BIOE 2520 Electrical Properties of the Membrane Reading: Chapter 11 of Alberts et al. Stephen Smith, Ph.D. 433 Biotech Center shs46@pitt.edu
Permeability of Lipid membrane Lipid bilayer is virtually impermeable for charged ions and molecules Permeability: Gas > small uncharged molecules > Large uncharged molecules >> ions > charged larger molecules
Osmosis Osmosis: Diffusion of water molecules down its concentration gradient. If membrane is only permeable to H 2 O: NaCl NaCl NaCl NaCl H 2 O Osmotic Pressure: ρgh = ΔnRT
Osmosis and Cell Volume
Diffusion across a lipid bilayer Measurement of diffusion across a bilayer: Diffusion rate concentration gradient; Diffusion rate depends on substance solubility in lipid, which is measured by partition coefficient (between water and lipid); For charged particles, diffusion rates also depend on electrical potential across the bilayer;
Intracellular and Extracellular Ionic Concentrations [K ] i > [K ] o [Na ] i < [Na ] o [Ca 2 ] i << [Ca 2 ] o [Cl - ] i < [Cl - ] o
Membrane Transport Proteins
ATPases ATPases transport molecules across membrane against their electrochemical gradient.
Intracellular Na and K concentrations are maintained by Na /K ATPase Na/K ATPase: transports 3 Na out and 2 K into the cell by hydrolyzing an ATP to ADP and P i ; Na/K ATPase: tetramer α 2 β 2.
ATPases
Ion Channels Gated Ion Channel: opening and closing is determined by membrane potential (voltage-gated) or gating molecules (signal molecules); Non-gated ion Channels; Determine the resting membrane potential.
Potassium Channel Tetramer with identical subunits; High throughput rate: can pass 10 8 K ions per second (near diffusion limit): No binding site for K ; High selectivity: K is 10 4 -fold more permeable than Na ; Diameters of K and Na ions: 0.133 nm and 0.095 nm, how is the selectivity achieved?
K channel ion-select filter
Conservation of K channel Sequence There are consensus sequences in K channels that are conserved from bacteria, plants, to mammals. Gly-Tyr-Gly in pore region forms the filter. Doyle et al. Science, 1998, 280: 69-77.
Membrane Potential
Thermodynamics of Ideal solutions Under isothermal and isobaric conditions, a system reaches equilibrium when its electrochemical potential is at a minimum; The electrochemical potential of an ideal solution is: μ = μ i i μ = ( μ ), z Fψ i o T P i RT ln c Where z i and c i are the electric charge and concentration of the ith substance, ψ is the electrical potential, F and R are the Faraday and gas constants, (μ o ) T,P only depends on the property of the solvent. i
Thermodynamics of Ideal solutions If the membrane is only permeable to substance i, then the system reaches equilibrium when electrochemical potentials of substance i equal on both sides: in out μ = μ For i =Na : z ψ Na in Fψ ψ in i out RT ln[ Na = Na i ] in = RT [ Na ln z F [ Na z ] ] out in Na Fψ = out RT z Na RT ln[ Na ] [ Na ln10 lg F [ Na out ] out ] in RT F ln10 59 mv, Nernst Equation: ψ in ψ out = RT ln zf c c out in
Nernst Potential If the membrane is only permeable to K, then ψ in out RT [ K ] ψ = ln z F [ K ] K out in = 59 mv
Nernst Equilibrium potentials If plasma membrane is only permeable to: 4 139 145 = 59lg( ) 12 K in out : E = ψ ψ = 59lg( ) 91 K Na in out : E = ψ ψ 64 Na 116 4 Cl in out : E = ψ ψ = 59lg( ) 86 Cl mv mv mv E K, E Na, E cl : equilibrium potentials for K, Na, Cl -.
Membrane permeable to more then one ion If the membrane is permeable to K, Na, and Cl -, then an equilibrium can not be maintained!
