Coherence, collective rhythm, and phase difference distribution in populations of stochastic genetic oscillators with cellular communication.

An ensemble of stochastic genetic relaxation oscillators via phase-attractive or repulsive cell-to-cell communication are investigated. In the phase-attractive coupling case, it is found that cellular communication can enhance self-induced stochastic resonance as well as collective rhythms, and that different intensities of noise resulting from the fluctuation of intrinsic chemical reactions or the extrinsic environment can induce stochastic limit cycles with different amplitudes for a large cell density. In contrast, in the phase-repulsive coupling case, the distribution of phase differences among the stochastic oscillators can display such characteristic as unimodality, bimodality or polymodality, depending on both noise intensity and cell number, but the modality of phase difference distribution almost keeps invariant for an arbitrary noise intensity as the cell number is beyond a threshold.