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!
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?
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.
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.
