Are distance-dependent statistical potentials considering three interacting bodies superior to two-body statistical potentials for protein structure prediction?

Distance-based statistical potentials have long been used to model condensed matter systems, e.g. as scoring functions in differentiating native-like protein structures from decoys. These scoring functions are based on the assumption that the total free energy of the protein can be calculated as the sum of pairwise free energy contributions derived from a statistical analysis of pair-distribution functions. However, this fundamental assumption has been challenged theoretically. In fact the free energy of a system with N particles is only exactly related to the N-body distribution function. Based on this argument coarse-grained multi-body statistical potentials have been developed to capture higher-order interactions. Having a coarse representation of the protein and using geometric contacts instead of pairwise interaction distances renders these models insufficient in modeling details of multi-body effects. In this study, we investigated if extending distance-dependent pairwise atomistic statistical potentials to corresponding interaction functions that are conditional on a third interacting body, defined as quasi-three-body statistical potentials, could model details of three-body interactions. We also tested if this approach could improve the predictive capabilities of statistical scoring functions for protein structure prediction. We analyzed the statistical dependency between two simultaneous pairwise interactions and showed that there is surprisingly little if any dependency of a third interacting site on pairwise atomistic statistical potentials. Also the protein structure prediction performance of these quasi-three-body potentials is comparable with their corresponding two-body counterparts. The scoring functions developed in this study showed better or comparable performances compared to some widely used scoring functions for protein structure prediction.