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Announcements. Today Review membrane potential What establishes the ion distributions? What confers selective permeability? Ionic basis of membrane potential Next Lectures Action Potentials. Membrane Potential Inside of cell is negative compared to outside Depends on:

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    1. Announcements

    2. Today • Review membrane potential • What establishes the ion distributions? • What confers selective permeability? • Ionic basis of membrane potential Next Lectures • Action Potentials

    3. Membrane Potential • Inside of cell is negative compared to outside • Depends on: • High concentration K+ inside • Selective permeability of membrane

    4. What causes the different ion distributions in cells? • Passive distribution – Donnan equilibrium • Active Transport

    5. I I II II Passive distribution – Donnan equilibrium • The ratio of positively charged permeable ions equals the ratio of negatively charged permeable ions Start Equilibrium K+ [K+] = [K+] Cl- [Cl-] = [Cl-]

    6. Donnan Equilibrium • Mathematically expressed: • Another way of saying the number of positive charges must equal the number of negative charges on each side of the membrane

    7. I I II II Passive Distribution • BUT, in real cells there are a large number of negatively charged, impermeable molecules (proteins, nucleic acids, other ions) • call them A- Start Equilibrium A- A- [K+] > [K+] K+ Cl- [Cl-] < [Cl-]

    8. I II Passive Distribution Equilibrium [K+]I = [A-]I + [Cl-]I A- [K+]II = [Cl-]II [K+] > [K+] [Cl-] < [Cl-] If [A-]Iis large, [K+]I must also be large +’ve = -’ve +’ve = -’ve space-charge neutrality

    9. The presence of impermeable negatively charged molecules requires more positively charged molecules inside the cell.

    10. Donnan Equilibrium Example Initial Concentrations I II A- = 0 K+ = 150 Cl- = 150 A- = 100 K+ = 150 Cl- = 50 Are these ions in electrochemical equilibrium? No, EK+ = 0 mV ECl-= -27 mV

    11. Let X be the amount of K+ and Cl- that moves Solve for X, 7500 + 200X + X2 = 22500 - 300X + X2 X=30

    12. Final Concentrations I II A- = 0 K+ = 120 Cl- = 120 A- = 100 K+ = 180 Cl- = 80 space-charge neutrality Are these ions in electrochemical equilibrium? Yes, EK+ = -10 mV ECl-= -10 mV

    13. What causes the different ion distributions in cells? • Passive distribution – Donnan equilibrium • Active Transport

    14. Active Transport • ATP-powered pumps • Proteins that are capable of pumping ions from one side of the cell membrane to the other • Use energy

    15. Active Transport • Na+ - K+ pump 2 K+ outside inside 3 Na+ ATP ADP + Pi

    16. Active Transport • Na+ - K+ pump • 3 Na+ move out • 2 K+ move in • Hydrolyzes ATP • Maintains the concentration gradient

    17. Active Transport • Na+ - K+ pump 2 K+ outside inside 3 Na+ • Electrogenic • net loss of 1 positive charge from inside • Inside becomes more negative • contributes a few mV to resting potential

    18. Na+/K+ pump is required • Due to low permeability for Na+ to leak into the cell • Without pump, • Gradual accumulation of +’ve charge inside • Eventually lose the membrane potential Active ingredient in rodent poison, ouabain, poisons the Na/K pump

    19. What causes the different ion distributions in cells? • Passive distribution – Donnan equilibrium • Active Transport

    20. What confers selective permeability? Ion channels • Non-gated • Leakage channels • Open at rest – allow K+ to flow out along its concentration gradient K+

    21. Membrane Potential Summary • Selective permeability • Ion channel – K+ leak channel • Unequal distribution of ions • Passive distribution (Donnan) • Active transport – Na+/K+ pump • The equilibrium potential of each ion is described by the Nernst equation • The total membrane potential is described by the Goldman equation

    22. Ionic basis of membrane potential

    23. Mammalian Cell Equilibrium (Nernst) Potential Inside (mM) Outside (mM)

    24. Is the resting membrane potential controlled by one ion, or several? • Do an experiment • Measure membrane potential (Vm) of a cell • Change extracellular concentration of an ion in the bathing solution • If Vm really depends on Eion than Vm should change as Eion changes

    25. Resting potential Measuring Membrane Potential amplifier microelectrode Reference electrode 0 mV cell -80 mV time

    26. Expt #1vary extracellular Na Assume [Na]in = 10 mM [Na]out prediction

    27. 1 2 5 10 20 50 100 200 40 20 0 -20 Prediction of ENa From Nernst equation -40 Membrane Potential (mV) -60 -80 -100 Measured Vm -120 External Na+ concentration (mM)

    28. Therefore, • Conclude that Vm does not follow ENa

    29. Expt #2vary extracellular K • Assume intracellular [K] = 140 mM Extracell [K] prediction

    30. Deviation at low [K+] due to slight permeability of Na+ 1 2 5 10 20 50 100 200 0 -20 Prediction of EK From Nernst equation -40 Membrane Potential (mV) -60 -80 -100 Measured Vm -120 External K+ concentration (mM)

    31. Therefore, the resting membrane potential (Vm) is very close to the equilibrium potential for K+ (EK)

    32. Summary • At rest PK>>PNa, PCl, PCa • Therefore, at rest, the membrane potential is close to EK • In general, the membrane potential will be dominated by the equilibrium (Nernst) potential of the most permeable ion

    33. Sample Question At rest Vm of this typical cell is -75 mV. What would Vm be if PNa >> Pk,PCl? K = 140 Na = 10 Cl = 30 K = 5 Na = 145 Cl = 110 Answer: Calculate ENa using Nernst equation. Assume Vm ENa = +67 mV

    34. The resting membrane potential is the basis for all electrical signaling • Next Lecture: Action Potentials