Dynamical synapses causing self-organized criticality in neural networks

Abstract

Self-organized criticality 1 is one of the key concepts to describe the emergence of complexity in natural systems. The concept asserts that a system self-organizes into a critical state where system observables are distributed according to a power law. Prominent examples of self-organized critical dynamics include piling of granular media 2 , plate tectonics 3 and stick-slip motion 4 . Critical behaviour has been shown to bring about optimal computational capabilities 5 , optimal transmission 6 , storage of information 7 and sensitivity to sensory stimuli 8-10 . In neuronal systems, the existence of critical avalanches was predicted 11 and later observed experimentally 6,12,13 . However, whereas in the experiments generic critical avalanches were found, in the model of ref. 11 they only show up if the set of parameters is fine-tuned externally to a critical transition state. Here, we demonstrate analytically and numerically that by assuming (biologically more realistic) dynamical synapses 14 in a spiking neural network, the neuronal avalanches turn from an exceptional phenomenon into a typical and robust self-organized critical behaviour, if the total resources of neurotransmitter are sufficiently large.In multi-electrode recordings on slices of rat cortex and neuronal cultures 6,12 , neuronal avalanches were observed whose sizes were distributed according to a power law with an exponent of −3/2. The distribution was stable over a long period of time.Variations of the dynamical behaviour are induced by application or wash-out of neuromodulators. Qualitatively identical behaviour can be reached in models such as those in refs 11,15 by variations of a global connectivity parameter. In these models, criticality only shows up if the interactions are fixed precisely at a specific value or connectivity structure.Here, we study a model with activity-dependent depressive synapses and show that existence of several dynamical regimes can be reconciled with parameter-independent criticality. We find that synaptic depression causes the mean synaptic strengths to approach a critical value for a certain range of interaction parameters, whereas outside this range other dynamical behaviours are prevalent, see Fig. 1. We analytically derive an expression for the average coupling strengths among neurons and the average inter-spike intervals in a mean-field approach. The mean-field approximation is applicable here even in the critical state, because the quantities that are averaged do not exhibit power laws, but unimodal distributions. These mean values obey a self-consistency equation that allows us to identify the mechanism that drives the dynamics of the system towards the critical regime. Moreover, the critical regime induced by the synaptic dynamics is robust to parameter changes.Consider a network of N integrate-and-fire neurons. Each neuron is characterized by a membrane potential 0 < h i (t ) < θ. The neurons receive external inputs by a random process ξ τ ∈ {1,. . .,N} that selects a neuron ξ τ (t ) = i at a rate τ and a...

Adaptation to sensory input tunes visual cortex to criticality

“…The principles governing such adaptation at the macroscopic level of neuronal network dynamics are not well understood. Computational models and theory suggest that such adaptation can maintain critical network dynamics [14][15][16] , but these previous studies did not consider the strongly driven regime that is expected during intense sensory input. Indeed, sufficiently strong input may increase the overall excitability of a network by bringing neurons closer to their firing thresholds and potentially tipping the network into a high firing rate regime that is inconsistent with critical dynamics (Supplementary Information 1).…”

“…A subset of neurons (20%) was inhibitory. Motivated by previous experiments 21 and models 14 , we modelled adaptation as short-term synaptic depression with recovery (Methods). However, our model differed from previously studied models, as detailed in Supplementary Information 7.…”

“…This could be achieved by some 'top-down' mechanism (for example, neuromodulators such as dopamine 29 ) that tunes the network or as the result of local self-organization 14,16,30,31 . In either case, one concern with this hypothesis has been that, theoretically, the critical regime occupies an infinitesimal volume in state space (the boundary between two different regimes), which may be too small a target to hit for a real biological tuning process contending with noise and imperfections.…”

Critical phenomena in globally coupled excitable elements

“…This makes it difficult to perform a systematic study of the problem. Thus, it is necessary to investigate the typical cooperative phenomena in nonequilibrium systems.Recently, critical behaviors have been observed experimentally [1,2,3,4,5,6,7] and numerically [8,9,10,11,12,13,14,15] in typical examples of coupled excitable elements such as neural networks and cardiac tissues. In general, such critical behaviors are classified into several groups on the basis of the exponents of divergences.…”

Slow synaptic dynamics in a network: From exponential to power-law forgetting

“…Typically, models of integrate-and-fire neurons on networks * Electronic address: jean-marc.luck@cea.fr † Electronic address: anita@bose.res.in have been studied, and their different dynamical regimes explored [21]. The discovery of neural avalanches in the brain [22] was followed by several dynamical models of neural networks [23,24], where the statistics of avalanches were investigated [25][26][27][28][29][30] in the context of theories of self-organised criticality [31]. A review of such approaches can be found in [32].…”