A crucial regulation for life is enabled at the molecular level through allosteric proteins, whose catalytic activity at the active sites can be significantly enhanced or inhibited by the appearance of specific chemicals binding at their allosteric sites. Predicting the allosteric pathways from protein structures would help us determine regulation networks and design smart drugs. However, it remains a challenge as the nature of allostery — this elasticity-mediated long-range interaction is understood superficially. To approach the problem with systematic samples, we introduce a numerical scheme with the model proteins evolving in-silico to accomplish specific allosteric functions. We then obtain statistical features among thousands of solutions to the tasks and deduce rules for the allosteric mechanics. For the geometric task when a specific strain is propagated through the media, we find commonly applied is an edge-mode mechanism which quickly amplifies the strain signal close to the active site. While for the cooperative task with elastic energy conveyed, we reveal that the appearance of a mechanism, an extended and nearly zero energy mode, dominates the pathway. This mechanism can appear as shear, hinge, and twist — designs found in some allosteric proteins, or be more complicated and hard to visualize. But independent of specific designs, we predict such a scaling relation for the frequency of the allosteric mechanism that the cooperative energy is optimized to be independent of the protein size.

Bio: After obtained Bachelor degree at Peking University in 2010, Le moved to the United States for his PhD at New York University, where he worked with Matthieu Wyart studying the glassy dynamics and rigidity transition. After that, he has been a postdoc fellow at Kavli Institute for Theoretical Physics in Santa Barbara, where he is applying his physics knowledge to understand mysteries in various scales of biology: from the protein structure to epithelial tissue network to evolution of flu.