Hodgin

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 144473-96
3
Loligo forbesi
4
Parallel conductance model
5
Action Potentials Overshoot
Hodgkin Huxley, 1939 Nature 144473-96
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(tDt)
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