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I'm new here, and would love some help from you guys.

Currently I can't seem to get NDSolve to work despite looking at multiple resources on the web. Can anyone tell me why I'm getting the error message "NDSolve::underdet: There are more dependent variables, {Cdc25[t],Cdc25a[t],Cdc25ps216[t],Cdc25ps216a[t],Chk1[t],Chk1p[t],F1433[t],Mdm2[t],MPF[t],p21[t],P21MPF[t],p53[t],p53a[t],preMPF[t],Wee1[t],Wee1p[t]}, than equations, so the system is underdetermined."?

. . .

Here's my code:

k1 = 1.5; k2 = 0.001; k3 = 10.0; k4 = 0.02; k5 = 6.0; k6 = 0.04; k7 = \
0.005; k8 = 0.00000001; k9 = 1; k10 = 1.0; k11 = 1.0; k12 = 0.0005; \
k13 = 1.0; k14 =  0.01; k15 = 1.0; k16 = 0.01; k17 = 1; k18 = 1; k19 \
= 0.1; k20 = 0.01; k21 = 0.1; k22 = 1.0; k23 = 0.01; k24 = 0.01; k25 \
= 1.0; k26 = 0.01; k27 = 1.0; k28 = 100.0; k29 = 1.0; k30 = 0.01; k31 \
= 0.01;  k32 = 0.0001; k33 = 1.0; k34 = 0.1; k35 = 1.0;  k36 = 1.0; \
kp = 0.0001; kM = 0.00094; kW = 0.00054; kj = 0.04; jW = 1.8; kd = \
0.01; kdeg = 0.772; kdamp = 0.02; kA = 0.2; ki = 0.01; vm = 0.00005; \
kWee1 = 0.0002; kin = 0.0013; k1d = 0.026; k2d = 0.0013; kca = 0.004; \
kcm = 0.005; kwip11 = 0.00054; kwip12 = 0.04; jwip1 = 1.8; kwip13 = \
0.001; k1p21 = 0.0001; k2p21 = 0.135; jp21 = 2; kdin1 = 0.000054; \
kdin2 = 0.0027; jdin1 = 0.4; kdin3 = 0.135; jdin2 = 0.5; kdin4 = \
0.00135; kAIP1 = 0.0011; kAIP2 = 0.027; jAIP1 = 0.3; kAIP3 = 0.01;
ks = 1;


Manipulate[
 sol = NDSolve[{
    MPF'[t] == 
     k17 * (Cdc25a[t] + Cdc25ps216a[t]) * preMPF[t] + 
      k18 * P21MPF[t] - k14 * MPF[t] * Wee1[t] - 
      k19 * MPF[t] * p21[t] - k20 * MPF[t]^2,

    Cdc25a'[t] == 
     k15 * MPF[t] * Cdc25[t] + k30 * Cdc25ps216a[t] - 
      ki * Cdc25a[t] - k30 * Chk1p[t] * Cdc25a[t] - k32 * Cdc25a[t],

    Chk1p'[t] ==   k9 * Chk1[t] * 1 - k10 * Chk1p[t],
    (* EQ for ATR'[t] is not given*)
    Chk1'[t] == k9 * Chk1p[t] - k10 * Chk1[t]*1,

    Cdc25'[t] ==  
     ki * Cdc25a[t] + vm - k15 * MPF[t] * Cdc25[t] - 
      k23 * Chk1p[t] * Cdc25[t],

    Cdc25ps216a'[t] ==  
     k31 * Chk1p[t] * Cdc25a[t] + k25 * MPF[t] * Cdc25ps216[t] - 
      k30 * Cdc25ps216a[t] - k24 * Cdc25ps216a[t],

    preMPF'[t] == (k12)/(1 + k13 * p53[t]) + k14  * k15 * k16 - 
      k17*(Cdc25a[t] + Cdc25ps216a[t]) * preMPF[t],

    P21MPF'[t] == k19*p21[t] - k18 * P21MPF[t],

    p21'[t] == 
     k21 * p53a[t] + k16 + k18 * P21MPF - k22 * p21[t] - 
      k19 * MPF[t] * p21[t],

    p53a'[t] == k1d * p53[t] - kin * p53a[t] - k2d * p53a[t],

    p53'[t] == 
     ks + k1 * (DDS * 
         Exp[-k8 * 
           t]) - (((Dego - kdeg * (DDS * Exp[-k8 * t]) - 
            DDS * Exp[-kdamp * DDS * t])) * p53[t] * Mdm2 [t])/(ka + 
         p53[t]) + kin * p53a[t] - k1d * p53[t] - k2 * p53[t],

    Cdc25ps216'[t] == 
     k23 * Chk1p[t] * Cdc25[t] - k25 * MPF[t] * Cdc25ps216[t] + 
      k24 * Cdc25ps216a[t] - k28 * F1433[t] * Cdc25ps216[t],

    (*14-3-3 = F1433*)
    F1433'[t] ==  
     k26 * p53[t] + k27 - k28 * Cdc25ps216[t] * F1433[t] - 
      k29 * F1433[t],

