Membrane Properties - PowerPoint Presentation

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 GHK equation Intro to simulation

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

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

Cell Volume Changes with Osmolarity Osmolarity = the total concentration of dissolved particles cell volume 10 20 30 40 10 20 30 40 Time (minutes) hypotonic hypertonic 300 mM sucrose = 150 mM NaCl = 100 mM Na 2 SO 4

Tonicity v.s . Osmolarity Osmolarity = [dissolved particles] (physical chemistry) Tonicity = effective osmotic pressure relative to blood plasma (cell physiology – depends on permeability) 150 mM NaCl – isotonic, isosmotic10 mM EtOH – hypo-osmotic and hypotonicBoth together – isotonic, hyperosmoticvan’t Hoff Formula: p = sRT*(C2 – C1 )osmotic pressure (p) is proportional to the difference in concentration, s is an index of impermeability

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

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 + - + -

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 + - + -

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.

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 / cm 2 .

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 / cm 2 Surface area = 4 p r 2 Faraday’s Constant = 9.648 x 104 Coulombs / mole Avogadro’s # = 6.022 x 1023 ions / mole

Calculations Area = 4 p r 2 = 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 Þ 7 x 10-12 Coulombs / 9.65 x 10 4 Coulombs per mole= 7.3 x 10-17 moles of ions must cross the membrane = 0.073 femptomoles or ~ 44 x 106 ions 1 2 3

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

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 Ca 2+ and Mg2+, -1 for Cl-F is Faraday’s Constant = 9.648 x 104 Coulombs / moleR is the gas constant = 8.315 Joules / °Kelvin * moleT is the temperature in °Kelvin

Nernst Equation Derivation zF * V in + 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°

Nernst Potential Calculations First K and Cl E K = 60 mV log (3 / 90) = 60 * -1.477 = -89 mV E Cl = (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 E Na = 60 mV log (117 / 30) = 60 * 0.591 = +36 mVWhen Vm = -89 mV, both the concentration gradient and electrical gradient for Na are from outside to inside

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

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

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

Environmental Changes: Dilution Na 58.5 K 1.5 Cl 60 Anions 0 Total 120 Na 30 K 90 Cl 4 Anions 116 Total 240 E K = -107 mV E Cl = -71 mV 0 mV -89 mV Add water H 2 O

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

Deviation from the Nernst Equation 3 10 30 100 300 External [K] (mM) 0 -25 -50 -75 -100 Resting Potential (mV) E K (Nernst) P K : P Na : P Cl 1 : 0.04 : 0.05 Resting membrane potentials in real cells deviate from the Nernst equation, particularly at low external potassium concentrations. The Goldman, Hodgkin, Katz equation provides a better description of membrane potential as a function of potassium concentration in cells. Squid Axon Curtis and Cole, 1942

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.

GHK Equation: Sample Calculation = 60 mV * log (18.7 / 213) = 60 mV * -1.06 = -63 mV Suppose P K : P Na : P Cl = 1 : 0.1 : 1

Membrane Potential as a Function of Time Membrane Potential (mV) E Na E K + 36 mV 0 mV - 89 mV P Na = 0 P Na = 0.1 Time (milliseconds) -63 mV

Membrane Potential as a Function of Time Membrane Potential (mV) E Na E K + 36 mV 0 mV - 89 mV P Na 0 0.1 Time (milliseconds) -63 mV 1.0 -17 mV

Summary: Cells are always at water equilibrium Osmolarity inside = Osmolarity outside The cell membrane is a barrier to polar, charged molecules Þ cells need specific transport mechanismsIons crossing the membrane create a voltage differenceFew ions must cross to generate a significant potential Þ bulk neutrality of internal and external solutionPermeable ions move toward electrochemical equilibriumE ion = (60 mV / z) * log ([Ion]out / [Ion]in) @ 30°CElectrochemical equilibrium does not depend on permeability

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

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 Acad Sci U S A. 100:6257-62 . Finkelstein A. (1976) Water and nonelectrolyte permeability of lipid bilayer membranes. J Gen Physiol.68:127-35.