Quantitative Analysis of Dynamic Allostery.

Dynamic allostery refers to one important class of allosteric regulation that does not involve noticeable conformational changes upon effector binding. In recent years, many "quasi"-dynamic allosteric proteins have been found to only experience subtle conformational changes during allosteric regulation. However, as enthalpic and entropic contributions are coupled to each other and even tiny conformational changes could bring in noticeable free energy changes, a quantitative description is essential to understand the contribution of pure dynamic allostery. Here, by developing a unified anisotropic elastic network model (uANM) considering both side-chain information and ligand heavy atoms, we quantitatively estimated the contribution of pure dynamic allostery in a dataset of known allosteric proteins by excluding the conformational changes upon ligand binding. We found that the contribution of pure dynamic allostery is generally small (much weaker than previously expected) and robustly exhibits an allosteric activation effect, which exponentially decays with the distance between the substrate and the allosteric ligand. We further constructed toy models to study the determinant factors of dynamic allostery in monomeric and oligomeric proteins using the uANM. Analysis of the toy models revealed that a short distance, a small angle between the two ligands, strong protein-ligand interactions, and weak protein internal interactions lead to strong dynamic allostery. Our study provides a quantitative estimation of pure dynamic allostery and facilitates the understanding of dynamic-allostery-controlled biological processes and the design of allosteric drugs and proteins.