ELECPHYS - o /[X] i ) E Na+ = 58 log (460/50) = 58 log 9.2...

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MEMBRANE POTENTIALS Ion [X] i -70mV [X] o Na + 50mM c <==== 460mM e <==== Cl - 40 c <==== 540 e ====> K + 400 c ====> 10 e <==== Proteins - 400 xxxxxxx 0 As you can see, there is a concentration gradient for each ion, as well a -70 mv electrical gradient . If the concentration gradient for an ion exactly offsets the electrical gradient, then the system is at equilibrium for that ion. The voltage that exactly offsets a particular concentration gradient is the equilibrium potential , or reversal potential , for that ion. If the membrane is permeable to a particular ion, and ONLY that ion, then that ion will flow in (influx) or out (efflux ) until the equilibrium potential is attained. An equation used to calculate equilibrium potential for each ion is the Nernst equation: E i = RT/ZF * ln ([X] o /[X] i ) where R =universal gas constant (8.31 joules/mole- o K ) T = temp in degrees Kelvin Z = charge on ion F = faraday constant (96,500 coulombs/mole) At 293 o K (20 o C) this simplifies to E i = 58 log ([X]
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Unformatted text preview: o /[X] i ) E Na+ = 58 log (460/50) = 58 log 9.2 = 58 (0.964) = +55.9mV E Cl-= -58 log (40/540) = -58 log (13.5) = -58 (1.13) = -65.6mV E K+ = 58 log (10/400) = 58 log (0.025) = 58 (-1.60) = -92.9mV However, the membrane is permeable to more than one at a time. Using permeability to potassium as the reference, typical permeabilities of a membrane at rest are as follows: At rest: P K+ = 1.00 P Na+ = .03 P Cl-= .10 The Goldman-Katz equation accounts for the contributions of all three ions: (P Na+ [Na + ] o + P K+ [K + ] o + P Cl-[Cl-] I ) E m = 58 log -------------------------------------------(P Na+ [Na + ] i + P K+ [K + ] i + P Cl-[Cl-] o ) (.03(460) + 1.0 (10) + .10 (40)) (13.8 + 10 + 4) 27.8 E rm = 58 log --------------------------------------- = 58 log ------------------- = 58 log ------(.03 (50) + 1.0(400) + .10(540)) (1.5 + 400 + 54) 455.5 = 58 log (.061) = 58 (-1.21) = -70.3mV...
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