# [Neuroscience] Re: Equation that explains the behaviour of a circuit in voltage clamp

r norman via neur-sci%40net.bio.net (by r_s_norman from comcast.net)
Fri Apr 3 09:32:09 EST 2009

```On Thu, 2 Apr 2009 21:04:39 -0700 (PDT), "Bill.Connelly"
<connelly.bill from gmail.com> wrote:

>Thanks,
>
>> Icap = C dV/dt = 0 because during voltage clamp, the voltage is
>> ordinarily constant.  Of course, there is an enormous transient
>> capacitative current at the time of the voltage step.
>
>Aah, that is exactly where I am having the issue. What happens during
>the voltage step. Now I appreciate at the point of the step, dV/dt =
>infinity (or close enough), so Icap is infinity, and the capcitor
>fills instantly. However, because of the series resistance of the
>electrode, peak delta I = delta V * Rs. But this is where I fall over.
>Because what happens during Non-step voltages (ramps etc).
>
>I also get that in a parallel RC circuit
>
>Itot = V/Rm + C *  dV/dt
>
>But that leaves me in the same position, with dV/dt = infinity. So it
>needs some kind of modifier, but I can't figure it out.

You just accept that there is an enormous spike of capacitative
current that the equipment can handle and recover from quickly.  If
course it is not infinite, but if you integrate the very large current
over the very short duration of the interval, you get the total charge
necessary to change the voltage by the step, Cm times the step
voltage.  The capacitative current is so large that it is "off screen"
and doesn't show in the clamp records except as a very short gap.

My impression of the history is that K.C. Cole, who actually invented
the voltage clamp, worried that the "backwards" inward current flow
immediately after the step was some sort of instrumental artifact
resulting from that enormous capacitative current spike and spent a
tremendous amount of time trying to figure out if it was real or not.
Hodgkin and Huxley, on the other hand, used Cole's idea of the
circuitry but didn't worry about it and just accepted the results as
real.  They then went on to show that that inward component was the
Sodium inrush and the rest (including Nobel Prizes) is history.
Certainly Cole would have done the same thing, but just a little while
later.

If you use non-step clamp voltages, you just calculate the dV/dt term
and subtract the capacitative component from the total current to get
the pure ionic component.  It is not hard to measure the capacitance.
For a ramp it is very simple because dV/dt is constant during the
ramp.  Again, any variation in current must be caused by variation in
ion conductance.

```