Example: Vogels_et_al_2011 (frompapers)

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 brian import *

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

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

w = 1.*nS           # Basic weight unit
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

eta = 1e-2          # Learning rate
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*w*v+g_gaba*(v-er)*w)+bgcurrent)/memc : volt
dg_ampa/dt = -g_ampa/tau_ampa : 1
dg_gaba/dt = -g_gaba/tau_gaba : 1
'''

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

neurons=NeuronGroup(NE+NI,model=eqs_neurons,threshold=vt,reset=el,refractory=5*ms)
Pe=neurons.subgroup(NE)
Pi=neurons.subgroup(NI)

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

con_e = Connection(Pe,neurons,'g_ampa',weight=0.3,sparseness=epsilon)
con_ie = Connection(Pi,Pe,'g_gaba',weight=1e-10,sparseness=epsilon)
con_ii = Connection(Pi,Pi,'g_gaba',weight=3,sparseness=epsilon)

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

sm = SpikeMonitor(Pe)

# ###########################################
# Run without plasticity
# ###########################################

run(1*second)

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

alpha = 3*Hz*tau_stdp*2  # Target rate parameter
gmax = 100               # Maximum inhibitory weight

eqs_stdp_inhib = '''
dA_pre/dt=-A_pre/tau_stdp : 1
dA_post/dt=-A_post/tau_stdp : 1
'''

stdp_ie = STDP(con_ie, eqs=eqs_stdp_inhib, pre='A_pre+=1.; w+=(A_post-alpha)*eta;',
        post='A_post+=1.; w+=A_pre*eta;', wmax=gmax)

# ###########################################
# Run with plasticity
# ###########################################

run(simtime-1*second,report='text')

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

subplot(211)
raster_plot(sm,ms=1.)
title("Before")
xlabel("")
xlim(float(0.8*second/ms), float(1*second/ms))
subplot(212)
raster_plot(sm,ms=1.)
title("After")
xlim(float((simtime-0.2*second)/ms), float(simtime/ms))
show()