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

Abstract

During sleep, under anesthesia and in vitro, cortical neurons in sensory, motor, association and executive areas fluctuate between Up and Down states (UDS) characterized by distinct membrane potentials and spike rates [1, 2, 3, 4, 5]. Another phenomenon observed in preparations similar to those that exhibit UDS, such as anesthetized rats [6], brain slices and cultures devoid of sensory input [7], as well as awake monkey cortex [8] is self-organized criticality (SOC). This is characterized by activity “avalanches” whose size distributions obey a power law with critical exponent of about −32 and branching parameter near unity. Recent work has demonstrated SOC in conservative neuronal network models [9, 10], however critical behavior breaks down when biologically realistic non-conservatism is introduced [9]. We here report robust SOC behavior 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 2 stable activity levels corresponding to Up and Down states, that the networks switch spontaneously between them, and that Up states are critical and Down states are subcritical.