Fast gap‐free enumeration of conformations and sequences for protein design

Despite significant successes in structure‐based computational protein design in recent years, protein design algorithms must be improved to increase the biological accuracy of new designs. Protein design algorithms search through an exponential number of protein conformations, protein ensembles, and amino acid sequences in an attempt to find globally optimal structures with a desired biological function. To improve the biological accuracy of protein designs, it is necessary to increase both the amount of protein flexibility allowed during the search and the overall size of the design, while guaranteeing that the lowest‐energy structures and sequences are found. DEE/A*‐based algorithms are the most prevalent provable algorithms in the field of protein design and can provably enumerate a gap‐free list of low‐energy protein conformations, which is necessary for ensemble‐based algorithms that predict protein binding. We present two classes of algorithmic improvements to the A* algorithm that greatly increase the efficiency of A*. First, we analyze the effect of ordering the expansion of mutable residue positions within the A* tree and present a dynamic residue ordering that reduces the number of A* nodes that must be visited during the search. Second, we propose new methods to improve the conformational bounds used to estimate the energies of partial conformations during the A* search. The residue ordering techniques and improved bounds can be combined for additional increases in A* efficiency. Our enhancements enable all A*‐based methods to more fully search protein conformation space, which will ultimately improve the accuracy of complex biomedically relevant designs. Proteins 2015; 83:1859–1877. © 2015 Wiley Periodicals, Inc.