Compact Representation of Continuous Energy Surfaces for More Efficient Protein Design.

In macromolecular design, conformational energies are sensitive to small changes in atom coordinates; thus, modeling the small, continuous motions of atoms around low-energy wells confers a substantial advantage in structural accuracy. However, modeling these motions comes at the cost of a very large number of energy function calls, which form the bottleneck in the design calculations. In this work, we remove this bottleneck by consolidating all conformational energy evaluations into the pre-computation of a local polynomial expansion of the energy about the "ideal" conformation for each low-energy, "rotameric" state of each residue pair. This expansion is called "energy as polynomials in internal coordinates" (EPIC), where the internal coordinates can be side-chain dihedrals, backrub angles, and/or any other continuous degrees of freedom of a macromolecule, and any energy function can be used without adding any asymptotic complexity to the design. We demonstrate that EPIC efficiently represents the energy surface for both molecular-mechanics and quantum-mechanical energy functions, and apply it specifically to protein design for modeling both side chain and backbone degrees of freedom.