In vivo imaging of dentate gyrus mossy cells in behaving mice (Danielson et al 2017)

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Accession:206397
Mossy cells in the hilus of the dentate gyrus constitute a major excitatory principal cell type in the mammalian hippocampus, however, it remains unknown how these cells behave in vivo. Here, we have used two-photon Ca2+ imaging to monitor the activity of mossy cells in awake, behaving mice. We find that mossy cells are significantly more active than dentate granule cells in vivo, exhibit significant spatial tuning during head-fixed spatial navigation, and undergo robust remapping of their spatial representations in response to contextual manipulation. Our results provide the first characterization of mossy cells in the behaving animal and demonstrate their active participation in spatial coding and contextual representation.
Reference:
1 . Danielson NB, Turi GF, Ladow M, Chavlis S, Petrantonakis PC, Poirazi P, Losonczy A (2017) In Vivo Imaging of Dentate Gyrus Mossy Cells in Behaving Mice. Neuron 93:552-559.e4 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type:
Brain Region(s)/Organism: Dentate gyrus;
Cell Type(s): Dentate gyrus granule cell; Dentate gyrus basket cell; Dentate gyrus hilar cell; Dentate gyrus mossy cell; Abstract integrate-and-fire adaptive exponential (AdEx) neuron;
Channel(s):
Gap Junctions:
Receptor(s): AMPA; GabaA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: Brian; Python;
Model Concept(s): Pattern Separation;
Implementer(s): Chavlis, Spyridon [schavlis at imbb.forth.gr]; Petrantonakis, Panagiotis C. ; Poirazi, Panayiota [poirazi at imbb.forth.gr];
Search NeuronDB for information about:  Dentate gyrus granule cell; GabaA; AMPA; NMDA;
#==============================================================================
# Network of Dentate gyrus based on Myers and Scharfman, Hippocampus 2008
#==============================================================================

# External input --> 100 cells, PoissonGroup??
# Granule cells --> 500 cells into 20 clusters, ModelNeuronSimple_ver2
# Basket cell (GABAergic) --> 1 per cluster (20 cells)
# Hilar mossy cells --> 20 per 500 granule cells
# HIPP --> 10 per 500 granule cells
#
#==============================================================================
# ****************************************************************************
#==============================================================================
# CONNECTIONS
# 1. input ---> granule cells : each to 20% of granule cells randomly (excitation)
# 2. input ---> HIPP : each to 20% of HIPP randomly (excitation)
# 3. mossy ---> granule cells: each to 20% randomly (excitation)
# 4. HIPP ---> granule cells: each to 20% randomly (inhibition- GABA / excitation)
# 5. granule cells ---> mossy cells: eack to 20% randomly (excitation)
# 6. basket cells <---> granule cell: one-to-all (feedback inhibition - excitation)
#

#==============================================================================
# Network of Dentate gyrus based on Myers and Scharfman, Hippocampus 2008
#==============================================================================

# External input --> 100 cells, PoissonGroup??
# Granule cells --> 500 cells into 20 clusters, ModelNeuronSimple_ver2
# Basket cell (GABAergic) --> 1 per cluster (20 cells)
# Hilar mossy cells --> 20 per 500 granule cells
# HIPP --> 10 per 500 granule cells
#
#==============================================================================
# ****************************************************************************
#==============================================================================
# CONNECTIONS
# 1. input ---> granule cells : each to 20% of granule cells randomly (excitation)
# 2. input ---> HIPP : each to 20% of HIPP randomly (excitation)
# 3. mossy ---> granule cells: each to 20% randomly (excitation)
# 4. HIPP ---> granule cells: each to 20% randomly (inhibition- GABA / excitation)
# 5. granule cells ---> mossy cells: eack to 20% randomly (excitation)
# 6. basket cells <---> granule cell: one-to-all (feedback inhibition - excitation)
#

from brian import *
from brian.library.ionic_currents import *
from brian.library.IF import *
import time
import os

print "\nBuilding the Network... "
start_timestamp = time.time()

reinit(states = True)
clear(erase = True, all = True)

#=======================================================================================================================
# CONNECTIVITY PARAMETERS

