Flux balance analysis

Flux Balance Analysis (FBA) is a widely used computational method that predicts the metabolic flux through biochemical reactions in metabolic networks [58–61]. FBA uses information about the stoichiometric coefficients of the metabolites participating in each reaction, encapsulated in the stoichiometric matrix S, which is of dimension m×n, where m and n, respectively, denote the number of metabolites and the number of reactions in a metabolism. FBA assumes that a metabolism has reached a steady-state, as might be attained by a growing population of bacteria in chemostat with constant nutrient supply, where mass conservation constraints apply. These constraints are mathematically expressed as Sv = 0, where v is the vector of fluxes (v _i) through reaction i. The solution space of this equation is called the null space of the stoichiometric matrix (S). This null space is further constrained by upper and lower bounds on the fluxes through each reaction. FBA applies linear programming to find the optimal flux vector(s) that maximize an objective function Z. This task can be mathematically formulated as finding a flux vector (v ^* ) with the property

where the vector c contains scalar coefficients representing a maximization criterion, and entries a _i and b _i of vectors a and b, respectively, indicate the minimally and maximally possible flux through reaction i.

We use a set of 13 well-known precursors from central carbon metabolism as biomass molecules required for viability (Additional file 2: Table S1). We use the software package CLP (1.4, Coin-OR; https://projects.coin-or.org/Clp) to solve all linear programming problems.