Collective brain activity shows very intriguing phenomena. Many experimental results, both in-vivo and in-vitro, support the idea that the brain cortex operates near a critical point, and, at the same time, works as a reservoir of multiple precise collective oscillatory spatio-temporal patterns, with both cue-induced and spontaneous reactivation of precise dynamical phase-locked periodic patterns of spikes
In this work we review recent results which link together memory functions, collective phase-locked oscillations and scale-free critical behavior, in a model with leaky neurons (whose structured recurrent connectivity comes from learning multiple spatio-temporal phase-coded patterns using a rule based on Spike Timing-Dependent Plasticity) in presence of a Poissonian noise distribution (modelling spontaneous neurotransmitter release at individual synapses, as well as other sources of inhomogeneity and randomness that determine an irregular background synaptic noise).
In absence of cue stimulation[2,3,4], we study the spontaneous dynamics induced by noise. Notably when heterogeneity in neurons parameters is included in the model, noise focusing can induce noise-initiated intermittent transient replay of oscillatory collective pattern, and up/down alternation. For low values of noise (alpha <alpha_c), sweeping excitability we observe a non-equilibrium discontinuous phase transition, while, at higher values of noise we get a crucially different behaviour, with alternation of up and down states [2]. Indeed noise coupling parameter changes the lifetime of the metastable states [3]. As the noise alpha approaches the critical value, critical features and scale-free neural avalanches are observed [2,3,4,5]. The presence of both a non-equilibrium discontinuous transition (at alpha< alphac) and a critical scale-free regime when alpha approaches alphac, in our model, are crucially related to the interplay between noise and a structured connectivity which promotes collectivity. Criticality emerges naturally near the edge of the instability when noise alpha approaches alphac, in an associative memory network, with many metastable dynamical states. Notably the scaling relation between the critical exponents of avalanches' sizes and durations is satisfied[3,4] with a mean size vs duration exponent slightly higher then 1, in agreement with some experimental results [7,8,9].
Interestingly, there are some analogies with the Random Field Ising Model of Sethna et al. [6], and with the discontinuous phase transition models that have been proposed for flocks and sworms to explain the scale-free critical features observed in flocks and sworms.
[1] Information capacity of a network of spiking neurons, S.Scarpetta A.de Candia Physica A 2020, https://doi.org/10.1016/j.physa.2019.123681
[2]Effects of Poisson noise in a IF model with STDP and spontaneous replay of periodic spatiotemporal patterns, in absence of cue stimulationS Scarpetta, F Giacco, F Lombardi, A De Candia, Biosystems 112 (3), 258-264
[3] Hysteresis, neural avalanches and critical behaviour near a first-order transition of a spiking neural network, S.Scarpetta I. Apicella A.de Candia, Phys. Rev. E 2018 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.062305
[4] Neural Avalanches at the Critical Point between Replay and Non-Replay of Spatiotemporal Patterns PLOS ONE 2013
[5] Critical Behavior and Memory Function in a Model of Spiking Neurons with a Reservoir of Spatio-Temporal Patterns. S.Scarpetta 2020 in "The Functional Role of Critical Dynamics in Neural Systems" Springer Series on Bio- and Neuro-systems, vol 11. Springer, https://doi.org/10.1007/978-3-030-20965-0_10
[6] Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations
James P. Sethna, Karin Dahmen, Sivan Kartha, James A. Krumhansl, Bruce W. Roberts, and Joel D. Shore
Phys. Rev. Lett. 70, 3347 – Published 24 May 1993
[7]W.L. Shew, W.P. Clawson, J. Pobst, Y. Karimipanah, N.C. Wright, and R. Wessel, "Adaptation
to sensoryinput tunes visual cortex to criticality," NATURE PHYS. 11, 659 (2015).
[8] Shaukat, A. & Thivierge, Statistical evaluation of waveform collapse reveals scale-free properties
of neuronal avalanches. Front. Comput. Neurosci. 10 (2016)
[9] N. Friedman, S. Ito, B.A.W. Brinkman, M. Shimono,R.E. Lee DeVille, K.A. Dahmen, J.M. Beggs, and T.C. Butler, Universal critical dynamics in high resolution neuronal avalanchePhys. Rev. Lett. 108, 208102 (2012)