11_-_Volume_control

11_-_Volume_control - BMEN E4001x: Quantitative Physiology...

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BMEN E4001x: Quantitative Physiology I / Molecular and Cellular Systems Control of cell volume Na/K pump, Na + and K + channels, o p=pump rate, per exchange Cl - channels, no pumps g Na , g K , g Cl indicate appropriate permeabilities. internal charged polymers, with a total of X molecules trapped within the cell, with valence z x =< -1. Cell volume of w V= transmembrane voltage, as usual. q=charge of proton, absolute charge of electron Taking the pump-leak model, and assuming Ohmic conduction, [ ] [ ] [ ] [ ] [ ] [ ] - = - - = + - = + + + + + + e i Cl Cl i e K K i e Na Na Cl Cl ln F RT V g I pq 2 K K ln F RT V g I pq 3 Na Na ln F RT V g I Noting that F= faraday’s constant, F=N A q, so RT/F = k b T/q There is also the equation for osmosis-driven transport: [ ] [ ] [ ] [ ] [ ] [ ] - - - - + + = - + + - + + i i i e e e P V Cl K Na w X Cl K Na RT L I Take the B&B equation, assume no pressure difference. Also, K&S uses different form of the right hand side, but it is still essentially water flow. Moreover, proportionality constants will drop out. There are also two equations for charge neutrality [ ] [ ] [ ] [ ] [ ] [ ] 0 w X z Cl K Na 0 Cl K Na x i i i e e e = + - + = - + - + + - + +
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For this analysis, we’re going to look at steady state. Note that that means no net flow of all ions,
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This note was uploaded on 12/21/2010 for the course BMEN 4001 taught by Professor Kam during the Fall '10 term at Columbia.

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11_-_Volume_control - BMEN E4001x: Quantitative Physiology...

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