Hodgin & Huxley

1. Hodgin & Huxley • The problem: Explain action potentials • The preparation: loligo giant axons • The suspects: • Time dependent conductance: Curtis & Cole • Multiple batteries in play • Likely players Na+, K+ : Hodgkin & Katz • The method: Voltage Clamp • Electronic feedback circuitry to fix membrane potential & measure the required current

2. Action Potentials “Overshoot” Hodgkin & Huxley, 1939 Nature 144:473-96

3. Loligo forbesi

4. Parallel conductance model

5. Action Potentials “Overshoot” Hodgkin & Huxley, 1939 Nature 144:473-96

6. Voltage Clamp • 3 electrodes used: • Vo • Vi • Ii (injected current, measured with I-mon) • Advantages • Space clamp – axial wires used – • Can effectively eliminate Ic – V is fixed • Used to isolate time dependent changes in I

7. V steps to depolarized potentials • Bipolar current responses • Early inward current followed by late outward current • Isolate inward/outward components • Time • Ion substitution • V-command

8. Voltage clamp currents in loligo Modern convention: • Original presentation: • - Vm relative to rest • -referenced to inside of cell • amplitude & polarity appropriate • for necessary charging of membrane

9. Isolate iNa by algebraic subtraction • Appears Ohmic • Sigmoidal onset • Increase in gNa is reversible • g(V) is independent of i sign

10. Current flow through pNa is Ohmic • Open channel I/V curve • Instantaneous conductance

11. gNa kinetics • Both activation and inactivation speed up with depolarization

12. Characterize gK • In absence of Na • Determine equilibrium g/V curve and kinetics of activation and inactivation

13. gK(t) • Sigmoid onset • Noninactivating • Exponential offset

14. Model of gK

15. Equilibrium n(V), noo • Similar to a Boltzmann distribution

16. Rate constants for gate n • Derived from onset or offset of gK upon DV

17. gK fitted to HH equation • Reasonable fit to onset, offset & steady state

18. Model of gNa

19. hoo • Determined with prepulse experiments

20. Rate constants for gate m • Derived from onset or offset of gNa upon DV

21. Rate constants for gate h • Derived from onset or offset of gNa upon DV

22. Summary of equilibrium states and time constants for HH gates

23. HH model equations - All as and bs are dependent on voltage but not time - Calculate I from sum of leak, Na, K - Can calculate dV/dt, and approximate V1 =V(t+Dt)

24. HH fit to expermentally determined gNa

25. Voltage clamp currents are reproduced by simulations

26. …as are action potentials

27. Evolution of channel gates during action potential

28. Modern view of voltage gated ion channels

29. Markov model of states & transitions • Allosteric model of Taddese & Bean • Only 2 voltage dependent rates

30. Allosteric model results • Reproduces transient & sustained current

31. Generality of model • Many ion channels described in different neuronal systems • Each has unique • Equilibrium V activation range • Equilibrium V inactivation range • Kinetics of activation and inactivation • Reversal potential • These contribute to modification of spike firing in different V and f domains