Parabolic avalanche scaling in the synchronization of cortical cell assemblies

Neurons in cortex synchronize their spiking in response to local and distant inputs. These synchronized assemblies are fundamental to cortex function, yet basic dynamical aspects about their size and duration are largely unknown. Using 2-photon imaging of neurons in superficial cortex of awake mice, we show that synchronized assemblies organize as scale-invariant avalanches that quadratically grow with duration. This quadratic expansion was found only for correlated neurons and required temporal coarse graining to compensate for spatial subsampling when network dynamics are critical, as demonstrated in simulations. The corresponding time course of an inverted parabola with exponent of χ = 2 described avalanches of up to 5 s duration and maximized temporal complexity in the ongoing activity of prefrontal and somatosensory cortex and in visual responses of primary visual cortex. Our results identify a scale-invariant order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches. Significance Statement The synchronization of cell assemblies is fundamental to many brain theories. Here we show such synchronization to grow according to an inverted parabola that maximizes temporal complexity. This quadratic scaling found for cell assemblies of highly diverse size and duration is in line with prediction for neuronal avalanches and the cortex being in a critical state.