Merge pull request #1385 from schmitts/naud_adex_patterns

Firing patterns in the adaptive exponential integrate-and-fire model

examples/frompapers/Naud_et_al_2008_adex_firing_patterns.py

@@ -0,0 +1,178 @@
+#!/usr/bin/env python
+"""
+Firing patterns in the adaptive exponential integrate-and-fire model
+-----------------------
+Naud R et al. (2008): Firing patterns in the adaptive exponential integrate-and-fire model.
+Biol Cybern. 2008; 99(4): 335–347.
+doi:10.1007/s00422-008-0264-7
+
+Parameters adapted by P. Müller to match figures, cf. http://www.kip.uni-heidelberg.de/Veroeffentlichungen/details.php?id=3445.
+
+Sebastian Schmitt, Sebastian Billaudelle, 2022
+"""
+from brian2 import *
+import matplotlib.pyplot as plt
+
+
+def sim(ax_vm, ax_w, ax_vm_w, parameters):
+    """
+    simulate with parameters and plot to axes
+    """
+
+    # taken from Touboul_Brette_2008
+    eqs = """
+    dvm/dt = (g_l*(e_l - vm) + g_l*d_t*exp((vm-v_t)/d_t) + i_stim - w)/c_m : volt
+    dw/dt  = (a*(vm - e_l) - w)/tau_w : amp
+    """
+
+    neuron = NeuronGroup(
+        1,
+        model=eqs,
+        threshold="vm > 0*mV",
+        reset="vm = v_r; w += b",
+        method="euler",
+        namespace=parameters,
+    )
+
+    neuron.vm = parameters["e_l"]
+    neuron.w = 0
+
+    states = StateMonitor(neuron, ["vm", "w"], record=True, when="thresholds")
+
+    defaultclock.dt = 0.1 * ms
+    run(0.6 * second)
+
+    # clip membrane voltages to threshold (0 mV)
+    vms = np.clip(states[0].vm / mV, a_min=None, a_max=0)
+
+    ax_vm.plot(states[0].t / ms, vms)
+    ax_w.plot(states[0].t / ms, states[0].w / nA)
+    ax_vm_w.plot(vms, states[0].w / nA)
+
+    ax_w.sharex(ax_vm)
+    ax_vm.tick_params(labelbottom=False)
+
+    ax_vm.set_ylabel("V [mV]")
+
+    ax_w.set_xlabel("t [ms]")
+    ax_w.set_ylabel("w [nA]")
+
+    ax_vm_w.set_xlabel("V [mV]")
+    ax_vm_w.set_ylabel("w [nA]")
+
+    ax_vm_w.yaxis.tick_right()
+    ax_vm_w.yaxis.set_label_position("right")
+
+
+patterns = {
+    "tonic spiking": {
+        "c_m": 200 * pF,
+        "g_l": 10 * nS,
+        "e_l": -70.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": 2.0 * nS,
+        "tau_w": 30.0 * ms,
+        "b": 0.0 * pA,
+        "v_r": -58.0 * mV,
+        "i_stim": 500 * pA,
+    },
+    "adaptation": {
+        "c_m": 200 * pF,
+        "g_l": 12 * nS,
+        "e_l": -70.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": 2.0 * nS,
+        "tau_w": 300.0 * ms,
+        "b": 60.0 * pA,
+        "v_r": -58.0 * mV,
+        "i_stim": 500 * pA,
+    },
+    "initial burst": {
+        "c_m": 130 * pF,
+        "g_l": 18 * nS,
+        "e_l": -58.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": 4.0 * nS,
+        "tau_w": 150.0 * ms,
+        "b": 120.0 * pA,
+        "v_r": -50.0 * mV,
+        "i_stim": 400 * pA,
+    },
+    "regular bursting": {
+        "c_m": 200 * pF,
+        "g_l": 10 * nS,
+        "e_l": -58.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": 2.0 * nS,
+        "tau_w": 120.0 * ms,
+        "b": 100.0 * pA,
+        "v_r": -46.0 * mV,
+        "i_stim": 210 * pA,
+    },
+    "delayed accelerating": {
+        "c_m": 200 * pF,
+        "g_l": 12 * nS,
+        "e_l": -70.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": -10.0 * nS,
+        "tau_w": 300.0 * ms,
+        "b": 0.0 * pA,
+        "v_r": -58.0 * mV,
+        "i_stim": 300 * pA,
+    },
+    "delayed regular bursting": {
+        "c_m": 100 * pF,
+        "g_l": 10 * nS,
+        "e_l": -65.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": -10.0 * nS,
+        "tau_w": 90.0 * ms,
+        "b": 30.0 * pA,
+        "v_r": -47.0 * mV,
+        "i_stim": 110 * pA,
+    },
+    "transient spiking": {
+        "c_m": 100 * pF,
+        "g_l": 10 * nS,
+        "e_l": -65.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": 10.0 * nS,
+        "tau_w": 90.0 * ms,
+        "b": 100.0 * pA,
+        "v_r": -47.0 * mV,
+        "i_stim": 180 * pA,
+    },
+    "irregular spiking": {
+        "c_m": 100 * pF,
+        "g_l": 12 * nS,
+        "e_l": -60.0 * mV,
+        "v_t": -50.0 * mV,
+        "d_t": 2.0 * mV,
+        "a": -11.0 * nS,
+        "tau_w": 130.0 * ms,
+        "b": 30.0 * pA,
+        "v_r": -48.0 * mV,
+        "i_stim": 160 * pA,
+    },
+}
+
+# loop over all patterns and plot
+for pattern, parameters in patterns.items():
+
+    fig = plt.figure(figsize=(10, 5))
+    fig.suptitle(pattern)
+    gs = fig.add_gridspec(2, 2)
+
+    ax_vm = fig.add_subplot(gs[0, 0])
+    ax_w = fig.add_subplot(gs[1, 0])
+    ax_vm_w = fig.add_subplot(gs[:, 1])
+
+    sim(ax_vm, ax_w, ax_vm_w, parameters)
+plt.show()