Simple Hodgkin-Huxley neuron.
In [1]:
from ANNarchy import *
clear()
dt=0.01
setup(dt=dt)
HH = Neuron(
parameters = """
C = 1.0 # Capacitance
VL = -59.387 # Leak voltage
VK = -82.0 # Potassium reversal voltage
VNa = 45.0 # Sodium reveral voltage
gK = 36.0 # Maximal Potassium conductance
gNa = 120.0 # Maximal Sodium conductance
gL = 0.3 # Leak conductance
vt = 30.0 # Threshold for spike emission
I = 0.0 # External current
""",
equations = """
# Previous membrane potential
prev_V = V
# Voltage-dependency parameters
an = 0.01 * (V + 60.0) / (1.0 - exp(-0.1* (V + 60.0) ) )
am = 0.1 * (V + 45.0) / (1.0 - exp (- 0.1 * ( V + 45.0 )))
ah = 0.07 * exp(- 0.05 * ( V + 70.0 ))
bn = 0.125 * exp (- 0.0125 * (V + 70.0))
bm = 4.0 * exp (- (V + 70.0) / 80.0)
bh = 1.0/(1.0 + exp (- 0.1 * ( V + 40.0 )) )
# Alpha/Beta functions
dn/dt = an * (1.0 - n) - bn * n : init = 0.3, midpoint
dm/dt = am * (1.0 - m) - bm * m : init = 0.0, midpoint
dh/dt = ah * (1.0 - h) - bh * h : init = 0.6, midpoint
# Membrane equation
C * dV/dt = gL * (VL - V ) + gK * n**4 * (VK - V) + gNa * m**3 * h * (VNa - V) + I : midpoint
""",
spike = """
# Spike is emitted when the membrane potential crosses the threshold from below
(V > vt) and (prev_V <= vt)
""",
reset = """
# Nothing to do, it is built-in...
"""
)
pop = Population(neuron=HH, geometry=1)
pop.V = -50.0
compile()
m = Monitor(pop, ['spike', 'V', 'n', 'm', 'h'])
# Preparation
simulate(100.0)
# Current impulse for 1 ms
pop.I = 200.0
simulate(1.0)
# Reset
pop.I = 0.0
simulate(100.0)
data = m.get()
tstart = int(90.0/dt)
tstop = int(120.0/dt)
import matplotlib.pyplot as plt
plt.figure(figsize=(15, 10))
plt.subplot(2,2,1)
plt.plot(90.0 + dt*np.arange(tstop-tstart), data['V'][tstart:tstop, 0])
plt.title('V')
plt.subplot(2,2,2)
plt.plot(90.0 + dt*np.arange(tstop-tstart), data['n'][tstart:tstop, 0])
plt.title('n')
plt.ylim((0.0, 1.0))
plt.subplot(2,2,3)
plt.plot(90.0 + dt*np.arange(tstop-tstart), data['m'][tstart:tstop, 0])
plt.title('m')
plt.ylim((0.0, 1.0))
plt.subplot(2,2,4)
plt.plot(90.0 + dt*np.arange(tstop-tstart), data['h'][tstart:tstop, 0])
plt.title('h')
plt.ylim((0.0, 1.0))
plt.show()