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Which Formalism to Use for Modeling Voltage-Dependent Conductances?

Alain Destexhe and John Huguenard

Catacomb models

There are interactive examples of different ways of modeling voltage gated ion channels in chapter 5 of the models section of Catacomb.

Tables

Rate constants of the Hodgkin-Huxley equations

variable	forward rate constant	Backward rate constant
m	-0.1 (V-V_r-25) / exp[-(V-V_r-25)/4] - 1	4 exp[-(V-V_r)/18]
h	0.07 exp[-(V-V_r)/20]	1 / (1 + exp[-(V-V_r+30)/10])
n	-0.01 (V-V_r+10) / exp[-(V-V_r+10)/10] - 1	0.125 exp[-(V-V_r)/80]

The rate constants are given for the variables m, n and h. The rate constants are those estimated by Hodgkin and Huxley (1952) in squid giant axon at a temperature around 6 degrees C. In the original study, the voltage axis was reversed in polarity and voltage values were given with respect to the resting membrane potential (V_r here).

Parameters for Figs 2-3

The detailed Markov model of Na channel (Vandenberg and Bezanilla 1991):

a_1=11490 s^-1
b_1=59.19mV
a_2=8641 s^-1
b_2=-5860mV
a_3=31310 s^-1
b_3=17.18mV
a_4=2719 s^-1
b_4=-51.54mV
a_5=33350 s^-1
b_5=74.58mV
a_6=1940 s^-1
b_6=-21.03mV
a_7=863.1 s^-1
b_7=27050mV
a_8=1538 s^-1
b_8=27050mV
a_9=7.992 s^-1
b_9=-27.07mV
r_10=r_8r_9/r_7

The simplified 3-state model (Destexhe et al. 1994):

a_1=1500 s^-1
a_2=200 s^-1
a_4=150 s^-1
b=5mV
c_1=c_2=-27mV
c_4=-65mV
r_3=3000 s^-1

The detailed Markov model of K channel (Perozo and Bezanilla 1989):

a_1=484.5 s^-1
b_1=112mV
a_2=19.23 s^-1
b_2=-8.471mV
a_3=1757 s^-1
b_3=25.83mV
a_4=569 s^-1
b_4=-491.0mV
a_5=672.9 s^-1
b_5=212mV
a_6=784.4
b_6=0

The simplified K+ channel model (Destexhe et al. 1994):

a_1=100 s^-1
a_2=240 s^-1
b=5mV
c_1 = c_2 = -27mV