Lecture 4: the hodkin and Huxley model

Special thanks to Prof. Sobie for sharing his slides

Sir Alan Hodgkin

Sir Andrew Huxley

The Hodgkin-Huxley model

1914-1998

1914-1998

Noble prize 1963

Brief historical note

Action potential recorded at the Marine Biological Association  at Plymouth

Hodkin and Huxley (1939) Nature 144:710-711

Hodgkin & Huxley left Plymouth: August 30, 1939

Hilter invaded Poland: September 1, 1939

"We published this result in a letter in Nature (1939) with no discussion or explanation. In a full paper (1945) we gave four possible explanations, all wrong" Huxley (2002), J. Physiol. 539: 2

Single cell

The membrane: contains channels which can open and close

Nerst potential: 2 opposite forces:

  • diffusion
  • electrical force

You can find the equilibrium which gives you the Nerst potential

 

 

 

 

 

 

 

 

 

 

Nerst potential: 2 opposite forces:

  • diffusion
  • electrical force

You can find the equilibrium which gives you the Nerst potential

 

 

 

 

 

 

 

 

 

 

Most easy model: Hodgkin huxley (nerve cell)

Most easy model: Hodgkin huxley (nerve cell)

Most easy model: Hodgkin huxley (nerve cell)

Current I required to keep Vcommand = Vi is equal in magnitude

to current flowing across the membrane

How to separate INa and IK?

V

time

I

time

Why did they have to develop the voltage clamp technique?

Imagine that we can magically separate INa and IK

Intermezzo:

Problem 1:

Problem 2:

Intermezzo:

Intermezzo:

Hudgkin and Huxley found a way to control the voltage so they could measure the currents

We will now derive the model equations from the experimental recordings.

 

We will convert the currents to conductance:

  1. K+ conductance: will increase with a delay
  2. Na+ conductance: increase and then decrease or inactivate

 

 

How do we go from these measurements to the famous equations of Hudgkin and Huxley?

1) Changing V changes both steady-state gK and rate of rise

2) Time course of gK: increase similar to an exponential raised to a power

time

time

time

n is a gating variable, which is always between 0 and 1

We can rewrite this equation as:

and

can be extracted from the data

How?

and

can be extracted from the data

How?

Initial situation: V= -80 mV

Fast activation of m-channel: INa large

Inactivation of h-channel -> INa equal to zero

n-channel open -> makes V lower again, gates closes