# [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 20:00:41 EST 2010

```On Fri, 3 Sep 2010 16:18:27 -0700 (PDT), "pennsylvaniajake from gmail.com"
<pennsylvaniajake from gmail.com> wrote:

>On Sep 3, 1:09 pm, r norman <r_s_nor... from comcast.net> wrote:
>> On Fri, 3 Sep 2010 09:39:47 -0700 (PDT), "pennsylvaniaj... from gmail.com"
>>
>> <pennsylvaniaj... 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?
>
>Sorry for the error.   I made several errors, one being the
>reference.  I was solving the equation: current - voltage/resistance =
>Capacitance times dv/dt using a Mathematica.  It came about using the
>book "Biophsics of Computation by C. Koch, 1999.  See fig. 1.3 on page
>11.  The result that I got from the program came from a newsgroup,
>other equation, and that made me question from way back in 2005.
>Sorry for the error.
>
>Thanks for you help and patience.

Not at all.  I taught this stuff for years and years (before my
retirement) and know all the pitfalls students fall into.

Please ask away.  That is what this news group is supposed to be for!

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