Data reconciliation and parameter estimation in flux-balance analysis

Flux blance analysis (FBA) has been shown to be a very effective tool to interpret and predict the metabolism of various microorganisms when the set of available measurements is not sufficient to determine the fluxes within the cell. In this methodology, an underdetermined stoichiometric model is solved using a linear programming (LP) approach. The predictions of FBA models can be improved if noisy measurements are checked for consistency, and these in turn are used to estimate model parameters. In this work, a formal methodology for data reconciliation and parameter estimation with underdetermined stoichiometric models is developed and assessed. The procedure is formulated as a nonlinear optimization problem, where the LP is transformed into a set of nonlinear constraints. However, some of these constraints violate standard regularity conditions, making the direct numerical solution very difficult. Hence, a barrier formulation is used to represent these constraints, and an iterative procedure is defined that allows solving the problem to the desired degree of convergence. This methodology is assessed using a stoichiometric yeast model. The procedure is used for data reconciliation where more reliable estimations of noisy measurements are computed. On the other hand, assuming unknown biomass composition, the procedure is applied for simultaneous data reconciliation and biomass composition estimation. In both cases it is verified that the f measurements required to get unbiased and reliable estimations is reduced if the LP approach is included as additional constraints in the optimization.