Hodgkin-Huxley Action Potential Model

​
stimulus amplitude
15
The voltage across membranes of excitable cells (e.g. nervous system, muscles, heart, endocrine system) transiently changes, creating a pulse-like wave called an "action potential". The action potential serves as a major signal for the initiation of many cellular and intercellular processes. The canonical mathematical-physical model of the phenomenon was presented by Alan Hodgkin and Andrew Huxley in 1952 in a series of seminal papers[2], where membrane potential dynamics is described in terms of voltage-dependent ionic conductance, dominated by four coupled ordinary differential equations. In the Demonstration presented here, the action potential is triggered by a short current stimulus. Shown are time evolutions of membrane voltage (blue trace) and conductance gates (
m
,
h
, and
n
).

Details

Units:
msec
,
mS
,
mV
, and
μF
2
cm
.
Rate functions:
α
m
=0.1(v+40)/(1-exp(-0.1(v+40)));​​
β
m
=4exp(-0.05(v+65));​​​​
α
n
=-0.01(v+55)/((exp(-0.1(v+55))-1);​​
β
n
=0.25exp(-0.0125(v+65));​​​​
α
h
=0.07exp(-0.05(v+65));​​
β
h
=1/((exp(-0.1(v+55))+1)
Parameters:
Maximal conductances are
20
,
12
, and
0.1
for sodium, potassium, and leak, respectively. Nernst equilibrium potentials are
50
,
-90
, and
-60
for sodium, potassium, and leak, respectively. Membrane capacitance is set to 1.

References

[1] B. Hille, Ion Channels of Excitable Membranes, Sunderland, MA: Sinauer, 2001.
[2] A. L. Hodgkin and A. F. Huxley, "A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve," Journal of Physiology, 117, 1952 pp. 500–544.

Permanent Citation

Shimon Marom
​
​"Hodgkin-Huxley Action Potential Model"​
​http://demonstrations.wolfram.com/HodgkinHuxleyActionPotentialModel/​
​Wolfram Demonstrations Project​
​Published: April 20, 2012