Smoothing protein energy landscapes by integrating folding models with structure prediction.

Decades of work has investigated the energy landscapes of simple protein models, but what do the landscapes of real, large, atomically detailed proteins look like? We explore an approach to this problem that systematically extracts simple funnel models of actual proteins using ensembles of structure predictions and physics-based atomic force fields and sampling. Central to our effort are calculations of a quantity called the relative entropy, which quantifies the extent to which a given set of structure decoys and a putative native structure can be projected onto a theoretical funnel description. We examine 86 structure prediction targets and one coupled folding-binding system, and find that in a majority of cases the relative entropy robustly signals which structures are nearest to native (i.e., which appear to lie closest to a funnel bottom). Importantly, the landscape model improves substantially upon purely energetic measures in scoring decoys. Our results suggest that physics-based models-including both folding theories and all-atom force fields-may be successfully integrated with structure prediction efforts. Conversely, detailed predictions of structures and the relative entropy approach enable one to extract coarse topographic features of protein landscapes that may enhance the development and application of simpler folding models.