# [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)
Sun Apr 5 10:16:47 EST 2009

```On Sun, 5 Apr 2009 01:29:16 -0700 (PDT), "Bill.Connelly"
<connelly.bill from gmail.com> wrote:

>I appriciate the technical limitations of ACTUALLY performing voltage
>clamp, it's just I was hoping to get an equation that relates dVcmd/dt
>to Itotal, on the basis of Rm, Rs and Cm. I'm starting to assume such
>an equation doesn't exist. If you think it does, I would deeply
>appriciate if you could give it to me. But some people think you can't
>analytically explain I for any arbitraty Vcmd.
>http://www.physicsforums.com/attachment.php?attachmentid=18292&d=1238839219
>
>But I completely agree
>I=Vm/Rm + C dVm/dt.
>the voltage across the entire thing is (Vcmd).... Vcmd = IRs + Vm.
>But what explains Vm?
>Ohh... so
>So its Vm=Vcmd - Rs * Vm/Rm+C dVm/dt
>
>Is that right? And is that even solveable?

Yes, if you have actual data.

Your final equation is wrong, that is the problem.

Vcmd = I Rs + Vm  -- you have this correct.

Now just write    Vm = Vcmd - I Rs.

When doing a voltage clamp, you get a plot (or a data listing) of I
vs. t and of Vcmd vs t.  So if you know Rs, you can easily calculate
Vm.

The first post you cite says : "However, I want to be able to
calculate I and any time, in response to an arbitrary voltage." That
is the problem.  You dont CALCULATE I, you MEASURE it in a voltage
clamp.  There is no way in general to calculate it for a real membrane
because the membrane is active and Rm (or gm) changes as a function of
V.
```