.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/urbanczik_synapse_example.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_urbanczik_synapse_example.py: Weight adaptation according to the Urbanczik-Senn plasticity ------------------------------------------------------------ This script demonstrates the learning in a compartmental neuron where the dendritic synapses adapt their weight according to the plasticity rule by Urbanczik and Senn [1]_. In this simple setup, a spike pattern of 200 poisson spike trains is repeatedly presented to a neuron that is composed of one somatic and one dendritic compartment. At the same time, the somatic conductances are activated to produce a time-varying matching potential. After the learning, this signal is then reproduced by the membrane potential of the neuron. This script produces Fig. 1B in [1]_ but uses standard units instead of the unitless quantities used in the paper. References ~~~~~~~~~~ .. [1] R. Urbanczik, W. Senn (2014): Learning by the Dendritic Prediction of Somatic Spiking. Neuron, 81, 521-528. .. GENERATED FROM PYTHON SOURCE LINES 42-369 .. code-block:: default import numpy as np from matplotlib import pyplot as plt import nest def g_inh(amplitude, t_start, t_end): """ returns weights for the spike generator that drives the inhibitory somatic conductance. """ return lambda t: np.piecewise(t, [(t >= t_start) & (t < t_end)], [amplitude, 0.0]) def g_exc(amplitude, freq, offset, t_start, t_end): """ returns weights for the spike generator that drives the excitatory somatic conductance. """ return lambda t: np.piecewise(t, [(t >= t_start) & (t < t_end)], [lambda t: amplitude * np.sin(freq * t) + offset, 0.0]) def matching_potential(g_E, g_I, nrn_params): """ returns the matching potential as a function of the somatic conductances. """ E_E = nrn_params['soma']['E_ex'] E_I = nrn_params['soma']['E_in'] return (g_E * E_E + g_I * E_I) / (g_E + g_I) def V_w_star(V_w, nrn_params): """ returns the dendritic prediction of the somatic membrane potential. """ g_D = nrn_params['g_sp'] g_L = nrn_params['soma']['g_L'] E_L = nrn_params['soma']['E_L'] return (g_L * E_L + g_D * V_w) / (g_L + g_D) def phi(U, nrn_params): """ rate function of the soma """ phi_max = nrn_params['phi_max'] k = nrn_params['rate_slope'] beta = nrn_params['beta'] theta = nrn_params['theta'] return phi_max / (1.0 + k * np.exp(beta * (theta - U))) def h(U, nrn_params): """ derivative of the rate function phi """ k = nrn_params['rate_slope'] beta = nrn_params['beta'] theta = nrn_params['theta'] return 15.0 * beta / (1.0 + np.exp(-beta * (theta - U)) / k) # simulation params n_pattern_rep = 100 # number of repetitions of the spike pattern pattern_duration = 200.0 t_start = 2.0 * pattern_duration t_end = n_pattern_rep * pattern_duration + t_start simulation_time = t_end + 2.0 * pattern_duration n_rep_total = int(np.around(simulation_time / pattern_duration)) resolution = 0.1 nest.resolution = resolution # neuron parameters nrn_model = 'pp_cond_exp_mc_urbanczik' nrn_params = { 't_ref': 3.0, # refractory period 'g_sp': 600.0, # soma-to-dendritic coupling conductance 'soma': { 'V_m': -70.0, # initial value of V_m 'C_m': 300.0, # capacitance of membrane 'E_L': -70.0, # resting potential 'g_L': 30.0, # somatic leak conductance 'E_ex': 0.0, # resting potential for exc input 'E_in': -75.0, # resting potential for inh input 'tau_syn_ex': 3.0, # time constant of exc conductance 'tau_syn_in': 3.0, # time constant of inh conductance }, 'dendritic': { 'V_m': -70.0, # initial value of V_m 'C_m': 300.0, # capacitance of membrane 'E_L': -70.0, # resting potential 'g_L': 