# General parameters
E_nmda     =   0      * mV       # NMDA reversal potential
E_ampa     =   0      * mV       # AMPA reversal potential
E_gaba     = -87      * mV       # GABA reversal potential
gama       =   0.072  * mV**-1   # Mg Concentration factor
alpha_nmda =   0.6    * ms**-1   # NMDA scale factor
alpha_ampa =   1      * ms**-1   # AMPA scale factor
alpha_gaba =   1      * ms**-1   # GABA scale factor

# CONDUCTANCES

# SOURCE: EC
# EC CELLS ---> GRANULE CELLS
# Supralinear dendrites - working good, discussion with Yiota
g_ampa_eg = 0.9670 * nS  # AMPA maximum conductance
g_nmda_eg = 1.0800 * g_ampa_eg

# EC CELLS ---> HIPP CELLS
g_ampa_eh = 0.24 * nS
g_nmda_eh = 1.15 * g_ampa_eh

# SOURCE: GRANULE CELLS
# GRANULE CELLS ---> BASKET CELLS
g_ampa_gb = 0.5 * nS
g_nmda_gb = 1.2 * g_ampa_gb

# GRANULE CELLS ---> MOSSY CELLS
g_ampa_gm = 0.50 * nS
g_nmda_gm = 1.05 * g_ampa_gm

# SOURCE: MOSSY CELLS
# MOSSY CELLS ---> GRANULE CELLS
g_ampa_mg = 0.9670 * nS
g_nmda_mg = 1.0800 * g_ampa_eg

# MOSSY CELLS ---> BASKET CELLS
g_ampa_mb = 0.15 * nS
g_nmda_mb = 1.10 * g_ampa_mb

# SOURCE: BASKET CELLS
# BASKET CELLS ---> GRANULE CELLS
g_gaba_bg = 0.6 * nS

# SOURCE: HIPP CELLS
# HIPP CELLS ---> GRANULE CELLS
g_gaba_hg = 0.5 * nS
#=======================================================================================================================

scale_fac = 4
N_input   = 100*scale_fac
N_granule = 500*scale_fac
N_basket  =  25*scale_fac
N_mossy   =  20*scale_fac
N_hipp    =  10*scale_fac


#=======================================================================================================================
# INPUT CELLS (ENTORHINAL CORTEX)
Input_ec = PoissonGroup(N_input)

#=======================================================================================================================

#=======================================================================================================================
# Parameters
gl_g      =   2.57   * nS  # leakage conductance
El_g      = -87.00   * mV  # reversal-resting potential
Cm_g      =   0.08   * nF  # membrane capacitance
v_th_g    = -56.00   * mV  # threshold potential
v_reset_g = -74.00   * mV  # reset potential

# Synaptic Reversal Potentials
E_nmda =  0.0  * mV  # NMDA reversal potential
E_ampa =  0.0  * mV  # AMPA reversal potential
E_gaba = -86.0 * mV  # GABA reversal potential

# AMPA/NMDA/GABA Model Parameters
gamma        = 0.04 * mV**-1 # the steepness of Mg sensitivity of Mg unblock
Mg           = 2.0  # [mM]--mili Molar - the extracellular Magnesium concentration
eta          = 0.2 # [mM**-1] -1- mili Molar **(-1) - Magnesium sensitivity of unblock
alpha_nmda_g = 2.0  * ms**-1
alpha_ampa   = 1.0  * ms**-1
alpha_gaba   = 1.0  * ms**-1


t_nmda_decay_g = 50.0  * ms  # NMDA decay time constant
t_nmda_rise_g  =  0.33 * ms  # NMDA rise time constant
t_ampa_decay_g =  2.0  * ms  # AMPA decay time constant
t_ampa_rise_g  =  0.1  * ms  # AMPA rise time constant

