Excitable mechanics embodied in a walking cilium

Abstract

Rapid transduction of sensory stimulation to action is essential for an animal to survive. To this end, most animals use the sub-second excitable and multistable dynamics of a neuromuscular system. Here, studying an animal without neurons or muscles, we report analogous excitable and multistable dynamics embedded in the physics of a 'walking' cilium. We define a 'walking cilium' as a phenomena where the locomotive force is generated through contact with a substrate which is periodically reset by steps in the direction of motion. We begin by showing that cilia can walk without specialized gait control and identify the characteristic scales of spatio-temporal height fluctuations of the tissue. With the addition of surface interaction, we construct a low-order dynamical model of this single-cilium sub-unit. In addition to studying the dynamics of a single cilium in isolation, we subsequently examine collections of these walking cilia. En route to an emergent model for ciliary walking, we demonstrate the limits of substrate mediated synchronization between cilia. In the desynchronized limit, our model shows evidence of localized multi-stability mediated by the crosstalk between locomotive forcing and height. The out-of-equilibrium mechanics -- which govern this emergent excitable bistability -- directly control the locomotive forcing of a walking cilia. This direct coupling bypasses the role of the synaptic junctions between neurons and muscles. We show a minimal mechanism -- trigger waves -- by which these walking cells may work together to achieve organism-scale collaboration, such as coordination of hunting strikes across $10^5$ cells without central control.

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