A shared speed encoding model for running and backing away behaviours in segregated neural circuits.

How neuronal firing within a circuit encodes behavioural intensity, like running speed, is largely unknown. Projections from temporal association cortex (TeA) and superior colliculus (SC) to dorsal periaqueductal grey (dPAG) circuit can both trigger running behaviour. Using in vivo loose-patch recordings with circuit manipulations in mice, we quantified a firing - speed relationship and established its encoding model. Here, we report two behavioural patterns induced by circuit activation: backing away and rebound running. Mechanistically, dPAG CaMKIIα neurons receiving inputs from either TeA or SC, function as distinct "behavioural units", controlling two "unit behaviours" of running and backing away, respectively. The unidirectional inhibition from the backing away unit to the running unit is mediated by somatostatin (SOM) neurons in dPAG, enabling transitions among four behavioural states: running, backing away, stopping, and rebound running. Both running and backing away behaviours follow a unified motor encoding model, quantified by a single-phase association equation.