# GABAergic Input from basket cells/hipp cells
g_gaba_g       = 2.8  * nS  # GABA maximum conductance
t_gaba_decay_g = 6.8  * ms  # GABA decay time constant
t_gaba_rise_g  = 0.9  * ms  # GABA rise time constant


g_ampa_gn = 0*nS
g_nmda_gn = 0*nS

g_gaba_g = 0*nS
# AHP patrameters
tau_ahp = 45.0 * ms
g_ahp   =  0.2 * nS

# Synaptic current equations @ SOMA
eq_soma = Equations('''
I_syn_g = I_nmda_eg + I_ampa_eg + I_nmda_mg + I_ampa_mg + I_nmda_gn + I_ampa_gn + I_gaba_bg +I_gaba_hg + I_Sahp : amp
I_nmda_eg = g_nmda_eg*(vm - E_nmda)*s_nmda_eg/(1.0 + eta*Mg*exp(-gamma*vm))                                     : amp
I_ampa_eg = g_ampa_eg*(vm - E_ampa)*s_ampa_eg                                                                   : amp
s_nmda_eg                                                                                                       : 1
s_ampa_eg                                                                                                       : 1
I_nmda_mg = g_nmda_mg*(vm - E_nmda)*s_nmda_mg/(1.0 + eta*Mg*exp(-gamma*vm))                                     : amp
I_ampa_mg = g_ampa_mg*(vm - E_ampa)*s_ampa_mg                                                                   : amp
s_nmda_mg                                                                                                       : 1
s_ampa_mg                                                                                                       : 1
I_gaba_bg = g_gaba_bg*(vm - E_gaba)*s_gaba_bg                                                                   : amp
s_gaba_bg                                                                                                       : 1
I_gaba_hg = g_gaba_hg*(vm - E_gaba)*s_gaba_hg                                                                   : amp
s_gaba_hg                                                                                                       : 1
I_nmda_gn = g_nmda_gn*(vm - E_nmda)*s_nmda_gn*(1.0 + eta*Mg*exp(-gamma*vm))                                     : amp
I_ampa_gn = g_ampa_gn*(vm - E_ampa)*s_ampa_gn                                                                   : amp
s_nmda_gn                                                                                                       : 1
s_ampa_gn                                                                                                       : 1
I_Sahp                                                                                                          : amp
dI_Sahp/dt = (g_ahp*(vm-El_g)-I_Sahp)/tau_ahp                                                                   : amp
''')

# Soma equation
granule_eqs  = MembraneEquation(Cm_g)
granule_eqs += leak_current(gl_g, El_g)
granule_eqs += IonicCurrent('I = I_syn_g : amp')
granule_eqs += eq_soma


granule = NeuronGroup(N_granule, model = granule_eqs, threshold = 'vm > v_th_g',
                     reset = 'vm = v_reset_g; I_Sahp += 0.0450*nA',
                     refractory = 20 * ms, compile = True, freeze = True)

# Initialization of membrane potential
granule.vm = El_g


#Clustering of granule cells
counter = 20
N_cl = len(granule)/counter
granule_cl = {}
for gran in xrange(N_cl):
    granule_cl[gran] = granule.subgroup(counter)
#=======================================================================================================================

#=======================================================================================================================
# BASKET CELLS

# Parameters
gl_b         =  18.054  * nS # leakage conductance
El_b         = -52      * mV # reversal-resting potential
Cm_b         =   0.1393 * nF # membrane capacitance
v_th_b       = -39      * mV # threshold potential
v_reset_b    = -45      * mV # reset potential
DeltaT       =   2      * mV # slope factor


#AMPA/NMDA Kinetics
t_nmda_decay_b = 130.0  * ms # NMDA decay time constant
t_nmda_rise_b  =  10.0  * ms # NMDA rise time constant
t_ampa_decay_b =   4.2  * ms # AMPA decay time constant
t_ampa_rise_b  =   1.2  * ms # AMPA rise time constant

# NOISE
noise_b = PoissonGroup(20, 3*Hz)
g_nmda_bn       =   2.5 * nS # NMDA maximum conductance
g_ampa_bn       =   3.5 * nS # AMPA maximum conductance
t_nmda_decay_bn = 130   * ms # NMDA decay time constant
t_nmda_rise_bn  =  10   * ms # NMDA rise time constant
t_ampa_decay_bn =   4.2 * ms # AMPA decay time constant
t_ampa_rise_bn  =   1.2 * ms # AMPA rise time constant


