.. currentmodule:: brian2

.. Fig4:

Example: Fig4
=============


        .. only:: html

            .. |launchbinder| image:: http://mybinder.org/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/frompapers/Brette_2012/Fig4.ipynb

            .. 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. 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()
    

.. image:: ../resources/examples_images/frompapers.Brette_2012.Fig4.1.png