#file Hodgkin_Huxley.ode
#Hodgkin-Huxley model of excitable barnacle muscle fiber
#reviewed in Rinzel (1990) Bulletin of Mathematical Biology 52 pp. 5-23.
#Figure 1.9 and problem 8.6.4

par E_N=55
par E_K=-72
par g_N_bar=120.0
par g_K_bar=36.0
par g_leak=0.30
par E_leak=-49.0   
par C_M=1.0

#model equations
V' = (- I_N - I_K - I_leak - Istim)/C_M

m_inf = (0.10*(V+35)/(1.0 - exp(-(V+35)/10.0)))/((0.10*(V+35)/(1.0 - exp(-(V+35)/10.0)))+(4.0*exp( -(V+60)/18.0)))
t_m   = 1.0/((0.10*(V+35)/(1.0 - exp(-(V+35)/10.0)))+(4.0*exp( -(V+60)/18.0)))
m' = (m_inf - m)/t_m
   
h_inf = (0.07*exp(-(V+60)/20))/((0.07*exp(-(V+60)/20))+(1/(exp(-(V+30)/10)+1)))
t_h   = 1.0/((0.07*exp(-(V+60)/20))+(1/(exp(-(V+30)/10)+1)))
h' = (h_inf - h)/t_h

I_N = g_N_bar*(V-E_N)*m^3*h

t_n = 1.0/((0.01*(V+50)/(1.0 - exp(-(V+50)/10.0)))+(0.125*exp( -(V+60)/80)))
n_inf = (0.01*(V+50)/(1.0 - exp(-(V+50)/10.0)))/((0.01*(V+50)/(1.0 - exp(-(V+50)/10.0)))+(0.125*exp( -(V+60)/80)))
n' = (n_inf - n)/t_n

I_K = g_K_bar*(V-E_K)*n^4

I_leak = g_leak*(V-E_leak)
  
Istim = (-6.65)*(heav(t-20.01)-heav(t-21.01))+(-6.86)*(heav(t-60.01)-heav(t-61.01))
   
# initial condition
init V=-59.9, m=0.0536, h=0.5925, n=0.3192

# final time
@ total=100
@ maxstor=1000000
@ dt=0.005
# set the plotting window size:
@ xlo=0, xhi=100, ylo=-80, yhi=45

# run the simulation in the GUI by selecting (I)nitialconds|(G)o

done