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Ionic Equilibria and Resting Membrane Potential

Lecture #11, BB, Chap. 6, pgs. 147 - 156

I. Introduction

A. membrane electrical properties enable:

1. cellular communication

2. muscle contraction

3. hormonal secretion

4. maintenance of ionic constituency

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B. early experiments with electrical properties of cells

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B. determination of cell potentials

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II. Resting Membrane Potential

A. diffusion potential

1. active transport establishes ionic concentration gradients

2. ions diffuse across membrane based upon selective permeability

3. results in small potential difference (mV) across membrane

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Na+

K+

2

3Na+

K+

Na+

4. role of active transport and ion diffusion

a. Na-K ATPase establishes ion gradientsi. [Na+]i < [Na

+]oii. [K+]i > [K

+]ob. K+diffuses out of cell

c. Na+much less permeable

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d. net K+efflux establishes potential gradient

i. K+influx occurs due to potential gradient

ii. influx continues until:

(a) K efflux due to [ ] gradient = K influx due to potential gradient

(b) termed electrochemical equilibrium

Na+

K+

Na+

K+

Na+

+

++

+

+

-

--

-

-potential

chemical

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Where:

K = diffusion potential for potassium

R = gas constant (.082L-atm/mole-Ko)

z = ion charge

F = Faraday constant (96,500 coulombs/g charge)

T = temperature (Kelvin, Co

+ 273)

RT

[K+]i

EK = -___ln ____zF [K+]

o

B. Nernst Equation

1. potential difference across membrane @ electrochemical equilibrium

2. specific for ion being considered (e.g. potassium)

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[K+]i

EK= - 60log___

mV[K+]

o

3. In a mammalian system, the Nernst equation is often simplified:

a. 37oC. (body temperature)

b. monovalent ions

c. convert ln to log (base of 10)

4. Example: if [K+]o= 10 mM and [K+]i= 100 mM, then:

[K+]i___ = 10; log of 10 = 1

[K+]o

EK= -60(1) = - 60 mv

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D. resting membrane potential (Em)

1. introduction

a. property of all living cells

b. result of active transport & selective permeability

c. Emresults from EC equilibrium of all of ions

i. Na+, K+and Cl-all contribute to Emii. however, effect upon Em, dependent upon permeability

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2. Chord (Goldman-Hodgekin-Katz) Equation

PK[K+]o+ PNa[Na+]o+ PCl[Cl-]iEm= 60 log

__ ___________________________________

PK[K+]i+ PNa

[Na+]i + PCl[Cl-]

o

a. Since: PK

>> PNa

:

i. Em K diffusion potential

ii. Emdiffers between of cell types

(1) neural -90 mV

(2) muscles - 50 to - 70 mV

(3) epithelia few mV

iii. dependent on relative ion permeability

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3. Since Vm is essentially a potassium diffusion potential

changes in [K+] can markedly effect resting membrane potential

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E. Na-K ATPase is an electrogenic transporter

1. active transport contributes directly to Vm2. cations are unequally translocated across membrane

a. 2:3 (2 K influx:3 Na efflux)

b. net efflux of charge (outside positive, relative to inside)

3. magnitude

a. depends on membrane

b. approx 2 - 5 mV of Vmdue to electrogenic activity

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III. Gibbs Donnan Equilibrium (BB, page 133 - 134)

A. introduction

1. cytoplasm contains:a. both charged & non-charged solute

b. both permeant & non-permeant solute

2. G-D equilibrium describes steady state properties of this mixture

B. consider two solutions separated by a semipermeable membrane1. initial conditions:

2. membrane permeable to K+and Cl-but not Y-

a. A and B isosmotic and electrically neutral

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2. equilibrium conditions

a. Cl-diffuses into A, down [ ] gradientb. K+diffuses into A to maintain electroneutrality

c. at equilibrium permeant ions (K and Cl) are both EC equilbrium

d. in a typical cell this contributes -10 mV to the cell potential

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3. Gibbs Donnan effects upon osmotic pressure

a. ion shift has resulted in a disparity of solute concentration

b. water diffuses from B to A to equalize osmolality

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4. physiological application

a. proteins negatively charged at biological pH

b. confined by cell membranes w/i compartmentsc. result is shift in non-confined ions (& H2O) across membrane

d. ~ 5% shift of confined solute in mammals, discussed in body fluid

balance lecture

e. elevates resting membrane potential and cell volume