Model: HODHUX, the Hodgkin-Huxley model for membrane conductance

1. TABLE OF CONTENTS

Reference

Input parameters

Calculated Parameters

Output Variables

Diagram

Equations and Descriptions

Model demonstrations with parameter sets

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, 500-544.

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 Y-parameters and press the right mouse button to bring up a list of plottable variables.

7. Diagram

 

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:

9.1. Figure 12 : hodhux.FIG12.xsim.par

Run the model. Under Results, display Plot Area 1. This parameter sets reproduces Figure 12 from the reference.

9.2. Fluctuating output: hodhux.fluctuating.par

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.

Contact garyr@bioeng.washington.edu with comments, questions, or critiques.