    (**)
    Wee1'[t] == kWee1 + k33 * Wee1p[t] - k34 * MPF[t] * Wee1[t],


    (**)
    MPF[0] == MPFo,  Cdc25a[0] == Cdc25ao, Chk1p[0] == Chk1po, 
    Chk1[0] == Chk1o, Cdc25[0] == Cdc25o, 
    Cdc25ps216a[0] == Cdc25ps216ao, preMPF[0]  == preMPFo,   
    P21MPF[0] == P21MPFo, p21[0] == p21o, p53a[0] == p53ao, 
    p53[0] == p53o, Cdc25ps216[0] == Cdc25ps216o, F1433[0] == F1433o, 
    Wee1[0] == Wee1o}, {MPF,  Cdc25a, Chk1p, Chk1, Cdc25, 
    Cdc25ps216a, preMPF, P21MPF, p21, Cdc25ps216, F1433,  Wee1}, {t, 
    8}];

  Plot[Evaluate[{MPF[t], Wee1[t]} /. sol], {t, 0, TFinal}, 
  PlotRange -> All, PlotLegends -> {"[MPF], [Wee1]"}, 
  PlotStyle -> {Green, Cyan}],
 {{TFinal, 5, "Time"}, 0.2, 8},
 {{DDS, 0, "DDS"}, 0, 0.008},
 {{MPFo, 1, "[MPF] Initial"}, 0, 10},
 {{Cdc25ao, 1, "[Cdc25a] Initial"}, 0, 10},
 {{Chk1po, 1, "[Chk1p] Initial"}, 0, 10},
 {{Chk1o, 1, "[Chk1] Initial"}, 0, 10},
 {{Cdc25o, 1, "[Cdc25] Initial"}, 0, 10},
 {{Cdc25ps216o, 1, "[Cdc25ps21a] Initial"}, 0, 10},
 {{Cdc25ps216ao, 1, "[Cdc25ps216a] Initial"}, 0, 10},
 {{preMPFo, 1, "[preMPF] Initial"}, 0, 10},
 {{P21MPFo, 1, "[P21MPF] Initial"}, 0, 10},
 {{p53ao, 1, "[P53a] Initial"}, 0, 10},
 {{p53o, 1, "[P53] Initial"}, 0, 10}, 
 {{F1433o, 1, "[F1433] Initial"}, 0, 10},
 {{Wee1o, 1, "[Wee1] Initial"}, 0, 8},
 {{K, 1, "K"}, 0, 8},
 {{Dego, 1, "Dego"}, 0, 8}

 ]

All of these equations come from an article, and I'm trying to reproduce the graphs using the models.

Thanks for reading! Any help is appreciated.

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  • $\begingroup$ You have one P21MPF in an equation that is lacking a trailing [t] and that probably explains the error message, even if more changes are needed $\endgroup$ – Bill Apr 23 '18 at 2:02
  • $\begingroup$ Bill, thank you for pointing that out! I think I misinterpreted what the error msg meant, but now I get what it means. I'm now back to being stuck on the error msg "NDSolve::underdet: There are more dependent variables, {Cdc25[t],Cdc25a[t],Cdc25ps216[t],Cdc25ps216a[t],Chk1[t],Chk1p[t],F1433[t],Mdm2[t],MPF[t],p21[t],P21MPF[t],p53[t],p53a[t],preMPF[t],Wee1[t],Wee1p[t]}, than equations, so the system is underdetermined." $\endgroup$ – MontX Apr 23 '18 at 2:15
  • $\begingroup$ Imagine if the error message said "You are missing a [t] right here with an animated bouncing red finger pointing right at it AND you don't have an equation defining P21MPF!!" This wouldn't be that hard to have a "novice mode" to explain the mistakes which have been made tens of thousands of times. $\endgroup$ – Bill Apr 23 '18 at 2:36
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You have 13 dependent variables and 11 equations. You need to be solving for {MPF, Cdc25a, Chk1p, Chk1, Cdc25, Cdc25ps216a, preMPF, P21MPF, p53, p21, Cdc25ps216, F1433, Wee1} and you need equations for the variables Chk1p[t] and P21MPF[t].

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  • $\begingroup$ Does that mean that the equation "Chk1p'[t] == k9 * Chk1[t] * 1 - k10 * Chk1p[t], (* EQ for ATR'[t] is not given*) Chk1'[t] == k9 * Chk1p[t] - k10 * Chk1[t]*1," and "P21MPF'[t] == k19*p21[t] - k18 * P21MPF[t]," do not count? $\endgroup$ – MontX Apr 23 '18 at 2:15
  • $\begingroup$ Sorry missed those two. You'd still need to add p53 in the solve-for list, I think. $\endgroup$ – ulvi Apr 23 '18 at 2:27
  • $\begingroup$ Just to make sure, are you saying that I need the non-differential equation of P21MPF and Chk1p in order to be able to solve this problem? I do not have those available to me ... $\endgroup$ – MontX Apr 23 '18 at 2:30
  • $\begingroup$ You'd still need to add p53 and Mdm2 in the solve-for list, I think, and need an eq. for Mdm2[t]. Also P53 needs to be p53? And what about p53a, etc... $\endgroup$ – ulvi Apr 23 '18 at 2:33
  • $\begingroup$ The Mdm2 was what I was missing! Thanks so much!! $\endgroup$ – MontX Apr 23 '18 at 2:39

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