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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.
LIFE – A complex interplay of chemistry and physics
The action potential – Physics in cell biology
1
1
2
2
3
3
4
4
K+
Na+
Excitation-contraction coupling
The islet of Langerhans
Glucose-dependent hormone secretion
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
Ion Channel Diversity
Cation channel Subunit Topology
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 KcsADoyle et al., 1998, Zhou et al., 2002
Selectivity filter diversity
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
Views of the Channel Open and Shut
Jiang et al., 2002
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
Ion gradients and membrane potential
Ion gradients and membrane potential
Ion gradients and membrane potential
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
K Na
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?
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
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
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
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
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
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
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
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°
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
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
Na 117K 3Cl 120Anions 0Total 240
Na 30K 90Cl 4Anions 116Total 240
[+ charge] = [- charge]
0 mV
[+ charge] = [- charge]
-89 mV
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
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
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
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
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
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.
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
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 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
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 /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
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