Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p ) and chapter 21 (p ). Alberts et al., Molecular Biology of the Cell, 4 th ed, chapter 11 (p ) and p Hille Ionic channels of excitable membranes 3 rd ed.

LIFE – A complex interplay of chemistry and physics

The action potential – Physics in cell biology K+ Na+

Excitation-contraction coupling

The islet of Langerhans

Glucose-dependent hormone secretion

The Lipid Bilayer is a Selective Barrier hydrophobic molecules (anesthetics) gases (O 2, CO 2 ) small uncharged polar molecules large uncharged polar molecules Ions charged polar molecules (amino acids) water inside outside

Ion Channel Diversity

Cation channel Subunit Topology

The ‘inner core’ of cation channel superfamily members

Structure of a Potassium Channel Doyle et al., 1998

Selectivity Filter and Space-Filling Model Doyle et al., 1998

Ion selectivity filter in KcsA Doyle et al., 1998, Zhou et al., 2002

Selectivity filter diversity

Ion selectivity filter in Na channels NavMs, NavAb, Kv1.2 Nature Communications, Oct 2, Structure of a bacterial voltage-gated sodium channel pore reveals mechanisms of opening and closing Emily C McCusker, 1, 3, Claire Bagnéris, 1 Claire E Naylor, 1, Ambrose R Cole, 1 Nazzareno D'Avanzo, 2, 4, Colin G Nichols 2, & B A Wallace 1Emily C McCusker 13 Claire Bagnéris 1 Claire E Naylor 1 Ambrose R Cole 1 Nazzareno D'Avanzo 24, Colin G Nichols 2B A Wallace 1

Views of the Channel Open and Shut Jiang et al., 2002

Views of the Channel Open and Shut Nature Communications, Oct 2, Structure of a bacterial voltage-gated sodium channel pore reveals mechanisms of opening and closing Emily C McCusker, 1, 3, Claire Bagnéris, 1 Claire E Naylor, 1, Ambrose R Cole, 1 Nazzareno D'Avanzo, 2, 4, Colin G Nichols 2, & B A Wallace 1Emily C McCusker 13 Claire Bagnéris 1 Claire E Naylor 1 Ambrose R Cole 1 Nazzareno D'Avanzo 24, Colin G Nichols 2B A Wallace 1

Ion gradients and membrane potential

-89 mV How does this membrane potential come about? The inside of the cell is at ~ -0.1V with respect to the outside solution

Ion gradients and membrane potential -89 mV How does this membrane potential come about? K Cl KNa

Ion gradients and membrane potential Na117 K 3 Cl120 Anions 0 Total 240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] -89 mV How does this membrane potential come about?

Na117 K 3 Cl120 Anions 0 Total240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] 0 mV Movement of Individual K + ions

Na117 K 3 Cl120 Anions 0 Total240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] 0 mV Movement of Individual Cl - ions mV

Setting a membrane potential – questions! How many ions must cross the membrane to set up this membrane potential? What makes it stop at this potential?

Capacitance CapacitanceCCoulombs / VoltFaradsF C = Q / VQ = C * VI = dQ / dt = C * dV / dt VC + - I C µ area { C µ 1 / thickness For biological membranes: Specific Capacitance = 1 µF / cm 2

How many ions? 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  r 2 Faraday’s Constant = x 10 4 Coulombs / mole Avogadro’s # = x ions / mole

Calculations Area = 4  r 2 = 4 p (25 x cm) 2 = 7.85 x cm 2 = 78.5 x µFarads = 78.5 x Farads Q = C * V = 78.5 x Farads * Volts = 7 x Coulombs ~ 7 x Coulombs / 9.65 x 10 4 Coulombs per mole = 7.3 x moles of ions must cross the membrane = femptomoles or ~ 44 x 10 6 ions ~ 1.1 µM change in [ ] 12 3

Why does it stop? - 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: zFV Chemical Energy Term: RT.ln[Ion] Z is the charge, 1 for Na + and K +, 2 for Ca 2+ and Mg 2+, -1 for Cl - F is Faraday’s Constant = x 10 4 Coulombs / mole R is the gas constant = Joules / °Kelvin * mole T is the temperature in °Kelvin

