Conductance-based generalized leaky integrate and fire (GLIF) neuron example

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Simple example of how to use the glif_cond neuron model for five different levels of GLIF neurons.

Four stimulation paradigms are illustrated for the GLIF model with externally applied current and spikes impinging

Voltage traces, injecting current traces, threshold traces, synaptic conductance traces and spikes are shown.

First, we import all necessary modules to simulate, analyze and plot this example.

import matplotlib.gridspec as gridspec
import matplotlib.pyplot as plt
import nest

We initialize NEST and set the simulation resolution.

nest.ResetKernel()
resolution = 0.05
nest.resolution = resolution

We create the five levels of GLIF model to be tested, i.e., lif, lif_r, lif_asc, lif_r_asc, lif_r_asc_a. For each level of GLIF model, we create a glif_cond node. The node is created by setting relative model mechanism parameters. Other neuron parameters are set as default. The five glif_cond node handles are combined as a list. Note that the default number of synaptic ports is two for spike inputs. One port is excitation receptor with time constant being 0.2 ms and reversal potential being 0.0 mV. The other port is inhibition receptor with time constant being 2.0 ms and -85.0 mV. Note that users can set as many synaptic ports as needed for glif_cond by setting array parameters tau_syn and E_rev of the model.

n_lif = nest.Create(
    "glif_cond", params={"spike_dependent_threshold": False, "after_spike_currents": False, "adapting_threshold": False}
)
n_lif_r = nest.Create(
    "glif_cond", params={"spike_dependent_threshold": True, "after_spike_currents": False, "adapting_threshold": False}
)
n_lif_asc = nest.Create(
    "glif_cond", params={"spike_dependent_threshold": False, "after_spike_currents": True, "adapting_threshold": False}
)
n_lif_r_asc = nest.Create(
    "glif_cond", params={"spike_dependent_threshold": True, "after_spike_currents": True, "adapting_threshold": False}
)
n_lif_r_asc_a = nest.Create(
    "glif_cond", params={"spike_dependent_threshold": True, "after_spike_currents": True, "adapting_threshold": True}
)

neurons = n_lif + n_lif_r + n_lif_asc + n_lif_r_asc + n_lif_r_asc_a

For the stimulation input to the glif_cond neurons, we create one excitation spike generator and one inhibition spike generator, each of which generates three spikes; we also create one step current generator and a Poisson generator, a parrot neuron(to be paired with the Poisson generator). The three different injections are spread to three different time periods, i.e., 0 ms ~ 200 ms, 200 ms ~ 500 ms, 600 ms ~ 900 ms. Configuration of the current generator includes the definition of the start and stop times and the amplitude of the injected current. Configuration of the Poisson generator includes the definition of the start and stop times and the rate of the injected spike train.

espikes = nest.Create("spike_generator", params={"spike_times": [10.0, 100.0, 150.0], "spike_weights": [20.0] * 3})
ispikes = nest.Create("spike_generator", params={"spike_times": [15.0, 99.0, 150.0], "spike_weights": [-20.0] * 3})
cg = nest.Create(
    "step_current_generator",
    params={
        "amplitude_values": [
            400.0,
        ],
        "amplitude_times": [
            200.0,
        ],
        "start": 200.0,
        "stop": 500.0,
    },
)
pg = nest.Create("poisson_generator", params={"rate": 15000.0, "start": 600.0, "stop": 900.0})
pn = nest.Create("parrot_neuron")

The generators are then connected to the neurons. Specification of the receptor_type uniquely defines the target receptor. We connect current generator to receptor 0, the excitation spike generator and the Poisson generator (via parrot neuron) to receptor 1, and the inhibition spike generator to receptor 2 of the GLIF neurons. Note that Poisson generator is connected to parrot neuron to transit the spikes to the glif_cond neuron.

nest.Connect(cg, neurons, syn_spec={"delay": resolution})
nest.Connect(espikes, neurons, syn_spec={"delay": resolution, "receptor_type": 1})
nest.Connect(ispikes, neurons, syn_spec={"delay": resolution, "receptor_type": 2})
nest.Connect(pg, pn, syn_spec={"delay": resolution})
nest.Connect(pn, neurons, syn_spec={"delay": resolution, "receptor_type": 1})

A multimeter is created and connected to the neurons. The parameters specified for the multimeter include the list of quantities that should be recorded and the time interval at which quantities are measured.

mm = nest.Create(
    "multimeter",
    params={
        "interval": resolution,
        "record_from": [
            "V_m",
            "I",
            "g_1",
            "g_2",
            "threshold",
            "threshold_spike",
            "threshold_voltage",
            "ASCurrents_sum",
        ],
    },
)
nest.Connect(mm, neurons)

A spike_recorder is created and connected to the neurons record the spikes generated by the glif_cond neurons.

sr = nest.Create("spike_recorder")
nest.Connect(neurons, sr)

Run the simulation for 1000 ms and retrieve recorded data from the multimeter and spike recorder.

nest.Simulate(1000.0)

data = mm.events
senders = data["senders"]

spike_data = sr.events
spike_senders = spike_data["senders"]
spikes = spike_data["times"]

We plot the time traces of the membrane potential (in blue) and the overall threshold (in green), and the spikes (as red dots) in one panel; the spike component of threshold (in yellow) and the voltage component of threshold (in black) in another panel; the injected currents (in strong blue), the sum of after spike currents (in cyan) in the third panel; and the synaptic conductances of the two receptors (in blue and orange) in responding to the spike inputs to the neurons in the fourth panel. We plot all these four panels for each level of GLIF model in a separated figure.

glif_models = ["lif", "lif_r", "lif_asc", "lif_r_asc", "lif_r_asc_a"]
for i in range(len(glif_models)):
    glif_model = glif_models[i]
    node_id = neurons[i].global_id
    plt.figure(glif_model)
    gs = gridspec.GridSpec(4, 1, height_ratios=[2, 1, 1, 1])
    t = data["times"][senders == 1]

    ax1 = plt.subplot(gs[0])
    plt.plot(t, data["V_m"][senders == node_id], "b")
    plt.plot(t, data["threshold"][senders == node_id], "g--")
    plt.plot(
        spikes[spike_senders == node_id],
        [max(data["threshold"][senders == node_id]) * 0.95] * len(spikes[spike_senders == node_id]),
        "r.",
    )
    plt.legend(["V_m", "threshold", "spike"])
    plt.ylabel("V (mV)")
    plt.title("Simulation of glif_cond neuron of " + glif_model)

    ax2 = plt.subplot(gs[1])
    plt.plot(t, data["threshold_spike"][senders == node_id], "y")
    plt.plot(t, data["threshold_voltage"][senders == node_id], "k--")
    plt.legend(["threshold_spike", "threshold_voltage"])
    plt.ylabel("V (mV)")

    ax3 = plt.subplot(gs[2])
    plt.plot(t, data["I"][senders == node_id], "--")
    plt.plot(t, data["ASCurrents_sum"][senders == node_id], "c-.")
    plt.legend(["I_e", "ASCurrents_sum", "I_syn"])
    plt.ylabel("I (pA)")
    plt.xlabel("t (ms)")

    ax4 = plt.subplot(gs[3])
    plt.plot(t, data["g_1"][senders == node_id], "-")
    plt.plot(t, data["g_2"][senders == node_id], "--")
    plt.legend(["G_1", "G_2"])
    plt.ylabel("G (nS)")
    plt.xlabel("t (ms)")

plt.show()