Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 Å ligand interface Cα root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.Author Summary: Protein–protein interactions play a central role in various aspects of the structural and functional organization of the cell, and their elucidation is crucial for a better understanding of processes such as metabolic control, signal transduction, and gene regulation. Genomewide proteomics studies, primarily yeast two-hybrid assays, will provide an increasing list of interacting proteins, but only a small fraction of the potential complexes will be amenable to direct experimental analysis. Thus, it is important to develop computational docking methods that can elucidate the details of specific interactions at the atomic level. Protein–protein docking generally starts with a rigid body search that generates a large number of docked conformations with good shape, electrostatic, and chemical complementarity. The conformations are clustered to obtain a manageable number of models, but the current methods are unable to select the most likely structure among these models. Here we describe a refinement algorithm that, applied to the individual clusters, improves the quality of the models. The better models are suitable for higher-accuracy energy calculation, thereby increasing the chances that near-native structures can be identified, and thus the refinement increases the reliability of the entire docking algorithm.