Mesoscopic dynamics from AdEx recurrent networks (Zerlaut et al JCNS 2018)

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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]
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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;
from brian2 import *

def set_spikes_from_time_varying_rate(time_array, rate_array, N, Nsyn, SEED=1):
    seed(SEED) # setting the seed !
    ## time_array in ms !!
    # so multplying rate array
    indices, times = [], []
    DT = (time_array[1]-time_array[0])
    # trivial way to generate inhomogeneous poisson events
    for it in range(len(time_array)):
        rdm_num = np.random.random(N)
        for ii in np.arange(N)[rdm_num<DT*Nsyn*rate_array[it]*1e-3]:
            indices.append(ii) # all the indicces
            times.append(time_array[it]) # all the same time !

    return array(indices), array(times)*ms

def build_up_excitatory_feedforward_connections_for_2_pop(Pops, syn_conn_matrix,\
                                                          input_on_exc, input_on_inh,\
    exc_neurons, inh_neurons = Pops
    P = syn_conn_matrix
    # number of synapses per neuron
    Nsyn = P[0,0]['p_conn']*(1-P[0,0]['gei'])*P[0,0]['Ntot']

    # feedforward input on INH pop
    indices, times = set_spikes_from_time_varying_rate(time_array, input_on_inh,\
                                                       inh_neurons.N, Nsyn,\
    input_inh = SpikeGeneratorGroup(inh_neurons.N, indices, times)
    fdfrwd_to_inh = Synapses(input_inh, inh_neurons, on_pre='Gei_post += w',\
    # feedforward input on EXC pop
    indices2, times2 = set_spikes_from_time_varying_rate(time_array, input_on_exc,\
                                                       exc_neurons.N, Nsyn,\
    input_exc = SpikeGeneratorGroup(exc_neurons.N, indices2, times2)
    fdfrwd_to_exc = Synapses(input_exc, exc_neurons, on_pre='Gee_post += w',\

    return input_exc, fdfrwd_to_exc, input_inh, fdfrwd_to_inh

def build_up_excitatory_feedforward_connections_for_exc_only(exc_neurons, syn_conn_matrix,\
                                                             time_array, rate_array, SEED=1):

    P = syn_conn_matrix
    # number of synapses per neuron
    Nsyn = P[0,0]['p_conn']*(1-P[0,0]['gei'])*P[0,0]['Ntot']
    # feedforward input on EXC pop
    indices, times = set_spikes_from_time_varying_rate(time_array, rate_array,\
                                                       exc_neurons.N, Nsyn,\
    input_exc_aff = SpikeGeneratorGroup(exc_neurons.N, indices, times)
    fdfrwd_to_exc_aff = Synapses(input_exc_aff, exc_neurons, on_pre='Gee_post += w',\

    return input_exc_aff, fdfrwd_to_exc_aff

# def build_up_inhibitory_feedforward_connections_for_2_pop(Pops, syn_conn_matrix,\
#                                                           time_array, rate_array):

#     exc_neurons, inh_neurons = Pops
#     P = syn_conn_matrix

#     inh_input_exc, inh_fdfrwd_to_exc = set_stim_from_time_varying_rate(time_array, rate_array, exc_neurons,\
#                                                     ON_PRE='Gie_post += w')
#     inh_fdfrwd_to_exc.w = P[1,0]['Q']*nS

#     inh_input_inh, inh_fdfrwd_to_inh = set_stim_from_time_varying_rate(time_array, rate_array, inh_neurons,\
#                                                     ON_PRE='Gii_post += w')
#     inh_fdfrwd_to_inh.w = P[1,1]['Q']*nS
#     return inh_input_exc, inh_fdfrwd_to_exc, inh_input_inh, inh_fdfrwd_to_inh