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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: –High concentration K+ inside –Selective permeability of membrane

What causes the different ion distributions in cells? 1.Passive distribution – Donnan equilibrium 2.Active Transport

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

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

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

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

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

Donnan Equilibrium Example A - = 100 K + = 150 Cl - = 50 A - = 0 K + = 150 Cl - = 150 III Initial Concentrations Are these ions in electrochemical equilibrium? No, E K + = 0 mV E Cl - = -27 mV

Solve for X, X + X 2 = X + X 2 X=30 Let X be the amount of K+ and Cl- that moves

A - = 100 K + = 180 Cl - = 80 A - = 0 K + = 120 Cl - = 120 III Final Concentrations Are these ions in electrochemical equilibrium? Yes, E K + = -10 mV E Cl - = -10 mV space-charge neutrality

What causes the different ion distributions in cells? 1.Passive distribution – Donnan equilibrium 2.Active Transport

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

Active Transport Na + - K + pump outside inside 3 Na + 2 K + ATPADP + Pi

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

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

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

What causes the different ion distributions in cells? 1.Passive distribution – Donnan equilibrium 2.Active Transport

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

Membrane Potential Summary 1.Selective permeability Ion channel – K + leak channel 2.Unequal distribution of ions Passive distribution (Donnan) Active transport – Na+/K+ pump 3.The equilibrium potential of each ion is described by the Nernst equation 4.The total membrane potential is described by the Goldman equation

Ionic basis of membrane potential

K mV Na mV Cl mV Ca mV Outside (mM) Equilibrium (Nernst) Potential Inside (mM) Mammalian Cell

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 E ion than Vm should change as E ion changes

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

Expt #1 vary extracellular Na Assume [Na] in = 10 mM 1-58 mV [Na] out prediction

External Na+ concentration (mM) Membrane Potential (mV) Prediction of E Na From Nernst equation Measured Vm

Therefore, –Conclude that Vm does not follow E Na

Expt #2 vary extracellular K Assume intracellular [K] = 140 mM 1-124mV Extracell [K] prediction

External K+ concentration (mM) Membrane Potential (mV) Prediction of E K From Nernst equation Deviation at low [K+] due to slight permeability of Na Measured Vm

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

Summary 1.At rest P K >>P Na, P Cl, P Ca 2.Therefore, at rest, the membrane potential is close to E K 3.In general, the membrane potential will be dominated by the equilibrium (Nernst) potential of the most permeable ion

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

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