Example: Vogels_et_al_2011

Inhibitory synaptic plasticity in a recurrent network model

(F. Zenke, 2011) (from the 2012 Brian twister)

Adapted from: Vogels, T. P., H. Sprekeler, F. Zenke, C. Clopath, and W. Gerstner. Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks. Science (November 10, 2011).

from brian2 import *

# ###########################################
# Defining network model parameters
# ###########################################

NE = 8000          # Number of excitatory cells
NI = NE/4          # Number of inhibitory cells

tau_ampa = 5.0*ms   # Glutamatergic synaptic time constant
tau_gaba = 10.0*ms  # GABAergic synaptic time constant
epsilon = 0.02      # Sparseness of synaptic connections

tau_stdp = 20*ms    # STDP time constant

simtime = 10*second # Simulation time

# ###########################################
# Neuron model
# ###########################################

gl = 10.0*nsiemens   # Leak conductance
el = -60*mV          # Resting potential
er = -80*mV          # Inhibitory reversal potential
vt = -50.*mV         # Spiking threshold
memc = 200.0*pfarad  # Membrane capacitance
bgcurrent = 200*pA   # External current

eqs_neurons='''
dv/dt=(-gl*(v-el)-(g_ampa*v+g_gaba*(v-er))+bgcurrent)/memc : volt (unless refractory)
dg_ampa/dt = -g_ampa/tau_ampa : siemens
dg_gaba/dt = -g_gaba/tau_gaba : siemens
'''

# ###########################################
# Initialize neuron group
# ###########################################

neurons = NeuronGroup(NE+NI, model=eqs_neurons, threshold='v > vt',
                      reset='v=el', refractory=5*ms)
Pe = neurons[:NE]
Pi = neurons[NE:]

# ###########################################
# Connecting the network
# ###########################################

con_e = Synapses(Pe, neurons, pre='g_ampa += 0.3*nS', connect='rand()<epsilon')
con_ii = Synapses(Pi, Pi, pre='g_gaba += 3*nS', connect='rand()<epsilon')

# ###########################################
# Inhibitory Plasticity
# ###########################################

eqs_stdp_inhib = '''
w : 1
dA_pre/dt=-A_pre/tau_stdp : 1 (event-driven)
dA_post/dt=-A_post/tau_stdp : 1 (event-driven)
'''
alpha = 3*Hz*tau_stdp*2  # Target rate parameter
gmax = 100               # Maximum inhibitory weight

con_ie = Synapses(Pi, Pe, model=eqs_stdp_inhib,
                  pre='''A_pre += 1.
                         w = clip(w+(A_post-alpha)*eta, 0, gmax)
                         g_gaba += w*nS''',
                  post='''A_post += 1.
                          w = clip(w+A_pre*eta, 0, gmax)
                       ''',
                  connect='rand()<epsilon')
con_ie.w = 1e-10

# ###########################################
# Setting up monitors
# ###########################################

sm = SpikeMonitor(Pe)

# ###########################################
# Run without plasticity
# ###########################################
eta = 0          # Learning rate
run(1*second)

# ###########################################
# Run with plasticity
# ###########################################
eta = 1e-2          # Learning rate
run(simtime-1*second, report='text')

# ###########################################
# Make plots
# ###########################################

i, t = sm.it
subplot(211)
plot(t/ms, i, 'k.', ms=0.25)
title("Before")
xlabel("")
yticks([])
xlim(0.8*1e3, 1*1e3)
subplot(212)
plot(t/ms, i, 'k.', ms=0.25)
xlabel("time (ms)")
yticks([])
title("After")
xlim((simtime-0.2*second)/ms, simtime/ms)
show()
../_images/frompapers.Vogels_et_al_2011.1.png