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"""
Brette R (2013). Sharpness of spike initiation in neurons explained by compartmentalization.
PLoS Comp Biol, doi: 10.1371/journal.pcbi.1003338.
Fig. 3C-F. Kink with Nav1.6 and Nav1.2
"""
from brian2 import *
from params import *
defaultclock.dt = 0.01*ms
# Morphology
morpho = Soma(50*um) # chosen for a target Rm
morpho.axon = Cylinder(diameter=1*um, length=300*um, n=300)
location16 = 40*um # where Nav1.6 channels are placed
location12 = 15*um # where Nav1.2 channels are placed
va2 = va + 15*mV # depolarized Nav1.2
# Channels
duration = 100*ms
eqs='''
Im = gL * (EL - v) + gNa*m*(ENa - v) + gNa2*m2*(ENa - v) : amp/meter**2
dm/dt = (minf - m) / taum : 1 # simplified Na channel
minf = 1 / (1 + exp((va - v) / ka)) : 1
dm2/dt = (minf2 - m2) / taum : 1 # simplified Na channel, Nav1.2
minf2 = 1/(1 + exp((va2 - v) / ka)) : 1
gNa : siemens/meter**2
gNa2 : siemens/meter**2 # Nav1.2
Iin : amp (point current)
'''
neuron = SpatialNeuron(morphology=morpho, model=eqs, Cm=Cm, Ri=Ri,
method="exponential_euler")
compartment16 = morpho.axon[location16]
compartment12 = morpho.axon[location12]
neuron.v = EL
neuron.gNa[compartment16] = gNa_0/neuron.area[compartment16]
neuron.gNa2[compartment12] = 20*gNa_0/neuron.area[compartment12]
# Monitors
M = StateMonitor(neuron, ['v', 'm', 'm2'], record=True)
run(20*ms, report='text')
neuron.Iin[0] = gL * 20*mV * neuron.area[0]
run(80*ms, report='text')
subplot(221)
plot(M.t/ms, M[0].v/mV, 'r')
plot(M.t/ms, M[compartment16].v/mV, 'k')
plot(M.t/ms, M[compartment16].m*(80+60)-80, 'k--') # open channels
ylim(-80, 60)
xlabel('Time (ms)')
ylabel('V (mV)')
title('Voltage traces')
subplot(222)
plot(M[0].v/mV, M[compartment16].m, 'k')
plot(M[0].v/mV, 1 / (1 + exp((va - M[0].v) / ka)), 'k--')
plot(M[0].v/mV, M[compartment12].m2, 'r')
plot(M[0].v/mV, 1 / (1 + exp((va2 - M[0].v) / ka)), 'r--')
xlim(-70, 0)
xlabel('V (mV)')
ylabel('m')
title('Activation curves')
subplot(223)
dm = diff(M[0].v) / defaultclock.dt
dm40 = diff(M[compartment16].v) / defaultclock.dt
plot((M[0].v/mV)[1:], dm/(volt/second), 'r')
plot((M[compartment16].v/mV)[1:], dm40/(volt/second), 'k')
xlim(-80, 40)
xlabel('V (mV)')
ylabel('dV/dt (V/s)')
title('Phase plot')
subplot(224)
plot((M[0].v/mV)[1:], dm/(volt/second), 'r')
plot((M[compartment16].v/mV)[1:], dm40/(volt/second), 'k')
plot((M[0].v/mV)[1:], 10 + 0*dm/(volt/second), 'k--')
xlim(-70, -40)
ylim(0, 20)
xlabel('V (mV)')
ylabel('dV/dt (V/s)')
title('Phase plot(zoom)')
tight_layout()
show()
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