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

1. TABLE OF CONTENTS

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.