# Synaptic current equations
eq_soma_b = Equations('''
I_syn_b = I_nmda_gb + I_ampa_gb + I_nmda_mb + I_ampa_mb + I_nmda_bn + I_ampa_bn     : amp
I_nmda_gb = g_nmda_gb*(vm - E_nmda)*s_nmda_gb*(1.0/(1 + exp(-gama*vm)*(1.0/3.57)))  : amp
I_ampa_gb = g_ampa_gb*(vm - E_ampa)*s_ampa_gb                                       : amp
s_nmda_gb                                                                           : 1
s_ampa_gb                                                                           : 1
I_nmda_mb = g_nmda_mb*(vm - E_nmda)*s_nmda_mb*(1.0/(1 + exp(-gama*vm)*(1.0/3.57)))  : amp
I_ampa_mb = g_ampa_mb*(vm - E_ampa)*s_ampa_mb                                       : amp
s_nmda_mb                                                                           : 1
s_ampa_mb                                                                           : 1
I_nmda_bn  = g_nmda_bn*(vm - E_nmda)*s_nmda_bn*(1.0/(1 + exp(-gama*vm)*(1.0/3.57))) : amp
I_ampa_bn  = g_ampa_bn*(vm - E_ampa)*s_ampa_bn                                      : amp
s_nmda_bn                                                                           : 1
s_ampa_bn                                                                           : 1
''')

# Brette-Gerstner
basket_eqs = Brette_Gerstner(Cm_b, gl_b, El_b, v_th_b, DeltaT, tauw = 100 * ms, a = .1 * nS)
basket_eqs += IonicCurrent('I = I_syn_b : amp')
basket_eqs += eq_soma_b

basket = NeuronGroup(N_basket, model = basket_eqs, threshold = 'vm > v_th_b',
                     reset = AdaptiveReset(Vr=v_reset_b, b = 0.0205*nA),
                     refractory = 2 * ms, compile = True)

# Initialization of membrane potential
basket.vm = El_b

basket_cl = {}
for bb in xrange(N_cl):
    basket_cl[bb] = basket.subgroup(1)
#=======================================================================================================================


#=======================================================================================================================
# MOSSY CELLS

# Parameters
gl_m           =   7.53   * nS           # leakage conductance
El_m           = -64      * mV           # reversal-resting potential
Cm_m           =   0.621  * nfarad       # membrane capacitance
v_th_m         = -42      * mV           # threshold potential
v_reset_m      = -49      * mV           # reset potential
DeltaT_m       =   2      * mV

#AMPA/NMDA Kinetics
t_nmda_decay_m = 100     * ms  # NMDA decay time constant
t_nmda_rise_m  =   4     * ms  # NMDA rise time constant
t_ampa_decay_m =   6.2   * ms  # AMPA decay time constant
t_ampa_rise_m  =   0.5   * ms  # AMPA rise time constant

# NOISE
noise_m = PoissonGroup(30, 4*Hz)
g_nmda_mn       =   1.165  * nS # NMDA maximum conductance
g_ampa_mn       =   3.7    * nS # AMPA maximum conductance
t_nmda_decay_mn = 100      * ms # NMDA decay time constant
t_nmda_rise_mn  =   4      * ms # NMDA rise time constant
t_ampa_decay_mn =   6.2    * ms # AMPA decay time constant
t_ampa_rise_mn  =   0.5    * ms # AMPA rise time constant


# Synaptic current equations
eq_soma_m = Equations('''
I_syn_m   = I_ampa_gm + I_nmda_gm + I_ampa_mn + I_nmda_mn                           : amp
I_nmda_gm = g_nmda_gm*(vm - E_nmda)*s_nmda_gm*(1.0/(1 + exp(-gama*vm)*(1.0/3.57)))  : amp
I_ampa_gm = g_ampa_gm*(vm - E_ampa)*s_ampa_gm                                       : amp
s_nmda_gm                                                                           : 1
s_ampa_gm                                                                           : 1
I_nmda_mn = g_nmda_mn*(vm - E_nmda)*s_nmda_mn*(1.0/(1 + exp(-gama*vm)*(1.0/3.57)))  : amp
I_ampa_mn = g_ampa_mn*(vm - E_ampa)*s_ampa_mn                                       : amp
s_nmda_mn                                                                           : 1
s_ampa_mn                                                                           : 1
''')

