Physics-based prediction of protein folding and unfolding rates: Examining the roles of fold topology and core packing.

Abstract

The (un)folding rates of natural proteins determine their native stability and functional homeostasis, making them important targets for protein engineering and design. From a prediction standpoint, the rates have been a long-standing puzzle. We have known for decades that folding rates empirically correlate with properties of the native three dimensional (3D) structures and that both, folding and unfolding rates, scale with protein size. Whereas such rate correlations are too rough for being of practical use, no significant progress in prediction accuracy has occurred since then, despite many efforts even including machine learning approaches. Here, we retake on this challenge by expanding the simple one-dimensional free energy surface (1D-FES) model that originally led to demonstrate the size scaling of both rates, and a curated database with rates for 75 single-domain proteins. We define the weighted sequence order (WSO) as a novel parameter that allows incorporating structural information into the 1D-FES model explicitly. Via the WSO, we examine the role of global structural properties such as fold topology and core packing in defining the (un)folding rates within the context of a physics-based model of protein folding. After introducing fold topology and packing at a coarse-grained level, the model uses three floating parameters to predict the folding and unfolding rates within 6.5- and 10-fold, respectively, resulting in ±6.5 kJ/mol accuracy in native stability, equivalent to the typical perturbation induced by one single-point mutation. The net improvement over the 2-parameter size-only prediction is of 2.5-fold. These new rate predictions are significantly closer to the threshold of usefulness for engineering and design. More importantly, this WSO-modified 1D-FES model can now directly accommodate atomistic, high-resolution, force-fields to further optimize the rate predictions, and/or to use rate information as a testbed for force-field refinement. Finally, the WSO-1D-FES model could also serve as foundation for developing more complex models capable of dealing with multi-domain proteins as well as with the evolutionary information cryptically encoded in natural protein sequences.