Ion channels

• Ligand or voltage gated membrane pores

• Electrical properties of cells

• Functional characterization of channels

• Key concepts– Nernst equation– Equilibrium (Nernst) potential– Resting potential– Membrane capacitance and resistance

Ion balance

• Intracellular– 10 mM Na+

– 3 mM Cl-

– 140 mM K+

– 50 nM Ca2+

• Extracellular– 120 mM Na+

– 120 mM Cl-

– 5 mM K+

– 2 mM Ca2+

NaK3 Na+

2 K+

ATPSodium potassium ATPase moves a net positive charge out of the cell

The NaK is responsible for establishing the Na+/K+ concentration gradient

Nernst Equation: Free Energy

To move an ion across membrane Concentration Energy

GC = RT ln(C)

– R=8.314 J/mol/K

Electrical Energy GE = zF(V)

• F=96.5 kJ/mol/V; z=ion valence

• Transport across membrane• Goutin = Gin-Gout

• Goutin = RT ln(Cin)+zFEin–RT ln(Cout)-zFEout

Nernst Equation: Free Energy

Concentration Energy GC = RT ln(Ci/Co)

• R=8.314 J/mol/K

Capacitance Energy GE = zF(Vi-Vo)

• F=96.5 kJ/mol/V; z=ion valence

Equilibrium• zF(Vi-Vo) +RT ln(Ci/Co) = 0

• Vi-Vo =V= RT/zF ln(Co/Ci)

• Co/Ci=exp(zFV/RT)

Lower concentration inside gives G<0

Lower potential inside gives G<0 for positive ions

Compare Nernst for electrochemistry:E0 = RT/nF ln(Qprod/Qreac)

Reciprocal concentration ratio of G, but you can reason whether you have the right order

Nernst Equation

• Intracellular– 140 mM K+

• Extracellular– 5 mM K+

NaK3 Na+

2 K+

ATP

zF

KKRTV iO )/ln(

V=-89 mV

Equilibrium potential

• Intracellular– 10 mM Na+

– 3 mM Cl-

– 140 mM K+

– 50 nM Ca2+

• Extracellular– 120 mM Na+

– 120 mM Cl-

– 5 mM K+

– 2 mM Ca2+

NaK3 Na+

2 K+

ATP

+66mV-98mV-89mV

+142mV

Resting potential-50 - -90 mV

NaCl sets osmotic equilibriumKCl sets electrical equilibriumKCl must be relatively free to move

Ion specific currents

• Ionic Nernst potential defines reversal

-150 -100 -50 0 50 100 150

-200

-150

-100

-50

0

50

100

150

200

250K+Na+Ca++

TransmembranePotential (mV)

Ion

ic c

urr

en

t (m

A*

)

Current positive outwards.Reduce intracellular potential without changing ion concentration (much).Each ion seeks its own Nernst potential

Origin of resting potential

• Equilibrium potential defines Possible resting potential• Ions contribute to resting potential in proportion to

their conductance– As resting potential diverges from Nernst potential, current

increases. Ion with highest g(=1/R) drives the most ions

• Equivalent circuit model– Chord conductance

gK gCl gNa gCaCm

EK ECl ENa ECa

NaK

i

ii

g

EgV

Energy• Transport (out-to-in)

• G =zF(Vi) +RT ln(Ci/Co) per mole

• G =q(Vi) +kBT ln(Ci/Co) per molecule

– Potassium (K+)• dG=F(-0.09)+R(310) ln(140/5)

• dG=-80 J/mole

– Sodium (Na+)• dG=F(-0.09)+R(310) ln(10/120)

• dG=-15 kJ/mole

• ATP hydrolysis– Heat: H=-20kJ/mole– With Entropy: RT ln(ADP Pi H/ATP) ~ -50 kJ/mole

Transport of 1 Na+ down diffusion gradient is coupled to 15 kJ energy release (useful or heat) ~1/3 ATP

Membrane Capacitance

• Charge stored per potential difference• C=Q/V

• Potential change per charge moved• V=Q/C

• C = A/s• : permitivity ~7 pF/cm, pure lipid bilayer, 0.7 w/protein

• S: Thickness ~5 nm

• A: Membrane area…kinda fuzzy

• 1 uF/cm2 neuron ~ 0.1-10 pF

• 8 uF/cm2 skeletal muscle fiber ~ 1 p FHighly structured membrane, so real surface area != apparent SA

Polyester, ~0.4

Membrane Capacitance

• To charge membrane to –90 mV• Q=C V

• Q~10-12*0.1=10-13 Coulombs

• 10-13 C/1.6 10-19 C/electron = 6 105 ions

• 6 105 ions/10-12L = 6 1017 molecules/L= 1 uM

• Higher capacitance requires more charge• Lower capacitance easier to discharge

– Smaller structures vs larger

– Nerve vs muscle

• Despite resting potential, intracellular +/- ions are exactly balanced Provably true within ~10 nM/100mM,

practically accepted as true

Single channel activity

• Patch recording through micropipet

• Single channel current• 1 pA = 1e-12 C/s; e0=1.6e-19 C

= 6e7 ions/secondRemember, 6e5 ions to depolarize neuron

Typical channel has only two conductance states: open and closed.

Characterizing a single channel

• Conductance

• Open dwell time

• Closed dwell time

• Open Probability, Po

• All of these vary with chemical and electrical environment

Kinetics of a BK channel,Díez-Sampedro, et al., 2006

Whole cell recording

• Aggregate behavior of channel population– Single channel discrete; population continuous

• Clamp voltage (V)

• Record current (I)

Applied V

Time

Cur

rent

Recorded I

Derived I-V Derived Conductance

RectificationG=I/VR=V/I

Voltage gated channel

Channel Closing

• Esp voltage gated channels

• Tail current while channels close

Beam & Donaldson, 1983

1.PreconditioningDepolarization

2. Re-/Hyper-polarize

3. Record current as channel closes

Can record tail current in any gated channel which you can change the gating condition fast enough

Channel state models

Closed Open

Closed Closed Open

Closed Open

ATP

ATP-gated

Mg2+ blocked

Mg

pi = proportion of channels in state IW= matrix of rate constants

ii Wpp