complexes, using both the bound and (when available) unbound subunits. The correct conformation of the complex is frequently identified when docking bound subunits, and a good docking orientation is ranked within the top 20 in 11 out of 18 cases when starting from unbound subunits. Proteins 2000;39:178–194. © 2000 Wiley‐Liss, Inc.