Flux Analysis of Yeast Central Carbon Metabolism

Absolute values of intracellular fluxes were calculated with a flux model comprising all the major pathways of yeast central carbon metabolism (Additional data file 2). Deleted reactions were not omitted from the mutant models; thus the mutations were independently verified from the ¹³C data. The stoichiometric matrix of 34 linear equations and 30 metabolites has an infinite condition number [57 (link)]; it is thus underdetermined, and has a solution space with an infinite number of different flux vectors that fulfill the constraints from determined uptake and production rates. To uniquely solve the system for fluxes (ν), a set of linearly independent equations that quantify flux ratios (FlRs) were used to obtain eight constraints on the relative flux distribution from METAFoR analysis (see Additional data file 2).
The fraction of cytosolic oxaloacetate originating from cytosolic pyruvate is given by:
The fraction of mitochondrial oxaloacetate derived through anaplerosis is given by:
The fraction of PEP originating from cytosolic oxaloacetate is given by:
The fraction of serine derived through glycolysis is given by:
The upper and lower bounds for mitochondrial pyruvate derived through the malic enzyme (from mitochondrial malate) are given by:
The contribution of glycine to serine biosynthesis is given by:
and, finally, the contribution of serine to glycine biosynthesis is given by:
The stoichiometric matrix including Equations 3-10 has a condition number of 31, implying that the model is numerically robust [57 (link)]. Error minimization was carried out as described by Fischer et al. [10 (link)]. Balanced NADPH production and consumption were not added as additional constraints. In general, NADPH production was constrained by Equations 3 and 7/8, which estimate the relative use of the PP pathway and malic enzyme, respectively. As an additional source of NADPH, the flux through the NADPH-dependent acetaldehyde dehydrogenase [33 (link)] was estimated from the acetate production rate and the biomass requirement for cytosolic acetyl-CoA. Deviation of the NADPH production estimated in this way from the consumption for biosynthesis was generally below ± 20%, suggesting that the model assumptions and the experimental data are highly consistent. All extreme flux patterns were independently verified in 30-ml cultures (data not shown).