A fast protein-protein docking algorithm using series expansion in terms of spherical basis functions.

We describe a fast protein-protein docking algorithm using a series expansion in terms of newly designed bases to efficiently search the entire six-dimensional conformational space of rigid body molecules. This algorithm is an ab initio docking algorithm designed to list candidates of putative conformations from a global conformational space for unbound docking. In our algorithm, a scoring function is constructed from terms that are the inner products of two scalar fields expressing individual molecules. The mapping from a molecule to a scalar field can be arbitrarily defined to express an energy term. Since this scoring scheme has the same expressiveness as that of a method using a fast Fourier transform (FFT), it has the flexibility to introduce various physicochemical energies. Currently, we are using scalar fields that approximate desolvation free energy and steric hindrance energy. Fast calculation of the scoring function for each conformation of the six-dimensional search space is realized by expansion of the fields in terms of basis functions which are combinations of spherical harmonics and modified Legendre polynomials, and the use of only low-order terms, which carry most of the information on the scalar field. We have implemented this algorithm and evaluated the computation time and precision by using actual protein structure data of complexes and their monomers. This paper presents the results for six unbound cases and in all the cases we obtained at least one conformation close to the native structures (interface RMSD < 3.0 A) within the top 1000 candidates with about 40 seconds of computation time using a single Pentium4 2.4 GHz CPU.