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Add Wang 2002 example
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""" | ||
Decision network as in: | ||
Wang, X.-J. | ||
Probabilistic decision making by slow reverberation in cortical circuits. | ||
Neuron, 2002, 36, 955-968. | ||
Authors: Klaus Wimmer (kwimmer@crm.cat) and Marcel Stimberg | ||
""" | ||
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from brian2 import * | ||
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# ----------------------------------------------------------------------------------------------- | ||
# Set up the simulation | ||
# ----------------------------------------------------------------------------------------------- | ||
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# Stimulus and simulation parameters | ||
coh = 12.8 # coherence of random dots | ||
sigma = 4.0 * Hz # standard deviation of stimulus input | ||
mu0 = 40.0 * Hz # stimulus input at zero coherence | ||
mu1 = 40.0 * Hz # selective stimulus input at highest coherence | ||
stim_interval = 50.0 * ms # stimulus changes every 50 ms | ||
stim_on = 1000 * ms # stimulus onset | ||
stim_off = 3000 * ms # stimulus offset | ||
runtime = 4000 * ms # total simulation time | ||
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# External noise inputs | ||
N_ext = 1000 # number of external Poisson neurons | ||
rate_ext_E = 2400 * Hz / N_ext # external Poisson rate for excitatory population | ||
rate_ext_I = 2400 * Hz / N_ext # external Poisson rate for inhibitory population | ||
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# Network parameters | ||
N = 2000 # number of neurons | ||
f_inh = 0.2 # fraction of inhibitory neurons | ||
NE = int(N * (1.0 - f_inh)) # number of excitatory neurons (1600) | ||
NI = int(N * f_inh) # number of inhibitory neurons (400) | ||
fE = 0.15 # coding fraction | ||
subN = int(fE * NE) # number of neurons in decision pools (240) | ||
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# Neuron parameters | ||
El = -70.0 * mV # resting potential | ||
Vt = -50.0 * mV # firing threshold | ||
Vr = -55.0 * mV # reset potential | ||
CmE = 0.5 * nF # membrane capacitance for pyramidal cells (excitatory neurons) | ||
CmI = 0.2 * nF # membrane capacitance for interneurons (inhibitory neurons) | ||
gLeakE = 25.0 * nS # membrane leak conductance of excitatory neurons | ||
gLeakI = 20.0 * nS # membrane leak conductance of inhibitory neurons | ||
refE = 2.0 * ms # refractory periodof excitatory neurons | ||
refI = 1.0 * ms # refractory period of inhibitory neurons | ||
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# Synapse parameters | ||
V_E = 0. * mV # reversal potential for excitatory synapses | ||
V_I = -70. * mV # reversal potential for inhibitory synapses | ||
tau_AMPA = 2.0 * ms # AMPA synapse decay | ||
tau_NMDA_rise = 2.0 * ms # NMDA synapse rise | ||
tau_NMDA_decay = 100.0 * ms # NMDA synapse decay | ||
tau_GABA = 5.0 * ms # GABA synapse decay | ||
alpha = 0.5 * kHz # saturation of NMDA channels at high presynaptic firing rates | ||
C = 1 * mmole # extracellular magnesium concentration | ||
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# Synaptic conductances | ||
gextE = 2.1 * nS # external -> excitatory neurons (AMPA) | ||
gextI = 1.62 * nS # external -> inhibitory neurons (AMPA) | ||
gEEA = 0.05 * nS / NE * 1600 # excitatory -> excitatory neurons (AMPA) | ||
gEIA = 0.04 * nS / NE * 1600 # excitatory -> inhibitory neurons (AMPA) | ||
gEEN = 0.165 * nS / NE * 1600 # excitatory -> excitatory neurons (NMDA) | ||
gEIN = 0.13 * nS / NE * 1600 # excitatory -> inhibitory neurons (NMDA) | ||
gIE = 1.3 * nS / NI * 400 # inhibitory -> excitatory neurons (GABA) | ||
gII = 1.0 * nS / NI * 400 # inhibitory -> inhibitory neurons (GABA) | ||
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# Synaptic footprints | ||
Jp = 1.7 # relative synaptic strength inside a selective population (1.0: no potentiation)) | ||
Jm = 1.0 - fE * (Jp - 1.0) / (1.0 - fE) | ||
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# Neuron equations | ||