30.0, # dendritic leak conductance 'tau_syn_ex': 3.0, # time constant of exc input current 'tau_syn_in': 3.0, # time constant of inh input current }, # parameters of rate function 'phi_max': 0.15, # max rate 'rate_slope': 0.5, # called 'k' in the paper 'beta': 1.0 / 3.0, 'theta': -55.0, } # synapse params syns = nest.GetDefaults(nrn_model)['receptor_types'] init_w = 0.3 * nrn_params['dendritic']['C_m'] syn_params = { 'synapse_model': 'urbanczik_synapse_wr', 'receptor_type': syns['dendritic_exc'], 'tau_Delta': 100.0, # time constant of low pass filtering of the weight change 'eta': 0.17, # learning rate 'weight': init_w, 'Wmax': 4.5 * nrn_params['dendritic']['C_m'], 'delay': resolution, } """ # in case you want to use the unitless quantities as in [1]: # neuron params: nrn_model = 'pp_cond_exp_mc_urbanczik' nrn_params = { 't_ref': 3.0, 'g_sp': 2.0, 'soma': { 'V_m': 0.0, 'C_m': 1.0, 'E_L': 0.0, 'g_L': 0.1, 'E_ex': 14.0 / 3.0, 'E_in': -1.0 / 3.0, 'tau_syn_ex': 3.0, 'tau_syn_in': 3.0, }, 'dendritic': { 'V_m': 0.0, 'C_m': 1.0, 'E_L': 0.0, 'g_L': 0.1, 'tau_syn_ex': 3.0, 'tau_syn_in': 3.0, }, # parameters of rate function 'phi_max': 0.15, 'rate_slope': 0.5, 'beta': 5.0, 'theta': 1.0, } # synapse params: syns = nest.GetDefaults(nrn_model)['receptor_types'] init_w = 0.2*nrn_params['dendritic']['g_L'] syn_params = { 'synapse_model': 'urbanczik_synapse_wr', 'receptor_type': syns['dendritic_exc'], 'tau_Delta': 100.0, 'eta': 0.0003 / (15.0*15.0*nrn_params['dendritic']['C_m']), 'weight': init_w, 'Wmax': 3.0*nrn_params['dendritic']['g_L'], 'delay': resolution, } """ # somatic input ampl_exc = 0.016 * nrn_params['dendritic']['C_m'] offset = 0.018 * nrn_params['dendritic']['C_m'] ampl_inh = 0.06 * nrn_params['dendritic']['C_m'] freq = 2.0 / pattern_duration soma_exc_inp = g_exc(ampl_exc, 2.0 * np.pi * freq, offset, t_start, t_end) soma_inh_inp = g_inh(ampl_inh, t_start, t_end) # dendritic input # create spike pattern by recording the spikes of a simulation of n_pg # poisson generators. The recorded spike times are then given to spike # generators. n_pg = 200 # number of poisson generators p_rate = 10.0 # rate in Hz pgs = nest.Create('poisson_generator', n=n_pg, params={'rate': p_rate}) prrt_nrns_pg = nest.Create('parrot_neuron', n_pg) nest.Connect(pgs, prrt_nrns_pg, {'rule': 'one_to_one'}) sr = nest.Create('spike_recorder', n_pg) nest.Connect(prrt_nrns_pg, sr, {'rule': 'one_to_one'}) nest.Simulate(pattern_duration) t_srs = [ssr.get('events', 'times') for ssr in sr] nest.ResetKernel() nest.resolution = resolution """ neuron and devices """ nrn = nest.Create(nrn_model, params=nrn_params) # poisson generators are connected to parrot neurons which are # connected to the mc neuron prrt_nrns = nest.Create('parrot_neuron', n_pg) # excitatory input to the soma spike_times_soma_inp = np.arange(resolution, simulation_time, resolution) sg_soma_exc = nest.Create('spike_generator', params={'spike_times': spike_times_soma_inp, 'spike_weights': soma_exc_inp(spike_times_soma_inp)}) # inhibitory input to the soma sg_soma_inh = nest.Create('spike_generator', params={'spike_times': spike_times_soma_inp, 'spike_weights': soma_inh_inp(spike_times_soma_inp)}) # excitatory input to the dendrite sg_prox = nest.Create('spike_generator', n=n_pg) # for recording all parameters of the Urbanczik neuron rqs = nest.GetDefaults(nrn_model)['recordables'] mm = nest.Create('multimeter', params={'record_from': rqs, 'interval': 0.1}) # for recoding the synaptic weights of the Urbanczik synapses wr = nest.Create('weight_recorder') # for recording the spiking of the soma sr_soma = nest.Create('spike_recorder') # create