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Membrane Potential and Ion Channels

Colin Nichols. Membrane Potential and Ion Channels.

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Membrane Potential and Ion Channels

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  1. Colin Nichols Membrane Potentialand Ion Channels Background readings:Lodish et al., Molecular Cell Biology, 4th ed, chapter 15 (p. 633-665) and chapter 21 (p. 925-965).Alberts et al., Molecular Biology of the Cell, 4th ed, chapter 11 (p. 615-650) and p. 779-780.Hille Ionic channels of excitable membranes 3rd ed.

  2. LIFE – A complex interplay of chemistry and physics

  3. 1 2 2 3 1 4 3 4 Na+ K+ The action potential – Physics in cell biology

  4. Excitation-contraction coupling

  5. The islet of Langerhans

  6. Glucose-dependent hormone secretion

  7. The Lipid Bilayer is a Selective Barrier inside outside hydrophobic molecules (anesthetics) gases (O2, CO2) small uncharged polar molecules large uncharged polar molecules Ions charged polar molecules (amino acids) water

  8. Ion Channel Diversity

  9. Cation channel Subunit Topology

  10. Cation channel Subunit Topology The ‘inner core’ of cation channel superfamily members

  11. Structure of a Potassium Channel Doyle et al., 1998

  12. Selectivity Filter and Space-Filling Model Doyle et al., 1998

  13. Ion selectivity filter in KcsA Doyle et al., 1998, Zhou et al., 2002

  14. Selectivity filter diversity

  15. Ion selectivity filter in Na channels NavMs, NavAb, Kv1.2 Nature Communications , Oct 2, 2012. Structure of a bacterial voltage-gated sodium channel pore reveals mechanisms of opening and closing Emily C McCusker,1, 3, Claire Bagnéris,1Claire E Naylor,1, Ambrose R Cole,1Nazzareno D'Avanzo,2, 4, Colin G Nichols2, & B A Wallace1

  16. Views of the Channel Open and Shut Jiang et al., 2002

  17. Views of the Channel Open and Shut Nature Communications , Oct 2, 2012. Structure of a bacterial voltage-gated sodium channel pore reveals mechanisms of opening and closing Emily C McCusker,1, 3, Claire Bagnéris,1Claire E Naylor,1, Ambrose R Cole,1Nazzareno D'Avanzo,2, 4, Colin G Nichols2, & B A Wallace1

  18. Ion gradients and membrane potential

  19. Ion gradients and membrane potential

  20. Ion gradients and membrane potential

  21. Ion gradients and membrane potential The inside of the cell is at ~ -0.1V with respect to the outside solution -89 mV How does this membrane potential come about?

  22. Ion gradients and membrane potential K Na Cl K -89 mV How does this membrane potential come about?

  23. Ion gradients and membrane potential Na 117 K 3 Cl 120 Anions 0 Total 240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] -89 mV How does this membrane potential come about?

  24. Movement of Individual K+ ions + - Na 117 K 3 Cl 120 Anions 0 Total 240 Na 30 K 90 Cl 4 Anions 116 Total 240 + - [+ charge] = [- charge] 0 mV [+ charge] = [- charge] 0 mV

  25. Movement of Individual Cl- ions + - Na 117 K 3 Cl 120 Anions 0 Total 240 Na 30 K 90 Cl 4 Anions 116 Total 240 + - [+ charge] = [- charge] 0 mV [+ charge] = [- charge] 0 mV -89 mV

  26. Setting a membrane potential –questions! • How many ions must cross the membrane to set up this membrane potential? • What makes it stop at this potential?

  27. C µ area I { + - + + + + + + + + - - - - - - - - V C C µ 1 / thickness For biological membranes: Specific Capacitance = 1 µF / cm2 Capacitance Capacitance C Coulombs / Volt Farads F C = Q / V Q = C * V I = dQ / dt = C * dV / dt

  28. How many ions? • How many ions must cross the membrane of a spherical cell 50 µm in diameter (r = 25 µm) to create a membrane potential of –89 mV?Q (Coulombs) = C (Farads) * V (Volts) Specific Capacitance = 1.0 µFarad / cm2Surface area = 4 p r2Faraday’s Constant = 9.648 x 104 Coulombs / mole Avogadro’s # = 6.022 x 1023 ions / mole

  29. Area = 4 p r2 = 4 p (25 x 10-4 cm)2 = 7.85 x 10-5 cm2 = 78.5 x 10-6 µFarads = 78.5 x 10-12 Farads Q = C * V= 78.5 x 10-12 Farads * 0.089 Volts= 7 x 10-12 Coulombs Calculations 1 2 3 ~ 7 x 10-12 Coulombs / 9.65 x 104 Coulombs per mole= 7.3 x 10-17 moles of ions must cross the membrane= 0.073 femptomoles or ~ 44 x 106 ions ~ 1.1 µM change in [ ]

