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04-04-2019
09:05 PM

04-04-2019
09:05 PM

Constraints in Odesolve to solve Enzymatic Reaction ODEs

I'm modeling glucose conversion to ethanol through solving a series of ODEs of enzymatic reactions. How do I set the constraint that all concentrations are >= 0 and the total mass of all compounds in the pathway are constant over time. Any help would be greatly appreciated!

8 REPLIES 8

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04-05-2019
04:25 AM

04-05-2019
04:25 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

1. I think you have an error in the formulas, if you get a negative concentration.

2. I recommend that you go to Mathcad Prime - where differential equations are solved with units

3. I recommend the book Chemical Kinetics with Mathcad and Maple

4. Do you design moonshine?

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04-05-2019
04:41 AM

04-05-2019
04:41 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

Your reaction rates are extremely fast! The value of Glu drops to zero within a value of x of about 6.5*10^-4, yet you are looking for results over values of x out to 200. The ODE solvers can't cope with this!

I suggest:

1. Solve Glu on its own (as it is independent of the others) to x around 6.5*10^-4; Then set it to zero beyond this.

2. Solve the others to the same limited time (distance?), then use their results at this time as initial conditions for subsequent solutions.

I didn't check the time constants of anything other than that for Glu, so you might have to repeat step 2 if the end time is still too large for the ODE solvers to cope.

Alan

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04-05-2019
01:15 PM

04-05-2019
01:15 PM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

Hi,

In fact the first equation (First order, Type II: y = f (y ')) can be solved in parametric form:

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04-08-2019
02:49 AM

04-08-2019
02:49 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

Obviously the result coincides with that obtained using "odesolve" for the single differential equation y '= f (y) with the necessary initial conditions. The result is then used by the system of differential equations without the previous equation. But there are still negative concentrations.

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04-08-2019
09:12 AM

04-08-2019
09:12 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

Hi,

Are you sure you have the conversion of hour and seconds the right way round?

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04-11-2019
05:01 AM

04-11-2019
05:01 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

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04-11-2019
05:05 AM

04-11-2019
05:05 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

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04-15-2019
07:30 AM

04-15-2019
07:30 AM

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

Hi,

I did a simulation with initial constants chosen by me and similar values between them:

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