Splitting between two subgroups of the SCN neurons with instantaneous feedback

Phase-splitting and various arrhythmic behaviors have been observed in mammals. Although it is known that desynchronization of SCN neurons plays an important role, the exact mechanisms underlying this behavior are still not completely understood. A previous study suggested that phase-splitting behavior was explained by the SCN output signal feeding back to the SCN with a time delay of about 12 h. However, experimental evidence showed that the feedback is instantaneous and does not have a time delay. In the present study, a Kuramoto model with instant feedback is proposed to explain the mechanisms underlying phase splitting and arrhythmic behavior. Our results show that phase-splitting and arrhythmic behavior results from the feedback which is described by two key parameters, the strength of the feedback as well as the phase difference of the feedback to the SCN activity. Additionally, in accordance with experimental findings, we observe that the SCN period in the split state is equal to 24 h, while it is larger than 24 h for a state that has a robust circadian rhythm. Our study provides an alternative explanation for the phase-splitting and arrhythmic behavior and opens a window to understand how feedback influences the SCN, and consequently its behavior.