The constructed stoichiometric model of E. coli contains all presently known reactions in central carbon metabolism with 98 reactions and 60 metabolites (Supplementary Table I ). To apply FBA, the reaction network was automatically translated into a stoichiometric matrix (Schilling and Palsson, 1998 (link)) by means of a parser program implemented in Matlab (MATLAB®, version 7.0.0.19920 (R14), The MathWorks Inc., Natick, MA). Assuming steady-state mass balances, the production and consumption of each of the m intracellular metabolites Mi is balanced to yield
with
S corresponds to the stoichiometric matrix (m × n) and ν (n × 1) to the array of n metabolic fluxes with νilb as lower and νiub as upper bounds, respectively. The above equations represent the conservation law of mass that is fundamental to constraint-based modeling. For all herein presented stoichiometric analyses, maximization of biomass yield is synonymous to the frequently used maximization of growth rate objective (Price et al, 2004 (link)). This is because stoichiometric models are sets of linear balance equations that are inherently dimensionless, hence maximization of the biomass reaction optimizes the amount of product (i.e., the yield) rather than a time-dependent rate of formation. The P-to-O ratio constraint was implemented by omitting the energy-coupling NADH dehydrogenase I (Nuo), cytochrome oxidase bo3 (Cyo) and/or cytochrome oxidase bd (Cyd) components of the respiratory chain. For a ratio of unity, Cyd and Nuo were set equal to zero. Under anaerobic conditions, electron flow is only possible via the NADH oxidases Nuo or NADH dehydrogenase II (Ndh) to fumarate reductase (Frd), hence coupled to succinate fermentation. For nitrate respiration, the terminal oxidase nitrate reductase (Nar) was used instead of Cyd or Cyo (Unden and Bongaerts, 1997 ).
For the genome-scale analysis we used two recently reconstructed models of E. coli metabolism (Edwards and Palsson, 2000b (link); Reed et al, 2003 (link)). In silico growth was simulated on glucose minimal medium for all six environmental conditions. ADP remained unbalanced, since otherwise formation of adenosine would be carbon-limited. For the proton-balanced model of Reed et al (2003) (link), severe alternate optima occurred in central carbon metabolism given an unlimited proton exchange flux between the cell and the medium and a P-to-O ratio of 2, that is the upper bound of the biologically feasible range of P-to-O ratios (Unden and Bongaerts, 1997 ). To prevent the unlimited production of ATP equivalents through the ATPS4r reaction under this condition, all external protons involved in the respiratory chain and the transhydrogenase reaction were balanced (specifically, we balanced the external protons around the reactions ATPS4r, TDH2, CYTBD, CYTBO3, NO3R1, NO3R2, NADH6, NADH7, NADH8). A P-to-O ratio of 2 was implemented by assuming both the transport of four protons through CYTBO3 and NADH6 across the membrane and the diffusion of four protons through ATPS4r for the formation of one ATP equivalent.
For the genome-scale analysis we used two recently reconstructed models of E. coli metabolism (Edwards and Palsson, 2000b (link); Reed et al, 2003 (link)). In silico growth was simulated on glucose minimal medium for all six environmental conditions. ADP remained unbalanced, since otherwise formation of adenosine would be carbon-limited. For the proton-balanced model of Reed et al (2003) (link), severe alternate optima occurred in central carbon metabolism given an unlimited proton exchange flux between the cell and the medium and a P-to-O ratio of 2, that is the upper bound of the biologically feasible range of P-to-O ratios (Unden and Bongaerts, 1997 ). To prevent the unlimited production of ATP equivalents through the ATPS4r reaction under this condition, all external protons involved in the respiratory chain and the transhydrogenase reaction were balanced (specifically, we balanced the external protons around the reactions ATPS4r, TDH2, CYTBD, CYTBO3, NO3R1, NO3R2, NADH6, NADH7, NADH8). A P-to-O ratio of 2 was implemented by assuming both the transport of four protons through CYTBO3 and NADH6 across the membrane and the diffusion of four protons through ATPS4r for the formation of one ATP equivalent.