.. currentmodule:: brian2

.. Fig3CF:

Example: Fig3CF
===============


        .. only:: html

            .. |launchbinder| image:: file:///usr/share/doc/python-brian-doc/docs/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/frompapers/Brette_2012/Fig3CF.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. 3C-F. Kink with Nav1.6 and Nav1.2

::

    from brian2 import *
    from params import *
    
    defaultclock.dt = 0.01*ms
    
    # Morphology
    morpho = Soma(50*um) # chosen for a target Rm
    morpho.axon = Cylinder(diameter=1*um, length=300*um, n=300)
    
    location16 = 40*um  # where Nav1.6 channels are placed
    location12 = 15*um  # where Nav1.2 channels are placed
    
    va2 = va + 15*mV  # depolarized Nav1.2
    
    # Channels
    duration = 100*ms
    eqs='''
    Im = gL * (EL - v) + gNa*m*(ENa - v) + gNa2*m2*(ENa - v) : amp/meter**2
    dm/dt = (minf - m) / taum : 1  # simplified Na channel
    minf = 1 / (1 + exp((va - v) / ka)) : 1
    dm2/dt = (minf2 - m2) / taum : 1 # simplified Na channel, Nav1.2
    minf2 = 1/(1 + exp((va2 - v) / ka)) : 1
    gNa : siemens/meter**2
    gNa2 : siemens/meter**2  # Nav1.2
    Iin : amp (point current)
    '''
    
    neuron = SpatialNeuron(morphology=morpho, model=eqs, Cm=Cm, Ri=Ri,
                           method="exponential_euler")
    compartment16 = morpho.axon[location16]
    compartment12 = morpho.axon[location12]
    neuron.v = EL
    neuron.gNa[compartment16] = gNa_0/neuron.area[compartment16]
    neuron.gNa2[compartment12] = 20*gNa_0/neuron.area[compartment12]
    # Monitors
    M = StateMonitor(neuron, ['v', 'm', 'm2'], record=True)
    
    run(20*ms, report='text')
    neuron.Iin[0] = gL * 20*mV * neuron.area[0]
    run(80*ms, report='text')
    
    subplot(221)
    plot(M.t/ms, M[0].v/mV, 'r')
    plot(M.t/ms, M[compartment16].v/mV, 'k')
    plot(M.t/ms, M[compartment16].m*(80+60)-80, 'k--')  # open channels
    ylim(-80, 60)
    xlabel('Time (ms)')
    ylabel('V (mV)')
    title('Voltage traces')
    
    subplot(222)
    plot(M[0].v/mV, M[compartment16].m, 'k')
    plot(M[0].v/mV, 1 / (1 + exp((va - M[0].v) / ka)), 'k--')
    plot(M[0].v/mV, M[compartment12].m2, 'r')
    plot(M[0].v/mV, 1 / (1 + exp((va2 - M[0].v) / ka)), 'r--')
    xlim(-70, 0)
    xlabel('V (mV)')
    ylabel('m')
    title('Activation curves')
    
    subplot(223)
    dm = diff(M[0].v) / defaultclock.dt
    dm40 = diff(M[compartment16].v) / defaultclock.dt
    plot((M[0].v/mV)[1:], dm/(volt/second), 'r')
    plot((M[compartment16].v/mV)[1:], dm40/(volt/second), 'k')
    xlim(-80, 40)
    xlabel('V (mV)')
    ylabel('dV/dt (V/s)')
    title('Phase plot')
    
    subplot(224)
    plot((M[0].v/mV)[1:], dm/(volt/second), 'r')
    plot((M[compartment16].v/mV)[1:], dm40/(volt/second), 'k')
    plot((M[0].v/mV)[1:], 10 + 0*dm/(volt/second), 'k--')
    xlim(-70, -40)
    ylim(0, 20)
    xlabel('V (mV)')
    ylabel('dV/dt (V/s)')
    title('Phase plot(zoom)')
    tight_layout()
    show()
    

