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# [Neuroscience] Re: membrane voltage equations which one

r norman via neur-sci%40net.bio.net (by r_s_norman from comcast.net)
Fri Sep 3 12:09:29 EST 2010

```On Fri, 3 Sep 2010 09:39:47 -0700 (PDT), "pennsylvaniajake from gmail.com"
<pennsylvaniajake from gmail.com> wrote:

>What equation is used to find the membrane voltage in a neuron?
>
>eq1.  membrane voltage = membrane current x specific membrane
>resistance x (1 - Exp ^ (-time/tau).
>
>eq2.  membrane voltage = (1/capacitance) x (current x voltage/
>resistance)
>
>eq1 from "The Neuron cell and Molecular Biology" I.B. Levitan & L.K>
>Kaczmarek, 3rd ed.
>eq2 from Principles of Neural Science", Kandel, Schwartz, Jessell, 4th
>ed
>
>They both are talking about the patch clamp technique.

Thumbing through Kandel et al. 4th ed. chapters 7. 8, and 9 I can't
find anything at all like your eq. 2.  That is a good thing because
your eq. 2 doesn't make any sense at all and would never appear in
that or any other text.

The simple fact of physics is that membrane current is capacitative
current plus ionic current.  Writing out the equations for those two
current components in terms of voltage you get

Im = C dVm/dt + Vm/Rm
where Im is total membrane current,
Vm is membrane potential
Rm is membrane resistance.

If you know Im, then Vm is the solution to this differential equation.

Under voltage clamp conditions when Vm is constant, then dVm/dt is
zero so Im = Vm/Rm or Vm = Im Rm, which is something similar to your
Eq. 1 without the exponential stuff.

If you are NOT in voltage clamp and pass a rectangular current pulse
through the membrane, the voltage will vary as the solution to the
differential equation and you get your Eq. 1 including the exponential
stuff.  This has nothing whatsoever to do with patch clamp.

I can't imagine where you got Eq. 2.  Could you provide a page number?

```