Attractive and repulsive couplings between circadian pacemaker neurons promote entrainment to light-dark cycles with after-effect

The mammalian circadian pacemaker, the suprachiasmatic nucleus (SCN), comprises a core region that receives light signals from the retina and a shell region that outputs pacemaking rhythms to peripheral tissues. The free-running period (FRP) of animals in constant darkness (DD) correlates with the period of the preceding LD cycle, a phenomenon known as after-effect. To elucidate the mechanisms underlying robust entrainment and after-effect, we analyzed phase oscillator models incorporating attractive and repulsive couplings that respectively decrease or increase phase differences between oscillators. Attractive coupling from the core to shell regions accounts for experimentally observed phase relationships between these regions under LD cycles. Remarkably, repulsive coupling from the shell to core regions promotes SCN entrainability to LD cycles. Furthermore, after transfer to DD, the FRP slowly returns to the intrinsic SCN period, reflecting the after-effect. Our analysis identifies an SCN coupling architecture that underlies stable daily activity rhythms.