09_-_Resting_potential_and_the_Pump-leak_model - BMEN...

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BMEN E4001x: Quantitative Physiology I / Molecular and Cellular Systems Some typical numbers for concentrations. Ion concentration (mM) interstitial space (ext) cell (“typical”) (int) V nernst (mV) Na + , mammalian cell 145 15 +58 K + , mammalian cell 4.5 120 -84 Cl - , mammalian cell 116 20 -45 Na + , squid giant axon 440 50 +54 K + , squid giant axon 20 400 -75 Cl - , squid giant axon 560 52 -59 - = - = ext B Nernst ext c c ne T k V V V V int int ln ;where n = valency. Also shown as z. In short, bottom term should be charge of an individual ion. In the last lectures, we looked at the diffusion of a single species through a membrane, most likely through channels or carriers, and came up with the Nernst potential. Now, look at what underlies the situation in which we have multiple species. Clearly, something is wrong. First, with the defined internal and external concentrations, how can we have different “resting” potentials; our discussion until now suggests that resting is that flow through channels is zero. The system seems to be overspecified. Moreover, the resting potential of cells (-50 to - 80 mV) is not near any of these. Cl - and K + are about right, but not exact. Nernst potentials for Na + is way off; this is in fact referred to as the sodium anomaly. In this section , we’re going after a “resting” state of the cell, which, except as noted, will describe as a situation in which the cell may require energy to maintain, but the membrane voltage and ion concentrations both externally and internally are maintained. Note that in the GHK model, maintenance of ion concentrations is not guaranteed. Gibbs-Donnan equilibrium Important equilibrium state, based on the assumptions: Concentrations of each permeant species adjusts until V Nernst is identical for all permeant species, and equal to the resting voltage. o Since the external concentration is held constant, internal concentrations should change to meet the Nernst potential Charged species add up to provide electroneutrality both inside and outside cell o This works for the external solution, but internally, there seems to be a problem. o Extra internal charge is provided by proteins and DNA inside cell, on the order of 125 mM excess single electron charge. o Electroneutrality can be violated at small scales, but not “macroscopic” ones.
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Effectively, this pushes for: e i i e i e ] Cl [ ] Cl [ ] K [ ] K [ ] Na [ ] Na [ - - + + + + = = [Na + ] e +[K + ] e -[Cl - ] e =0; roughly done. Mammalian cell: 145 mM (Na + ) + 4.5 mM (K + ) – 116 mM (Cl - ) = 34 mM excess positive. [Na + ] i +[K + ] i -[Cl - ] i -125mM=0; these conc. to be determined. Solving for internal concentrations,
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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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09_-_Resting_potential_and_the_Pump-leak_model - BMEN...

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