Steady State Membrane Potential Ionic flux is proportional to its driving forces; Driving forces across a membrane: i Concentration gradient: E, i = ln in zf ci Voltage V m ; Ionic flux: ji = gi ( Vm Ei ) At steady state, V m is constant (no net charge movement across the membrane), Net current is zero: i = i j 0 RT c out
Steady State Membrane Potential Ionic flux: j i = g i ( Vm Ei Can be modeled with an equivalent electric circuit; ) C out V ---- m j i ---- V m g i E i C in
Steady State Membrane Potential Multiple ionic currents: ji = gi ( Vm Ei )
Steady State Membrane Potential At steady state, net current is zero: or gi ( Vm Ei ) = 0 i Membrane potential: V m = i i g i g E i i (Chord conductance equation) ji = 0 i
An Example g K = 10 g Na 4 E K = 59lg( ) 91 139 145 E Na = 59lg( ) 64 12 V m = g K E g K K g g Na Na 10 ( 91) 64 = 11 E Na 10g NaE = 10g = 76.9mV K Na g g Na Na E K 10EK E = 11 Na
Animal Cell membrane potential is predominately determined by non-gated K channels The membrane potentials of animal cells are proximately -70 mv. ψ in ψ out = g K EK g g K Membrane potential will shift if the conductance (permeability) of one or more ions change If more K channels open, potential will be more negative (hyperpolarization); If more Na channels open or some K channels are blocked, potential will be less negative (more positive) (depolarization). E g Na Na g g Na Cl Cl E Cl
Measurement of cell membrane potential Microelectrode method:
Gibbs-Donnan Equilibrium If membrane is permeable to Na and Cl, the two side will eventually have equal [Na ] and [Cl - ] at equilibrium. 100 mm NaCl 200 mm NaCl 150 mm NaCl 150 mm NaCl No electrical potential exits at the interface.
Gibbs-Donnan Equilibrium If one side contain large non-diffusible (impermeable) ions (X -, in our example), an unsymmetrical equilibrium (Gibbs-Donnan equilibrium) can be established: 18 mv 100 NaCl 100 NaX 67 Na 67 Cl - - - - - - - - 133 Na 33 Cl - 100 X - [ Na ] 1 [ Cl ] 1 = [ Na ] 2[ Cl ] 2 [ Na [ Na ] ] or 1 2 [ Cl = [ Cl ] ] 2 1 An equilibrium electrical potential (Gibbs-Donnan equilibrium potential) is present at the interface, and often an osmotic gradient exits.
Patch Clamps: Measurement of single channel current
Patch Clamps
Patch Clamps
Na /Ca 2 antiporter Many animal cells utilize plasma Na /Ca 2 antiporter to maintain low intracellular [Ca 2 ]; Exchange 3 extracellular Na for 1 intracellular Ca 2 ; [Ca 2 ] in < 0.2 μm; [Ca 2 ] out ~ 2 mm; 3Na out Ca 2 in 3Na in Ca 2 out
Cellular ph In animals: extracellular ph o 7.4, intracellular ph i 7.2; If unregulated and [H ] is at equilibrium, then RT [ H ] Δ ψ = ln10 lg F [ H ] out in = 59( ph in ph out ) mv Δψ ph = 59 = 6.2 in ph out Δψ = 70 mv
Cellular ph Cells regulate intracellular ph: With Na /H, Cl - /HCO 3-, and Na HCO 3- /Cl - antiporters (exchanger);
Transepithelial Transport Epithelium: a single layer of cells that lines the inside of internal organs such as intestine, stomach, kidney, etc. Uptake of glucose from intestinal lumen
Transepithelial Transport Acidfication of the stomach lumen by parietal cells
Water Movement Across Plasma Membrane Osmosis: water flows in the direction that minimizes difference of solute concentrations (electrochemical potential)..
Water Movement Across Plasma Membrane Cell swells in hypotonic (low osmolarity) solution; Cell shrinks in hypertonic (high osmolarity) solution; Water permeability in cell membrane is often 10 times higher than pure lipid bilayer: presence of water channels. Cells can regulate its volume in response to external disturbance by activation of ion channels, contransporters, and ATPases.