[63] to demonstrate the duality between weak producibility and the existence of certain extreme semipositive conservation relations (ESCRs) in a media. ESCRs were defined as the simplest semi-positive linear combinations of species concentrations that were invariant

to all metabolic flux configurations. A biochemical species was called producible Inhibitors,research,lifescience,medical in a constraints-based metabolic model if a feasible steady-state flux configuration existed that sustained its nonzero concentration during growth. Weak nutrient sets are analogous to MCSs in a metabolic network in that a MCS C for an objective reaction j is a set of reactions whose elimination renders flux through j infeasible at steady state so, Inhibitors,research,lifescience,medical a necessary and sufficient condition for C to be a cut set for j is that C is a hitting set for all j-containing elementary modes. Similarly, U is a weak nutrient set for species or metabolite i if and only if U is a hitting set for all of the i-containing ESCRs. The ‘weak nutrient sets’ algorithm identified

all minimal nutrient media that left an arbitrary metabolite weakly producible with respect to Inhibitors,research,lifescience,medical a given metabolic network. Details of the concept and its application can be seen in [63]. 5.4. Flux Balance Analysis Flux balance analysis (FBA) [49,64,65] shares a common underlying mathematical find more framework with MCSs and EMs except that, while EMs identify all possible and feasible non-decomposable metabolic routes for a given network at steady state, FBA derives a feasible set of steady-state fluxes optimizing a stated cellular objective e.g, optimizing the biomass production per substrate uptake.

EM analysis establishes a link Inhibitors,research,lifescience,medical between structural analysis and metabolic flux analysis (MFA) where thermodynamically and stoichiometrically feasible stationary flux distributions for a network can Inhibitors,research,lifescience,medical be obtained from the linear combinations of the EMs. Calculating EMs and MCSs for larger networks can lead to problems with combinatorial explosion. However, because they are unique for a given network structure, they provide the full range of potential functionalities of the metabolic system and are therefore useful for investigating all physiological states that are meaningful for the cell in the long term. FBA, on the other hand, is more efficient, providing good predictions of mutant phenotypes and using linear programming to obtain a single (not necessarily unique) Cytidine deaminase solution to an optimization problem. However, because it focuses on a specific behavior, FBA cannot cope with cellular regulation without additional constraints; it fails whenever network flexibility has to be taken into account, e.g., in the analysis of pathway redundancy or in quantitative prediction of gene expression [42]. We conclude that MCSs and EMs offer a convenient way of interpreting metabolic functions while FBA can be used to explore the relationship between the metabolic genotype and phenotype of organisms.