| Current-voltage characteristic
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| ==================================
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| The current through an electronic component, with the corresponding
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| potential difference (voltage) across it is called the
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| `current-voltage characteristic <https://en.wikipedia.org/wiki/Current%E2%80%93voltage_characteristic>`_.
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| This relationship is usually represented with an I/V curve, which is
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| just that: a plot of current versus voltage.
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| This property is one characteristic used to when examining the
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| behaviour of electonic circuits. Given the electronic-biological
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| equivalence `discussed earlier <Electrophysiology.html>`_, it is
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| easy to see how this property would also be useful in defining
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| the behaviour of excitable membranes and their embedded ion channels.
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| The patch-clamp protocol
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| In a patch-clamp experiment, a piece of membrane is sealed off from its
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| surrounding environment, such that there is almost no influence of external
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| electrochemical process on what is happening in this small "patch" of
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| membrane.
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| By applying a voltage through this membrane patch, almost perfect
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| control of the membrane potential can be obtained. In this way, an
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| experimenter can hold the membrane at various voltages (fig. 1) and
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| observe the current response that occurs (fig. 2).
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| .. figure:: ../_media/fig_1_voltage_steps.png
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| :width: 500
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| :align: center
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| :alt: Voltage steps
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| Fig. 1
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| Voltage stepping in a patch-clamp protocol. Electrical potential
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| applied across a patch of membrane, holding the membrane at that
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| potential.
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| .. figure:: ../_media/fig_2_current_vs_time.png
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| :width: 500
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| :align: center
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| :alt: Current-time plot
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| Fig. 2
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| Current-time plot for a voltage-clamped membrane patch. This
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| represents the current change over time in response to voltage
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| clamping.
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| Making I/V plots
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| With this data, we can now plot a current-voltage relationship, to help
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| us characterize and model the electrophysiological behaviour of the
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| patch of membrane.
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| We will consider two types of I/V curves here. The first is the so-called
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| "peak" I/V curve, where the largest current magnitude produced at each voltage
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| step is plotted against the voltage that produced it. We can see an
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| example of this in figure 3.
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| The second type of I/V curve is called a "steady-state" I/V curve, and
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| is a representation of the somewhat leveled out current at the end of
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| each voltage step, again plotted against the voltage step that produced
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| it. See figure 4 for an example of this type of I/V plot.
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| .. figure:: ../_media/fig_3_peak_iv_curve.png
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| :width: 500
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| :align: center
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| :alt: Peak I/V curve
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| Fig. 3
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| Peak I/V Curve. Plotting the maximum current at each voltage step
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| produces a curve like this.
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| .. figure:: ../_media/fig_4_steady_state_iv_curve.png
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| :width: 500
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| :align: center
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| :alt: Steady-state I/V curve
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| Fig. 4
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| Steady-state I/V curve. Plotting the current at the end of each
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| voltage step gives us a curve similar to this one.
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| How does current even flow across the membrane?
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| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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| In the `electrophysiology <Electrophysiology.html>`_ section we looked
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| at how voltage-gated ion channels influence the kinetics of excitable
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| cells. It is this behaviour that we are closely examining here, by
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| holding the membrane potential at a particular level and observing
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| what happens to ion flow (current) across the membrane.
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| If we patch-clamp a larger piece of membrane, there will be many ion
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| channels exerting their effect. Technology now exists, however, that
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| allows electrophysiologists to patch-clamp a *single* ion channel and
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| perform the same experiments. In this way, it is possible to obtain
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| data about individual ion channel types, and characterize their kinetics
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| using I/V curves.
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| The above figures are all examples of this type of ion channel patch
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| clamping.
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| Using code to produce these plots
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| At the risk of losing your trust, it must be admitted that the plots
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| above were not actual biological recordings, but were instead
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| generated by *simulating* a single ion channel patch-clamp experiment.
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| Using a `NeuroML2 model of an ion channel <https://github.com/VahidGh/ChannelWorm/blob/8e0daf66e0070c6760c26d4c27d9dec525a0ac12/models/Cav1.channel.nml>`_
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| and a suite of virtual electrophysiology tools (`pyNeuroML <https://github.com/NeuroML/pyNeuroML>`_), you
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| can produce this set of curves, and a similar characterization for any
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| number of ion channel models that exist.
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| First, make sure you have the latest version of pyNeuroML installed.
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| Jump over to that project's `installation instructions <https://github.com/NeuroML/pyNeuroML#installation>`_ to get up
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| and running.
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| Now, by doing the set of commands below in your shell, you should be presented
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| with the same set of plots we have been usign in this tutorial.
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| .. code:: bash
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| # grab a sample channel model
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| wget https://goo.gl/yrAfhn -O Cav1.channel.nml
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| # analyse it
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| pynml-channelanalysis -ivCurve Cav1.channel.nml
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