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# [Neuroscience] Re: membrane voltage equations which one

pennsylvaniajake from gmail.com via neur-sci%40net.bio.net (by pennsylvaniajake from gmail.com)
Fri Sep 3 18:18:27 EST 2010

```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,