Synchronization of biological clock cells with a coupling mediated by the local concentration of a diffusing substance

• We proposed a model for the synchronization of biological clock cells in the suprachiasmatic nucleus that considers a nonlocal coupling mediated by the local concentration of a rapidly diffusing substance.
• The model considers also the photic stimulation and its effect on the synchronized rhythm displayed by the coupled network.
• Three photic stimulation protocols are considered.

The circadian rhythm in mammals is determined by the output of biological clock cells, e.g. in the brain suprachiasmatic nucleus. Each biological clock cell has its own period and can respond to photic stimulation, such that the output rhythm is given both by the coupling among cells and the external forcing. We propose a model for the coupling among biological clock cells of the suprachiasmatic nucleus where the coupling is mediated by the local concentration of a diffusing neurotransmitter which is both secreted and absorbed by the cells, influencing their individual rhythms. Such a coupling is non-local because it considers all the cells in the assembly, and the interaction strength decays exponentially with the spatial distance. We investigate the synchronization properties of this network with respect to the coupling strength and the inverse characteristic length of the coupling, which varies from zero (a global, all-to-all, coupling) to infinity (a local, nearest-neighbor, coupling). Quantitative diagnostics of phase and frequency synchronization are applied to describe the transition from a non-synchronized to a partially synchronized behavior as the coupling parameters are changed.