Pulsatile contractions and pattern formation in excitable active gels

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate and transmit mechanical forces. The cortex can exhibit a wide range of dynamic behaviours, from generating pulsatory contractions and traveling waves to forming highly organised structures such as ordered fibers, contractile rings and networks that must adapt to the local cellular environment. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, our quantitative understanding of the emergent dynamics of this mechanochemical system is limited. Here we develop a mathematical model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active polymer gel, to investigate how the interplay between chemical signalling and mechanical forces govern the propagation of contractile stresses and patterns in the cortex. We demonstrate that mechanical feedback in the excitable RhoA system, through dilution and concentration of chemicals, acts to destabilise homogeneous states and robustly generate pulsatile contractions. While moderate active stresses generate spatial propagation of contraction pulses, higher active stresses assemble localised contractile structures. Moreover, mechanochemical feedback induces memory in the active gel, enabling long-range propagation of transient local signals.