Asynchronous irregular and up/down states in excitatory and inhibitory NNs (Destexhe 2009)

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Accession:126466
"Randomly-connected networks of integrate-and-fire (IF) neurons are known to display asynchronous irregular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. ... Here, we investigate the occurrence of AI states in networks of nonlinear IF neurons, such as the adaptive exponential IF (Brette-Gerstner-Izhikevich) model. This model can display intrinsic properties such as low-threshold spike (LTS), regular spiking (RS) or fast-spiking (FS). We successively investigate the oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks using such models. ..."
Reference:
1 . Destexhe A (2009) Self-sustained asynchronous irregular states and Up-Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons. J Comput Neurosci 27:493-506 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Abstract integrate-and-fire adaptive exponential (AdEx) neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: PyNN;
Model Concept(s): Spatio-temporal Activity Patterns;
Implementer(s):
/
demo_TCX
prevPyNN
README
demo_cx_Up-Down.py
demo_cx05_N=500b_LTS.py
LICENSE.txt
plot.py
                            
"""
 Network of IF cells - Sustained Activity

 Cortical network consisting of N=500 EX and IN cells, with
 80-20% proportion, and random connectivity
 The excitatory cells also include a proportion of LTS cells

 calculate the nb of spikes for each cell -> "numspikes_cx05_LTS500b.dat"
 calculate spiketimes -> "spiketimes_cx05_LTS500b.dat"
 write the Vm of one cell to "Vm170_cx05_LTS500b.dat" for control
 print the values of the connectivity

 cortical excitatory inputs 61.03425  -> from 1.9 % of exc cells
 cortical inhibitory inputs 14.465    -> from 1.8 % of inh cells

 This file: all cells described by IF-BG4 mechanism (RS + FS cells
 for cortex), with correct storage of spike times (also faster)
 This file: interneurons are FS, adaptation of 0.005 for RS.
 Proportion of LTS cells: 5%
  => sustained activity (AI state)
  
 Refactoring of original Python conversion of Alain's Hoc file, putting more
 of the code into the cell classes.
 Replaced multiStimexp, multiAMPAexp and multiGABAAexp with ExpSyn
 Replaced IF_BG4 with AdExpIF
 Replaced gen mechanism with NetSimFD
 Replaced locally-defined AdExp cell class with BretteGerstnerIF from pyNN.neuron
 Replaced list of cells and list of spike sources by PyNN Populations
 Replaced direct NetCon creation with pyNN.connect()
 Can now run with any PyNN-supported simulator.
 
Original Hoc version by Alain Destexhe
Python version by Andrew Davison

License: Modified BSD (see LICENSE.txt)

 Updated for PyNN 0.8, 2016
"""


from __future__ import print_function
import sys
from math import sqrt, pi
from pyNN.random import NumpyRNG, RandomDistribution
SIMULATOR = sys.argv[-1]
exec("import pyNN.%s as pyNN" % SIMULATOR)
    
#-----------------------------------------------------------------
#  Parameters
#-----------------------------------------------------------------

# General parameters

SEED_LTS = 428577
SEED_CONN = 193566
SEED_GEN = 983651

DT = 0.1                                        # (ms) Time step
TSTART  = 0                                     
TSTOP   = 5000
V_INIT  = -60.0

# Cell parameters

LENGTH          = sqrt(20000/pi)                # in um
DIAMETER        = sqrt(20000/pi)                # in um
AREA            = 1e-8 * pi * LENGTH * DIAMETER # membrane area in cm2
TAU             = 20                            # time constant in ms
CAPACITANCE     = 1                             # capacitance in muF/cm2
G_L             = 1e-3 * CAPACITANCE / TAU      # leak conductance in S/cm2
V_REST          = -60                           # resting potential     

a_RS            = 0.001 
b_RS            = 0.1   # full adaptation
b_RS            = 0.005 # weaker adaptation
a_LTS           = 0.02
b_LTS           = 0.0
a_FS            = 0.001
b_FS            = 0.0

TAU_W           = 600
DELTA           = 2.5

# Spike parameters

VTR             = -50           # threshold in mV
VTOP            = 40            # top voltage during spike in mV
VBOT            = -60           # reset voltage in mV
REFRACTORY      = 5.0/2         # refractory period in ms (correction for a bug in IF_CG4)

# Synapse parameters

scale = 1               # scaling factor (>1 = more synapses)

TAU_E           = 5             # excitation time constant in ms
TAU_I           = 10            # inhibition time constant in ms
V_E             = 0             # excitatory reversal potential
V_I             = -80           # inhibitory reversal potential
AMPA_GMAX       = 0.006/scale
GABA_GMAX       = 0.067/scale

# Network parameters
# Cortex
N_CX = 500              # Number of cortical cells
N_I = int(N_CX/5.0)     # Number of Cx inibitory cells
N_E = N_CX - N_I        # Number of excitatory cells
PROB_CONNECT = 0.02*scale       # Connection probability in cortex
PROB_CONNECT = 0.02*2000/N_CX   # prob renormalized to size

