Scale Free Avalanches in Excitatory-Inhibitory Populations of Spiking Neurons with Conductance Based Synaptic Currents

TL;DR

This paper models excitatory-inhibitory neural networks with conductance-based synapses, revealing critical avalanche dynamics at bifurcation points that resemble cortical activity patterns.

Contribution

It introduces a mean-field framework for EI spiking neurons with conductance-based synapses, identifying bifurcations associated with critical avalanche behavior.

Findings

Avalanche size and duration follow power-law distributions.

The network operates near bifurcation points with balanced excitation and inhibition.

Neuron firing is fluctuation-driven and Poisson-like near the Bogdanov-Takens point.

Abstract

We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron gain function and a linear Poisson neuron approximation which we use to study mean-field dynamics of the EI population and its bifurcations. In the low firing rate regime, the quiescent state loses stability due to saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and the saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low firing spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the firing of the individual cells is fluctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval $[V_{Rest}, V_{th}]$. Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.