Neural Network Dynamics

Theoretical analysis and numerical simulations to study the emergent dynamics in spiking neural networks

Purpose

Build a common framework to study the following aspects of neural network dynamics:

• numerical simulations of networks of Adexp single neuron models
• customized network and cellular features such as connectivity matrices or intrinsic currents
• mean-field predictions of network dynamics
• cellular integration in morphologically-detailed models

Numerical simulations

Both the spiking network and single cell simulation toolkit are built as a layer on top of the Brian2 simulator.

Installation

Using git to clone the repository and "pip" to install the package in your python environment:

git clone https://github.com/yzerlaut/neural_network_dynamics.git
pip install -r neural_network_dynamics/requirements.txt

Note you might want to use the code compilation to C code for speed, so you will need the gcc compiler, e.g. on ubuntu/debian, get it with sudo apt install build-essential.

N.B. the multicompartmental modeling in Brian2 only works with python=3.8 !

Usage

import numpy as np
import matplotlib.pylab as plt

import ntwk # THIS MODULE

# write your model details/parameters in a dictionary (N.B unit system is : ms, mV, pF, nS, pA, Hz)
Model = {
    # numbers of neurons in population
    'N_Exc':4000, 'N_Inh':1000, 'N_AffExc':400,
    # synaptic weights
    'Q_Exc_Exc':1., 'Q_Exc_Inh':1., 
    'Q_AffExc_Exc':1., 'Q_AffExc_Inh':1., 
    'Q_Inh_Exc':4., 'Q_Inh_Inh':4., 
    # synaptic time constants
    'Tse':5., 'Tsi':5.,
    # synaptic reversal potentials
    'Ee':0., 'Ei': -80.,
    # connectivity parameters
    'p_Exc_Exc':0.05, 'p_Exc_Inh':0.05, 
    'p_Inh_Exc':0.05, 'p_Inh_Inh':0.05, 
    'p_AffExc_Exc':0.5, 'p_AffExc_Inh':0.5, 
    # simulation parameters
    'dt':0.1, 'tstop': 1500., 'SEED':3, # low by default, see later
    ## ---------------------------------------------------------------------------------
    # === cellular properties (based on AdExp), population by population ===
    # --> Excitatory population (Exc, recurrent excitation)
    'Exc_Gl':10., 'Exc_Cm':200.,'Exc_Trefrac':5.,
    'Exc_El':-70., 'Exc_Vthre':-50., 'Exc_Vreset':-70., 'Exc_deltaV':2.,
    'Exc_a':0., 'Exc_b': 40., 'Exc_tauw':500,
    # --> Inhibitory population (Inh, recurrent inhibition)
    'Inh_Gl':10., 'Inh_Cm':200.,'Inh_Trefrac':5.,
    'Inh_El':-70., 'Inh_Vthre':-50., 'Inh_Vreset':-70., 'Inh_deltaV':0.5,
    'Inh_a':0., 'Inh_b': 0., 'Inh_tauw':1e9,
}

t_array = ntwk.arange(int(Model['tstop']/Model['dt']))*Model['dt']

# build the model
NTWK = ntwk.build.populations(Model, ['Exc', 'Inh'],
                              AFFERENT_POPULATIONS=['AffExc'],
                              with_raster=True, with_Vm=4,
			      verbose=True)
ntwk.build.recurrent_connections(NTWK, SEED=5, verbose=True)
Faff_array = 4.+4*np.exp(-(t_array-1000)**2/2/100**2) # afferent input
# afferent excitation onto cortical excitation and inhibition
for i, tpop in enumerate(['Exc', 'Inh']): # both on excitation and inhibition
    ntwk.stim.construct_feedforward_input(NTWK, tpop, 'AffExc',
                                          t_array, Faff_array,
					  verbose=True, SEED=32)
# initialize
ntwk.build.initialize_to_rest(NTWK)
# run
network_sim = ntwk.collect_and_run(NTWK, verbose=True)
# store data
ntwk.recording.write_as_hdf5(NTWK, filename='RS-FS_data.h5')
# plot
fig, AX = ntwk.plots.activity_plots(ntwk.recording.load_dict_from_hdf5('RS-FS_data.h5'))
plt.show()

see the demo script

Examples/demo

See the demo folder for more examples

Content

1. Network Dynamics

Organized into different parts:

Simulations:

• cells

  The list of cells available. See "cells"

• build

  Build the network elements and architecture (equations, connectivity, ...)

• stim

  Stimulate the network with afferent activity.

• recording

  The recording module.

• scan

  Perform parameter scans.

• analysis

  Tools to analyze network simulations

• plots

  Plot network simulation results.

Theory

• theory

  Implementation of the mean-field approach to network dynamics characterization. Based on the Markovian approach formulated in El Boustani & Destexhe (2009) Neural Comp.

• transfer_functions.

  The core of the mean-field approach. The function that accounts for the statistical "rate-behavior" of a population of neurons in the network. Procedure to make semi-analytical characterizations of transfer functions. See Zerlaut et al. (2016) J. Physiol for the transfer function characterization and Zerlaut et al. (2018) J. Comp. Neurosci. for its use in predicting network dynamics.

• Configs

  • configs.

    Stores some cellular and configurations to be easily re-used.

2. Single Cell Integration

• Morphologies

  See the available morphologies

• Synaptic Inputs

  See the synaptic inputs properties

• Active Mechanisms

  See the active mechanisms properties

3. Vision

in progress [...]