C_I = int(N_I*PROB_CONNECT)     # nb inh synapses per neuron
C_E = int(N_E*PROB_CONNECT)     # nb exc synapses per neuron
N_GEN = N_CX            # total number of cells

PROP = 0.05             # proportion of cortical LTS cells

# Stimulation parameters

N_STIM          = int(N_CX/5)   # number of neurons stimulated
STOPSTIM        = 50            # duration of stimulation (ms)
NSYN_STIM       = 20            # nb of stim (exc) synapses per neuron
STIM_INTERVAL   = 70            # mean interval between stims (ms)

MODEL_ID        = "cx05_LTS500b_%s" % SIMULATOR

NEURONS_TO_RECORD = [170, 0, N_STIM-1]

# NEURON-specific parameters

NEURONS_TO_PLOT = [0, 10, 20, 30, N_E, N_E+10]
USE_GUI = False   # } NEURON-specific 
USE_CVODE = False # }


#-----------------------------------------------------------------
#  Create cells
#-----------------------------------------------------------------

# we now use a standard cell model from PyNN, so there is nothing to do here


#-----------------------------------------------------------------
#  Create Network
#-----------------------------------------------------------------

rLTS = NumpyRNG(seed=SEED_LTS)
nLTS = 0

def netCreate ():
    global nLTS, neurons
    RS_parameters = {
        'cm': 1000*AREA*CAPACITANCE, 'tau_m': TAU, 'v_rest': V_REST,
        'v_thresh': VTR, 'tau_refrac': REFRACTORY+DT,
        'v_reset': VBOT, 'v_spike': VTR+1e-6, 'a': 1000.0*a_RS, 'b': b_RS,
        'tau_w': TAU_W, 'delta_T': DELTA, 'tau_syn_E': TAU_E, 'e_rev_E': V_E,
        'tau_syn_I': TAU_I, 'e_rev_I': V_I
    }
    
    LTS_parameters = RS_parameters.copy()
    LTS_parameters.update({'a': 1000.0*a_LTS, 'b': b_LTS}) # 1000 is for uS --> nS
    FS_parameters = RS_parameters.copy()
    FS_parameters.update({'a': 1000.0*a_FS, 'b': b_FS})

    neurons = pyNN.Population(N_CX, pyNN.EIF_cond_exp_isfa_ista, RS_parameters)
    for nbactual in range(0, N_E):      # create cortical cells (excitatory)
        # check if LTS cell
        if rLTS.uniform(0,1) < PROP:
            print("Cell", nbactual, "is LTS")
            neurons[nbactual].set_parameters(**LTS_parameters)
            nLTS = nLTS + 1

    for nbactual in range(N_E, N_CX):     # create cortical cells (inhibitory)
        neurons[nbactual].set_parameters(**FS_parameters)
    
    neurons.initialize(v=V_INIT, w=0.0)


#  Connect cells

rCon = NumpyRNG(seed=SEED_CONN)

PRINT = 2        # flag to print; 0=minimal, 1=verbose, 2=summary

ampa_list = []
gabaa_list = []
stimsyn_list = []

def netConnect(): # local i, j, rand, distvert, nbconn
    ne = 0
    ni = 0
    ie = 0
    ii = 0
    print("Calculate connectivity of cortical cells...")
    # scan cortical cells
    for i in range(0, N_CX):
        if PRINT==1:
           if i<N_E:
                print("Cortical EX cell ", i)
           else:
                print("Cortical IN cell ", i)
        nbconex = 0
        nbconin = 0

        # Insert excitatory inputs
        j = 0
        while (nbconex < C_E) and (j < N_E):
            rand = rCon.uniform(0.0, 1.0)
            if (i != j) and (rand <= PROB_CONNECT):
                nc = pyNN.connect(neurons[j], neurons[i], weight=AMPA_GMAX,
                                  delay=DT, receptor_type="excitatory")
                ampa_list.append(nc)
                nbconex = nbconex + 1    
            j = j + 1
        if PRINT==1:
            print(" - exc inputs from CX:", nbconex)
        ne = ne + nbconex
        ie = ie + 1

        # Insert inhibitory inputs
        j =  N_E
        while (nbconin < C_I) and (j < N_CX):
            rand = rCon.uniform(0.0, 1.0)
            if (i != j) and (rand <= PROB_CONNECT):
                nc = pyNN.connect(neurons[j], neurons[i], weight=GABA_GMAX,
                                  delay=DT, receptor_type="inhibitory")
                gabaa_list.append(nc)
                nbconin = nbconin + 1
            j = j + 1
        if PRINT==1:
            print(" - inh inputs from CX:", nbconin)
        ni= ni + nbconin
        ii = ii + 1

    if PRINT==2:
        print("MEAN SYNAPSES PER NEURON:")
        print("cortical excitatory inputs ", float(ne)/ie)
        print("cortical inhibitory inputs ", float(ni)/ii)

