In macromolecular design, conformational energies are sensitive to small
changes in atom coordinates, so 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 calculation. In
this work, we remove this bottleneck by consolidating all conformational energy
evaluations into the precomputation 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 sidechain 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 to model both sidechain and backbone degrees of
freedom.