1. LECTURE 3: ION CHANNELS & THE RESTING MEMBRANE POTENTIAL REQUIRED READING: Kandel text, Chapters 7, pgs 105-139 - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + V m = V in - V out In resting neuron: V m ~ - 60 to - 75 mV Membrane potential is a BATTERY providing power to drive currents when the cell is activated This lecture discusses how membrane potential is established and maintained - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

2. MEASURING THE RESTING MEMBRANE POTENTIAL: MICROPIPET FILLED WITH HIGH SALT For this method, recording pipet has a very fine tip and is filled with a high salt solution (e.g. 3M KCl), so that pipet has very low resistance. In this way, the voltage measured by amplifier accurately reflects the voltage across the cell membrane. (method not useful in very small cells due to pipet salt poisoning of cells) V pipet V m (actual) R m (actual) R pipet V m (measured) = V m (actual) + V pipet when R pipet <<< R m (actual) V m (measured) = V m (actual)

3. MEASURING THE RESTING MEMBRANE POTENTIAL: PATCH PIPET IN “WHOLE-CELL” CONFIGURATION Patch pipet filled with cytoplasm-like solution is touched to cell membrane; with negative pressure, the pipet makes a very tight “cell-attached” or “on-cell” seal onto membrane (leak resistance > 10 G  ) Applying gentle suction can break the membrane inside the pipet, making pipet fluid contiguous with the cytoplasm. This is the “whole-cell” configuration. When break is made into cell, the pipet can record the membrane potential

4. TWO TYPES OF PROTEIN COMPLEXES CONTRIBUTE TO ESTABLISHING THE RESTING MEMBRANE POTENTIAL ION PUMP -- drives a specific ion or group of ions from one side of the plasma membrane to the other side Pumps drive ions ONE-WAY and use energy from ATP hydrolysis to make the process energetically favorable ION CHANNEL -- protein complex containing a small pore which allows a specific ion or group of ions to pass Flow of ions through channels is PASSIVE and is driven by the prevailing chemical and electrical gradients A channel is an ion-specific resistor with a certain conductance ( g ) For most channels, the conductance is the same for ions flowing IN or OUT Other channels allow ions to pass with greater conductance in one direction; these are called RECTIFYING CHANNELS e.g., a channel with greater conductance of inward current is called an inwardly rectifying channel

5. Na/K ATPase PUMP Na +23 ATP ADP + P i inside outside K+K+ Na+/K+ ATPase USES ENERGY FROM ATP HYDROLYSIS TO PUMP SODIUM IONS OUT OF CELL & POTASSIUM IONS INTO CELL AT A 3 Na+ : 2 K+ RATIO CONSEQUENCES OF PUMP ACTIVITY [ K + ] in >> [ K + ] out [ Na + ] in << [ Na + ] out Net positive charge pumped out of cell causes a matching amount of permeable chloride anions to move out passively through channels [ Cl - ] in << [ Cl - ] out

6. IONS CHANNELS inside outside K+K+ Na + POTASSIUM CHANNEL (non-gated, “leak”) Some types of ion channels are “gated”, meaning the ion-selective pore can be either open or shut (not in-between) Such channels can be gated by ligands, phosphorylation, or voltage Other types of ion channels are open all the time These channels referred to as “leak” channels

7. POTASSIUM CHANNELS FAVOR A NEGATIVE MEMBRANE POTENTIAL Potassium channels are the most abundant leak channels in neurons. Because the Na/K pump makes [K + ] in >> [K + ] out, potassium ions move outwards through channels due to the chemical driving potential, E K. (E K can be thought of as a potassium “battery”) Net outward ion flow continues until opposed by a membrane potential, V m, of equal force built up in the membrane capacitor. When V m = 0, large K + efflux AT EQUILIBRIUM When V m = E K, zero net K + flux in out K+K+ K+K+ Na + Cl - A-A- in out K+K+ K+K+ Na + Cl - A-A- + + - - + -

8. CIRCUIT REPRESENTATION OF POTASSIUM CONDUCTANCE, POTASSIUM BATTERY, AND MEMBRANE CAPACITANCE When V m = 0, large K + effluxWhen V m = E K, zero net K + flux in out K+K+ K+K+ Na + Cl - A-A- in out K+K+ K+K+ Na + Cl - A-A- + + - - + - + - IKIK CMCM EKEK gKgK + - I K = 0 CMCM EKEK gKgK + + + _ _ _ V M = 0V M = E K What is the strength of the potassium battery E K ???