#-----------------------------------------------------------------
#  External Input
#-----------------------------------------------------------------

nstim = NSYN_STIM
rStim = NumpyRNG(seed=SEED_GEN)
stim = []

def generate_stimulus(start, stop, interval):
    rd = RandomDistribution('exponential', [interval], rng=rStim)
    t = start
    times = []
    while t < stop:
        t += rd.next()
        if t < stop:
            times.append(t)
    return times

def insertStimulation():
    print("Add stimulation of cortical neurons...")
    for i in range(0, N_STIM):
        G = pyNN.Population(nstim, pyNN.SpikeSourceArray())
        stim.append(G)
        for cell in G:
            spike_times = generate_stimulus(TSTART, STOPSTIM, STIM_INTERVAL)
            cell.spike_times = spike_times
        ncs = pyNN.connect(G, neurons[i], weight=AMPA_GMAX*scale, delay=DT,
                           receptor_type='excitatory')
        stimsyn_list.append(ncs)

#-----------------------------------------------------------------
# Simulation settings
#-----------------------------------------------------------------

pyNN.setup(DT, min_delay=DT, use_cvode=USE_CVODE, rng_seeds_seed=SEED_GEN)

#-----------------------------------------------------------------
#  Add graphs
#-----------------------------------------------------------------

g = [None]*20
ngraph = 0

def addgraph(v_min, v_max, label, colour):
    global ngraph
    ngraph = ngraph+1
    ii = ngraph-1
    g[ii] = h.Graph()
    g[ii].size(TSTART, h.tstop, v_min, v_max)
    g[ii].xaxis()
    g[ii].yaxis()
    g[ii].addexpr(label, colour, 0)
    g[ii].save_name("graphList[0].")
    h.graphList[0].append(g[ii])
   

print("")
print("=======================================================================")
print("            Network of ",N_GEN,"IF neurons in an active state")
print("=======================================================================")
print("")

#------------------------------------------------------------------------------
#  creating cells
#------------------------------------------------------------------------------
print("----[ CREATING CELLS ]----")
netCreate()

#------------------------------------------------------------------------------
#  creating network
#------------------------------------------------------------------------------
print("----[ CREATING NETWORK ]----")
netConnect()

#------------------------------------------------------------------------------
#  adding network input
#------------------------------------------------------------------------------
print("----[ ADDING NETWORK INPUT ]----")
insertStimulation()

#------------------------------------------------------------------------------
#  procedures to write spike times
#------------------------------------------------------------------------------

nspikes = []

def write_numspikes():  
    f = open("numspikes_%s.dat" % MODEL_ID, 'w')
    f.write("%g %g\n" % (N_GEN, pyNN.get_current_time())) # write nb of cells and time
    sum1 = 0
    sum2 = 0
    sum3 = 0
    sum4 = 0
    spike_counts = neurons.get_spike_counts()
    for i in range(0, N_GEN):
        nspikes = spike_counts.get(i, 0)
        f.write("%g\n" % nspikes)       # write tot number of spikes
        rate = nspikes * 1000.0 / TSTOP
        if i<N_E:
            sum1 = sum1 + rate
            sum2 = sum2 + rate**2
        else:
            sum3 = sum3 + rate
            sum4 = sum4 + rate**2
    f.close()

    sum1 = float(sum1) / N_E
    sum2 = sqrt( float(sum2)/N_E - sum1**2 )
    sum3 = float(sum3) / N_I
    sum4 = sqrt( float(sum4)/N_I - sum3**2 )
    return sum1, sum2, sum3, sum4


#-----------------------------------------------------------------
#  Graphs
#-----------------------------------------------------------------

def create_graphs():
    h('objref py')
    h.py = h.PythonObject() # lets Hoc access Python
    h.nrnmainmenu()
    h.nrncontrolmenu()
    h.steps_per_ms = 1.0/DT

    # adding graphs
    for id in NEURONS_TO_PLOT:
        addgraph(-80, 40, "py.neurons[%d]._cell.seg.v" % id, 4)

# record spikes
neurons.record('spikes')

# record the Vm         
neurons[NEURONS_TO_RECORD].record('v')

#-----------------------------------------------------------------
# Procedure to run simulation and menu
#-----------------------------------------------------------------

def run_sim(with_graphs=False):
    if with_graphs and SIMULATOR == 'neuron':
        from neuron import h, gui
        create_graphs()
        h.v_init = V_INIT
        h.init()
        h.tstop = TSTOP
        h.run()
    else:
        pyNN.run(TSTOP)

    print("Writing spikes to file...")
    rate_RS, std_RS, rate_FS, std_FS = write_numspikes()
    neurons.write_data("data_%s.pkl" % MODEL_ID)

    print("Mean rate per RS cell (Hz) = ", rate_RS)
    print(" standard deviation = ", std_RS)
    print("Mean rate per FS cell (Hz) = ", rate_FS)
    print(" standard deviation = ", std_FS)


def make_Vpanel():                    # make panel
    h.xpanel("Brette-Gerstner network")
    h.xbutton("Run simulation", "py.run_sim(1)")
    h.xpanel()


if USE_GUI and SIMULATOR == 'neuron':
    make_Vpanel()
else:
    run_sim(with_graphs=False)

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