Abstract

Collective oscillations of cells in a population appear under diverse biological contexts. Here, we establish a set of common principles by categorising 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 in several cellular systems with increasing biological complexity reaffirms the pivotal role of adaptation in powering oscillations in an otherwise dissipative cell-to-cell communication channel. The physical conditions identified also apply to synthetic oscillatory systems.

Highlights

  • Collective oscillations of cells in a population appear under diverse biological contexts

  • Dubbed dynamical quorum sensing (DQS) to emphasise the role of increased cell density in triggering the auto-induced oscillations, this class of behaviour lies outside the well-known Kuramoto paradigm of oscillator synchronisation[14,15]

  • By focusing on the frequency-resolved cellular response, we report a generic condition for collective oscillations to emerge, and show that it is satisfied when cells affect the signal in a way that adapts to slow environmental variations, i.e., cells respond to signal variation rather than to its absolute level

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Summary

Introduction

Collective oscillations of cells in a population appear under diverse biological contexts. Multicellular pulsation has been observed in nerve tissues[8], during dorsal closure in late stage drosophila embryogenesis[9,10,11,12], and more[13] In these examples, communication through chemical or mechanical signals is essential to activate quiescent cells. Sound is generated by hair bundles, the sensory units of hair cells that detect sound with ultra-high sensitivity[18,19,20] Another example is glycolytic oscillations of yeast cells which can be induced across different laboratory conditions[21,22,23,24,25,26]. Together with the measurable response of individual cells, quantitative predictions of the oscillation frequency and its dependence on cell density become possible

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