9. THE NERNST EQUATION The cytoplasmic and extracellular concentrations of an ion determine the chemical driving force for that ion and the equilibrium membrane potential if this is the ONLY ion that is permeable through the membrane E K + = 58 mV 1 log 5 130 Nernst Equation Where E X is the chemical potential and z is the charge of ion X [K + ] in = 130 mM [K + ] out = 5 mM z = +1 E X = 58 mV z log [X] out [X] in = - 82 mV For potassium:

10. in out K+K+ K+K+ Na + Cl - A-A- + + - - in out K+K+ K+K+ Na + Cl - A-A- + - When V m = 0, large K + efflux I K = 2 pA When V m = E K, zero net K + flux I K = 0 pA VmVm IKIK E K = - 82 mV slope =  K = 25 pS I K = 2 pA VOLTAGE-CURRENT RELATION OF THE POTASSIUM BATTERY inout + - E K = - 82 mV  K = 25 pS I K = 2 pA inout + - E K = - 82 mV  K = 25 pS I K = 0 Conductivity of single K channel  K = 25 pS Total K conductivity ( g K ) g K =  K X N K where N K is # K channels I K = g K x ( V m - E K ) V m = E K + I K R K

11. g K and C m DETERMINE HOW FAST V m CHANGES TO E K in out K+K+ K+K+ Na + Cl - A-A- + - V m (mV) t - 82 0  ~ C m / g K channels open  The greater the value of g K, the greater the potassium current ( I K ) and the faster the transition to the potassium Nernst potential ( E K ) The greater the value of C m, the longer the potassium current ( I K ) and the slower the transition to the potassium Nernst potential ( E K )

12. RESTING POTENTIAL SET BY RELATIVE PERMEABILITIES OF K +, Na +, & Cl - IONS E K = - 82.1 mV 1.0 E Na = + 84.8 mV 0.05 E Cl = - 63.6 mV 0.2 Nernst Potential Relative Permeability (P) Resting membrane potential reflects the relative permeabilities of each ion and the Nernst potential of each ion When the resting membrane potential is achieved, there is ongoing influx of sodium and a matching efflux of potassium. Na/K ATPase is continually needed to keep the ion gradients from running down over time g K E K + g Na E Na + g Cl E Cl g K + g Na + g Cl V m = P K E K + P Na E Na + P Cl E Cl P K + P Na + P Cl = ~

13. THE GOLDMAN EQUATION P K E K + P Na E Na + P Cl E Cl P K + P Na + P Cl V m = from before Nernst equatiion E X = 58 mV z log [X] out [X] in Goldman equation V m = 58 mV log 10 P K [K + ] o + P Na [Na + ] o + P Cl [Cl - ] i P K [K + ] i + P Na [Na + ] i + P Cl [Cl - ] o ( ) The greater an ion’s concentration and permeability, the more it contributes to the resting membrane potential When one ion is by far the most permeable, Goldman eq. reduces to Nernst eq.

14. RELATIVE PERMEABILITY & THE RESTING POTENTIAL P K E K + P Na E Na + P Cl E Cl P K + P Na + P Cl V m = [K + ] o [K + ] i PKPK = 5 mM = 130 mM = 145 mM = 5 mM = 8 mM [Na + ] o [Na + ] i P Na [Cl - ] o = 100 mM [Cl - ] i P Cl = 0.2 = 0.05 = 1 EKEK = - 82.1 mV E Na = 84.8 mV E Cl = - 63.6 mV V m = - 72.4 mV

15. GRAPHIC AND CIRCUIT REPRESENTATIONS OF ION FLOWS ACROSS THE MEMBRANE AT THE RESTING POTENTIAL in out K+K+ K+K+ + + + - - - Cl - K+K+ K+K+ K+K+ K+K+ Na + + + + - - - + + + V m = - 72.4 mV E K = - 82.1 mV E Na = + 84.8 mV I K + I Na + I Cl = 0 AT STEADY STATE: inout + - E K = - 82.1 mV g K = 2 nS I K = 19.4 pA R K = 0.5 G  inout - + E Na = + 84.8 mV g Na = 0.1 nS I Na = - 15.7 pA R Na = 10 G  E K + I K R K E Na + I Na R Na E Cl + I Cl R Cl E K + I K R K = V m = E Na + I Na R Na = E Cl + I Cl R Cl -82.1 mV + (19.4 pA)(0.5 G  )+84.8 mV + (-15.7 pA)(10 G  )-63.6 mV + (-3.5 pA)(2.5 G  ) -82.1 mV + (19.4 pA)(0.5 G  ) = -72.4 mV = +84.8 mV + (-15.7 pA)(10 G  ) = -63.6 mV + (-3.5 pA)(2.5 G  ) V m = in out -72.4 mV +++ --- out - + E Cl = - 63.6 mV g Cl = 0.4 nS I Cl = -3.5 pA R Cl = 2.5 G 

16. INCREASING SODIUM PERMEABILITY UNDERLIES SODIUM INFLUX AND MEMBRANE DEPOLARIZATION DURING ACTION POTENTIAL During action potential, the number of open sodium channels increases dramatically E K = - 82 mV 1.0 1.0 5.0 E Na = + 85 mV 0.05 5.0 E Cl = - 64 mV 0.2 0.2 Nernst Potential P rest P action-potential GOLDMAN EQUATION-PREDICTED V m Rest During Action Potential - 70 mV + 36 mV When sodium channels open, sodium ions flow in rapidly because of the negative membrane potential and the strong inward sodium battery Inward sodium current depolarizes membrane and moves it towards the positive potential predicted by Goldman’s equation (this positive potential is never fully achieved due to additional channel dynamics)

17. Next Lecture: MEASURING MEMBRANE CONDUCTANCE AND CAPACITANCE & VOLTAGE-CLAMP RECORDING REQUIRED READING: Kandel text, Chapters 8, 9 (beginning), pgs 140-153