Encoding seasonal information in a two-oscillator model of the multi-oscillator circadian clock

The suprachiasmatic nucleus (SCN) is a collection of about 10 000 neurons, each of which functions as a circadian clock with slightly different periods and phases, that work in concert with form and maintain the master circadian clock for the organism. The diversity among neurons confers on the SCN the ability to robustly encode both the 24-h light pattern as well as the seasonal time. Cluster synchronization brings the different neurons into line and reduces the large population to essentially two oscillators, coordinated by a macroscopic network motif of asymmetric repulsive-attractive coupling. We recount the steps leading to this simplification and rigorously examine the two-oscillator case by seeking an analytical solution. Through these steps, we identify physiologically relevant parameters that shape the behaviour of the SCN network and delineate its ability to store past details of seasonal variation in photoperiod.