# Brette-Gerstner
mossy_eqs  = Brette_Gerstner(Cm_m, gl_m, El_m, v_th_m, DeltaT_m, tauw = 40 * ms, a = 2 * nS)
mossy_eqs += IonicCurrent('I = I_syn_m : amp')
mossy_eqs += eq_soma_m

mossy = NeuronGroup(N_mossy, model = mossy_eqs, threshold = 'vm > v_th_m',
                     reset = AdaptiveReset(Vr=v_reset_m, b = 0.2829*nA),
                     refractory = 2 * ms, compile = True)

# Initialization of membrane potential
mossy.vm = El_m
#=======================================================================================================================

#=======================================================================================================================
# HIPP CELLS
# Parameters
gl_h           =   1.930  * nS # leakage conductance
El_h           = -59      * mV # reversal-resting potential
Cm_h           =  0.1084  * nF # membrane capacitance
v_th_h         = -50      * mV # threshold potential
v_reset_h      = -56      * mV # reset potential
DeltaT_h       =   2      * mV # slope factor

#AMPA/NMDA Kinetics
t_nmda_decay_h = 110    * ms  # NMDA decay time constant
t_nmda_rise_h  =   4.8  * ms  # NMDA rise time constant
t_ampa_decay_h =  11.0  * ms  # AMPA decay time constant
t_ampa_rise_h  =   2.0  * ms  # AMPA rise time constant
# NOISE
noise_h = PoissonGroup(20, 4*Hz)
g_nmda_hn       =   0.2 * nS  # NMDA maximum conductance
g_ampa_hn       =   0.2 * nS  # AMPA maximum conductance
t_nmda_decay_hn = 100   * ms  # NMDA decay time constant
t_nmda_rise_hn  =  5.0  * ms  # NMDA rise time constant
t_ampa_decay_hn = 11.0  * ms  # AMPA decay time constant
t_ampa_rise_hn  =  2.0  * ms  # AMPA rise time constant

# Synaptic current equations
eq_soma_h = Equations('''
I_syn_h   = I_nmda_eh + I_ampa_eh + I_nmda_hn + I_ampa_hn                          : amp
I_nmda_eh = g_nmda_eh*(vm - E_nmda)*s_nmda_eh*1.0/(1 + exp(-gama*vm)*(1.0/3.57))   : amp
I_ampa_eh = g_ampa_eh*(vm - E_ampa)*s_ampa_eh                                      : amp
s_nmda_eh                                                                          : 1
s_ampa_eh                                                                          : 1
I_nmda_hn = g_nmda_hn*(vm - E_nmda)*s_nmda_hn*(1.0/(1 + exp(-gama*vm)*(1.0/3.57))) : amp
I_ampa_hn = g_ampa_hn*(vm - E_ampa)*s_ampa_hn                                      : amp
s_nmda_hn                                                                          : 1
s_ampa_hn                                                                          : 1
''')

# Brette-Gerstner
hipp_eqs  = Brette_Gerstner(Cm_h, gl_h, El_h, v_th_h, DeltaT_h, tauw = 93 * ms, a = .82 * nS)
hipp_eqs += IonicCurrent('I = I_syn_h : amp')
hipp_eqs += eq_soma_h

hipp = NeuronGroup(N_hipp, model = hipp_eqs, threshold = EmpiricalThreshold(threshold = v_th_h,refractory = 3*ms),
                     reset = AdaptiveReset(Vr=v_reset_h, b = 0.009*nA), compile = True, freeze = True)

# Initialization of membrane potential
hipp.vm = El_h
#=======================================================================================================================

#=======================================================================================================================
# ***************************************  C  O  N  N  E  C  T  I  O  N  S  ********************************************
#=======================================================================================================================
if not os.path.exists('ConnectivityMatrices/scale_'+str(scale_fac)):
    os.makedirs('ConnectivityMatrices/scale_'+str(scale_fac))
os.chdir('ConnectivityMatrices/scale_'+str(scale_fac))

