A Novel Minimized Dead-End Elimination Criterion and Its Application to Protein Redesign in a Hybrid Scoring and Search Algorithm for Computing Partition Functions over Molecular Ensembles

Novel molecular function can be achieved by redesigning an enzyme's active site so that it will perform its chemical reaction on a novel substrate. One of the main challenges for protein redesign is the efficient evaluation of a combinatorial number of candidate structures. The modeling of protein flexibility, typically by using a rotamer library of commonly-observed low-energy side-chain conformations, further increases the complexity of the redesign problem. A dominant algorithm for protein redesign is Dead-End Elimination (DEE), which prunes the majority of candidate conformations by eliminating rigid rotamers that provably are not part of the Global Minimum Energy Conformation (GMEC). The identified GMEC consists of rigid rotamers that have not been energy-minimized and is referred to as the rigid-GMEC. As a post-processing step, the conformations that survive DEE may be energy-minimized. When energy minimization is performed after pruning with DEE, the combined protein design process becomes heuristic, and is no longer provably accurate: That is, the rigid-GMEC and the conformation with the lowest energy among all energy-minimized conformations (the minimized-GMEC, or minGMEC) are likely to be different. While the traditional DEE algorithm succeeds in not pruning rotamers that are part of the rigid-GMEC, it makes no guarantees regarding the identification of the minGMEC. In this paper we derive a novel, provable, and efficient DEE-like algorithm, called minimized-DEE (MinDEE), that guarantees that rotamers belonging to the minGMEC will not be pruned, while still pruning a combinatorial number of conformations. We show that MinDEE is useful not only in identifying the minGMEC, but also as a filter in an ensemble-based scoring and search algorithm for protein redesign that exploits energy-minimized conformations. We compare our results both to our previous computational predictions of protein designs and to biological activity assays of predicted protein mutants. Our provable and efficient minimized-DEE algorithm is applicable in protein redesign, protein-ligand binding prediction, and computer-aided drug design.

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