  30. Why does it stop?- The Nernst Equation Calculates the membrane potential at which an ion will be in electrochemical equilibrium. At this potential: total energy inside = total energy outside Electrical Energy Term: zFV Chemical Energy Term: RT.ln[Ion] Z is the charge, 1 for Na+ and K+, 2 for Ca2+ and Mg2+, -1 for Cl- F is Faraday’s Constant = 9.648 x 104 Coulombs / mole R is the gas constant = 8.315 Joules / °Kelvin * mole T is the temperature in °Kelvin

  31. Nernst Equation Derivation zF.Vin + RT.ln [K+]in = zF.Vout + RT.ln [K+]out zF (Vin – Vout) = RT (ln [K+]out – ln [K+]in) EK = Vin – Vout = (RT/zF).ln([K+]out/[K+]in) EK = 2.303 (RT / F) * log10([K+]out/[K+]in) In General: Eion ~ 60 * log ([ion]out / [ion]in) for monovalent cation at 30°

  32. Nernst Potential Calculations • First K and ClEK = 60 mV log (3 / 90) = 60 * -1.477 = -89 mVECl = (60 mV / -1) log (120 / 4) = -60 * 1.477 = -89 mV Both Cl and K are at electrochemical equilibrium at -89 mV • Now for Sodium ENa = 60 mV log (117 / 30) = 60 * 0.591 = +36 mV When Vm = -89 mV, both the concentration gradient and electrical gradient for Na are from outside to inside

  33. At Electrochemical Equilibrium: • The concentration gradient for the ion is exactly balanced by the electrical gradient • There is no net flux of the ion • There is no requirement for any energy-driven pump to maintain the concentration gradient

  34. Ion Concentrations Na 117 K 3 Cl 120 Anions 0 Total 240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] -89 mV

  35. Ion Concentrations Add water – 50% dilution Na 117 K 3 Cl 120 Anions 0 Total 240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] -89 mV

  36. Environmental Changes: Dilution H2O Add water – 50% dilution Na 58.5 K 1.5 Cl 60 Anions 0 Total 120 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] [+ charge] = [- charge] -89 mV

  37. Environmental Changes: Dilution Add water – 50% dilution Na 58.5 K 1.5 Cl 60 Anions 0 Total 120 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] [+ charge] = [- charge] -89 mV EK = -107 mV ECl = -71 mV

  38. Na 30 K <90 Cl <4 Anions 116 Total <240 Environmental Changes: Dilution H2O Add water – 50% dilution Na 58.5 K 1.5 Cl 60 Anions 0 Total 120 [+ charge] = [- charge] [+ charge] = [- charge] -89 mV EK = -107 mV ECl = -71 mV

  39. Deviation from the Nernst Equation 0 Resting membrane potentialsin real cells deviate from the Nernst equation, particularlyat low external potassiumconcentrations. The Goldman, Hodgkin, Katzequation provides a better description of membrane potential as a function of potassium concentration in cells. Squid Axon Curtis and Cole, 1942 -25 PK : PNa : PCl 1 : 0.04 : 0.05 -50 Resting Potential (mV) -75 EK (Nernst) -100 • 3 10 30 100 300 • External [K] (mM)

  40. The Goldman Hodgkin Katz Equation • Resting Vm depends on the concentration gradients and on the relative permeabilities to Na, K and Cl. The Nernst Potential for an ion does not depend on membrane permeability to that ion. • The GHK equation describes a steady-state condition, not electrochemical equilibrium. • There is net flux of individual ions, but no net charge movement. • The cell must supply energy to maintain its ionic gradients.

  41. GHK Equation: Sample Calculation Suppose PK : PNa : PCl = 1 : 0.1 : 1 = 60 mV * log (18.7 / 213) = 60 mV * -1.06 = -63 mV

  42. Recording Membrane Potential

  43. To here L1

  44. On-Cell Patch Recording (Muscle) 50 µm

  45. Forming a Tight Seal

  46. Whole-Cell and Outside-Out Patch 10 µm

  47. Channels Exist in at least 2 States

  48. To here… Current ~3.2 pA = 3.2 x 10-12 Coulombs/sec Charge on 1 ion ~1.6 x 10-19 Culombs Ions per second = 3.2/1.6 x 10^7 ~20 million

  49. Exponential Distribution of Lifetimes mean open time = topen = 1 / a = 1 / closing rate constant

  50. Summary: • Cell membranes form an insulating barrier that acts like a parallel plate capacitor (1 µF /cm2) • Ion channels allow cells to regulate their volume and to generate membrane potentials • Only a small number of ions must cross the membrane to create a significant voltage difference ~ bulk neutrality of internal and external solution • Permeable ions move toward electrochemical equilibrium • Eion = (60 mV / z) * log ([Ion]out / [Ion]in) @ 30°C • Electrochemical equilibrium does not depend on permeability, only on the concentration gradient

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