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Goldman (-Hodgkin-Katz) Equation

Goldman (-Hodgkin-Katz) Equation. Passive movements of sodium and potassium account for –67 mV of the –70 mV of the resting membrane potential. The Sodium Pump. The other –3 mV is due to the Na + pump.

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Goldman (-Hodgkin-Katz) Equation

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  1. Goldman (-Hodgkin-Katz) Equation • Passive movements of sodium and potassium account for –67 mV of the –70 mV of the resting membrane potential.

  2. The Sodium Pump • The other –3 mV is due to the Na+ pump. Active processes directly contribute a small amount to the resting membrane potential: –3 mV. • The Na+ pump is an electrical generator. • Because the Na+ pump pumps more + out than in (3 Na+ out, 2 K+ in), the sodium pump is electrogenic. • But, -3 mV is a nearly insignificant amount. Therefore, of the three major functions of the Na+ pump, generating electricity is the least important.

  3. Functions of the Sodium Pumps(in order of importance) • Prevent cell swelling They reverse the Donnan effect. • Charge the battery They maintain the disequilibria of Na+ and K+ across the cell membrane. • Generate electricity

  4. The Donnan Effect • Which fluid compartments are high in protein? • intracellular fluid • plasma • Which fluid compartment is low in protein? • interstitial fluid Fig. 1-27 Ganong

  5. The Donnan Effect • Proteins are impermeant polyanions. • Proteins are impermeant to the membrane. • due both to size and charge • Most proteins have a net negative charge. • This negative charge is balanced by cations, typically monovalent cations. • K+ for intracellular fluid • Na+ for plasma Fig. 12.11

  6. The Donnan Effect – simplified scenario BEFORE in out 1 Eq K+ 1 Eq K+ 0.5 Eq Cl- 1 Eq Cl- 0.5 Eq Pr- 0 mV AFTER in out > 1 Eq K+ <1 Eq K+ >0.5 Eq Cl- <1 Eq Cl- 0.5 Eq Pr- H2O - mV + • Cl- moves in down its concentration gradient. • The inside of the cell becomes negative. • K+ moves in down its electrical gradient. • By osmosis, H2O follows the K+ and Cl-.    

  7. The Donnan Effect • When Donnan and Gibbs analyzed the situation mathematically, they showed that “in” and “out” could not be in electrochemical and osmotic equilibrium at the same time. (see Ganong) • As a result of the osmotic imbalance, water will flow into a compartment (cytosol, blood plasma) that contains more protein. • The portion of the osmotic pressure that is due to the effects of protein is called “colloidal osmotic pressure.”

  8. Animal cells must have sodium pumps. • The problem: Because of the Donnan effect, cells will swell and burst. • The solution: For animal cells, the sodium pump solves the problem. • Na+ pumped out • Cl- follows Na+ • H2O follows NaCl Alberts et al., Molecular Biology of the Cell

  9. Fig. 2-6 Ganong The Action Potential ~ 1 ms An action potential is the sequence of changes in the membrane potential that occurs during the transmission of an electrical signal along the cell membrane, as measured at a specific point on a nerve or muscle cell membrane. repolarization depolarization Fig. 12-13

  10. The Action Potential Fig. 12.12 Fig. 11.1 • skeletal muscle fibers • axons of neurons Fig. 12.13

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