Nernst Equation Derivation zF.V in + RT.ln [K + ] in = zF.V out + RT.ln [K + ] out zF (V in – V out ) = RT (ln [K + ] out – ln [K + ] in ) E K = V in – V out = (RT/zF).ln([K + ] out /[K + ] in ) E K = (RT / F) * log 10 ([K + ] out /[K + ] in ) In General: E ion ~ 60 * log ([ion] out / [ion] in ) for monovalent cation at 30°

Nernst Potential Calculations First K and Cl E K = 60 mV log (3 / 90) = 60 * = -89 mV E Cl = (60 mV / -1) log (120 / 4) = -60 * = -89 mV Both Cl and K are at electrochemical equilibrium at -89 mV Now for Sodium E Na = 60 mV log (117 / 30) = 60 * = +36 mV When 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 any energy- driven pump to maintain the concentration gradient

Ion Concentrations Na117 K 3 Cl120 Anions 0 Total240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] -89 mV

Ion Concentrations Na117 K 3 Cl120 Anions 0 Total240 Na 30 K 90 Cl 4 Anions 116 Total 240 [+ charge] = [- charge] 0 mV [+ charge] = [- charge] -89 mV Add water – 50% dilution

Na 30 K 90 Cl 4 Anions 116 Total 240 Environmental Changes: Dilution Na58.5 K 1.5 Cl 60 Anions 0 Total120 [+ charge] = [- charge] Add water – 50% dilution [+ charge] = [- charge] -89 mV H2OH2O

Na 30 K 90 Cl 4 Anions 116 Total 240 Environmental Changes: Dilution Na58.5 K 1.5 Cl 60 Anions 0 Total120 [+ charge] = [- charge] Add water – 50% dilution E K = -107 mV E Cl = -71 mV [+ charge] = [- charge] -89 mV

Environmental Changes: Dilution Na58.5 K 1.5 Cl 60 Anions 0 Total120 [+ charge] = [- charge] Add water – 50% dilution E K = -107 mV E Cl = -71 mV Na 30 K<90 Cl <4 Anions 116 Total<240 [+ charge] = [- charge] -89 mV H2OH2O

Deviation from the Nernst Equation External [K] (mM) 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 * = -63 mV Suppose P K : P Na : P Cl = 1 : 0.1 : 1

Competing Batteries Model Ohm’s Law: V = I * R, so I Na = V 1 * g Na I K = V 2 * g K I Cl = V 3 * g Cl At rest there is no net current I Na + I K + I Cl = 0 Þ V 1 * g Na + V 2 * g K + V 3 * g Cl = 0 V m = V 1 + E Na = V 2 + E K = V 3 + E Cl Þ V 1 = V m – E Na and V 2 = V m – E K and V 3 = V m – E Cl  0 = (V m – E Na ) * g Na + (V m – E K ) * g K + (V m – E cl ) * g Cl V m = g Na E Na + g K E K + g Cl E Cl I ion = g ion * (V m -E ion ) g Na + g K + g Cl

Recording Membrane Potential

To here L1

On-Cell Patch Recording (Muscle) 50 µm

Forming a Tight Seal

Whole-Cell and Outside-Out Patch 10 µm

Channels Exist in at least 2 States

To here… Current ~3.2 pA = 3.2 x Coulombs/sec Charge on 1 ion ~1.6 x Culombs Ions per second = 3.2/1.6 x 10^7 ~20 million

Exponential Distribution of Lifetimes mean open time =  open = 1 / a = 1 / closing rate constant

Summary: I. Cell membranes form an insulating barrier that acts like a parallel plate capacitor (1 µF /cm 2 ) II. Ion channels allow cells to regulate their volume and to generate membrane potentials III. Only a small number of ions must cross the membrane to create a significant voltage difference ~ bulk neutrality of internal and external solution IV. Permeable ions move toward electrochemical equilibrium E ion = (60 mV / z) * log ([Ion] out / [Ion] in 30°C Electrochemical equilibrium does not depend on permeability, only on the concentration gradient

Summary (continued): V. 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 The cell must supply energy to maintain its ionic gradients