#  EC CELLS ----> GRANULE CELLS
# Synapses at 1st branch
nmda_eqs = '''
dj_eg/dt = -j_eg / t_nmda_decay_g + alpha_nmda_g * x_eg * (1 - j_eg) : 1
dx_eg/dt = -x_eg / t_nmda_rise_g                                     : 1
wNMDA_eg                                                             : 1
'''
synNMDA_eg = Synapses(Input_ec, granule, model = nmda_eqs, pre = 'x_eg += wNMDA_eg', implicit=True, freeze=True)
granule.s_nmda_eg = synNMDA_eg.j_eg
synNMDA_eg.connect_random(Input_ec, granule, sparseness = 0.2)
synNMDA_eg.wNMDA_eg[:, :] = 1.0
synNMDA_eg.delay[:, :]    = 3 * ms
synNMDA_eg.save_connectivity('syn_eg.txt')

ampa_eqs = '''
dy_eg/dt = -y_eg / t_ampa_decay_g + alpha_ampa * h_eg * (1 - y_eg) : 1
dh_eg/dt = -h_eg / t_ampa_rise_g                                   : 1
wAMPA_eg                                                           : 1
'''
synAMPA_eg = Synapses(Input_ec, granule, model = ampa_eqs, pre = 'h_eg += wAMPA_eg', implicit=True, freeze=True)
granule.s_ampa_eg = synAMPA_eg.y_eg
synAMPA_eg.connect_random(Input_ec, granule, sparseness = 0.2)
synAMPA_eg.wAMPA_eg[:, :] = 1.0
synAMPA_eg.delay[:, :]    = 3 * ms

# EC CELLS ---> HIPP CELLS
# The NMDA/AMPA synapses @ hipp cell
nmda_eqs_eh = '''
dj_eh/dt = -j_eh / t_nmda_decay_h + alpha_nmda * x_eh * (1 - j_eh) : 1
dx_eh/dt = -x_eh / t_nmda_rise_h                                   : 1
w_ehNMDA                                                           : 1
'''
synNMDA_eh = Synapses(Input_ec, hipp, model = nmda_eqs_eh, pre = 'x_eh += w_ehAMPA', implicit=True, freeze=True)
hipp.s_nmda_eh = synNMDA_eh.j_eh
synNMDA_eh.connect_random(Input_ec, hipp, sparseness = 0.2)
synNMDA_eh.w_ehNMDA[:, :] = 1.0
synNMDA_eh.delay[:, :]    = 3.0 * ms
synNMDA_eh.save_connectivity('syn_eh.txt')

ampa_eqs_eh = '''
dy_eh/dt = -y_eh / t_ampa_decay_h + h_eh*alpha_ampa*(1 - y_eh) : 1
dh_eh/dt = -h_eh / t_ampa_rise_h                               : 1
w_ehAMPA                                                       : 1
'''
synAMPA_eh = Synapses(Input_ec, hipp, model = ampa_eqs_eh, pre = 'h_eh += w_ehAMPA', implicit=True, freeze=True)
hipp.s_ampa_eh = synAMPA_eh.y_eh
synAMPA_eh.connect_random(Input_ec, hipp, sparseness = 0.2)
synAMPA_eh.w_ehAMPA[:, :] = 1.0
synAMPA_eh.delay[:, :]    = 3.0 * ms

# GRANULE CELLS ---> MOSSY CELLS
# The NMDA/AMPA synapses @ mossy cell
nmda_eqs_gm = '''
dj_gm/dt = -j_gm / t_nmda_decay_m + alpha_nmda * x_gm * (1 - j_gm) : 1
dx_gm/dt = -x_gm / t_nmda_rise_m                                   : 1
w_gmNMDA                                                           : 1
'''
synNMDA_gm = Synapses(granule, mossy, model = nmda_eqs_gm, pre = 'x_gm += w_gmNMDA', implicit=True, freeze=True)
mossy.s_nmda_gm = synNMDA_gm.j_gm
synNMDA_gm.connect_random(granule, mossy, sparseness = 0.05)
synNMDA_gm.w_gmNMDA[:, :] = 1.0
synNMDA_gm.delay[:, :]    = 1.5 * ms
synNMDA_gm.save_connectivity('syn_gm.txt')

