.. currentmodule:: brian2

.. Fig1:

Example: Fig1
=============


        .. 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/Fig1.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 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_0/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)')
    tight_layout()
    show()
    

.. image:: ../resources/examples_images/frompapers.Brette_2012.Fig1.1.png