# Note the "(unless refractory)" statement serves to clamp the membrane voltage during the refractory period; | ||
# otherwise the membrane potential continues to be integrated but no spikes are emitted. | ||
eqsE = """ | ||
label : integer (constant) # label for decision encoding populations | ||
dV/dt = (- gLeakE * (V - El) - I_AMPA - I_NMDA - I_GABA - I_AMPA_ext + I_input) / CmE : volt (unless refractory) | ||
I_AMPA = s_AMPA * (V - V_E) : amp | ||
ds_AMPA / dt = - s_AMPA / tau_AMPA : siemens | ||
I_NMDA = gEEN * s_NMDA_tot * (V - V_E) / ( 1 + exp(-0.062 * V/mvolt) * (C/mmole / 3.57) ) : amp | ||
s_NMDA_tot : 1 | ||
I_GABA = s_GABA * (V - V_I) : amp | ||
ds_GABA / dt = - s_GABA / tau_GABA : siemens | ||
I_AMPA_ext = s_AMPA_ext * (V - V_E) : amp | ||
ds_AMPA_ext / dt = - s_AMPA_ext / tau_AMPA : siemens | ||
I_input : amp | ||
ds_NMDA / dt = - s_NMDA / tau_NMDA_decay + alpha * x * (1 - s_NMDA) : 1 | ||
dx / dt = - x / tau_NMDA_rise : 1 | ||
""" | ||
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eqsI = """ | ||
dV/dt = (- gLeakI * (V - El) - I_AMPA - I_NMDA - I_GABA - I_AMPA_ext) / CmI : volt (unless refractory) | ||
I_AMPA = s_AMPA * (V - V_E) : amp | ||
ds_AMPA / dt = - s_AMPA / tau_AMPA : siemens | ||
I_NMDA = gEIN * s_NMDA_tot * (V - V_E) / ( 1 + exp(-0.062 * V/mvolt) * (C/mmole / 3.57) ): amp | ||
s_NMDA_tot : 1 | ||
I_GABA = s_GABA * (V - V_I) : amp | ||
ds_GABA / dt = - s_GABA / tau_GABA : siemens | ||
I_AMPA_ext = s_AMPA_ext * (V - V_E) : amp | ||
ds_AMPA_ext / dt = - s_AMPA_ext / tau_AMPA : siemens | ||
""" | ||
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# Neuron populations | ||
popE = NeuronGroup(NE, model=eqsE, threshold='V > Vt', reset='V = Vr', refractory=refE, method='euler', name='popE') | ||
popI = NeuronGroup(NI, model=eqsI, threshold='V > Vt', reset='V = Vr', refractory=refI, method='euler', name='popI') | ||
popE1 = popE[:subN] | ||
popE2 = popE[subN:2 * subN] | ||
popE3 = popE[2 * subN:] | ||
popE1.label = 0 | ||
popE2.label = 1 | ||
popE3.label = 2 | ||
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# Recurrent excitatory -> excitatory connections mediated by AMPA receptors | ||
C_EE_AMPA = Synapses(popE, popE, 'w : siemens', on_pre='s_AMPA += w', delay=0.5 * ms, method='euler', name='C_EE_AMPA') | ||
C_EE_AMPA.connect() | ||
C_EE_AMPA.w[:] = gEEA | ||
C_EE_AMPA.w["label_pre == label_post and label_pre < 2"] = gEEA*Jp | ||
C_EE_AMPA.w["label_pre != label_post and label_post < 2"] = gEEA*Jm | ||
# Note that this produces the following structure of excitatory connections: | ||
# | ||
# | from E1 from E2 from E3 | ||
# --------------------------------- | ||
# to E1 | Jp Jm Jm | ||
# to E2 | Jm Jp Jm | ||
# to E3 | 1 1 1 | ||
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# Recurrent excitatory -> inhibitory connections mediated by AMPA receptors | ||
C_EI_AMPA = Synapses(popE, popI, on_pre='s_AMPA += gEIA', delay=0.5 * ms, method='euler', name='C_EI_AMPA') | ||
C_EI_AMPA.connect() | ||
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# Recurrent excitatory -> excitatory connections mediated by NMDA receptors | ||
C_EE_NMDA = Synapses(popE, popE, on_pre='x_pre += 1', delay=0.5 * ms, method='euler', name='C_EE_NMDA') | ||
C_EE_NMDA.connect(j='i') | ||
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# Dummy population to store the summed activity of the three populations | ||
NMDA_sum_group = NeuronGroup(3, 's : 1', name='NMDA_sum_group') | ||
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# Sum the activity according to the subpopulation labels | ||
NMDA_sum = Synapses(popE, NMDA_sum_group, 's_post = s_NMDA_pre : 1 (summed)', name='NMDA_sum') | ||
NMDA_sum.connect(j='label_pre') | ||
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# Propagate the summed activity to the NMDA synapses | ||
NMDA_set_total_E = Synapses(NMDA_sum_group, popE, | ||
'''w : 1 (constant) | ||
s_NMDA_tot_post = w*s_pre : 1 (summed)''', name='NMDA_set_total_E') | ||
NMDA_set_total_E.connect() | ||
NMDA_set_total_E.w = 1 | ||
NMDA_set_total_E.w["i == label_post and label_post < 2"] = Jp | ||
NMDA_set_total_E.w["i != label_post and label_post < 2"] = Jm | ||
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# Recurrent excitatory -> inhibitory connections mediated by NMDA receptors | ||
