Scale free avalanches in excitatory-inhibitory populations of spiking neurons with conductance based synaptic currents

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 $$[V_{Rest}, V_{th}]$$ [ V Rest , V th ] . Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.

Empirical mode decomposition of local field potential data from optogenetic experiments

“…Power laws in critically self-organized systems extend past the size distribution of neural activity avalanches found from in vitro (Beggs and Plenz, 2003 ; Mazzoni et al, 2007 ; Pasquale et al, 2008 ) and in vivo (Petermann et al, 2009 ; Hahn et al, 2010 ; Capek et al, 2023 ; Salners et al, 2023 ) experiments. Such power laws include different macroscopically measurable quantities, such as the duration distribution of functional connections in EEG recordings (Lee et al, 2010 ), the duration of neural avalanches (Ehsani and Jost, 2023 ), and the power spectrum. While most studies found that a power-law exponent of neural avalanche duration is around −1.5 (Beggs and Plenz, 2003 ; Millman et al, 2010 ; Cowan et al, 2013 ; Hesse and Gross, 2014 ), steeper exponents were induced by dopamine modulation (Stewart and Plenz, 2006 ), and by D1 receptor antagonists (Gireesh and Plenz, 2008 ).…”

“…In our experiments, the IMF energy scales with the instantaneous frequency obtained from Hilbert-Huang transform as energy ∝ f −ξ with an average power law exponent ξ≈1.4. While our study on mPFC of mice is the only one we could find that covers a very broad frequency range 2–2,000 Hz, our results support the criticality hypothesis and previously reported critical exponents for avalanche size of ξ = 1.5 in awake rhesus monkeys (Petermann et al, 2009 ), acute mPFC slices of adult rats (Stewart and Plenz, 2006 ), mature organotypic cultures and acute slices of rat cortex (Beggs and Plenz, 2003 ), superficial cortex of awake mice (Capek et al, 2023 ), in vivo and in vitro rat cortical layer 2/3 (Gireesh and Plenz, 2008 ), adult cats under anesthesia (Hahn et al, 2010 ), dissociated cortical neurons from rat embryos cultured onto micro-electrode arrays (Pasquale et al, 2008 ), and in conductance-based computational models (Ehsani and Jost, 2023 ).…”

Model-Agnostic Neural Mean Field With The Refractory SoftPlus Transfer Function

“…We are interested in modeling neurons in the asynchronous irregular state observed in biological systems, which computational experiments have shown occurs when spiking is driven by fluctuations rather than drift [34, 41, 50, 51]. Even where both drift-driven and fluctuation-driven neurons coexist, drift-driven neurons have been described as the predictable background input to the computational activity of fluctuation-driven neurons [52].…”

“…Mean-field models based on the diffusion approximation and the approximate transfer function of [17] have been applied to a variety of different model neurons [39], have been studied in terms of bifurcation theory [40, 41], and have been compared to biological data [19]. However, the sigmoidal shape of this transfer function does not match analytical results [31, 42].…”

A Neuromechanical Control Model For Rhythmic and Discrete Movements Based on Central Pattern Generator (CPG)

“…The intersection of the nullcline diagram, which is related to the system's input, shows different neuron states [49]. The neurons are inactive when the information is such that the h-nullcline and v-nullcline intersect in the left branch of the v-nullcline, Fig.…”