Novel Kuramoto model with inhibition dynamics modeling scale-free avalanches and synchronization in neuronal cultures

TL;DR

The paper tackles how neuronal cultures exhibit both scale-free avalanche activity and synchronized bursts, challenging purely critical or purely oscillatory explanations. It develops a biologically grounded two-population active Kuramoto model with inhibition dynamics and validates it against hiPSC-derived cortical networks at different E:I ratios, reproducing bimodal avalanche distributions, inter-time crossovers, and memory-like correlations. Key findings include robust bimodal $P(S)$ and $P(T)$ with hyperscaling relations, two-regime inter-event times, and a crossover in conditional avalanche probabilities that the model captures with inhibitory-amplitude modulation and external Poisson noise. This work supports a self-organized bistability view of brain dynamics and provides a unified mechanism linking avalanche organization, synchronization, and temporal correlations, with potential implications for understanding brain function and dysfunction.

Abstract

Neuronal cultures exhibit a complex activity, bursts, or avalanches, characterized by the coexistence of scale invariance and synchronization, quite stable with the percentage of inhibitory neurons. While this bistable behavior has been already observed in the past, the characterization of the statistical properties of avalanche activity and their temporal organization is still lacking, as well as a model able to reproduce these dynamics. Here, we analyze experimental data of human neuronal cultures with controlled percentage of inhibitory neurons and characterize their statistical properties and dynamical organization. In order to model the experimental data, we propose a novel version of the Kuramoto model for two populations of oscillators, excitatory and inhibitory, implementing successfully the inhibition dynamics. The model can fully reproduce the experimental results, confirming the existence of correlations in the temporal organization of avalanche activity and the presence of an amplification - attenuation regime, as found in the human brain.

Figures (5)

• Figure 1: Representative images of hiPSC-derived neuronal cultures. A) Neuronal network plated on a micro-electrode array (MEA) at a density of $1200$ cells/$\text{mm}^2$; electrodes are visible beneath the neuronal layer. B-C) Representative network images at DIV70 of (B) 100E and (C) 75E25I cultures. Neurons were labelled for NeuN (red) and GABA (green) to visualize the neuronal population and distinguish GABAergic from glutamatergic populations. D) Raster plots of the spontaneous activity of representative 100E (on the left) and 75E25I (on the right) neuronal cultures at DIV70. A black dot and a dense band represent a detected spike and a network burst, respectively.
• Figure 2: Size and duration distributions for experimental and numerical data with superimposed theoretical power-law behavior (dashed and dot-dashed lines). Circles and squares represent samples with high or low values of the exponents $\tau$ and $\alpha$, respectively. a) Size distribution of experiments on purely excitatory networks. b) Size distribution of experiments on physiological networks. c-d) Size distributions of single- and two- population active Kuramoto model with inhibition dynamics. e) Duration distribution of experiments on purely excitatory networks. f) Duration distribution of experiments on physiological networks. g-h) Duration distributions of single- and two- population active Kuramoto model with inhibition dynamics.
• Figure 3: Conditional expectation of avalanche size $\langle S \rangle_{S|T}$ for experimental and numerical data with superimposed theoretical power-law behavior (dashed and dot-dashed lines). Circles and squares represent groups with high or low values of the exponents $\tau$ and $\alpha$, respectively. a) Experiments on purely excitatory networks. b) Experiments on physiological networks. c-d) Single- and two- population active Kuramoto model with inhibition dynamics.
• Figure 4: Inter-time distributions with superimposed theoretical power-law behavior. The crossover time can be estimated from the intersection between the two power-law regimes. a-b) Experiments on purely excitatory networks. e-f) Experiments on physiological networks. c-d-g-h) Single- and two- population active Kuramoto model with inhibition dynamics.
• Figure 5: Difference $\delta P$ between conditional probabilities of observing a difference between subsequent avalanche sizes smaller than a given value $s_0$ conditioned on the fact that their inter-time is lower than $t_0$. The crossover time can be estimated as the time when the switching between amplification and attenuation regime occurs. a-b) Experiments on purely excitatory networks. e-f) Experiments on physiological networks. c-d-g-h) Single- and two- population active Kuramoto model with inhibition dynamics.