  Elementary flux modes (EFMs) are vectors defined from a metabolic reaction
network, giving the connections between substrates and products. EFMs-based
metabolic flux analysis (MFA) estimates the flux over each EFM from external
flux measurements through least-squares data fitting. In previous work we
presented an optimization method of column generation type that facilitates
EFMs-based MFA when the metabolic reaction network is so large that enumerating
all EFMs is prohibitive. In this work we extend this model by including errors
on measurements in a robust optimization framework. In the robust optimization
problem, the least-squares data fitting is minimized subject to the error on
each metabolite being as unfavourable as it can be, within a given interval. In
general, inclusion of robustness may make the optimization problem
significantly harder. However, we show that in our case the robust problem can
be stated as a convex quadratic programming problem, i.e., of the same form as
the original non-robust problem. Additionally, we demonstrate that the
column-generation technique of the non-robust problem can be extended also to
the robust problem. Furthermore, the option to indicate intervals on
metabolites that are not measured is introduced in this column generation
framework. The effect of including robustness in the model is evaluated in a
case-study, which indicated that the solutions of our non-robust problems are
in fact near-optimal also when robustness is considered. On the other hand, the
addition of intervals on unmeasured metabolites resulted in a change of optimal
solution. Implying that the inclusion of intervals on unmeasured metabolites is
more important than the direct consideration of measurement errors, this
despite up to 20% errors.
