Example: Fig4

Note

You can launch an interactive, editable version of this example without installing any local files using the Binder service (although note that at some times this may be slow or fail to open):

Brette R (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLoS Comp Biol, doi: 10.1371/journal.pcbi.1003338.

Fig. 4E-F. Spatial distribution of Na channels. Tapering axon near soma.

from brian2 import *
from params import *

defaultclock.dt = 0.025*ms

# Morphology
morpho = Soma(50*um) # chosen for a target Rm
# Tapering (change this for the other figure panels)
diameters = hstack([linspace(4, 1, 11), ones(290)])*um
morpho.axon = Section(diameter=diameters, length=ones(300)*um, n=300)

# Na channels
Na_start = (25 + 10)*um
Na_end = (40 + 10)*um
linear_distribution = True  # True is F, False is E

duration = 500*ms

# Channels
eqs='''
Im = gL*(EL - v) + gclamp*(vc - v) + gNa*m*(ENa - v) : amp/meter**2
dm/dt = (minf - m) / taum: 1  # simplified Na channel
minf = 1 / (1 + exp((va - v) / ka)) : 1
gclamp : siemens/meter**2
gNa : siemens/meter**2
vc = EL + 50*mV * t / duration : volt (shared)  # Voltage clamp with a ramping voltage command
'''

neuron = SpatialNeuron(morphology=morpho, model=eqs, Cm=Cm, Ri=Ri,
                       method="exponential_euler")
compartments = morpho.axon[Na_start:Na_end]
neuron.v = EL
neuron.gclamp[0] = gL*500

if linear_distribution:
    profile = linspace(1, 0, len(compartments))
else:
    profile = ones(len(compartments))
profile = profile / sum(profile)  # normalization

neuron.gNa[compartments] = gNa_0 * profile / neuron.area[compartments]

# Monitors
mon = StateMonitor(neuron, 'v', record=True)

run(duration, report='text')

dt_per_volt = len(mon.t) / (50*mV)
for v in [-64*mV, -61*mV, -58*mV, -55*mV, -52*mV]:
    plot(mon.v[:100, int(dt_per_volt * (v - EL))]/mV, 'k')
xlim(0, 50+10)
ylim(-65, -25)
ylabel('V (mV)')
xlabel('Location (um)')
title('Voltage across axon')
tight_layout()
show()