What is the minimum flux computed by Flux Balance Analysis or the accuracy of FBA?

[Michel_Lavoie]

Hi all,

         When I perform a Flux balance analysis (FBA) using the command optimizeCbModel(model, 'max', 0) or optimizeCbModel(model, 'max','one'), I get a range of fluxes varying from -1000 mmol / gDW / h (lower boundary) to +1000 mmol / gDW / h (upper boundary). I also get very low fluxes that are equals to some 10-6 mmol/ gDW/ h and a lot of fluxes equal to zeros. I would like to know the accuracy of FBA, i.e., the minimum detectable non-zero flux at (and above) which we can say that there is a 'significant' flux through a given reaction. I have the same question for shadow prices and reduced costs. What are the lowest non-zero shadow prices or reduced costs computed with the command 'optimizeCbModel of the cobra toolbox?

Thank you very much for your help,

Michel

[Thomas Pfau]

Dear Michel,

That depends on the parameters you use.

If you use default parameters and glpk/gurobi/cplex/mosek the allowed tolerances for fesibility are set to 10^-9, i.e. anything change (or difference from 0) below this value can be ignored.

As for optimality, the tolerance is normally 10^-6.

I hope this answers your question.

Best

Thomas

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[Michel_Lavoie]

Hi Thomas,

             Thank you very much for your help. Yes, I use default parameters and gurobi so I guess the minimum non-zero flux found with a FBA is 1 x 10^-6. Am I right? I also saw that shadow prices (the .y field of the output of optimizeCbModel()) can be as low as 10^-17 and I saw that reduced costs (the .w field of the output of optimizeCbModel()) can be as low as 10^-19. So, I have another question. What are the minimum non-zero shadow prices and reduced costs?

Regards,

Michel

[Thomas Pfau]

Hi Michel,

             Thank you very much for your help. Yes, I use default parameters and gurobi so I guess the minimum non-zero flux found with a FBA is 1 x 10^-6. Am I right?

Not exactly,

If you are optimising for it, then yes, if the absolute value is below 1e-6 then it can be assumed to be 0. If a flux is 1e-6, this can still be relevant, because here the feasibility tolerances are more relevant (which indicate how much of a deviation from S*v = 0 is allowed). So a flux below 1e-9 can definitely be assumed to be an artifact.

The sane applies to shadow prices and reduced costs (should be the 1e-9 threshold).

Best

Thomas

Am 13.03.2019 um 13:03 schrieb 'Michel_Lavoie' via COBRA Toolbox:

Hi Thomas,

[Michel_Lavoie]

Hi Thomas,

                Thank you again. Now I think I understand. I think the presence of a threshold below which all fluxes are artifacts is a very important point !  I have not seen anything about that in tutorials or papers. The unexperienced user of the Cobra toolbox could think that very low fluxes , shadow prices or reduced costs are 'significant' or relevant, but , in fact , they might be artifacts in some cases.

So, for reactions with fluxes that are optimized (such as the fluxes of the biomass equation), the minimum non-zero flux is 10-6 and any fluxes lower than that can be considered equal to 0. For all other reactions and for shadow prices or reduced costs, all computed values lower than 10-9 can be considered equal to zero.

Thank you very much for clarifying that in this forum.

Michel