Directed percolation theory and experiments of ultra-fast hydrodynamic quorum sensing*

Responding to external stimuli promptly is key to survival, so the biophysical relationships between physiological sensors and actuators were fundamental to the development of complex life forms. We study the protist Spirostomum ambiguum, which is unicellular but can grow up to 4mm in size. As a defence against predators, this ciliate releases toxins by contracting its long body within milliseconds. These rapid contractions also generate long-ranged vortex flows that trigger neighbouring cells, in turn, which collectively leads to an ultra-fast hydrodynamic signal transduction across a colony that moves hundreds of times faster than the swimming speed. By combining high-speed PIV and rheosensing experiments we determine the critical colony density required to sustain these signal waves. Synchronised toxin discharges could facilitate the repulsion of large-scale predators cooperatively, but false triggers are costly. We investigate this decision-making process in a framework of quorum sensing and percolation theory.