membrane potential and ion channels colin nichols background readings: lodish et al., molecular cell...
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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](https://reader035.vdocument.in/reader035/viewer/2022062301/5697c0131a28abf838cccac3/html5/thumbnails/1.jpg)
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.
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LIFE – A complex interplay of chemistry and physics
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The action potential – Physics in cell biology
1
1
2
2
3
3
4
4
K+
Na+
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Excitation-contraction coupling
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The islet of Langerhans
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Glucose-dependent hormone secretion
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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
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Ion Channel Diversity
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Cation channel Subunit Topology
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Cation channel Subunit Topology
The ‘inner core’ of cation channel superfamily members
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Structure of a Potassium Channel
Doyle et al., 1998
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Selectivity Filter and Space-Filling Model
Doyle et al., 1998
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Ion selectivity filter in KcsADoyle et al., 1998, Zhou et al., 2002
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Selectivity filter diversity
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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
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Views of the Channel Open and Shut
Jiang et al., 2002
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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
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Ion gradients and membrane potential
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Ion gradients and membrane potential
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Ion gradients and membrane potential
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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
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Ion gradients and membrane potential
-89 mV
How does this membrane potential come about?
K
Cl
K Na
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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?
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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
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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
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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?
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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
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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
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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
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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
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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°
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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
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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
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Ion Concentrations
Na 117K 3Cl 120Anions 0Total 240
Na 30K 90Cl 4Anions 116Total 240
[+ charge] = [- charge]
0 mV
[+ charge] = [- charge]
-89 mV
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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
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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
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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
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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
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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
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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.
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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
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Recording Membrane Potential
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To here L1
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On-Cell Patch Recording (Muscle)
50 µm
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Forming a Tight Seal
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Whole-Cell and Outside-Out Patch
10 µm
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Channels Exist in at least 2 States
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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
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Exponential Distribution of Lifetimes
mean open time = open = 1 / a = 1 / closing rate constant
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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
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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