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Flux balance analysis has proven an effective tool for analyzing metabolicnetworks. In flux balance analysis, reaction rates and optimal pathways areascertained by solving a linear program, in which the growth rate is maximizedsubject to mass-balance constraints. A variety of cell functions in response toenvironmental stimuli can be quantified using flux balance analysis byparameterizing the linear program with respect to extracellular conditions.However, for most large, genome-scale metabolic networks of practical interest,the resulting parametric problem has multiple and highly degenerate optimalsolutions, which are computationally challenging to handle. An improvedmulti-parametric programming algorithm based on active-set methods isintroduced in this paper to overcome these computational difficulties.Degeneracy and multiplicity are handled, respectively, by introducinggeneralized inverses and auxiliary objective functions into the formulation ofthe optimality conditions. These improvements are especially effective formetabolic networks because their stoichiometry matrices are generally sparse;thus, fast and efficient algorithms from sparse linear algebra can be leveragedto compute generalized inverses and null-space bases. We illustrate theapplication of our algorithm to flux balance analysis of metabolic networks bystudying a reduced metabolic model of Corynebacterium glutamicum and agenome-scale model of Escherichia coli. We then demonstrate how the criticalregions resulting from these studies can be associated with optimal metabolicmodes and discuss the physical relevance of optimal pathways arising fromvarious auxiliary objective functions. Achieving more than five-foldimprovement in computational speed over existing multi-parametric programmingtools, the proposed algorithm proves promising in handling genome-scalemetabolic models.

An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks