# Example: Izhikevich_2007

> Note

> You can launch an interactive, editable version of this example without installing any local files using the Binder service (although note that at some times this may be slow or fail to open):

STDP modulated with reward

Adapted from Fig. 1c of:

Eugene M. Izhikevich Solving the distal reward problem through linkage of STDP and dopamine signaling. Cerebral cortex 17, no. 10 (2007): 2443-2452.

Note: The variable “mode” can switch the behavior of the synapse from “Classical STDP” to “Dopamine modulated STDP”.

Author: Guillaume Dumas (Institut Pasteur) Date: 2018-08-24

    from brian2 import *

    # Parameters
    simulation_duration = 6 * second

    ## Neurons
    taum = 10*ms
    Ee = 0*mV
    vt = -54*mV
    vr = -60*mV
    El = -74*mV
    taue = 5*ms

    ## STDP
    taupre = 20*ms
    taupost = taupre
    gmax = .01
    dApre = .01
    dApost = -dApre * taupre / taupost * 1.05
    dApost *= gmax
    dApre *= gmax

    ## Dopamine signaling
    tauc = 1000*ms
    taud = 200*ms
    taus = 1*ms
    epsilon_dopa = 5e-3

    # Setting the stage

    ## Stimuli section
    input_indices = array([0, 1, 0, 1, 1, 0,
                           0, 1, 0, 1, 1, 0])
    input_times = array([ 500,  550, 1000, 1010, 1500, 1510,
                         3500, 3550, 4000, 4010, 4500, 4510])*ms
    spike_input = SpikeGeneratorGroup(2, input_indices, input_times)

    neurons = NeuronGroup(2, '''dv/dt = (ge * (Ee-v) + El - v) / taum : volt
                                dge/dt = -ge / taue : 1''',
                          threshold='v>vt', reset='v = vr',
                          method='euler')
    neurons.v = vr
    neurons_monitor = SpikeMonitor(neurons)

    synapse = Synapses(spike_input, neurons,
                       model='''s: volt''',
                       on_pre='v += s')
    synapse.connect(i=[0, 1], j=[0, 1])
    synapse.s = 100. * mV

    ## STDP section
    synapse_stdp = Synapses(neurons, neurons,
                       model='''mode: 1
                             dc/dt = -c / tauc : 1 (clock-driven)
                             dd/dt = -d / taud : 1 (clock-driven)
                             ds/dt = mode * c * d / taus : 1 (clock-driven)
                             dApre/dt = -Apre / taupre : 1 (event-driven)
                             dApost/dt = -Apost / taupost : 1 (event-driven)''',
                       on_pre='''ge += s
                              Apre += dApre
                              c = clip(c + mode * Apost, -gmax, gmax)
                              s = clip(s + (1-mode) * Apost, -gmax, gmax)
                              ''',
                       on_post='''Apost += dApost
                              c = clip(c + mode * Apre, -gmax, gmax)
                              s = clip(s + (1-mode) * Apre, -gmax, gmax)
                              ''',
                       method='euler'
                       )
    synapse_stdp.connect(i=0, j=1)
    synapse_stdp.mode = 0
    synapse_stdp.s = 1e-10
    synapse_stdp.c = 1e-10
    synapse_stdp.d = 0
    synapse_stdp_monitor = StateMonitor(synapse_stdp, ['s', 'c', 'd'], record=[0])

    ## Dopamine signaling section
    dopamine_indices = array([0, 0, 0])
    dopamine_times = array([3520, 4020, 4520])*ms
    dopamine = SpikeGeneratorGroup(1, dopamine_indices, dopamine_times)
    dopamine_monitor = SpikeMonitor(dopamine)
    reward = Synapses(dopamine, synapse_stdp, model='''''',
                                on_pre='''d_post += epsilon_dopa''',
                                method='exact')
    reward.connect()

    # Simulation
    ## Classical STDP
    synapse_stdp.mode = 0
    run(simulation_duration/2)
    ## Dopamine modulated STDP
    synapse_stdp.mode = 1
    run(simulation_duration/2)

    # Visualisation
    dopamine_indices, dopamine_times = dopamine_monitor.it
    neurons_indices, neurons_times = neurons_monitor.it
    figure(figsize=(12, 6))
    subplot(411)
    plot([0.05, 2.95], [2.7, 2.7], linewidth=5, color='k')
    text(1.5, 3, 'Classical STDP', horizontalalignment='center', fontsize=20)
    plot([3.05, 5.95], [2.7, 2.7], linewidth=5, color='k')
    text(4.5, 3, 'Dopamine modulated STDP', horizontalalignment='center', fontsize=20)
    plot(neurons_times, neurons_indices, 'ob')
    plot(dopamine_times, dopamine_indices + 2, 'or')
    xlim([0, simulation_duration/second])
    ylim([-0.5, 4])
    yticks([0, 1, 2], ['Pre-neuron', 'Post-neuron', 'Reward'])
    xticks([])
    subplot(412)
    plot(synapse_stdp_monitor.t/second, synapse_stdp_monitor.d.T/gmax, 'r-')
    xlim([0, simulation_duration/second])
    ylabel('Extracellular\ndopamine d(t)')
    xticks([])
    subplot(413)
    plot(synapse_stdp_monitor.t/second, synapse_stdp_monitor.c.T/gmax, 'b-')
    xlim([0, simulation_duration/second])
    ylabel('Eligibility\ntrace c(t)')
    xticks([])
    subplot(414)
    plot(synapse_stdp_monitor.t/second, synapse_stdp_monitor.s.T/gmax, 'g-')
    xlim([0, simulation_duration/second])
    ylabel('Synaptic\nstrength s(t)')
    xlabel('Time (s)')
    tight_layout()
    show()