#naglu5.ode (5 state Na/glucose cotransporter)
#initial values of state variables
init x1=0.15,x2=0.15,x3=0.15,x45=0.2
#parameters
parm k12=0.08,k21=500,k16=35,k61=5,k23=100,k32=20
parm k25=0.3,k52=0.3,k34=50,k43=50,k45=800,k54=40000
parm k56=10,k65=0.00005,ap=0.3,app=0,d=0.7,f=96489
parm gluIn=10,gluOut=1,NaIn=20,NaOut=100
parm n=2,z=-2,r=8314,tconst=310,v=-50 
#functions and rate constants
mu(v)=f*v/(r*tconst)
k12p(v)=k12*NaOut^2*exp(-n*ap*mu(v)/2)
k21p(v)=k21*exp(n*ap*mu(v)/2)
k56p(v)=k56*exp(-n*app*mu(v)/2)
k65p(v)=k65*NaIn^2*exp(n*app*mu(v)/2)
k34p(v)=k34*exp(-(z+n)*d*mu(v)/2)
k43p(v)=k43*exp((z+n)*d*mu(v)/2)
k25p(v)=k25*exp(-(z+n)*d*mu(v)/2)
k52p(v)=k52*exp((z+n)*d*mu(v)/2)
k61p(v)=k61*exp(z*d*mu(v)/2)
k16p(v)=k16*exp(-z*d*mu(v)/2)
#the other state variables
x5=x45*k45/(k45+k54*GluIn)
x4=x45*k54*GluIn/(k45+k54*GluIn)
x6=1-x1-x2-x3-x45
#the fluxes
j12(x1,x2,v)=k21p(v)*x2-k12p(v)*x1
j16(x1,x6,v)=k61p(v)*x6-k16p(v)*x1
j23(x2,x3)=k32*x3-k23*GluOut*x2
j25(x2,x5,v)=k52p(v)*x5-k25p(v)*x2
j34(x3,x4,v)=k43p(v)*x4-k34p(v)*x3
j56(x5,x6,v)=k65p(v)*x6-k56p(v)*x5
#equations
dx1/dt=j12(x1,x2,v)+j16(x1,x6,v)
dx2/dt=-j12(x1,x2,v)+j23(x2,x3)+j25(x2,x5,v)
dx3/dt=-j23(x2,x3)+j34(x3,x4,v)
dx45/ct=-j34(x3,x4,v)+j56(x5,x6,v)-j25(x2,x5,v)
#flux of glucose
aux jGlu=j23(x2,x3)
done