Flexible protein docking refinement using pose-dependent normal mode analysis

Modeling conformational changes in protein docking calculations is challenging. To make the calculations tractable, most current docking algorithms typically treat proteins as rigid bodies and use soft scoring functions that implicitly accommodate some degree of flexibility. Alternatively, ensembles of structures generated from molecular dynamics (MD) may be cross-docked. However, such combinatorial approaches can produce many thousands or even millions of docking poses, and require fast and sensitive scoring functions to distinguish them. Here, we present a novel approach called "EigenHex," which is based on normal mode analyses (NMAs) of a simple elastic network model of protein flexibility. We initially assume that the proteins to be docked are rigid, and we begin by performing conventional soft docking using the Hex polar Fourier correlation algorithm. We then apply a pose-dependent NMA to each of the top 1000 rigid body docking solutions, and we sample and re-score multiple perturbed docking conformations generated from linear combinations of up to 20 eigenvectors using a multi-threaded particle swarm optimization algorithm. When applied to the 63 "rigid body" targets of the Protein Docking Benchmark version 2.0, our results show that sampling and re-scoring from just one to three eigenvectors gives a modest but consistent improvement for these targets. Thus, pose-dependent NMA avoids the need to sample multiple eigenvectors and it offers a promising alternative to combinatorial cross-docking.