Architecture and Co-Evolution of Allosteric Materials
Seminar | January 14 | 4-5 p.m. | 106 Stanley Hall
Matthieu Wyart, Ecole Polytechnique Federale de Lausanne
We introduce a numerical scheme to evolve functional elastic materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures and the correlations among them can be computed. We first consider an allosteric task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies non-monotonically along the trumpet. We show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials, analogous to the edge modes of topological insulators. Next, we show that materials designed to display cooperative binding at two locations evolve quite different architectures. We report evidence for these designs in the data base of ~ 50 allosteric proteins. If time permits, I will discuss the relationship between protein mechanics and epistasis in these architectures, and how it can (or cannot) be inferred by inference methods using sequence alignments such as Direct Coupling Analysis.