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Monod kinetics and curve fitting

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kknd on 12 Jul 2012
Commented: Star Strider on 26 Nov 2019
Hi to everyone!
I think i should start immediately with a short description of what i' m dealing with. I have a system of two (2) equations. Generally, these equations are expressed as following:
  1. dS/dt = (mmax * X * S)/(Y * (Ks + S)
  2. dX/dt = (mmax * X * S)/ (Ks + S) - (b * X)
S = So and X = Xo
In the laboratory, i' ve measured concentration values versus time, e.g. (t, S). Moreover, i know the initial value Xo. As a result, i' m trying to estimate all the other parameters.
So the problem is how do i solve the differential equation system and then use this solution for the curve fitting procedure? I tried simbiology and the absence of a constraint search for the best solutions leads to estimates with no physical meaning.
What should i try next? Perhaps the solution is associated with non linear fitting tools, but i would like a more specific answer by an experienced user, before i start the effort.
Thank you in advance!

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Star Strider
Star Strider on 17 May 2017
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Accepted Answer

Star Strider
Star Strider on 12 Jul 2012
Edited: Star Strider on 12 Jul 2012
The differential equations may have long since been integrated and published:
so all you need to do is fit them to your data. (They are both free PDFs.) I didn't look through the lists in the articles to be sure they have specifically integrated the equations you're interested in fitting.
I can't claim to be an experienced user with respect to fitting chemical kinetics data, since I haven't done anything with chemical kinetics in a while, but I'm familiar with MATLAB's nonlinear curve fitting routines. Either ‘nlinfit’, ‘lsqcurvefit’, or others should be able to estimate the parameters you want. They can also provide confidence intervals on the parameter estimates with ‘nlparci’ and the fitted estimates with ‘nlpredci’.


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Star Strider
Star Strider on 26 Nov 2019
With the estimated parameters ‘B’:
tv = linspace(min(t), max(t), 250);
Mfit = MonodKinetics(B,t);
plot(t, Mfit)
hna on 26 Nov 2019
Thank you very much for this quick answer
Star Strider
Star Strider on 26 Nov 2019
My pleasure!
A vote for my Answer would be appreciated!

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