opensourcebrain/HodgkinHuxleyTutorial

1Current-voltage characteristic
2==================================
3
4The current through an electronic component, with the corresponding 
5potential difference (voltage) across it is called the 
6`current-voltage characteristic <https://en.wikipedia.org/wiki/Current%E2%80%93voltage_characteristic>`_.
7
8This relationship is usually represented with an I/V curve, which is 
9just that: a plot of current versus voltage.
10
11This property is one characteristic used to when examining the 
12behaviour of electonic circuits. Given the electronic-biological 
13equivalence `discussed earlier <Electrophysiology.html>`_, it is 
14easy to see how this property would also be useful in defining 
15the behaviour of excitable membranes and their embedded ion channels.
16
17The patch-clamp protocol
18------------------------
19
20In a patch-clamp experiment, a piece of membrane is sealed off from its
21surrounding environment, such that there is almost no influence of external
22electrochemical process on what is happening in this small "patch" of 
23membrane.
24
25By applying a voltage through this membrane patch, almost perfect
26control of the membrane potential can be obtained. In this way, an
27experimenter can hold the membrane at various voltages (fig. 1) and 
28observe the current response that occurs (fig. 2).
29
30.. figure:: ../_media/fig_1_voltage_steps.png
31    :width: 500
32    :align: center
33    :alt: Voltage steps
34
35    Fig. 1
36
37    Voltage stepping in a patch-clamp protocol. Electrical potential
38    applied across a patch of membrane, holding the membrane at that
39    potential.
40
41.. figure:: ../_media/fig_2_current_vs_time.png
42    :width: 500
43    :align: center
44    :alt: Current-time plot
45
46    Fig. 2
47
48    Current-time plot for a voltage-clamped membrane patch. This 
49    represents the current change over time in response to voltage 
50    clamping.
51
52---------
53
54Making I/V plots
55----------------
56
57With this data, we can now plot a current-voltage relationship, to help
58us characterize and model the electrophysiological behaviour of the 
59patch of membrane. 
60
61We will consider two types of I/V curves here. The first is the so-called
62"peak" I/V curve, where the largest current magnitude produced at each voltage
63step is plotted against the voltage that produced it. We can see an 
64example of this in figure 3.
65
66The second type of I/V curve is called a "steady-state" I/V curve, and
67is a representation of the somewhat leveled out current at the end of 
68each voltage step, again plotted against the voltage step that produced
69it. See figure 4 for an example of this type of I/V plot.
70
71.. figure:: ../_media/fig_3_peak_iv_curve.png
72    :width: 500
73    :align: center
74    :alt: Peak I/V curve
75
76    Fig. 3
77
78    Peak I/V Curve. Plotting the maximum current at each voltage step 
79    produces a curve like this.
80
81.. figure:: ../_media/fig_4_steady_state_iv_curve.png
82    :width: 500
83    :align: center
84    :alt: Steady-state I/V curve
85
86    Fig. 4
87
88    Steady-state I/V curve. Plotting the current at the end of each 
89    voltage step gives us a curve similar to this one.
90
91-----------
92
93How does current even flow across the membrane?
94^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
95
96In the `electrophysiology <Electrophysiology.html>`_ section we looked
97at how voltage-gated ion channels influence the kinetics of excitable
98cells. It is this behaviour that we are closely examining here, by 
99holding the membrane potential at a particular level and observing
100what happens to ion flow (current) across the membrane.
101
102If we patch-clamp a larger piece of membrane, there will be many ion 
103channels exerting their effect. Technology now exists, however, that
104allows electrophysiologists to patch-clamp a *single* ion channel and 
105perform the same experiments. In this way, it is possible to obtain 
106data about individual ion channel types, and characterize their kinetics
107using I/V curves.
108
109The above figures are all examples of this type of ion channel patch
110clamping. 
111
112Using code to produce these plots
113---------------------------------
114
115At the risk of losing your trust, it must be admitted that the plots
116above were not actual biological recordings, but were instead 
117generated by *simulating* a single ion channel patch-clamp experiment.
118
119Using a `NeuroML2 model of an ion channel <https://github.com/VahidGh/ChannelWorm/blob/8e0daf66e0070c6760c26d4c27d9dec525a0ac12/models/Cav1.channel.nml>`_
120and a suite of virtual electrophysiology tools (`pyNeuroML <https://github.com/NeuroML/pyNeuroML>`_), you 
121can produce this set of curves, and a similar characterization for any 
122number of ion channel models that exist.
123
124First, make sure you have the latest version of pyNeuroML installed.
125Jump over to that project's `installation instructions <https://github.com/NeuroML/pyNeuroML#installation>`_ to get up
126and running.
127
128Now, by doing the set of commands below in your shell, you should be presented
129with the same set of plots we have been usign in this tutorial.
130
131.. code:: bash
132
133    # grab a sample channel model
134    wget https://goo.gl/yrAfhn -O Cav1.channel.nml 
135
136    # analyse it
137    pynml-channelanalysis -ivCurve Cav1.channel.nml 
138
139
140