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I'm studying neuron electrochemistry rn and my book basically says that the more the cytoplasm impedes the flow of ions, the slower conduction will be, therefore larger neurons will have lower cytoplasmic resistance. Can someone explain this to me?

I'm confused why a larger neuron would mean less cytoplasmic resistance...wouldn't it be more since there is more cytoplasm? And the ratio of cytoplasm : ion channels in membrane would increase with size as volume : surface area ratio increases, so it's not that. I thought maybe it has to do with the diameter of the axon since larger diameter tubes have less resistance, but the flow of an action potential down the axon isn't really like a liquid flowing down a tube...

Thanks for any help you can give.

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Neurons are like leaky cables. If you make them longer, the resistance increase (along the long axis); if you make them thicker (larger cross-sectional area), the resistance decrease. The word "larger" is quite ambiguous here. However if we assume the neuron grows evenly along all axis by a factor of k, the theory goes that

$R_{k} = \rho \frac{kl}{k^2A} = \rho \frac{l}{kA} = \frac{1}{k} * \rho \frac{l}{A}$

where l is the original length and A is the original cross-sectional area, so the resistance is 1/k of the original value. If k is greater than 1, the resistence is reduced.

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  • $\begingroup$ Hi @X, can I changed your equation to latex format - can you double check I've preserved the original meaning? $\endgroup$
    – user438383
    Commented May 30, 2022 at 12:31
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    $\begingroup$ @user438383 thanks, it looks very pretty. Today I learned latex in comments on cell biology ;-) $\endgroup$
    – X Zhang
    Commented May 30, 2022 at 13:14

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