Monod kinetics and curve fitting

213 views (last 30 days)
kknd
kknd on 12 Jul 2012
Commented: Star Strider on 3 Dec 2020
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!
  1 Comment
Star Strider
Star Strider on 17 May 2017
PLEASE do not post new Questions here as Comments or Answers related to this Question.
Post new Questions, and copy the URL here as a reference.

Sign in to comment.

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’.
  11 Comments
Michele Notarantonio
Michele Notarantonio on 3 Dec 2020
Hello,
I have another type of problem similar to the one explained here. My problem is " I have a set of equations (biochemical reactions) and, initially, I want to simulate the mathematical model with parameters choosen by literature" How the code should change? Pratically I need to solve the combined system of algebraic and differentially equation but I'm finding a lot of trouble. I have written all the equations that I need to simulate the model (11 differential equation and 3/6 algebraic equations to define kinetics rate). I tried to simulate them with ode15s and ode 45 but the results haven't physycally meaning (i'm finding some negatives values). What should I do?
Thanks for the help!
Star Strider
Star Strider on 3 Dec 2020
Note that lsqcurvefit (and several other optimisation functions) can use parameter constraints, so setting the lower bound to a vector of zeros will prevent negative parameters.

Sign in to comment.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!