Figure 4

Determination of flux confidence intervals at a confidence level of γ using the Monte Carlo approach based on multiple parameter estimations. For each of L _MAX  = 500 trials (simulations), all MIDs and measured efflux values were corrupted by random noise with a given standard deviations, and fluxes were estimated via least-squares optimization. Then, the estimations of each flux obtained in L _MAX trials were sorted in ascending order followed by performing of “discarding” or “mean-varianced” strategies for determination of flux confidence intervals at the confidence level of γ, $\mathit{C}{\mathit{I}}_{\mathit{\gamma }}^{\mathit{M}\mathit{C}-1}$ or $\mathit{C}{\mathit{I}}_{\mathit{\gamma }}^{\mathit{M}\mathit{C}-2}$, respectively, (see Additional file 1: SF-1.7. ). The computation of the 68% and 95% confidence interval bounds for the ${\stackrel{⌢}{\mathit{\theta }}}_8$ and ${\stackrel{⌢}{\mathit{\theta }}}_{22}$ fluxes provided by both Monte Carlo-based strategies are presented as examples of estimates that are distributed rather symmetrically or non-symmetrically, respectively, around the optimized values of fluxes (indicated by the cursor).