Mechanical platforms that mimic living matter

Mechanical networks, consisting of nodes connected by central-force springs, have many attributes that are reminiscent of living systems. For example, such networks can be easily tuned, or trained, to mimic the allosteric response in proteins where a strain exerted between one pair of nodes at a source can cause a strain between nodes at a distant target. We extend this analogy to create evolvable networks where the removal or addition of individual bonds in the network are considered to be mutations. Applying a series of such mutations can change the response between incompatible functions such as changing in-phase to out-of-phase response between target and source strains. The response is quantified as the ratio of the target to the source strain. We find that the mutations between two functions are epistatic – the effect of a mutation depends on what other mutation have already occurred. With a response threshold for the network to be considered functional, so that non-functional networks are disallowed, only some evolutionary pathways are viable. We can evaluate the evolutionary trajectories over a large ensemble of source-target pairs. We introduce the idea of a critical threshold above which no viable pathways exist and find that the critical threshold is surprisingly large. Moreover, we find that the set of mutations between functions fall predominantly into two well-defined classes. The ensemble behavior of our networks can be compared with what has been discovered in studies of protein evolution. Not only do these studeis allow comparison and elucidation of biological behavior, but the introduction of epistasis presents a constructive context in which to study many-body effects in condensed matter by emphasizing the importance of sequence, or order in which the interacting elements are introduced.

This work was done jointly with Samar Alqatari.