Channels

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					               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+
Sodium potassium ATPase                   concentration gradient
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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