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The equations for the gating variables are all well and good in
theory, but in practice, how does one compute them? This is done by a
technique known as the voltage clamp. One holds the voltage as a fixed
value and then changes it by some incremental amount. The current that
passes is then measured. Lets take, for example, the squid axon model
of Hodgkin and Huxley. Suppose that we chemically block the sodium
channel. (There are many different pharmacological agents that can be
used to block different channels. Sodium is blocked by tetrodotoxin, TTX,
found in the puffer fish. Tetraethylammonium , TEA, blocks certain
kinds of potassium channels.) The the current passed is due solely to
the leak, the capacitance, and the leak. Since the capacitative
current is just a short pulse and is zero otherwise, we can ignore
that. The current is thus:

*I*(*t*) = *g*_{L} (*V*-*E*_{L})+*g*_{K}(*t*)(*V*-*E*_{K})

We know the voltage and the reversal potentials, so we can solve for
the time-dependent conductance:
Now, the idea is that the conductance should be of the form:
where
For a fixed value of voltage, this is just a linear differential
equation which has a solution:
By using a series of different initial voltages and voltage jumps, we
can first find the best power, *p* to fit the data. Then we can find
the maximal value of the conductance. Finally, we can use the above
formula to fit the conductance to a series of exponential curves and
use these to find and for each value of the
voltage. For gates that have both activation and inactivation, the
voltage clamp is a little trickier, but not all that bad. With the
advent of channel blockers, it is now a fairly standard (though by no
means easy!) experimental protocol. A paper illustrating the technique
applied to a calcium current in the thalamus is Coulter et al
J. Physiol. London, 414:587-604.

** Next:** Some common currents in
** Up:** Voltage gated channels
** Previous:** Voltage gated channels
*G. Bard Ermentrout*

*1/29/1998*