Equation representing the dark-entrained transition from inaction to action in male and female mice

The activation of behaviour in a daily rhythm governed by the light cycle is a universal phenomenon among humans, laboratory mammals and other vertebrates. For mice, the active period is during the dark. We have quantified the increase in activity when the lights shut off (Light to Dark, L to D) using a generalized CNS arousal assay with 20 ms resolution, rather than traditional running wheels. Data analysis yielded the rare demonstration of an equation which precisely tracks this behavioural transition and, surprisingly, its reverse during D to L. This behavioural dynamic survives in constant darkness (experiment 2) and is hormone-sensitive (experiment 3). Finally (experiment 4), mice on a light schedule analogous to one which proved troublesome for U.S. Navy sailors, had dysregulated activity bursts which did not conform to the transitions between D and L. These experiments show the lawfulness of a behavioural phase transition and the consequence of deviating from that dynamic pattern. And, in a new way, they bring mathematics to the realm of behavioural neuroscience.