[Neuroscience] Re: membrane voltage equations which one

Bill via neur-sci%40net.bio.net (by connelly.bill from gmail.com)
Sun Sep 5 18:07:56 EST 2010


Not to detract in anyway from anything R Norman said, but I have
always liked the simplicity of

dV/dt = I/C

where I = Σ Gx (Ex-V)

Gx being the conductance of the membrane to Ion x, which has a
reversal potential of Ex

On Sep 5, 3:29 am, "pennsylvaniaj... from gmail.com"
<pennsylvaniaj... from gmail.com> wrote:
> On Sep 3, 9:00 pm, r norman <r_s_nor... from comcast.net> wrote:
>
>
>
>
>
> > On Fri, 3 Sep 2010 16:18:27 -0700 (PDT), "pennsylvaniaj... from gmail.com"
>
> > <pennsylvaniaj... 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,
> > >from 5/7/2005.   When I was reading more about this I ran into the the
> > >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!
>
> I appreciate your offer and will take you up on it.
>
> I taught Mechanical Engineering for many years, and before that worked
> in medical research.  My work life as an engineer started back in 73.
> I used a slide rule when I went through school in PA.  I started to
> study Neural Networks back in 87, and wrote programs for DOD.  My life
> more or less came to an end in 92 when I became severely disabled.
>
> I was never happy when every one said that neural networks are the
> perfect model to show how the mind works.  So I started on my own to
> learn Neuroscience in hopes of building a mathematical model of a
> single neuron.    This has turned out to be a major chalange.  I am in
> the process of writing a text book "The Neuron and the math behind
> it".  I hope the book will help those in the medical field better
> understand how drugs affect the mind, especially with kids with mental
> problems.
>
> I get really stuck at times.  One due to my health and the other, I am
> stuck at home all the time.  I really miss talking to fellow facility
> members about my ideas and so on and going to a library too look up
> materials that I need.  My wife just picked up at the library "Patch
> Clamping Techniques" by Areles Molleman.  I have been trying to go by
> the papers from H and H from 52.  I cant afford journals to keep up,
> even with some thing like this, so finding this book was like
> discovering gold.
>
> Any way, I just wanted you to know more about me, since I will be
> asking many more "stupid" questions.  I apologize in advance for what
> errors that I make.  Some times my health and the drugs cause my brain
> to go south.
>
> If you happen to know of any good sites to help me, I would appreciate
> them.
>
> Thanks once again.
> Jake



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