Try this code. Look at the parameters that were not described: ka, Mdm2[t], p21o.

Manipulate[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; ka = 1; Mdm2[t_] := 1;
 f = {MPF, Wee1, Cdc25a, Chk1p, Chk1, Cdc25, Cdc25ps216a, preMPF, 
   P21MPF, p21, p53a , p53, Cdc25ps216, F1433};
 eq = {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 * Cdc25[t] - 
     k30 * Chk1p[t] * Cdc25a[t] - k32 * Cdc25a[t],
   Chk1p'[t] == k9 * Chk1[t]*1 - k10 * Chk1p[t], 
   Chk1'[t] == k9 * Chk1p[t] - k10 * Chk1[t], 
   Cdc25'[t] == 
    ki * Cdc25[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] == 
    k1p21 + k2p21*(p53a[t]^3)/(jp21^3 + p53a[t]^3) + 
     k18 * P21MPF[t] + k16 - 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]) + kM * 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],
   F1433'[t] == 
    k26 * p53[t] + k27 - k28 * Cdc25ps216[t] * F1433[t] - 
     k29 * F1433[t],
   Wee1'[t] == kWee1 + k33 * Wee1[t] - k34 * MPF[t]* Wee1[t]};
 eq0 = {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}; sol = NDSolveValue[{eq, eq0}, f, {t, 0, 8}]; 
 Plot[Evaluate[{sol[[1]][t], sol[[2]][t]} ], {t, 0, 8}, 
  PlotRange -> All, PlotLegends -> {"MPF", "Wee1"}, 
  PlotStyle -> {Green, Cyan}], {{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}, {{p21o, 1, "[p21] Initial"}, 
  0, 10},
 {{ks, 1, "ks"}, 0, 8},
 {{Dego, 1, "Dego"}, 0, 8}]

Attachments:

Trouble with NDsolve and dependent variables?

How would I use the equation that uses another function for its variable?

For example, I have

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

It uses both p53a and p53, and thus if I try to put the code as so:

f[1] := 
 NDSolveValue[{p53a'[t] == 
    k1d * p53[t] - kin * p53a[t] - k2d * p53a[t]}, p53a[0] == 1, 
  p53[0] == 1, {t, 0, 8}]


Plot[Evaluate[{ f[1] }], {t, 0 , 1}]

it will not plot since there are more dependent variables than independent!

Would you be so kind as to give me an example of an unnested function? I'm not sure how to bring it out.