Model: HODHUX, the HodgkinHuxley model for membrane conductance
2. IMPORTANT !!! To run a demonstration, enter "xhost +nsr.bioeng.washington.edu" in one of your windows to allow the demonstration program to open windows on your machine !!!
3. Reference
Hodgkin, A.L. and Huxley, A.F., "A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (1952) 117, 500544.
4. Input parameters
HODHUX is parameterized as follows.
Table 1. HODHUX Input Parameters
Parameter

Description

Units

I

Total current (capacity current + ionic currents)

mu A/cm^2


Membrane capacity,
is the capacity current

mu F/cm^2

(gbarK)

Potassium conductance
is the ionic current
carried by potassium ions

m.mho/cm^2

(VK)

Potential associated with potassium ions

mV

(gbarNa)

Sodium conductance
is the ionic
current carried by sodium ions

m.mho/cm^2

(VNa)

Potential associated with sodium ions

mV

(gbarl)

Leakage conductance
leakage current carried by
chloride and other ions

m.mho/cm^2

(Vl)

Potential associated with chloride
and other ions

mV

(V0)

Initial Potential

mV

Temperature

Temperature, reaction rates triple for
every 10 degrees centigrade change in
temperature

degrees Centigrade

(Vrest)

Resting membrane potential

mV

Access to all input variables is via selecting "Inputs" under the "Parameters" menu.
5. Calculated Parameters
The following parameters are calculated from the Input parametersAccess to all Access to all calculated variables is via selecting "Calculated" under the "Parameters" menu.
Table 2.



(phi)

controls the
reaction speed of the alpha and beta
constants which it multiplies.
At 16.3 degrees centigrade, the rate
constants are increased by a factor of
3.0.

none

(n0rest)

Initial value of n at time=0 (a function
of Vrest)

none

(m0rest

Initial value of m at time=0 (a
function of Vrest)

none

(h0rest)

Initial value of h at time=0 (a function
of Vrest)

none

6. Output Variables
Output variables are given by:
Table 3. HODHUX Output Variables
Parameter

Description

Units


Membrane potential

mV


Dimensionless time dependent
variable affecting ionic potassium
current

none


Dimensionless time dependent
variable affecting ionic sodium
current

none


Dimensionless time dependent
variable affecting ionic sodium
current

none

(alphan)

Voltage dependent parameter
governing time dependent variable n

1/msec

(betan)

Voltage dependent parameter
governing time dependent variable n

1/msec

(alpham)

Voltage dependent parameter
governing time dependent variable m

1/msec

(betam)

Voltage dependent parameter
governing time dependent variable m

1/msec

(alphah)

Voltage dependent parameter
governing time dependent variable h

1/msec

(betah)

Voltage dependent parameter
governing time dependent variable h

1/msec

(IK)

Ionic potassium current

mu A/cm^2

(INa

Ionic sodium Current

mu A/cm^2

(Il)

Ionic leakage current, due to chloride and other ions

mu A/cm^2

(gK)

Total potassium conductance

m.mho/cm^2

(gNa)

Total sodium conductance

m.mho/cm^2

To plot results, select "Plot Area 1" from the Results menu. Place the cursor in an unused box under Yparameters and press the right mouse button to bring up a list of plottable variables.
8. Equations and Descriptions
The five governing equations are
.
The equations for
an, bn, am, bm, ah,
and
bh
are given in the reference on page 519 as:
,
,
. Note that
an
and
am
are undefined for
V=10
and 25, respectively, but are continuous functions when the limiting values are taken for those values.
The Initial condition for
n
is given in the resting state, defined by
V=0
, in the model,
Vrest
, as
. Initial conditions for
m
and
h
are similarly defined. Depolarization means a negative voltage. The temperature dependence of the model is embodied in the parameter
, which triples the rate constants for every increase of 10oC.
9. Model demonstrations with parameter sets
The user should inspect the input parameters and the output curves. Output curves can be found under the Results button under Plot Area 1 and Plot Area 2.
The following parameter sets are can be demonstrated by clicking on them:
Run the model. Under Results, display Plot Area 1. This parameter sets reproduces Figure 12 from the reference.
Run the model. Under Results, display Plot Area 1. This parameter set reproduces a fluctuation membrane potential.
Copyright © 2000, National Simulation Resource, University of Washington.