Evolutionary conservation of mechanical strain distributions in functional transitions of protein structures

One of the tenets of molecular biology is that dynamic transitions between three-dimensional structures determine the function of proteins. Therefore, it seems only natural that evolutionary analysis of proteins, presently based mainly on their primary sequence, needs to shift its focus towards their function as assessed by corresponding structural transitions. This can be facilitated by recent progress in cryogenic electron microscopy that provides atomic structures of multiple conformational states for proteins and protein assemblies isolated from evolutionarily related species. In this work, we study evolutionary conservation of multi-protein assembly function by using mechanical strain as a quantitative footprint of structural transitions. We adopt the formalism of finite strain analysis, developed in condensed matter physics, and apply it, as a case study, to a classical multi-protein assembly, the ATP synthase. Our Protein Strain Analysis (PSA) provides a precise characterization of rotation domains that agrees with the present biophysical knowledge. In addition, we obtain a strain distribution on the protein structure associated with functional transitions. By analyzing in detail, the strain patterns of the chains responsible for ATP synthesis across distinct species, we show that they are evolutionarily conserved for the same functional transition. Such conservation is not revealed by displacement or rotation patterns. Furthermore, within each functional transition, we can identify conserved strain patterns for ATP synthases isolated from different organisms. The observed strain conservation across evolutionary distant species indicates that strain should be essential in future structure-based evolutionary studies of protein function.