membrane potential and ion channels colin nichols background readings: lodish et al., molecular cell...

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Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology , 4 th ed, chapter 15 (p. 633-665) and chapter 21 (p. 925-965). Alberts et al., Molecular Biology of the Cell , 4 th ed, chapter 11 (p. 615-650) and p. 779-780. Hille Ionic channels of excitable membranes 3 rd ed.

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Page 1: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Membrane Potential

and Ion Channels

Colin Nichols

Background readings:Lodish et al., Molecular Cell Biology, 4th ed, chapter 15 (p. 633-665) and chapter 21 (p. 925-965).

Alberts et al., Molecular Biology of the Cell, 4th ed, chapter 11 (p. 615-650) and p. 779-780.

Hille Ionic channels of excitable membranes 3rd ed.

Page 2: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

LIFE – A complex interplay of chemistry and physics

Page 3: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

The action potential – Physics in cell biology

1

1

2

2

3

3

4

4

K+

Na+

Page 4: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Excitation-contraction coupling

Page 5: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

The islet of Langerhans

Page 6: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Glucose-dependent hormone secretion

Page 7: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

The Lipid Bilayer is a Selective Barrier

hydrophobic molecules (anesthetics)

gases (O2, CO2)

small uncharged polar molecules

large uncharged polar molecules

Ions

charged polar molecules (amino acids)

water

inside outside

Page 8: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion Channel Diversity

Page 9: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Cation channel Subunit Topology

Page 10: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Cation channel Subunit Topology

The ‘inner core’ of cation channel superfamily members

Page 11: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Structure of a Potassium Channel

Doyle et al., 1998

Page 12: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Selectivity Filter and Space-Filling Model

Doyle et al., 1998

Page 13: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion selectivity filter in KcsADoyle et al., 1998, Zhou et al., 2002

Page 14: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Selectivity filter diversity

Page 15: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion selectivity filter in Na channels

NavMs, NavAb, Kv1.2 Nature Communications , Oct 2, 2012. 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 Nichols2, & B A Wallace1

Page 16: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Views of the Channel Open and Shut

Jiang et al., 2002

Page 17: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Views of the Channel Open and Shut

Nature Communications , Oct 2, 2012. 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 Nichols2, & B A Wallace1

Page 18: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion gradients and membrane potential

Page 19: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion gradients and membrane potential

Page 20: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion gradients and membrane potential

Page 21: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

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

Page 22: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion gradients and membrane potential

-89 mV

How does this membrane potential come about?

K

Cl

K Na

Page 23: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion gradients and membrane potential

Na 117K 3Cl 120Anions 0Total 240

Na 30K 90Cl 4Anions 116Total 240

[+ charge] = [- charge]

0 mV

[+ charge] = [- charge]

-89 mV

How does this membrane potential come about?

Page 24: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Na 117K 3Cl 120Anions 0Total 240

Na 30K 90Cl 4Anions 116Total 240

[+ charge] = [- charge]

0 mV

[+ charge] = [- charge]

0 mV

+ -

+ -

Movement of Individual K+ ions

Page 25: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Na 117K 3Cl 120Anions 0Total 240

Na 30K 90Cl 4Anions 116Total 240

[+ charge] = [- charge]

0 mV

[+ charge] = [- charge]

0 mV

Movement of Individual Cl- ions

+ -

+ -

-89 mV

Page 26: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

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?

Page 27: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Capacitance

Capacitance C Coulombs / Volt Farads F

C = Q / V Q = C * V I = dQ / dt = C * dV / dt

V C+

-

I

+ + + + + + + +

- - - - - - - -

C µ area

{

C µ 1 / thickness

For biological membranes:Specific Capacitance = 1 µF / cm2

Page 28: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

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 / cm2

Surface area = 4 r2

Faraday’s Constant = 9.648 x 104 Coulombs / mole

Avogadro’s # = 6.022 x 1023 ions / mole

Page 29: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Calculations

Area = 4 r2

= 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

~ 7 x 10-12 Coulombs / 9.65 x 104 Coulombs per mole

= 7.3 x 10-17 moles of ions must cross the membrane

= 0.073 femptomoles or ~ 44 x 106 ions ~ 1.1 µM change in [ ]

1 2

3

Page 30: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

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: zFVChemical Energy Term: RT.ln[Ion]

Z is the charge, 1 for Na+ and K+, 2 for Ca2+ 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

