[Paper Review] The balance between excitation and inhibition controls the temporal organization of neuronal avalanches

Fabrizio Lombardi, Hans J. Herrmann+3 more|arXiv (Cornell University)|Apr 27, 2012

Neural dynamics and brain function16 citations

TL;DR

This study reveals that the non-monotonic waiting time distribution between neuronal avalanches in rat cortical slices arises from the alternation between up-states (high activity) and down-states (quiescent periods), driven by a homeostatic balance between excitation and inhibition. Numerical simulations show that this behavior emerges when single-neuron dynamics toggle between depolarized and hyperpolarized states, with the critical balance controlled by a single parameter ratio R ≈ 10⁻⁴, matching experimental data and confirming that network-level criticality depends on intrinsic neuronal state transitions.

ABSTRACT

Neuronal avalanches, measured in vitro and in vivo, exhibit a robust critical behaviour. Their temporal organization hides the presence of correlations. Here we present experimental measurements of the waiting time distribution between successive avalanches in the rat cortex in vitro. This exhibits a non-monotonic behaviour, not usually found in other natural processes. Numerical simulations provide evidence that this behaviour is a consequence of the alternation between states of high and low activity, named up and down states, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homeostatic mechanisms.

Motivation & Objective

• To understand the origin of the non-monotonic waiting time distribution between neuronal avalanches observed in rat cortical slices.
• To investigate how the alternation between up-states and down-states shapes the temporal organization of avalanches.
• To determine whether the balance between excitation and inhibition governs the observed non-monotonic waiting time distribution.
• To validate that single-neuron state transitions (depolarized in up-states, hyperpolarized in down-states) are essential for reproducing experimental waiting time statistics.

Proposed method

• Experimental measurement of waiting time distributions between neuronal avalanches in organotypic rat somatosensory cortex slices using microelectrode arrays.
• Numerical simulations of spiking neuronal networks with state-dependent dynamics mimicking up- and down-states.
• Incorporation of homeostatic mechanisms that tune single-neuron excitability based on prior activity, with distinct membrane potential thresholds for excitation and inhibition.
• Use of a threshold-based transition mechanism between up- and down-states, where the balance is controlled by the ratio R = h / sΔv^min.
• Statistical comparison of simulated and experimental waiting time distributions using the Kolmogorov-Smirnov test at p = 0.05 significance level.
• Systematic variation of excitation (sΔv^min) and inhibition (h) parameters to identify optimal agreement with experimental data.

Experimental results

Research questions

• RQ1 What causes the non-monotonic waiting time distribution between neuronal avalanches in cortical networks?
• RQ2 How do up-states and down-states contribute differently to the temporal organization of avalanches?
• RQ3 To what extent is the observed waiting time distribution determined by the balance between excitation and inhibition?
• RQ4 Can a minimal model with state-dependent single-neuron dynamics reproduce the experimental waiting time statistics?
• RQ5 Is the non-monotonic behavior a consequence of network-level criticality or of intrinsic neuronal state transitions?

Key findings

• The experimental waiting time distribution exhibits an initial power law regime (exponent 2.15 ± 0.32) between 10 and 200 ms, followed by a local minimum at 200 ms < Δt_min < 1 s, and a pronounced maximum at Δt ≈ 1–2 s.
• Numerical simulations reproduce the non-monotonic waiting time distribution with high fidelity, passing the Kolmogorov-Smirnov test with p = 0.99 (top panel) and p = 0.68 (bottom panel) for experimental data.
• The minimum and maximum in the waiting time distribution are controlled by the balance between excitation and inhibition, quantified by the ratio R = h / sΔv^min ≈ 10⁻⁴ for optimal agreement with experiments.
• The power-law regime in waiting times arises from clustered avalanche activity during up-states, while the bell-shaped peak at longer intervals originates from down-states with long recovery times.
• Removing single-neuron state dependence (e.g., setting h = 0) results in a monotonic waiting time distribution, demonstrating that intrinsic neuronal dynamics are essential for the non-monotonic shape.
• The model confirms that up-states are metastable network states sustained by recurrent activity, while down-states represent a recovery phase where network excitability is reset, erasing memory of past activity.