[Paper Review] Mechanisms of self-organized quasicriticality in neuronal networks models

Osame Kinouchi, Renata Pazzini+1 more|arXiv (Cornell University)|Oct 20, 2020

Neural dynamics and brain function103 references4 citations

TL;DR

This paper reviews biological mechanisms—such as synaptic plasticity, homeostatic plasticity, and adaptive neuronal thresholds—that enable neuronal networks to self-organize into a quasicritical state, avoiding fine-tuning of parameters. The key result is that these mechanisms lead to self-organized quasicriticality (SOqC), where networks hover near criticality, producing neuronal avalanches with experimentally observed scaling exponents despite non-conservative, dissipative dynamics.

ABSTRACT

The critical brain hypothesis states that there are information processing advantages for neuronal networks working close to the critical region of a phase transition. If this is true, we must ask how the networks achieve and maintain this critical state. Here we review several proposed biological mechanisms that turn the critical region into an attractor of a dynamics in network parameters like synapses, neuronal gains and firing thresholds. Since neuronal networks (biological and models) are nonconservative but dissipative, we expect not exact criticality but self-organized quasicriticality (SOqC), where the system hovers around the critical point.

Motivation & Objective

• To explain how neuronal networks self-organize toward criticality without requiring fine-tuning of control parameters.
• To address the challenge that biological neuronal networks are nonconservative and thus cannot achieve exact criticality, but instead exhibit self-organized quasicriticality (SOqC).
• To review biologically plausible mechanisms—such as STDP, synaptic depression, and adaptive thresholds—that drive networks toward the critical region.
• To demonstrate that SOqC, characterized by stochastic sawtooth oscillations around the critical point, can reproduce experimentally observed neuronal avalanche statistics.
• To advocate for the use of SOqC models over conservative sandpile models in neuroscience, given the dissipative nature of real neurons.

Proposed method

• Uses a standardized notation for network variables: synaptic weights $W_{ij}(t)$, membrane potential $V_i$, firing state $s_i \in \{0,1\}$, gain $\Gamma_i$, and threshold $\theta_i$.
• Applies dynamic rules such as spike-timing-dependent plasticity (STDP), where synaptic changes depend on pre- and postsynaptic spike timing differences $\Delta t = t_{\text{post}} - t_{\text{pre}}$.
• Models synaptic weight updates via exponential decay functions: $\Delta W_{ij} = A_{+}(W_{\text{max}} - W_{ij})\exp\left(-\frac{\Delta t - \tau_{ij}}{\tau_{+}}\right)$ for potentiation and $A_{-}(W_{ij} - W_{\text{min}})\exp\left(-\frac{\Delta t - \tau_{ij}}{\tau_{-}}\right)$ for depression.
• Analyzes network dynamics through phase transitions, particularly second-order absorbing phase transitions (e.g., Directed Percolation universality class), identifying critical behavior via avalanche size and duration distributions.
• Compares SOqC to traditional self-organized criticality (SOC), emphasizing that non-conservative systems like neurons cannot achieve exact SOC but instead exhibit SOqC with large excursions near criticality.
• Employs mean-field exponents and scaling analysis to validate that SOqC networks produce avalanche statistics matching experimental data from Beggs and Plenz (2003).

Experimental results

Research questions

• RQ1 How can neuronal networks achieve critical dynamics without fine-tuning of synaptic strength or other control parameters?
• RQ2 What biologically plausible mechanisms can drive a nonconservative, dissipative network toward a state of quasicriticality?
• RQ3 Why are conservative SOC models like sandpiles inadequate for modeling real neuronal networks?
• RQ4 How does self-organized quasicriticality (SOqC) differ from exact criticality, and can it still account for experimental neuronal avalanche data?
• RQ5 To what extent do homeostatic mechanisms such as STDP, synaptic depression, and adaptive thresholds lead to robust, stable quasicritical states?

Key findings

• Neuronal networks with dynamic synapses, such as those governed by STDP, self-organize robustly to the border of a phase transition, producing critical-like neuronal avalanches.
• The system exhibits stochastic sawtooth oscillations in the control parameter, indicating persistent hovering around the critical point rather than exact tuning.
• Despite non-conservative dynamics, the network produces neuronal avalanches with mean-field exponents matching those observed in experiments (e.g., power-law distributions of avalanche size and duration).
• Mechanisms such as STDP, synaptic depression, and adaptive thresholds collectively lead to SOqC, where the system avoids fine-tuning and maintains criticality through homeostatic feedback.
• The largest eigenvalue $\Lambda$ of the synaptic matrix depends weakly on hyperparameters of the homeostatic rules, indicating robustness compared to direct control of the original parameter.
• SOqC is a more accurate description of biological neuronal networks than SOC, as real neurons are dissipative and lack infinite time-scale separation.