1. Hodgin & Huxley The problem: Explain action potentials
The preparation: loligo giant axons
What was known:
Time dependent conductance: Curtis & Cole
Multiple batteries in play
Likely players Na+, K+ : Hodgkin & Katz
A new method: Voltage Clamp

2. Action Potentials “Overshoot”
200 Hz time calibration
Later Hodgkin and Katz showed that reducing [Na]o reduced the overshoot
Hodgkin & Huxley, 1939 Nature 144:473-96

3. Loligo forbesi

4. Parallel conductance model

5. How to study the process of action potential generation
200 Hz time calibration
Later Hodgkin and Katz showed that reducing [Na]o reduced the overshoot

6. Voltage Clamp 3 electrodes used: Advantages 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. 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

8. Isolation of the “outward current”

9. gK(t)
Sigmoid onset
Noninactivating
Exponential offset

10. Model of gK

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

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

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

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

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

16. gNa kinetics
Both activation and inactivation speed up with depolarization

17. Model of gNa

18. hoo
Determined with prepulse experiments

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

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

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

22. 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)

23. HH fit to expermentally determined gNa

24. Voltage clamp currents are reproduced by simulations

25. …as are action potentials
Calculated by hand calculator by integrating at very small time steps

26. Evolution of channel gates during action potential

27. Modern view of voltage gated ion channels

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

29. Allosteric model results
Reproduces transient & sustained current

30. 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