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

Bill via neur-sci%40net.bio.net (by connelly.bill from gmail.com)
Tue Aug 18 21:38:05 EST 2009

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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