ampa_eqs_gm = '''
dy_gm/dt = -y_gm / t_ampa_decay_m + h_gm*alpha_ampa*(1 - y_gm) : 1
dh_gm/dt = -h_gm / t_ampa_rise_m                               : 1
w_gmAMPA                                                       : 1
'''
synAMPA_gm = Synapses(granule, mossy, model = ampa_eqs_gm, pre = 'h_gm += w_gmAMPA', implicit=True, freeze=True)
mossy.s_ampa_gm = synAMPA_gm.y_gm
synAMPA_gm.connect_random(granule, mossy, sparseness = 0.05)
synAMPA_gm.w_gmAMPA[:, :] = 1.0
synAMPA_gm.delay[:, :]    = 1.5 * ms

# GRANULE CELLS ---> BASKET CELLS
# The NMDA/AMPA synapses @ basket cell
synNMDA_gb = {}
synAMPA_gb = {}
for gtob in xrange(N_cl):
    nmda_eqs_gb = '''
    dj_gb/dt = -j_gb / t_nmda_decay_b + alpha_nmda * x_gb * (1 - j_gb) : 1
    dx_gb/dt = -x_gb / t_nmda_rise_b                                   : 1
    w_gbNMDA                                                           : 1
    '''
    synNMDA_gb[gtob] = Synapses(granule_cl[gtob], basket_cl[gtob], model = nmda_eqs_gb, pre = 'x_gb += w_gbNMDA', implicit=True, freeze=True)
    basket_cl[gtob].s_nmda_gb = synNMDA_gb[gtob].j_gb
    synNMDA_gb[gtob].connect_random(granule_cl[gtob], basket_cl[gtob], sparseness = 1.0)
    synNMDA_gb[gtob].w_gbNMDA[:, :] = 1.0
    synNMDA_gb[gtob].delay[:, :]    = 0.8 * ms

    ampa_eqs_gb = '''
    dy_gb/dt = -y_gb / t_ampa_decay_b + h_gb*alpha_ampa*(1 - y_gb) : 1
    dh_gb/dt = -h_gb / t_ampa_rise_b                               : 1
    w_gbAMPA                                                       : 1
    '''
    synAMPA_gb[gtob] = Synapses(granule_cl[gtob], basket_cl[gtob], model = ampa_eqs_gb, pre = 'h_gb += w_gbAMPA', implicit=True, freeze=True)
    basket_cl[gtob].s_ampa_gb = synAMPA_gb[gtob].y_gb
    synAMPA_gb[gtob].connect_random(granule_cl[gtob], basket_cl[gtob], sparseness = 1.0)
    synAMPA_gb[gtob].w_gbAMPA[:, :] = 1.0
    synAMPA_gb[gtob].delay[:, :]    = 0.8 * ms


# MOSSY CELLS ---> GRANULE CELLS
nmda_eqs_mg = '''
dj_mg/dt = -j_mg / t_nmda_decay_g + alpha_nmda_g * x_mg * (1 - j_mg) : 1
dx_mg/dt = -x_mg / t_nmda_rise_g                                     : 1
wNMDA_mg                                                             : 1
'''
synNMDA_mg = Synapses(mossy, granule, model = nmda_eqs_mg, pre = 'x_mg += wNMDA_mg', implicit=True, freeze=True)
granule.s_nmda_mg = synNMDA_mg.j_mg
synNMDA_mg.connect_random(mossy, granule, sparseness = 0.2)
synNMDA_mg.wNMDA_mg[:, :] = 1.0
synNMDA_mg.delay[:, :]    = 3.0 * ms
synNMDA_mg.save_connectivity('syn_mg.txt')

ampa_eqs_mg = '''
dy_mg/dt = -y_mg / t_ampa_decay_g + alpha_ampa   * h_mg * (1 - y_mg) : 1
dh_mg/dt = -h_mg / t_ampa_rise_g                                     : 1
wAMPA_mg                                                             : 1
'''
synAMPA_mg = Synapses(mossy, granule, model = ampa_eqs_mg, pre = 'h_mg += wAMPA_mg', implicit=True, freeze=True)
granule.s_ampa_mg = synAMPA_mg.y_mg
synAMPA_mg.connect_random(mossy, granule, sparseness = 0.2)
synAMPA_mg.wAMPA_mg[:, :] = 1.0
synAMPA_mg.delay[:, :]    = 3.0 * ms

