Emergent oscillations in dense adaptive cell populations

Dynamical quorum sensing is one of the simplest group behaviours in cell populations, where collective oscillations emerge via mutual signaling beyond a critical cell density. Although many examples are documented, no unifying principle has yet been proposed. Here, by considering the response of cells to the extracellular signal and vice versa, we develop a quantitative theory for the phenomenon, and present a necessary condition for collective oscillations in a communicating population. We further show that a sufficient condition for oscillations is fulfilled by adaptive cells which reset their signal secretion rate upon prolonged stimulation. These general results were elucidated from non-equilibrium thermodynamic principles, where active cells play the role of engines to power oscillations in the medium. This unexpected link between adaptation and oscillation is shown to underlie several known examples of dynamical quorum sensing, and as such may also be a source of inadvertent group behaviour in large populations of living organisms.