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Constraints in Odesolve to solve Enzymatic Reaction ODEs

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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

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?

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

 

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:

Glu.jpg

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.

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?

 

Capture.PNG

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

 

Re: Constraints in Odesolve to solve Enzymatic Reaction ODEs

Glu2.jpg

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:

Glu4.jpg