# Channels by ert554898

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• pg 1
```									               Ion channels
• Ligand or voltage gated membrane pores
• Electrical properties of cells
• Functional characterization of channels
Ion balance
• Intracellular                  • Extracellular
–   10 mM Na+                   –   120 mM Na+
–   3 mM Cl-                    –   120 mM Cl-
–   140 mM K+                   –   5 mM K+
–   50 nM Ca2+                  –   2 mM Ca2+

2 K+
NaK
3   Na+
ATP                 The NaK is responsible for
establishing the Na+/K+
moves a net positive
charge out of the cell
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
– Goutin = Gin-Gout
– Goutin = RT ln(Cin)+zFEin–RT ln(Cout)-zFEout
Nernst Equation: Free Energy
 Concentration Energy                Lower concentration
 GC = RT ln(Ci/Co)                inside gives G<0

– R=8.314 J/mol/K
 Capacitance Energy               Lower potential
 GE = zF(Vi-Vo)                inside gives G<0
for positive ions
– F=96.5 kJ/mol/V; z=ion valence
Reciprocal concentration
 Equilibrium                                ratio of G, but you can
reason whether you
– zF(Vi-Vo) +RT ln(Ci/Co) = 0              have the right order
– Vi-Vo =V= RT/zF ln(Co/Ci) Compare Nernst for
electrochemistry:
– Co/Ci=exp(zFV/RT)          E = E0 - RT/nF ln(Qprod/Qreac)
Nernst Equation
• Intracellular               • Extracellular
– 140 mM K+                   – 5 mM K+

ln(/ i)
K
RT O K
V
zF

V=-90 mV

2 K+
NaK
3   Na+
ATP
Equilibrium potential
• Intracellular                • Extracellular
+66mV – 10 mM Na+                    –   120 mM Na+
-98mV – 3 mM Cl-                     –   120 mM Cl-
-90mV – 140 mM K+                    –   5 mM K+
+50mV – 50 nM Ca2+                   –   2 mM Ca2+

2 K+
NaK
3   Na+
ATP
NaCl sets osmotic equilibrium
Resting potential                KCl sets electrical equilibrium
-50 - -90 mV                    KCl must be relatively free to
move
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          Transport of 1 Na+ down diffusion
gradient is coupled to 15 kJ energy
• ATP hydrolysis                 release (useful or heat) ~1/3 ATP

– Heat: H=-20kJ/mole
– With Entropy: RT ln(ADP Pi H/ATP) ~ -50 kJ/mole
Membrane Capacitance
• Charge stored per potential difference
– C=Q/V
• Potential change per charge moved
– V=Q/C
– C = e A/s
• e: permitivity ~7 pF/cm, pure lipid bilayer, 0.7 w/protein
• S: Thickness ~5 nm
Polyester, ~0.4
• A: Membrane area…kinda fuzzy
– 1 uF/cm2 neuron ~ 0.1-10 pF
– 8 uF/cm2 skeletal muscle fiber ~ 1 p F
Highly structured membrane, so
real surface area != apparent SA
Membrane Capacitance
• To charge membrane to –90 mV
–   V=Q/C; Q=C V
–   Q=10-12*0.1=10-13 Coulombs
–   10-13 C/1.6 10-19 C/electron = 6 104 ions
–   6 104 ions/10-12L = 6 1016 mol/L= 100 nM
• 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
Ion specific currents
• Ionic Nernst potential defines reversal

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

NaK
gK      gCl      gNa     gCa
Cm       V
E
g    i       i

 g       i

EK      ECl     ENa      ECa
Single channel activity
• Patch recording through micropipet
• Single channel current
• 1 pA = 1e-12 C/s; e0=1.6e-19 C
Remember, 6e4 ions to
= 6e7 ions/second           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)          Voltage gated channel
Derived I-V          Derived Conductance
Applied V
Current

Time                                             G=I/V
Rectification                 R=V/I
Recorded I
Channel Closing
• Esp voltage gated channels
• Tail current while channels close
2. Re-/Hyper-polarize
1.Preconditioning
Depolarization

3. Record current as channel closes

Can record tail current in
any gated channel which
you can change the gating
condition fast enough                         Beam & Donaldson, 1983
Channel state models

Closed         Open

ATP

Closed         Open          ATP-gated

Closed        Closed         Open         Mg2+ blocked

Mg

p  Wp
             pi = proportion of channels in state I
W= matrix of rate constants

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