Epistasis in allosteric mechanical networks*

Elastic networks of springs can be pruned to create a response between distant pairs of nodes that mimics allosteric behavior in proteins. We create pairs of such responses: one in which the source and target respond in phase with each other (+) and one in which they respond out-of-phase (-). These two networks differ by sets of “mutations” each of which removes or adds a single bond between network nodes. The effect of multiple mutations is epistatic, that is, it is not simply the sum of the effects due to each of the mutations considered separately. We generate ensembles of (+)/(-) network pairs that differ by a fixed number, N, of discrete mutations. Sampling thousands of mutational sequences from this ensemble, we study the dependence on N of the epistatic interactions. For this realistic mechanical system that is abstracted from biological and chemical complexity, we measure the statistics of local and global epistasis up to N=17 and study how epistasis is affected by the network structure (i.e., network coordination). We find that there is a large variation of response between different members of the ensemble.