Strain analysis of protein structures and low dimensionality of mechanical allosteric couplings

In many proteins, especially allosteric proteins that communicate regulatory states from allosteric to active sites, structural deformations are functionally important. To understand these deformations, dynamical experiments are ideal but challenging. Using static structural information, although more limited than dynamical analysis, is much more accessible. Underused for protein analysis, strain is the natural quantity for studying local deformations. We calculate strain tensor fields for proteins deformed by ligands or thermal fluctuations using crystal and NMR structure ensembles. Strains-primarily shears-show deformations around binding sites. These deformations can be induced solely by ligand binding at distant allosteric sites. Shears reveal quasi-2D paths of mechanical coupling between allosteric and active sites that may constitute a widespread mechanism of allostery. We argue that strain-particularly shear-is the most appropriate quantity for analysis of local protein deformations. This analysis can reveal mechanical and biological properties of many proteins.