NMDA_set_total_I = Synapses(NMDA_sum_group, popI, | ||
'''s_NMDA_tot_post = s_pre : 1 (summed)''', name='NMDA_set_total_I') | ||
NMDA_set_total_I.connect() | ||
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# Recurrent inhibitory -> excitatory connections mediated by GABA receptors | ||
C_IE = Synapses(popI, popE, on_pre='s_GABA += gIE', delay=0.5 * ms, method='euler', name='C_IE') | ||
C_IE.connect() | ||
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# Recurrent inhibitory -> inhibitory connections mediated by GABA receptors | ||
C_II = Synapses(popI, popI, on_pre='s_GABA += gII', delay=0.5 * ms, method='euler', name='C_II') | ||
C_II.connect() | ||
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# External inputs (fixed background firing rates) | ||
extinputE = PoissonInput(popE, 's_AMPA_ext', N_ext, rate_ext_E, gextE) | ||
extinputI = PoissonInput(popI, 's_AMPA_ext', N_ext, rate_ext_I, gextI) | ||
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# Stimulus input (updated every 50ms) | ||
stiminputE1 = PoissonGroup(subN, rates=0*Hz, name='stiminputE1') | ||
stiminputE2 = PoissonGroup(subN, rates=0*Hz, name='stiminputE2') | ||
stiminputE1.run_regularly("rates = int(t > stim_on and t < stim_off) * (mu0 + coh / 100.0 * mu1 + sigma*randn())", dt=stim_interval) | ||
stiminputE2.run_regularly("rates = int(t > stim_on and t < stim_off) * (mu0 - coh / 100.0 * mu1 + sigma*randn())", dt=stim_interval) | ||
C_stimE1 = Synapses(stiminputE1, popE1, on_pre='s_AMPA_ext += gextE', name='C_stimE1') | ||
C_stimE1.connect(j='i') | ||
C_stimE2 = Synapses(stiminputE2, popE2, on_pre='s_AMPA_ext += gextE', name='C_stimE2') | ||
C_stimE2.connect(j='i') | ||
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# ----------------------------------------------------------------------------------------------- | ||
# Run the simulation | ||
# ----------------------------------------------------------------------------------------------- | ||
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# Set initial conditions | ||
popE.s_NMDA_tot = tau_NMDA_decay * 10 * Hz * 0.2 | ||
popI.s_NMDA_tot = tau_NMDA_decay * 10 * Hz * 0.2 | ||
popE.V = Vt - 2 * mV | ||
popI.V = Vt - 2 * mV | ||
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# Record spikes of excitatory neurons in the decision encoding populations | ||
SME1 = SpikeMonitor(popE1, record=True) | ||
SME2 = SpikeMonitor(popE2, record=True) | ||
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# Record population activity | ||
R1 = PopulationRateMonitor(popE1) | ||
R2 = PopulationRateMonitor(popE2) | ||
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# Record input | ||
E1 = StateMonitor(stiminputE1, 'rates', record=0, dt=1*ms) | ||
E2 = StateMonitor(stiminputE2, 'rates', record=0, dt=1*ms) | ||
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# Run the simulation | ||
run(runtime, report='stdout', profile=True) | ||
print(profiling_summary()) | ||
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# Show results | ||
fig, axs = plt.subplots(4, 1, sharex=True, layout='constrained', gridspec_kw={'height_ratios': [2, 2, 2, 1]}) | ||
axs[0].plot(SME1.t / ms, SME1.i, '.', markersize=2, color='darkred') | ||
axs[0].set(ylabel='population 1', ylim=(0, subN)) | ||
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axs[1].plot(SME2.t / ms, SME2.i, '.', markersize=2, color='darkblue') | ||
axs[1].set(ylabel='population 2', ylim=(0, subN)) | ||
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axs[2].plot(R1.t / ms, R1.smooth_rate(window='flat', width=100 * ms) / Hz, color='darkred') | ||
axs[2].plot(R2.t / ms, R2.smooth_rate(window='flat', width=100 * ms) / Hz, color='darkblue') | ||
axs[2].set(ylabel='Firing rate (Hz)') | ||
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axs[3].plot(E1.t / ms, E1.rates[0] / Hz, color='darkred') | ||
axs[3].plot(E2.t / ms, E2.rates[0] / Hz, color='darkblue') | ||
axs[3].set(ylabel='Input (Hz)', xlabel='Time (ms)') | ||
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fig.align_ylabels(axs) | ||
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plt.show() |