Before revision:  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 stimulated energy release from active cells drives oscillations in the medium. The 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 URLanisms.
After revision:  Here, by considering the response of individual cells against a time-varying signal. A positive intracellular signal relay of sufficient gain from participating cells is required to sustain the oscillations, together with phase matching. The two conditions yield quantitative predictions for the onset cell density and frequency in terms of measured single-cell and signal response functions. Through mathematical constructions, we show that cells that adapt to a constant stimulus fulfil the phase requirement by developing a leading phase in an "active" frequency window that enables cell-to-signal energy flow. Analysis of dynamical quorum sensing , and as such may also be a source of inadvertent group behaviour in large populations of URLanisms.