Gradual development on genetic manipulation techniques has opened great possibilities for alteration of microorganisms for different purposes. These approaches have ranged from improvements and developments in the production of several metabolites, to multiple biochemical and microbiological investigations 
. Since early developments in this field, the need for global analysis of cellular systems was evident, because interaction between cellular components does not allow cell functions to be explained simply by characterizing the components comprised in it 
This environment led to the emergence of metabolic engineering, which is a combination of systematic analysis from different cellular networks (metabolic, signaling, etc.) with molecular biology techniques to improve cellular properties through rational design and the implementation of genetic modifications 
. Among the areas studied by metabolic engineering, one of the most relevant fields is searching for techniques to quantitatively predict the metabolic behavior of microorganisms under different conditions. In this category, the most widely used mathematical modeling approach has been flux balance analysis (FBA) 
FBA is based on the assumption that evolutionary pressure has led to the redirection of cellular metabolic fluxes, seeking for an optimal distribution according to a certain cellular goal 
. This assumption make it possible to solve (i.e. to find a flux distribution based on) the underdetermined system that results from a mass balance in steady state of the intracellular metabolites 
, shown in equation (1
), transforming the issue into the optimization problem of the equation (2
In equations (1
) and (2),
is the objective function that represents the cellular goal,
is the stoichiometric matrix,
is the flux value vector, and
are the lower and upper bounds of the flux values, respectively. It is evident that the flux distribution estimated by the FBA depends on the objective function used, and therefore the chosen goal will have a direct impact on the quality of the predictions. It has been shown that, qualitatively, simulations carried out with FBA are consistent with experimental data 
, but in many cases, quantitative predictions are not reliable.
To apply FBA as a predictive technique, it should be ensured that fluxes predicted clearly represent cell growth and exchange of metabolites by only using information related to the medium in which cells are growing as input data. For this aim, it is necessary to have metabolic models of higher quality, to improve the available knowledge about the restrictions on the metabolic fluxes, and to obtain objective functions that represent in a better way the biological goals.
In most analysis, maximization of biomass production has been assumed as the most appropriate objective function (e.g. 
). Recently, this objective function has been reviewed 
. However, it has been found that growth-based optimization may not occur in all substrates 
, and that in some cases other objective functions perform better adjustments (e.g. 
The problem of creating objective functions from experimental data has already been addressed; for example, finding the coefficients of importance (CoIs
), representing the consistency of the hypothesis that a given flux is maximized by the organism as part of its cellular objective 
, or with the BOSS method, in which an objective function is generated from the stoichiometric network, together with constraints over the fluxes and a set of experimental data 
. However, the objective functions obtained with these approaches are highly dependent on particular data sets, and cannot always be interpreted from a physiological point of view.
This work was aimed to determine whose FBA objective functions, composed of linear combination of objectives that represents targets of the cell compartments, allow better predictions of the metabolic fluxes. There are many objective functions previously proposed that are included in the linear combinations studied. Errors in predictions of both cell growth and exchange of metabolites (i.e. excretion) were evaluated quantitatively. The methodology presented here is most suitable for eukaryotic organisms, because prokaryotes do not possess multiple organelles. Therefore, as Saccharomyces cerevisiae
is generally used as the eukaryotic model organism, experimental data and a metabolic model of this microorganism were used for the calculations 
. While most FBA performance evaluations have been done using moderate size stoichiometric models, this study used a genome-scale model of the metabolism of S. cerevisiae
, which led to the use of much of the information available about its metabolism. The experimental data sets were classified in various categories, according to growth and environmental conditions.
To sum up, the performance of different FBA objective functions (composed by linear combination of different compartmental objectives) was assessed, using a genome-scale metabolic network as metabolic model, and experimental data to determine the quality of every objective function. The objective functions evaluated can be represented by equation (3
are the FBA objective functions tested in the study,
is the number of cellular compartments considered,
is an (1×
) row vector of relative weighting, and
is an (1×
) row vector whose o
-th element correspond to a possible objective of the o
-th cellular compartment (the T
superscript in equation (3
) indicates transposition).
Errors in the estimations produced for the FBA when every
was used as objective function were evaluated, comparing exchange fluxes and biomass production predictions with experimental data. The tested combinations of compartmental objectives were ranked according to the absolute value of the error percentage in the prediction of the specific growth rate, when the combination of objectives is used as objective function in the FBA. This approach can be expressed as shown by equation (4
), but instead of selecting only one combination of objectives (i.e. solving the outer optimization problem) for every category, the five best combinations of objectives for every category (of environmental/growth conditions) were analyzed; the errors in the estimated values obtained with those five best objective functions in the FBA were compared with the errors found using the most popular objective function (i.e. maximization of biomass production), and the errors found with an objective function that generally does not give good predictions (i.e. maximization of ATP production).
In equation (4
is the measured specific growth rate in the k
-th experimental data set of the category,
is the specific growth rate predicted by the internal optimization problem (i.e. a FBA done using
as objective function) for the k
-th data set, and
is the number of experimental data sets that belongs to the category (of environmental/growth conditions) analyzed.