Mean field model for Hodgkin Huxley networks of neurons (Carlu et al 2020)

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"We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology."
1 . Carlu M, Chehab O, Dalla Porta L, Depannemaecker D, Héricé C, Jedynak M, Köksal Ersöz E, Muratore P, Souihel S, Capone C, Zerlaut Y, Destexhe A, di Volo M (2020) A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models. J Neurophysiol 123:1042-1051 [PubMed]
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Model Type:
Brain Region(s)/Organism:
Cell Type(s):
Gap Junctions:
Simulation Environment: Python;
Model Concept(s): Methods;
Implementer(s): di Volo, Matteo [matteo.di-volo at];
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