# File calcium_oscillations.ode
# model of calcium-induced calcium release in hepatocytes
# adapted from Othmer and Tang (1997) in 'Case studies in mathematical
# modelling', Othmer et al. eds, Prentice Hall
# Figure 6.18


#parameters
par gamma0=0.1
par gamma1=20.5 
par p1=8.5
par p2=0.065
par k1=12
par k2=15
par k3=1.8
par km1=8
par km2=1.65
par km3=0.21
par Cs=8.37 
par vr=0.185


#set time-varying profile for ligand level
I=0.7*heav(t-20.001)+0.5*heav(t-60.001)+2.8*heav(t-90.001)

#dynamics
C'=vr*(gamma0+gamma1*RIC)*(Cs-C) - (p1*C^4)/(p2^4+C^4)
R'=-k1*I*R+km1*RI
RI'= -(km1+k2*C)*RI+ k1*I*R + km2*RIC 
RIC'=-(km2+k3*C)*RIC + k2*C*RI + km3*RICC 
RICC'=k3*C*RIC - km3*RICC

# initial condition
init C=0, R=1, RI=0, RIC=0, RICC=0

# final time
@ total=120
@ maxstor=100000
@ dt=0.005
# set the plotting window size:
@ xlo=0, xhi=120, ylo=0, yhi=2.5

# run the simulation in the GUI by selecting (I)nitialconds|(G)o
# plot other species by selecting (G)raphic stuff|(A)dd curve and 
# assigning the y-axis

done