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 Ca 2+ Extracellular –120 mM Na + –120 mM Cl - –5 mM K + –2 mM Ca 2+ NaK 3 Na + 2 K + ATP Sodium 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  G C = RT ln(C) –R=8.314 J/mol/K  Electrical Energy  G E = zF(V) F=96.5 kJ/mol/V; z=ion valence Transport across membrane  G out  in = G in -G out  G out  in = RT ln(C in )+zFE in –RT ln(C out )-zFE out

Nernst Equation: Free Energy  Concentration Energy   G C = RT ln(C i /C o ) R=8.314 J/mol/K  Capacitance Energy   G E = zF(Vi-Vo) F=96.5 kJ/mol/V; z=ion valence  Equilibrium zF(Vi-Vo) +RT ln(C i /C o ) = 0 Vi-Vo =V= RT/zF ln(C o /C i ) C o /C i =exp(zF  V/RT) Lower concentration inside gives  G<0 Lower potential inside gives  G<0 for positive ions Compare Nernst for electrochemistry:  E 0 = RT/nF ln(Q prod /Q reac ) 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 + NaK 3 Na + 2 K + ATP V=-89 mV

Equilibrium potential Intracellular –10 mM Na + –3 mM Cl - –140 mM K + –50 nM Ca 2+ Extracellular –120 mM Na + –120 mM Cl - –5 mM K + –2 mM Ca 2+ NaK 3 Na + 2 K + ATP +66mV -98mV -89mV +142mV Resting potential mV NaCl sets osmotic equilibrium KCl sets electrical equilibrium KCl must be relatively free to move

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 gKgK g Cl g Na g Ca CmCm EKEK E Cl E Na E Ca NaK

Energy Transport (out-to-in)  G =zF(Vi) +RT ln(C i /C o ) per mole  G =q(Vi) +k B T ln(C i /C o ) 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/cm 2 neuron ~ pF 8 uF/cm 2 skeletal muscle fiber ~ 1 p F Highly structured membrane, so real surface area != apparent SA Polyester, ~0.4

Membrane Capacitance To charge membrane to –90 mV Q=C V Q~ *0.1= Coulombs C/ C/electron = ions ions/ L = 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; e 0 =1.6e-19 C = 6e7 ions/second Remember, 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, P o 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 Current Recorded I Derived I-V Derived Conductance Rectification G=I/V R=V/I Voltage gated channel

Channel Closing Esp voltage gated channels Tail current while channels close Beam & Donaldson, Preconditioning Depolarization 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 ClosedOpen Closed Open ClosedOpen ATP ATP-gated Mg 2+ blocked Mg p i = proportion of channels in state I W= matrix of rate constants