Excitability and traveling waves in renewable active matter

Activity and renewability are distinctive features of living matter and constitute a new class of materials that we term renewable active matter. A striking example is the cell cytoskeleton, where myosin filaments bind to the actin meshwork, apply contractile stresses, and undergo continual stress- or strain-dependent turnover, thus acting as both force generators and sensors. As a consequence of nonreciprocity, arising from the independence of action and response, such living matter exhibits unusual mechanical properties like, segregation without attraction, fragility and force chains. Here we show that the interplay between activity and turnover gives rise to mechanical excitability in the form of traveling waves and pulses, and spatiotemporal chaos. We provide a systematic study of the nucleation, movement and shape of the traveling pulse, and present a boundary layer analysis to establish the existence of homoclinic orbits. Our analytical results are supported by detailed numerical analysis of the governing partial differential equations. This study has implications for the observed mechanical excitability in a variety of cellular contexts such as in isolated adherent cells and confluent cells within tissues.