Continuous anisotropic representation of coarse-grained potentials for proteins by spherical harmonics synthesis

A new method is presented for extracting statistical potentials dependent on the relative side chain and backbone orientations in proteins. Coarse-grained, anisotropic potentials are constructed for short-, medium-, and long-range interactions using the Boltzmann method and a database of non-homologous protein structures. The new orientation-dependent potentials are analyzed using a spherical harmonics decomposition method with real eigenfunctions. This method permits a more realistic, continuous angular representation of the coarse-grained potentials. Results of tests for discriminating the native protein conformations from large sets of decoy proteins, show that the new continuous distance- and orientation-dependent potentials present significantly improved performance. Novel graphical representations are developed and used to depict the orientational dependence of the interaction potentials. These new continuous anisotropic statistical potentials could be instrumental in developing new computational methods for structure prediction, threading and coarse-grained simulations.