Abstract
In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. Each cell in the SCN contains an autonomous molecular clock, and the SCN is composed of multiple single-cell circadian oscillators. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to achieve phase synchronization. In natural conditions, the interaction between the SCN neurons is non-negligible and coupling between cells in the SCN is achieved partly by neurotransmitters. Though there have been a lot of works about the synchronization of circadian oscillators coupled by neurotransmitter, most of the works are based on numerical simulation with little theoretical analysis. In this paper, from the theoretical analysis, we prove that the clocks can be synchronized by the neurotransmitter with mathematical knowledge. Our results also show that the coupling among neurons can synchronize circadian oscillators but the synchronized oscillators are not with period of 24 h, which indicates that environmental cues are necessary to entrain oscillators with period of 24 h. This work can offer theoretical basis to study circadian synchronization in a numerical or experimental way.
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