Example: Fig1ΒΆ

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

Fig 1C-E. Somatic voltage-clamp in a ball-and-stick model with Na channels at a particular location.

from brian2 import *
from params import *

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
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)
compartment = morpho.axon[location]
neuron.v = EL
neuron.gclamp[0] = gL*500
neuron.gNa[compartment] = gNa/neuron.area[compartment]

# Monitors
mon = StateMonitor(neuron, ['v', 'vc', 'm'], record=True)

run(duration, report='text')

subplot(221)
plot(mon[0].vc/mV,
     -((mon[0].vc - mon[0].v)*(neuron.gclamp[0]))*neuron.area[0]/nA, 'k')
xlabel('V (mV)')
ylabel('I (nA)')
xlim(-75, -45)
title('I-V curve')

subplot(222)
plot(mon[0].vc/mV, mon[compartment].m, 'k')
xlabel('V (mV)')
ylabel('m')
title('Activation curve (m(V))')

subplot(223)
# Number of simulation time steps for each volt increment in the voltage-clamp
dt_per_volt = len(mon.t)/(50*mV)
for v in [-64*mV, -61*mV, -58*mV, -55*mV]:
    plot(mon.v[:100 ,int(dt_per_volt*(v - EL))]/mV, 'k')
xlabel('Distance from soma (um)')
ylabel('V (mV)')
title('Voltage across axon')

subplot(224)
plot(mon[compartment].v/mV, mon[compartment].v/mV, 'k--')  # Diagonal
plot(mon[0].v/mV, mon[compartment].v/mV, 'k')
xlabel('Vs (mV)')
ylabel('Va (mV)')
show()
../_images/frompapers.Brette_2012.Fig1.1.png