Feedback between microscopic activity and macroscopic dynamics drives excitability and oscillations in mechanochemical matter

The macroscopic behaviour of active matter arises from nonequilibrium microscopic processes. In soft materials, active stresses typically drive macroscopic shape changes, which in turn alter the geometry constraining the microscopic dynamics, leading to complex feedback effects. Although such mechanochemical coupling is common in living matter and associated with biological functions such as cell migration, division, and differentiation, the underlying principles are not well understood due to a lack of minimal models that bridge the scales from the microscopic biochemical processes to the macroscopic shape dynamics. To address this gap, we derive tractable coarse-grained equations from microscopic dynamics for a class of mechanochemical systems, in which biochemical signal processing is coupled to shape dynamics. Specifically, we consider molecular interactions at the surface of biological cells that commonly drive cell-cell signaling and adhesion, and obtain a macroscopic description of cells as signal-processing droplets that adaptively change their interfacial tensions. We find a rich phenomenology, including multistability, symmetry-breaking, excitability, and self-sustained shape oscillations, with the underlying critical points revealing universal characteristics of such systems. Our tractable framework provides a paradigm for how soft active materials respond to shape-dependent signals, and suggests novel modes of self-organisation at the collective scale. These are explored further in our companion paper [arxiv 2402.08664v3].