Exploring Protein Flexibility and Allosteric Signalling Mechanism with Rigidity Theory

Advancements in the field of mathematical rigidity theory have opened up a number of exciting opportunities for computational predictions of protein flexibility and their dynamics. Starting with a 3D protein structure, several programs such as FIRST model the protein as a constraint multigraph, consisting of vertices (atoms) and edges (covalent bonds, hydrogen bonds, electrostatic interactions, and hydrophobic contacts). FIRST applies the pebble game algorithm on the resulting multigraph which rapidly decompose the protein into rigid clusters and flexible regions. Using an extension of FIRST and the pebble game algorithm we propose a computational approach for studying a biological phenomenon 'allostery'. Allostery refers to an effect of binding at one site to another, often significantly distant functional site on the protein, allowing for regulation of the protein function. Most dynamic proteins are allosteric and allostery has even been coined the 'second secret of life', however the molecular mechanisms that give rise to allostery are currently poorly understood. Extending our earlier seminal work, we have developed a rigidity-transmission allostery (RTA) algorithm which predicts if mechanical perturbation of rigidity (mimicking ligand binding) at one site of the protein can propagate across a protein structure and in turn cause a transmission and change in degrees of freedom and conformation at a second distant site, resulting in allosteric transmission. Since RTA algorithm is computationally fast, we can rapidly scan many unknown sites for rigidity-based allosteric communication, identifying potential new allosteric sites and quantify their allosteric effect. We will review the functional importance of protein flexibility and mathematical and algorithmic background of rigidity theory and method FIRST. In this originative expose we describe rigidity based mechanistic allostery communication model. We will also provide a few illustrations of rigidity-based allostery communication on actual protein structures, including the important signaling G-protein coupled receptors. This method will have important consequence in general understanding of allostery and in aid of design of allosteric drugs.