Self-organized criticality occurs in non-conservative neuronal networks during 'up' states

During sleep, under anaesthesia and in vitro, cortical neurons in sensory, motor, association and executive areas fluctuate between so-called up and down states, which are characterized by distinct membrane potentials and spike rates(1-5). Another phenomenon observed in preparations similar to those that exhibit up and down states-such as anaesthetized rats(6), brain slices and cultures devoid of sensory input(7), as well as awake monkey cortex(8)-is self-organized criticality (SOC). SOC is characterized by activity 'avalanches with a branching parameter near unity and size distribution that obeys a power law with a critical exponent of about -3/2. Recent work has demonstrated SOC in conservative neuronal network models(9,10), but critical behaviour breaks down when biologically realistic 'leaky' neurons are introduced(9). Here, we report robust SOC behaviour in networks of non-conservative leaky integrate-and-fire neurons with short-term synaptic depression. We show analytically and numerically that these networks typically have two stable activity levels, corresponding to up and down states, that the networks switch spontaneously between these states and that up states are critical and down states are subcritical.