Localizing Frustration in Proteins Using All-Atom Energy Functions.

The problems of protein folding and protein design are two sides of the same coin. Protein folding involves exploring a protein's configuration space given a fixed sequence, whereas protein design involves searching in sequence space given a particular target structure. For a protein to fold quickly and reliably, its energy landscape must be biased toward the folded ensemble throughout its configuration space and must lack deep kinetic traps that would otherwise frustrate folding. Evolution has "designed" the sequences of many naturally occurring proteins, through an eons-long process of random mutation and selection, to yield landscapes with a minimal degree of frustration. The task facing humans hoping to design protein sequences that fold into particular structures is to use the available approximate energy functions to sculpt funneled landscapes that work in the laboratory. In this work, we demonstrate how to calculate several localized frustration measures using an all-atom energy function. Specifically, we employ the Rosetta energy function, which has been used successfully to design proteins and which has a natural pairwise decomposition that is suitably solvent-averaged. We calculate these newly developed frustration measures for both a mutated WW domain, FiP35, and a three-helix bundle that was designed completely by humans, Alpha3D. The structure of FiP35 exhibits less localized frustration than that of Alpha3D. A mutation toward the consensus sequence for WW domains in FiP35, which has been shown unexpectedly in experiment to disrupt folding, induces localized frustration by disrupting the hydrophobic core. By performing a limited redesign on the sequence of Alpha3D, we show that some, but not all, mutations that lower the energy also result in decreased frustration. The results suggest that, in addition to being useful for detecting residual frustration in protein structures, optimizing the localized frustration measures presented here may be a useful and automatic means of balancing positive and negative design in protein design tasks.