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If the conductance of a single ion channel is 1pS and its capacitance per cm2 is 1uF and the time constant for a human neuron is 1ms

How many ion channels on average must there be in one µm2 of neuronal membranes?

How is it possible to know how many ion channels with only these information? would you be able to explain it?

Thank you

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    $\begingroup$ Is this a homework question? $\endgroup$ – Devon Ryan Apr 29 '17 at 10:56
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    $\begingroup$ Suggest you check the given units and use those as a hint... en.wikipedia.org/wiki/Siemens_(unit) and en.wikipedia.org/wiki/Farad comeback when you have made a slightly bigger effort. $\endgroup$ – Jeppe Nielsen Apr 29 '17 at 14:38
  • $\begingroup$ Hi, so I have found the resistance which is = 1/ conductance = 1/1*10^-12 so resistance = 1*10^12 ohms per cm^2. (I converted the pS to S). However, I am confused what does it mean by "how many ion channels" do they actually want the number of ion channels, or is there a formula for that, i tried researching a lot but I did not find anything related. Thank you! $\endgroup$ – user31972 Apr 30 '17 at 0:37
  • $\begingroup$ I know we have: Resistance, area (um^2), conductance and capacitance but i do not know how to put this information together to find the number of ion channels. $\endgroup$ – user31972 Apr 30 '17 at 0:41
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    $\begingroup$ To notify a user, you should type @ before their name. For e.g. @BryanKrause $\endgroup$ – user237650 May 1 '17 at 6:21
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I expect your homework was already due, so...

You're supposed to remember what a membrane time constant is. I'll quote from page 12 of my (by now quite old) copy of "Ion channels of excitable membranes", by Hille:

For biological membranes the product, RmCm, of membrane resistance and capacitance is often called the membrane time constant, taum.

Since you know tau and C, your goal is then to determine the membrane resistance. You also need to convert the capacitance to square microns (1e-14F per square micron). In this case: 1ms/1e-14F = 1e11Ohms, or 1e-11S, or 10pS. So on average there are 10 channels per square micron, assuming I didn't make any silly mistakes.

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