Mesoscopic dynamics from AdEx recurrent networks (Zerlaut et al., JCNS 2017)

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We present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units.
1 . Zerlaut Y, Chemla S, Chavane F, Destexhe A (2018) Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons. J Comput Neurosci 44:45-61 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s): Abstract integrate-and-fire adaptive exponential (AdEx) neuron;
Gap Junctions:
Simulation Environment: Brian 2; Python;
Model Concept(s): Vision;
import matplotlib.pylab as plt
import numpy as np

def time_freq_plot(t, freqs, data, coefs, xunits='s', yunits=''):
    if xunits=='ms':
        t = 1e3*t
    fig = plt.figure(figsize=(12,6))
    plt.subplots_adjust(wspace=.8, hspace=.5, bottom=.2)
    # signal plot
    plt.subplot2grid((3, 7), (0,0), colspan=6)
    plt.plot(t, data)
    plt.xlim([t[0], t[-1]])
    # time frequency power plot
    plt.subplot2grid((3, 7), (1,0), rowspan=2, colspan=6)
    c = plt.contourf(t, freqs, coefs, cmap='PRGn', aspect='auto')
    plt.xlabel('time ('+xunits+')')
    plt.ylabel('frequency (Hz)')
    # mean power plot over intervals
    plt.subplot2grid((3, 7), (1, 6), rowspan=2)
    # max of power over intervals
    plt.subplot2grid((3, 8), (1, 7), rowspan=2)
    plt.barh(freqs, np.power(coefs,2).mean(axis=1),\
             label='mean', height=freqs[-1]-freqs[-2])
    # plt.plot(np.power(coefs,2).max(axis=1), freqs,\
    #          label='max.')
    plt.xlabel(' power')
    plt.legend(prop={'size':'small'}, loc=(0.1,1.1))
    return fig

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