Example: Fig3ABΒΆ

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): launchbinder

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

Fig. 3. A, B. Kink with only Nav1.6 channels

from brian2 import *
from params import *

codegen.target='numpy'

defaultclock.dt = 0.025*ms

# Morphology
morpho = Soma(50*um)  # chosen for a target Rm
morpho.axon = Cylinder(diameter=1*um, length=300*um, n=300)

location = 40*um  # where Na channels are placed

# Channels
eqs='''
Im = gL*(EL - 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
gNa : siemens/meter**2
Iin : amp (point current)
'''

neuron = SpatialNeuron(morphology=morpho, model=eqs, Cm=Cm, Ri=Ri,
                       method="exponential_euler")

compartment = morpho.axon[location]
neuron.v = EL
neuron.gNa[compartment] = gNa_0/neuron.area[compartment]
M = StateMonitor(neuron, ['v', 'm'], record=True)

run(20*ms, report='text')
neuron.Iin[0] = gL * 20*mV * neuron.area[0]
run(80*ms, report='text')

subplot(121)
plot(M.t/ms, M[0].v/mV, 'r')
plot(M.t/ms, M[compartment].v/mV, 'k')
plot(M.t/ms, M[compartment].m*(80+60)-80, 'k--')  # open channels
ylim(-80, 60)
xlabel('Time (ms)')
ylabel('V (mV)')
title('Voltage traces')

subplot(122)
dm = diff(M[0].v) / defaultclock.dt
dm40 = diff(M[compartment].v) / defaultclock.dt
plot((M[0].v/mV)[1:], dm/(volt/second), 'r')
plot((M[compartment].v/mV)[1:], dm40/(volt/second), 'k')
xlim(-80, 40)
xlabel('V (mV)')
ylabel('dV/dt (V/s)')
title('Phase plot')
tight_layout()
show()
../_images/frompapers.Brette_2012.Fig3AB.1.png