How do you deal with equations when the denominator tends to 0?

[Bill.Connelly]

This is more of a maths question than a neuroscience question, but
I've come across it twice when dealing with neuroscience problems

1) I was trying to solve the Goldman Hodgkin Katz field equation,
which I shan't type out here in full, but it has a denonimator term of
1-e^(-z.V.F/RT) so when V=0, the denominator is 0. Obviously, I could
calculate the value fractionally above 0, and fractionally below 0,
and average the result to get the value for 0; but I was wondering if
there was a smarter way

2) Now here is the real problem. I've got some voltage ramp data, I
wanted to convert the current trace to a conductance trace using G = I/
(Vm-Ve). However as Vm approaches Ve the trace goes crazy (obviously
again, at Vm=Ve I couldn't calculate G, but even as Vm-Ve gets very
small, presumabley the noise of the trace is amplified, so you have a
rectangular hyperbola overlaid on a bolztman style curve). Is there
anything I can do about this? (and filtering doesn't work).
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[jonesmat]

On Aug 18, 9:38 pm, Bill <connelly.b...@...> wrote:

> This is more of a maths question than a neuroscience question, but
> I've come across it twice when dealing with neuroscience problems
>
> 1) I was trying to solve the Goldman Hodgkin Katz field equation,
> which I shan't type out here in full, but it has a denonimator term of
> 1-e^(-z.V.F/RT) so when V=0, the denominator is 0. Obviously, I could
> calculate the value fractionally above 0, and fractionally below 0,
> and average the result to get the value for 0; but I was wondering if
> there was a smarter way
>
> 2) Now here is the real problem. I've got some voltage ramp data, I
> wanted to convert the current trace to a conductance trace using G = I/
> (Vm-Ve). However as Vm approaches Ve the trace goes crazy (obviously
> again, at Vm=Ve I couldn't calculate G, but even as Vm-Ve gets very
> small, presumabley the noise of the trace is amplified, so you have a
> rectangular hyperbola overlaid on a bolztman style curve). Is there
> anything I can do about this? (and filtering doesn't work).

Bill,

How about a Taylor expansion of the function near zero, then only take
the first few terms of the polynomial, which won't be crazy yet.

However this will give no better results than just averaging over the
nearby points, so realistically you should probably just do that!

Matt


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