Page 31: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Nernst Equation Derivation

zF.Vin + 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 * log ([ion]out / [ion]in) for monovalent cation at 30°

Page 32: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Nernst Potential Calculations

First K and ClEK = 60 mV log (3 / 90) = 60 * -1.477 = -89 mV

ECl = (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 ENa = 60 mV log (117 / 30) = 60 * 0.591 = +36 mV

When Vm = -89 mV, both the concentration gradient and electrical gradient for Na are from outside to inside

Page 33: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

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

Page 34: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion Concentrations

Na 117K 3Cl 120Anions 0Total 240

Na 30K 90Cl 4Anions 116Total 240

[+ charge] = [- charge]

0 mV

[+ charge] = [- charge]

-89 mV

Page 35: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Ion Concentrations

Na 117K 3Cl 120Anions 0Total 240

Na 30K 90Cl 4Anions 116Total 240

[+ charge] = [- charge]

0 mV

[+ charge] = [- charge]

-89 mV

Add water – 50% dilution

Page 36: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Na 30K 90Cl 4Anions 116Total 240

Environmental Changes: Dilution

Na 58.5K 1.5Cl 60Anions 0Total 120

[+ charge] = [- charge]

Add water – 50% dilution

[+ charge] = [- charge]

-89 mV

H2O

Page 37: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Na 30K 90Cl 4Anions 116Total 240

Environmental Changes: Dilution

Na 58.5K 1.5Cl 60Anions 0Total 120

[+ charge] = [- charge]

Add water – 50% dilution

EK = -107 mVECl = -71 mV

[+ charge] = [- charge]

-89 mV

Page 38: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Environmental Changes: Dilution

Na 58.5K 1.5Cl 60Anions 0Total 120

[+ charge] = [- charge]

Add water – 50% dilution

EK = -107 mVECl = -71 mV

Na 30K <90Cl <4Anions 116Total <240

[+ charge] = [- charge]

-89 mV

H2O

Page 39: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Deviation from the Nernst Equation

1 3 10 30 100 300 External [K] (mM)

0

-25

-50

-75

-100

Res

ting

Pot

entia

l (m

V)

EK (Nernst)

PK : PNa : PCl

1 : 0.04 : 0.05

Resting membrane potentials in real cells deviate from the Nernst equation, particularlyat low external potassiumconcentrations.

The Goldman, Hodgkin, Katzequation provides a better description of membrane potential as a function of potassium concentration in cells.

Squid AxonCurtis and Cole, 1942

Page 40: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

The Goldman Hodgkin Katz Equation

outClinNainK

inCloutNaoutKm [Cl]P[Na]P[K]P

[Cl]P[Na]P[K]Plog60mVV

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.

Page 41: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

GHK Equation: Sample Calculation

120390

47.113log60mVVm

= 60 mV * log (18.7 / 213)

= 60 mV * -1.06

= -63 mV

Suppose PK : PNa : PCl = 1 : 0.1 : 1

Page 42: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Recording Membrane Potential

Page 43: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

To here L1

Page 44: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

On-Cell Patch Recording (Muscle)

50 µm

Page 45: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Forming a Tight Seal

Page 46: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Whole-Cell and Outside-Out Patch

10 µm

Page 47: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Channels Exist in at least 2 States

Page 48: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

To here…

Current ~3.2 pA = 3.2 x 10-12 Coulombs/sec

Charge on 1 ion ~1.6 x 10-19 Culombs

Ions per second = 3.2/1.6 x 10^7

~20 million

Page 49: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Exponential Distribution of Lifetimes

mean open time = open = 1 / a = 1 / closing rate constant

Page 50: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Summary:

I. Cell membranes form an insulating barrier that acts like a parallel plate capacitor (1 µF /cm2)

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• Eion = (60 mV / z) * log ([Ion]out / [Ion]in) @ 30°C• Electrochemical equilibrium does not depend on

permeability, only on the concentration gradient

Page 51: Membrane Potential and Ion Channels Colin Nichols Background readings: Lodish et al., Molecular Cell Biology, 4 th ed, chapter 15 (p. 633-665) and chapter

Summary (continued):

V. The Goldman, Hodgkin, Katz equation gives the steady-state membrane potential when Na, K and Cl are permeable

• In this case, Vm 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

outClinNainK

inCloutNaoutKm [Cl]P[Na]P[K]P

[Cl]P[Na]P[K]Plog60mVV