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.

Inhibitory Networks of Fast-Spiking Interneurons Generate Slow Population Activities due to Excitatory Fluctuations and Network Multistability

“…However, this is not supported by experimental data, because one would then need all the interneuron f-I functions to be more linear and similar to Figures 3Bi or 6C for the network to experience a second-order-like phase transition. It is also biologically infeasible unless extra mechanisms (Bak et al, 1987;Bak, 1996;Levina et al, 2007Levina et al, , 2009Millman et al, 2010) are in place to overcome the fine-tuning problem. Figure 10 B shows the hypothetical arrangement of mean-field solutions corresponding to a second-order-like phase transition when every interneuron in the network has an almost perfectly linear f-I curve above threshold.…”

Impact of membrane bistability on dynamical response of neuronal populations

“…Bistability in individual neurons provides an alternative explanation for persistent activity in some brain areas [18], and is related to perfect temporal information accumulation [19] and self-organized criticality [20]. Our work sheds insights into the possible role of the up state on signal encoding and transmission through population response.…”

Cooperation, competition and the emergence of criticality in communities of adaptive systems

“…In particular, in the brain -one of the flagships of the criticality hypothesis-it could lead to maximal dynamic ranges, high sensitivity to stimuli, optimal transmission and storage of information, and very diverse dynamical repertoires [16,17,18,19,20,21]. Different mechanisms and scenarios have been described in the recent literature to explain how such a critical behavior comes about [22,23,24,25,26]. On the other hand, some authors have argued that apparent criticality could be just an artifact of the attempt to fit overly simplified models to complex and highly heterogeneous systems [27,28].…”