Simple Model of Protein Energetics To Identify Ab Initio Folding Transitions from All-Atom MD Simulations of Proteins

A fundamental requirement to predict the native conformation, address questions of sequence design and optimization, and gain insights into the folding mechanisms of proteins lies in the definition of an unbiased reaction coordinate that reports on the folding state without the need to compare it to reference values, which might be unavailable for new (designed) sequences. Here, we introduce such a reaction coordinate, which does not depend on previous structural knowledge of the native state but relies solely on the energy partition within the protein: the spectral gap of the pair nonbonded energy matrix (ENergy Gap, ENG). This quantity can be simply calculated along unbiased MD trajectories. We show that upon folding the gap increases significantly, while its fluctuations are reduced to a minimum. This is consistently observed for a diverse set of systems and trajectories. Our approach allows one to promptly identify residues that belong to the folding core as well as residues involved in non-native contacts that need to be disrupted to guide polypeptides to the folded state. The energy gap and fluctuations criteria are then used to develop an automatic detection system which allows us to extract and analyze folding transitions from a generic MD trajectory. We speculate that our method can be used to detect conformational ensembles in dynamic and intrinsically disordered proteins, revealing potential preorganization for binding.