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Membrane Properties

Membrane Properties. chemical and electrical properties of biological membranes Jim Huettner. Lecture Overview. Selective permeability Osmolarity and osmotic pressure Ionic gradients Electrical properties: resistance and capacitance Electrochemical equilibrium Environmental change

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Membrane Properties

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  1. Membrane Properties chemical and electrical properties of biological membranes Jim Huettner

  2. Lecture Overview • Selective permeability • Osmolarity and osmotic pressure • Ionic gradients • Electrical properties: resistance and capacitance • Electrochemical equilibrium • Environmental change • GHK equation • Intro to simulation

  3. Membranes are Selective Barriers Cell membranes exhibit greater permeability to water than synthetic bilayers Alberts et al., 6th ed.

  4. Relative Scale of Permeability Alberts et al., 6th ed.

  5. Cell Volume Changes with Osmolarity hypotonic hypertonic cell volume Time (minutes) 10 20 30 40 10 20 30 40 Osmolarity = the total concentration of dissolved particles 300 mM sucrose = 150 mMNaCl = 100 mM Na2SO4

  6. Tonicity v.s. Osmolarity Osmolarity = [dissolved particles] (physical chemistry) Tonicity = effective osmotic pressure relative to blood plasma (cell physiology – depends on permeability) 150 mMNaCl – isotonic, isosmotic 10 mMEtOH – hypo-osmotic and hypotonic Both together – isotonic, hyperosmotic van’t Hoff Formula: p = sRT*(C2 – C1)osmotic pressure (p) is proportional to the difference in concentration, s is an index of impermeability

  7. 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

  8. 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

  9. 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

  10. Voltage • Measures the difference in potential energy experienced by a charged particle in two locations. It is the work required to move a charge from point A to point B.V = Joules / Coulomb = Volts (V) • Separation of + and – charges produces a potential difference or voltage. • To keep the charges apart, they must be on opposite sides of an insulating barrier.

  11. Capacitance • Measures how much charge must be separated to give a particular voltage:C (Farads) = Q (Coulombs) / V (Volts) • The cell membrane with dissolved ions on both sides acts as an electrical capacitor. By separating cations (+) and anions (-) across the membrane you develop a potential difference (voltage) from one side to the other. The lipid bilayer of most cells has a specific capacitance of 1.0 µFarad / cm2.

  12. Sample Problem • 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

  13. Calculations 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 1 2 3 Þ 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

  14. Types of Energy • Mechanical Energy: Force * Distance • Hydraulic Energy: Pressure * Volume • Gravitational Energy: Mass * g * height • Electrical Energy: Potential (Volts) * Charge (Coulombs) • Chemical Energy: R * T * ln [C] Chemical energy depends on the ability of a substance to react, which depends on concentration and temperature Charged particles in solution have chemical and electrical energy Electrochemical Energy: R * T * ln [C] + q * V

  15. 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: z * F * V Chemical Energy Term: R * T * 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

  16. 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 mV / z) * log ([ion]out / [ion]in) @ 30°

  17. 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

  18. 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 an energy-driven pump to maintain the concentration gradient • Any ion not already at electrochemical equilibrium will flow toward it, if there is a way to cross the membrane

  19. 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

  20. Eion (mV) +59 to +88 -87 +9 to +18 +120 to +129 -14 -81 to -52 Alberts et al., 6th ed.

  21. Environmental Changes: Dilution H2O Add water Na 58.5 K 1.5 Cl 60 Anions 0 Total 120 Na 30 K 90 Cl 4 Anions 116 Total 240 EK = -107 mV ECl = -71 mV 0 mV -89 mV

  22. Environmental Changes: ­K+ or ¯Cl- Na 114 29 K 6 91 Cl 120 7.9 Anions 0 112.1 EK = ECl = -71 mV Relative Volume = 1.034 Starting Conditions ­K+ Out In Na 117 30 K 3 90 Cl 120 4 Anions 0 116 EK = ECl = -89 mV Relative Volume = 1 Na 117 30.5 K 3 89.5 Cl 60 2.1 Anions 60 117.9 EK = ECl = -88 mV Relative Volume = 0.984 ¯Cl-

  23. Deviation from the Nernst Equation 0 Resting membrane potentials in 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)

  24. 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.

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

  26. Membrane Potential as a Function of Time ENa + 36 mV 0 mV Membrane Potential (mV) -63 mV EK - 89 mV Time (milliseconds) PNa = 0.1 PNa = 0

  27. Membrane Potential as a Function of Time ENa + 36 mV 0 mV -17 mV Membrane Potential (mV) -63 mV EK - 89 mV Time (milliseconds) 1.0 0.1 PNa 0

  28. Summary: • Cells are always at water equilibrium • Osmolarityinside = Osmolarityoutside • The cell membrane is a barrier to polar, charged moleculesÞ cells need specific transport mechanisms • Ions crossing the membrane create a voltage difference • Few ions must cross to generate a significant potential Þ 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

  29. Summary (continued): • The Goldman, Hodgkin, Katz equation gives the steady-state membrane potential when Na, K and Cl are permeable • In this case, Vm does depend on the relative permeability to each ion and there is steady flux of Na and KÞ The cell must supply energy to maintain its ionic gradients

  30. Additional Reading • Kay AR, Blaustein MP. (2019) Evolution of our understanding of cell volume regulation by the pump-leak mechanism. J Gen Physiol. 151:407-416. Erratum in: J Gen Physiol. (2019) 151:606-607. • Armstrong CM. (2003) The Na/K pump, Cl ion, and osmotic stabilization of cells. Proc Natl AcadSci U S A. 100:6257-62. • Finkelstein A. (1976) Water and nonelectrolyte permeability of lipid bilayer membranes. J Gen Physiol.68:127-35.

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