The continuum of allosteric behavior in mechanical networks

Allosteric regulation in proteins is often accompanied by conformational transitions, facilitating the transmission of mechanical signals between distant ligand binding sites. Analyses of allosteric proteins have revealed a variety of archetypal motions ranging from hinge-like or shear mechanisms to allosteric strain pathways connecting different binding sites. Here we investigate the range of possible motions that can be achieved in mechanical networks tuned to perform allostery. Using an analysis based on persistent homology, we develop a description of allosteric motion which quantifies and unifies all mechanisms into a single framework. We show that while some networks fall into distinct classes of archetypal designs, most fall along a continuum consisting of combinations of hinges, strain pathways and isostatic architectures. We apply this analysis to a collection of proteins, allowing us to identify potential sets of residues that are important for facilitating allosteric communication between different binding sites.