connections nest.Connect(sg_prox, prrt_nrns, {'rule': 'one_to_one'}) nest.CopyModel('urbanczik_synapse', 'urbanczik_synapse_wr', {'weight_recorder': wr[0]}) nest.Connect(prrt_nrns, nrn, syn_spec=syn_params) nest.Connect(mm, nrn, syn_spec={'delay': 0.1}) nest.Connect(sg_soma_exc, nrn, syn_spec={'receptor_type': syns['soma_exc'], 'weight': 10.0 * resolution, 'delay': resolution}) nest.Connect(sg_soma_inh, nrn, syn_spec={'receptor_type': syns['soma_inh'], 'weight': 10.0 * resolution, 'delay': resolution}) nest.Connect(nrn, sr_soma) # simulation divided into intervals of the pattern duration for i in np.arange(n_rep_total): # Set the spike times of the pattern for each spike generator for (sg, t_sp) in zip(sg_prox, t_srs): nest.SetStatus( sg, {'spike_times': np.array(t_sp) + i * pattern_duration}) nest.Simulate(pattern_duration) # read out devices # multimeter mm_events = mm.events t = mm_events['times'] V_s = mm_events['V_m.s'] V_d = mm_events['V_m.p'] V_d_star = V_w_star(V_d, nrn_params) g_in = mm_events['g_in.s'] g_ex = mm_events['g_ex.s'] I_ex = mm_events['I_ex.p'] I_in = mm_events['I_in.p'] U_M = matching_potential(g_ex, g_in, nrn_params) # weight recorder wr_events = wr.events senders = wr_events['senders'] targets = wr_events['targets'] weights = wr_events['weights'] times = wr_events['times'] # spike recorder spike_times_soma = sr_soma.get('events', 'times') # plot results fs = 22 lw = 2.5 fig1, (axA, axB, axC, axD) = plt.subplots(4, 1, sharex=True) # membrane potentials and matching potential axA.plot(t, V_s, lw=lw, label=r'$U$ (soma)', color='darkblue') axA.plot(t, V_d, lw=lw, label=r'$V_W$ (dendrit)', color='deepskyblue') axA.plot(t, V_d_star, lw=lw, label=r'$V_W^\ast$ (dendrit)', color='b', ls='--') axA.plot(t, U_M, lw=lw, label=r'$U_M$ (soma)', color='r', ls='-') axA.set_ylabel('membrane pot [mV]', fontsize=fs) axA.legend(fontsize=fs) # somatic conductances axB.plot(t, g_in, lw=lw, label=r'$g_I$', color='r') axB.plot(t, g_ex, lw=lw, label=r'$g_E$', color='coral') axB.set_ylabel('somatic cond', fontsize=fs) axB.legend(fontsize=fs) # dendritic currents axC.plot(t, I_ex, lw=lw, label=r'$I_ex$', color='r') axC.plot(t, I_in, lw=lw, label=r'$I_in$', color='coral') axC.set_ylabel('dend current', fontsize=fs) axC.legend(fontsize=fs) # rates axD.plot(t, phi(V_s, nrn_params), lw=lw, label=r'$\phi(U)$', color='darkblue') axD.plot(t, phi(V_d, nrn_params), lw=lw, label=r'$\phi(V_W)$', color='deepskyblue') axD.plot(t, phi(V_d_star, nrn_params), lw=lw, label=r'$\phi(V_W^\ast)$', color='b', ls='--') axD.plot(t, h(V_d_star, nrn_params), lw=lw, label=r'$h(V_W^\ast)$', color='g', ls='--') axD.plot(t, phi(V_s, nrn_params) - phi(V_d_star, nrn_params), lw=lw, label=r'$\phi(U) - \phi(V_W^\ast)$', color='r', ls='-') axD.plot(spike_times_soma, 0.0 * np.ones(len(spike_times_soma)), 's', color='k', markersize=2) axD.legend(fontsize=fs) # synaptic weights fig2, axA = plt.subplots(1, 1) for i in np.arange(2, 200, 10): index = np.intersect1d(np.where(senders == i), np.where(targets == 1)) if not len(index) == 0: axA.step(times[index], weights[index], label='pg_{}'.format(i - 2), lw=lw) axA.set_title('Synaptic weights of Urbanczik synapses') axA.set_xlabel('time [ms]', fontsize=fs) axA.set_ylabel('weight', fontsize=fs) axA.legend(fontsize=fs - 4) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.000 seconds) .. _sphx_glr_download_auto_examples_urbanczik_synapse_example.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: urbanczik_synapse_example.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: urbanczik_synapse_example.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_