Variable Neighborhood Search with Cost Function Networks to Solve Large Computational Protein Design Problems

Computational protein design (CPD) aims to predict amino acid sequences that fold to specific structures and perform desired functions. CPD depends on a rotamer library, an energy function, and an algorithm to search the sequence/conformation space. Variable neighborhood search (VNS) with cost function networks is a powerful framework that can provide tight upper bounds on the global minimum energy. We propose a new CPD heuristic based on VNS in which a subset of the solution space (a "neighborhood") is explored, whose size is gradually increased with a dedicated probabilistic heuristic. The algorithm was tested on 99 protein designs with fixed backbones involving nine proteins from the SH2, SH3, and PDZ families. The number of mutating positions was 20, 30, or all of the amino acids, while the rest of the protein explored side-chain rotamers. VNS was more successful than Monte Carlo (MC), replica-exchange MC, and a heuristic steepest-descent energy minimization, providing solutions with equal or lower best energies in most cases. For complete protein redesign, it gave solutions that were 2.5 to 11.2 kcal/mol lower in energy than those obtained with the other approaches. VNS is implemented in the toulbar2 software. It could be very helpful for large and/or complex design problems.