Robust modulation of integrate-and-fire models (Van Pottelbergh et al 2018)

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"By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks."
1 . Van Pottelbergh T, Drion G, Sepulchre R (2018) Robust Modulation of Integrate-and-Fire Models. Neural Comput 30:987-1011 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Abstract Izhikevich neuron; Abstract integrate-and-fire adaptive exponential (AdEx) neuron; Abstract integrate-and-fire neuron;
Gap Junctions:
Simulation Environment: Brian; Brian 2;
Model Concept(s): Bifurcation; Bursting; Action Potential Initiation; Delay; Multiscale; Neuromodulation;
Implementer(s): Van Pottelbergh, Tomas [tmjv2 at];
import matplotlib.pyplot as plt
from brian2 import *
from brian_models import *


C = 1*ms
tau_s = 10*ms
tau_u = 100*ms
v_th = 30
v_f0 = -40
v_s0 = -35
v_u0 = -40
g_f = 1
g_s = 0.5
g_u = 0

v_sr = 0
dv_u = 0

t_step = 100
MQIF_eqs = MQIF_eqs + '''I = 30.0 + 20.0*sign(t/ms-t_step) : 1'''

G = NeuronGroup(1, MQIF_eqs, threshold = MQIF_threshold, reset = MQIF_reset, dt=0.05*ms, method='rk4')
G.v = -50
G.v_s = -50
G.v_u = -50
M = StateMonitor(G, ['v','I'], record=0)

spikemon = SpikeMonitor(G)


t = M.t/ms
V = M[0].v
V = (V-min(V))/(max(V)-min(V))*100.
I = M[0].I
I = 105.+(I-min(I))/(max(I)-min(I))*10.

# Draw spikes
for ti in spikemon.t:
    i = int(ti / G.dt)
    V[i] = 100.

# Plot
plt.plot(t, V, t, I)

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