A Simnon™ program, Hodhux, to compute Vm = - (v + 70) mV, and the various current densities follows. Note that the current densities are in ^A/cm2, voltages are in mV, conductances in mS/cm2, and the capacitance is in mF/cm2. The strange treatment of units and voltage signs follows from the original HH (1952) paper.
continuous system HODHUX " 6/06/99 " Run w/ Euler integration w/ dt = 0.00001.
STATE v m n h " v in mV. v is depolarization if < 0.
DER dv dm dn dh " v = Vmo - Vm. Vm is actual transmembrane V.
" HH membrane patch ODE. (1 cm^2) dv = Jin/Cm - Jk/Cm - Jna/Cm - Jl/Cm
" Ionic current densities. Jk = gko* (n^4) * (v - Vk) Jna = gnao*(m^3)*h*(v - Vna) Jl = glo* (v - Vl) Jc = Cm*dv
" Ionic conductances: gk = gko*(n^4) gna = gnao*(m^3)*h gl = glo gnet = gk + gna + gl negv = -v
dn = - n* (an + bn) + an dm = - m* (am + bm) + am dh = - h* (ah + bh) + ah
Potassium conductance Sodium conductance Leakage conductance Net membrane conductance
K+ activation parameter. Na+ activation parameter. Na+ inactivation parameter
" VOLTAGE-DEPENDENT PARAMETER FUNCTIONS:
Vm = - (v + 70) Jksc = Jk/10 Jnasc = Jna/10 Jcsc = 10*Jc Vmsc = Vm/70
" Scaled current densities
" Scaled capacitor current density. " Scaled membrane voltage.
" CONSTANTS : zero:0 Vk: 12 Vna:-115 VL:-10.613
mV mV mV
glo : 0 . 3 gko: 3 6 gnao:120 Cm:.001 f:0.10 pi:3.14159
milliF/cm^2 = 1 microF/cm^2. Hz to) ELSE 0 ■ t2) ELSE 0
"Jinl = IF t > to THEN K*(t -current ramp input. " Jin2 = IF t > t2 THEN -K*(t microamps/cm^2.
t2: 10 " End of ramp to: 1 " Jin < 0 depolarizes membrane.
Jinl = IF t > to THEN Jino ELSE 0" Delayed current pulse input. Jin2 = IF t > (to + delt) THEN -Jino ELSE 0
delt:5 " Duration of current pulse, ms.
Jino:-2 " Microamps.
" Jinl = IF t > to THEN Jino ELSE 0" Delayed current step input. " Jin2 = Jinac*sin(2*pi*f*t) " Sinusoidal current input. Jin = Jinl + Jin2
" INITIAL CONDS.
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