# MOSSY CELL ---> BASKET CELLS
# The NMDA/AMPA synapses @ basket cell
nmda_eqs_mb = '''
dj_mb/dt = -j_mb / t_nmda_decay_b + alpha_nmda * x_mb * (1 - j_mb) : 1
dx_mb/dt = -x_mb / t_nmda_rise_b                                   : 1
wNMDA_mb                                                           : 1
'''
synNMDA_mb = Synapses(mossy, basket, model = nmda_eqs_mb, pre = 'x_mb += wNMDA_mb', implicit=True, freeze=True)
basket.s_nmda_mb = synNMDA_mb.j_mb
synNMDA_mb.connect_random(mossy, basket, sparseness = 1.0)
synNMDA_mb.wNMDA_mb[:, :] = 1.0
synNMDA_mb.delay[:, :]    = 3.0 * ms

ampa_eqs_mb = '''
dy_mb/dt = -y_mb / t_ampa_decay_b + alpha_ampa * h_mb * (1 - y_mb) : 1
dh_mb/dt = -h_mb / t_ampa_rise_b                                   : 1
wAMPA_mb                                                           : 1
'''
synAMPA_mb = Synapses(mossy, basket, model = ampa_eqs_mb, pre = 'h_mb += wAMPA_mb', implicit=True, freeze=True)
basket.s_ampa_mb = synAMPA_mb.y_mb
synAMPA_mb.connect_random(mossy, basket, sparseness = 1.0)
synAMPA_mb.wAMPA_mb[:, :] = 1.0
synAMPA_mb.delay[:, :]    = 3.0 * ms

# BASKET CELLS ----> GRANULE CELLS (INHIBITION @ soma)
# Synapses @ granule cell (soma)
syn_bg = {}
for btog in xrange(N_cl):
    gaba_eqs_bg = '''
    dz_bg/dt = -z_bg / t_gaba_decay_g + alpha_gaba * r_bg * (1 - z_bg) : 1
    dr_bg/dt = -r_bg / t_gaba_rise_g                                   : 1
    w_bg                                                               : 1
    '''
    syn_bg[btog] = Synapses(basket_cl[btog], granule_cl[btog], model = gaba_eqs_bg, pre = 'r_bg += w_bg', implicit=True, freeze=True)
    granule_cl[btog].s_gaba_bg = syn_bg[btog].z_bg
    syn_bg[btog].connect_random(basket_cl[btog], granule_cl[btog], sparseness = 1.0)
    syn_bg[btog].w_bg[:, :]  = 1.0
    syn_bg[btog].delay[:, :] = 0.85 * ms

# HIPP CELLS ----> GRANULE CELLS (INHIBITION @ distal dendrite)
gaba_eqs_hg = '''
dz_hg/dt = -z_hg / t_gaba_decay_g + alpha_gaba * r_hg * (1 - z_hg) : 1
dr_hg/dt = -r_hg / t_gaba_rise_g                                   : 1
w_hg                                                               : 1
'''
syn_hg = Synapses(hipp, granule, model = gaba_eqs_hg, pre = 'r_hg += w_hg', implicit=True, freeze=True)
granule.s_gaba_hg = syn_hg.z_hg
syn_hg.connect_random(hipp, granule, sparseness = 0.2)
syn_hg.w_hg[:, :]  = 1.0
syn_hg.delay[:, :] = 1.6 * ms
syn_hg.save_connectivity('syn_hg.txt')
#=======================================================================================================================

sim_duration = time.time() - start_timestamp
print "\nDuration of Network Building: " + str(sim_duration)

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