# Monod kinetics and curve fitting

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kknd on 12 Jul 2012
Commented: Star Strider on 24 Nov 2022 at 0:48
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.
Star Strider on 17 May 2017
Post new Questions, and copy the URL here as a reference.

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’.
Star Strider on 24 Nov 2022 at 0:48
@Anshuman — I looked at that earllier. I agree with @Torsten, that it is likely not possible to estimate a time-varying parameter without a significantly large number of (likely several hundred) experiments.
I will delete this Comment and yours in a few hours. They do not pertain to this thread.

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