Protein as evolvable functionally constrained amorphous matter

We explore current ideas around the representation of a protein as an amorphous material, in turn represented by an abstract graph G with edges weighted by elastic stiffnesses. By embedding this graph in physical space, we can map every graph to a spectrum of conformational fluctuations and responses (as a result of, say, ligandbinding). This sets up a 'genotype-phenotype' map, which we use to evolve the amorphous material to select for fitness. Using this, we study the emergence of allosteric interaction, hinge joint, crack formation and a slide bolt in functional proteins such as adenylate kinase, HSP90, calmodulin and GPCR proteins. We find that these emergent features are associated with specific geometries and mode spectra of floppy or liquid-like regions. Our analysis provides insight into understanding the architectural demands on a protein that enable a prescribed function and its stability to mutations.