
Glycolysis

seed_ := 25$

NUMBER OF EQUATIONS$

n_ := 15$

VARIABLES VECTOR$

b_ := {x1,
x2,
x3,
x4,
x5,
u1,
u2,
u3,
u4,
y1,
y2,
y3,
y4,
y5}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {k1,
k2,
k3,
k4,
km}$

RANKING AMONG THE VARIABLES$

bb_ := {x1,
x2,
x3,
x4,
x5,
u1,
u2,
u3,
u4,
df(x1,t),
df(x2,t),
df(x3,t),
df(x4,t),
df(x5,t),
df(u1,t),
df(u2,t),
df(u3,t),
df(u4,t),
df(x1,t,2),
df(x2,t,2),
df(x3,t,2),
df(x4,t,2),
df(x5,t,2),
df(u1,t,2),
df(u2,t,2),
df(u3,t,2),
df(u4,t,2),
df(x1,t,3),
df(x2,t,3),
df(x3,t,3),
df(x4,t,3),
df(x5,t,3),
df(u1,t,3),
df(u2,t,3),
df(u3,t,3),
df(u4,t,3),
df(x1,t,4),
df(x2,t,4),
df(x3,t,4),
df(x4,t,4),
df(x5,t,4),
df(u1,t,4),
df(u2,t,4),
df(u3,t,4),
df(u4,t,4),
df(x1,t,5),
df(x2,t,5),
df(x3,t,5),
df(x4,t,5),
df(x5,t,5),
df(u1,t,5),
df(u2,t,5),
df(u3,t,5),
df(u4,t,5),
y1,
y2,
y3,
y4,
y5,
df(y1,t),
df(y2,t),
df(y3,t),
df(y4,t),
df(y5,t)}$

NUMBER OF INPUT(S)$

nu_ := 4$

NUMBER OF OUTPUT(S)$

ny_ := 5$

NUMBER OF STATE(S) $

nx_ := 5$

MODEL EQUATION(S)$

c_ := {df(x1,t)=u1,
df(x2,t)=u2,
df(x3,t)=u3,
df(x4,t)=u4,
df(x5,t)=u5,
( - k1*x1)/(km + x1)=u1,
( - (km + x1)*k2*x2 + (km + x2)*k1*x1)/(km**2 + x1*x2 + (x1 + x2)*km)=u2,
( - (km + x2)*k3*x3 + (km + x3)*k2*x2)/(km**2 + x2*x3 + (x2 + x3)*km)=u3,
( - ((km**2 + x2*x3 + (x2 + x3)*km)*k4*x4 - (km**2 + x2*x4 + (x2 + x4)*km)*k3*x3) + (km**2 + x3*x4 + (x3 + x4)*km)*k2*x2
)/((x3 + x4 + x2)*km**2 + km**3 + x2*x3*x4 + ((x3 + x4)*x2 + x3*x4)*km)=u4,
(k4*x4)/(km + x4)=u5,
x1=y1,
x2=y2,
x3=y3,
x4=y4,
x5=y5}$

CHARACTERISTIC SET$

aa_(1) :=  - k4 + u5$

aa_(2) := x4*(k4 - u5) - km*u5$

aa_(3) :=  - u1*x1 - u1*km - x1*k1$

aa_(4) :=  - u2*x1*x2 - u2*x1*km - u2*x2*km - u2*km**2 + x1*x2*(k1 - k2) + x1*k1*km - x2*k2*km$

aa_(5) :=  - u3*x2*x3 - u3*x2*km - u3*x3*km - u3*km**2 + x2*x3*(k2 - k3) + x2*k2*km - x3*k3*km$

aa_(6) :=  - u4*x2*x3 - u4*x2*km - u4*x3*km - u4*km**2 + x2*x3*(k2 + k3 - u5) + x2*km*(k2 - u5) + x3*km*(k3 - u5) - km**
2*u5$

aa_(7) :=  - df(x1,t)*x1 - df(x1,t)*km - x1*k1$

aa_(8) :=  - df(x2,t)*x1*x2 - df(x2,t)*x1*km - df(x2,t)*x2*km - df(x2,t)*km**2 + x1*x2*(k1 - k2) + x1*k1*km - x2*k2*km$

aa_(9) :=  - df(x3,t)*x2*x3 - df(x3,t)*x2*km - df(x3,t)*x3*km - df(x3,t)*km**2 + x2*x3*(k2 - k3) + x2*k2*km - x3*k3*km$

aa_(10) := df(x5,t) - u5$

aa_(11) := x1 - y1$

aa_(12) := x2 - y2$

aa_(13) := x3 - y3$

aa_(14) := y4*( - k4 + u5) + km*u5$

aa_(15) := x5 - y5$

MODEL ALGEBRAICALLY OBSERVABLE$

NORMALIZED  INPUT /OUTPUT RELATION(S) $

aan_(1) :=  - k4 + u5$

aan_(2) := (x4*( - k4 + u5) + km*u5)/(km*u5)$

aan_(3) :=  - u1*x1 - u1*km - x1*k1$

aan_(4) :=  - u2*x1*x2 - u2*x1*km - u2*x2*km - u2*km**2 + x1*x2*(k1 - k2) + x1*k1*km - x2*k2*km$

aan_(5) :=  - u3*x2*x3 - u3*x2*km - u3*x3*km - u3*km**2 + x2*x3*(k2 - k3) + x2*k2*km - x3*k3*km$

aan_(6) :=  - u4*x2*x3 - u4*x2*km - u4*x3*km - u4*km**2 + x2*x3*(k2 + k3 - u5) + x2*km*(k2 - u5) + x3*km*(k3 - u5) - km
**2*u5$

aan_(7) :=  - df(x1,t)*x1 - df(x1,t)*km - x1*k1$

aan_(8) :=  - df(x2,t)*x1*x2 - df(x2,t)*x1*km - df(x2,t)*x2*km - df(x2,t)*km**2 + x1*x2*(k1 - k2) + x1*k1*km - x2*k2*km$

aan_(9) :=  - df(x3,t)*x2*x3 - df(x3,t)*x2*km - df(x3,t)*x3*km - df(x3,t)*km**2 + x2*x3*(k2 - k3) + x2*k2*km - x3*k3*km$

aan_(10) := df(x5,t) - u5$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {k1=8,k2=16,k3=3,k4=20,km=17}$

EXHAUSTIVE SUMMARY $

flist_ := { - k4 + 20,
 - km + 17,
 - k1 + 8,
 - km + 17,
 - km + 17,
 - km**2 + 289,
k1*km - 136,
 - k2*km + 272,
 - km + 17,
 - km + 17,
 - km**2 + 289,
k2*km - 272,
 - k3*km + 51,
 - km + 17,
 - km + 17,
 - km**2 + 289,
 - km**2 + 289,
 - km + 17,
 - k1 + 8,
 - km + 17,
 - km + 17,
 - km**2 + 289,
k1*km - 136,
 - k2*km + 272,
 - km + 17,
 - km + 17,
 - km**2 + 289,
k2*km - 272,
 - k3*km + 51,
k2 - k3 - 13,
k1 - k2 + 8,
k2 + k3 - 19,
k2 - k3 - 13,
k1 - k2 + 8,
k3*km - km*u5 + 17*u5 - 51,
k2*km - km*u5 + 17*u5 - 272,
( - 17*k4 - km*u5 + 20*km + 17*u5)/(17*km*u5)}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{k4=20,k1=8,k3=3,k2=16,km=17}}$

MODEL GLOBALLY IDENTIFIABLE$
Elapsed time for Glycolysis: 3.0120074 seconds
