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differential equations - Fitting experimental data by using ParametricNDSolveValue and NonlinearModelFit


I am a newcomer to Mathematica. Basically I just want to fit the data (enzyme kinetic data) shown below to a system of odes' by using NonlinearModelFit. The data, an 101x2 array, contains time in the first column and substrate concentration in the second. The model contains 4 species (e[t], es[t], s[t] and p[t]) and species s[t] is the one I want to fit the data to. I get the following error:



"The function value {<<1>>} is not a list of real numbers with dimensions {101} at {k1,k2,k3} = {4.,3.,1.`}". >>



Clicking on ">>" sends me to the basic NonlinearModelFit help page and I'm stuck there. The entire code is shown below. Thanks if anybody can help.


Francesco


(*some data*)
data={{0, 4.9112}, {20., 4.75011}, {40., 4.43818}, {60., 4.28744}, {80., 

  3.97296}, {100., 3.86888}, {120., 3.69122}, {140., 3.59596}, {160., 
  3.22247}, {180., 2.85438}, {200., 2.81939}, {220., 2.88236}, {240., 
  2.49125}, {260., 2.55379}, {280., 2.33662}, {300., 2.34136}, {320., 
  1.88169}, {340., 1.9444}, {360., 1.73578}, {380., 2.04545}, {400., 
  1.74068}, {420., 1.70471}, {440., 1.37455}, {460., 1.35169}, {480., 
  1.29391}, {500., 1.35778}, {520., 1.1509}, {540., 1.18335}, {560., 
  0.846087}, {580., 0.957338}, {600., 0.855021}, {620., 
  0.727364}, {640., 0.886429}, {660., 0.817111}, {680., 
  0.748117}, {700., 0.569694}, {720., 0.77641}, {740., 
  0.661459}, {760., 0.561378}, {780., 0.56037}, {800., 

  0.500522}, {820., 0.322087}, {840., 0.44058}, {860., 
  0.359604}, {880., 0.31989}, {900., 0.278633}, {920., 
  0.318697}, {940., 0.150813}, {960., 0.427698}, {980., 
  0.364589}, {1000., 0.292937}, {1020., 0.27481}, {1040., 
  0.182754}, {1060., 0.349605}, {1080., 0.220416}, {1100., 
  0.149073}, {1120., 0.343196}, {1140., 0.173815}, {1160., 
  0.126286}, {1180., 0.145337}, {1200., 0.0800335}, {1220., 
  0.043485}, {1240., 0.399296}, {1260., 0.303941}, {1280., 
  0.161308}, {1300., -0.00255049}, {1320., 0.0296389}, {1340., 
  0.0919508}, {1360., 

  0.182537}, {1380., -0.0356638}, {1400., -0.140977}, {1420., 
  -0.0581143}, {1440., 0.115227}, {1460., 0.116371}, {1480., 
  0.118025}, {1500., 0.0556984}, {1520., 0.0831993}, {1540., 
  0.0135393}, {1560., 0.143889}, {1580., -0.0817538}, {1600., 
  0.0968327}, {1620., -0.0364522}, {1640., 0.0121839}, {1660., 
  0.0983604}, {1680., 0.144547}, {1700., -0.0734307}, {1720., 
  0.162225}, {1740., 0.100122}, {1760., 0.0253859}, {1780., 
  0.0108251}, {1800., 0.00686486}, {1820., -0.00330938}, {1840., 
  0.0277739}, {1860., 0.0291533}, {1880., 0.105267}, {1900., 
  0.174073}, {1920., 0.0668537}, {1940., -0.00195318}, {1960., 

  0.080458}, {1980., 0.0352437}, {2000., -0.0870161}};
(* Dimensions[data] {101, 2} *)

tmax = Max[data[[All, 1]]];

(* the model, k1, k2, k3 are the parameters *)

model = ParametricNDSolveValue[{e'[t] == (k2 + k3) es[t] 
- k1 e[t] s[t], es'[t] == -e'[t], s'[t] == k2 es[t] - k1 e[t] s[t],
    p'[t] == k3 es[t], e[0] == 0.001, s[0] == 5, es[0] == 0, 

   p[0] == 0}, s[t], {t, 0, tmax}, {k1, k2, k3}]

fit = NonlinearModelFit[data,model[k1, k2, k3][t], {{k1, 4.}, {k2, 3}, {k3, 1}}, t];
plotfit = Plot[model[k1, k2, k3] /. fit, {t, 0, tmax}];
plotdata = ListPlot[data, PlotStyle -> PointSize[0.02]];
Show[plotfit, plotdata]


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