The recent advent of high-throughput experimental tools has steadily accumulated vast amounts of genome, transcriptome, proteome, metabolome, and fluxome data. Systematic approaches are required not only for characterizing the global context of the metabolic systems but also for designing the metabolic engineering strategies.1 This can be achieved by combining the accumulated wet data set with in silico analysis techniques. Amongst the available in silico approaches, constraint-based flux analysis using linear programming (LP) has been most widely used for predicting metabolic and physiological states under the given genetic and/or environmental conditions on the basis of experimentally observed extracellular flux measurements.
Escherichia coli is one of the best-characterized microorganisms. The last decade of research on this microbe has been further facilitated by the progressive development of its genome-scale model, composing of a multitude of reactions describing the entire metabolic network.2 When used in combination with the constraint-based analysis, this genome scale E. coli model allows us to simulate the metabolic behavior or characterize the cellular system by optimizing plausible phenotypic or cellular objective function. Commonly used objective functions in the model include maximizing the rate of cell growth, ATP production, and production of a desired by-product.3 It is widely acknowledged that the metabolism of wild-type E. coli has evolved toward the maximum rate of growth. This is supported by the consistency of flux simulations using the objective function of maximizing growth rate with experimental measurements.4 However, it has been demonstrated that under certain environmental or genetic conditions whereby the cells were probably not exposed to long-term evolutionary pressure, maximizing the growth rate would not represent the underlying cellular objective. For instance, incorrect simulations were observed in some cases of E. coli growing on uncommon carbon source such as glycerol5 and genetically engineered knockout strains.6 In the latter study, Segre et al.6 observed that the experimental growth rates of three knockout strains were lower by an average of 22% over the simulated values. Hence, for a clearer understanding of environmentally affected and genetically modified E. coli metabolism, it is indeed necessary to identify the principal cellular objective that best describes the metabolic strategy or altered physiological state of these cells. To date, only a few attempts were made to systematically validate available objective functions with experimentally observed metabolic fluxes.7–9 Burgard and Maranas7 suggested a novel bilevel (or nested) optimization procedure to infer and test various hypothesized objective functions based on experimental flux data; Knorr et al.8 identified the minimization of redox potential as the most plausible objective function for E. coli growing on succinate using Bayesian-based selection technique. Most recently, Schuetz et al.9 systematically evaluated 11 different objective functions by comparing the in silico simulated internal fluxes with 13C-determined in vivo fluxes in E. coli under various environmental conditions and as such identified the growth maximization and ATP yield per flux unit as best cellular descriptions under limited and unlimited growth conditions, respectively.
In this work, we explored the capability of constraint-based genome-scale modeling as an investigative tool to elucidate the physiological effect of plasmid metabolic burden on E. coli cells cultured under steady-state chemostat condition.10 There are evidences suggesting that the recombinant E. coli cells bearing multicopy plasmids could be under an altered physiological state. The introduction of plasmids to the cell creates a metabolic burden effect leading to retarded growth11 and changes in gene regulation, enzyme activities, and metabolic flux.10 Glick11 defined the metabolic burden as the drain of the cellular resources, in the form of biosynthetic precursors and energy, to maintain and express plasmid DNA. Thus, the plasmid-related biosynthetic drain could be considered as a possible cellular objective. On the other hand, the presence of plasmids also induces multifaceted stress responses and global gene regulation changes showing some resemblance to the heat-shock response,12 phage defense,13 and catabolite derepression.14 Stress responses are expected to contribute to an additional drain of energy, which would be manifested as an increase in nongrowth-related maintenance energy expenditure. This additional energy drain from plasmid presence can be taken into account as another objective function. In this study, the simulated results for available phenotypic and operational objectives, that is, the growth rate, plasmid production, and ATP maintenance (ATPm) expenditure are compared with experimental flux information, thereby identifying the most plausible describer of the physiological state within the P+ cells.
Materials and Methods
Strain information and experimental measurements for flux analysis
All wet experimental growth and internal flux data were obtained from the previously published work of Wang et al.10 In summary, 2-L chemostat cultures of E. coli strain BL21(DE3) with and without the ColE1-derived high-copy pOri2 plasmid (37°C, pH 7.0, and dissolved oxygen concentration of 30%) were grown in glucose-limited synthetic medium. During the course of the run under the steady-state condition, biomass, glucose, acetate, and exhaust gas CO2/O2 concentrations were monitored, and their uptake and production rates were measured (Table 1). Plasmid concentration was determined with real-time PCR using β-lactamase-specific primers. For the determination of internal metabolic fluxes, glucose in the feed medium was replaced either partially with 1.8 g L−1 [U-13C] glucose and 6.2 g L−1 unlabelled glucose or completely with 8 g L−1 [l-13C] glucose. Labeling patterns of free intracellular amino acids in the hydrolyzed samples were analyzed using GC mass spectrometry. After correction for the natural abundance of stable isotopes in the mass spectra, the metabolic flux ratios and internal metabolic fluxes were determined.
Table 1. Objective Functions and Experimental Measurements for Flux Simulation*
Constraint-based flux modeling was conducted using the objective functions of maximizing growth rate (Max growth), plasmid production (Max plasmid), and ATPm expenditure (Max ATPm). Experimentally-measured growth, glucose uptake, plasmid synthesis, and acetate excretion rates from Wang et al. (2006) were used as the constraints for flux simulation. P− and P+ cells refer to the wild-type and plasmid-bearing strains, respectively.
Specific growth rate (h−1)
Specific glucose uptake (mmol/g DCW/h)
Specific plasmid synthesis (pmol/g DCW/h)
Specific acetate excretion (mmol/g DCW/h)
Genome-scale in silico E. coli model
The current genome-scale in silico model, describing plasmid-bearing E. coli metabolism, is derived and slightly modified from the iJR904 model.15 The metabolic network of the model incorporates 761 metabolites (143 extracellular metabolites and 618 intermediates) and 931 metabolic reactions. Embedded in the metabolic network includes the central, energy, and redox metabolisms along with the necessary transport reactions for extracellular metabolites. In addition to these metabolic reactions, two more balance equations were considered to represent E. coli biomass and plasmid-related macromolecule synthesis. The biomass equation is derived from the drain of various biosynthetic precursors into E. coli biomass with their appropriate ratios and used to quantify its specific growth rate. The plasmid equation consists of the biosynthetic precursors and energetic requirement for pOri2 plasmid DNA replication and marker protein expression.16 The pOri2 (4,575 bp) requires four nucleotide precursors for its replication based on an approximated E coli K-12 GC content of 51%:
The biosynthetic precursor balance for the sole plasmid encoded antibiotic marker protein (β-lactamase) combined with energetic requirements of 4.306 mol ATP/mol amino acids16 for its expression can be formulated as follows:
Equations 1 and 2 are incorporated to formulate the plasmid production rate on the basis of the experimentally determined production rates of plasmid DNA and β-lactamase protein, which is estimated as 3% of total cellular protein from two-dimensional gel electrophoresis analysis.17
Constraint-based flux analysis
To implement constraint-based flux analysis for in silico simulations on the basis of experimentally determined measurements by Wang et al.10 (Table 1), the relationships among all metabolites and reactions are balanced initially in terms of stoichiometry under the stationary hypothesis. Subsequently, using the LP approach, a given cellular objective is linearly optimized to evaluate the unknown fluxes within the metabolic reaction network, subject to the constraints pertaining to mass conservation, reaction reversibility, and capacity as described elsewhere.4, 18 In this work, the quantification of metabolic fluxes under various conditions for the selected objective and comparative analysis of the resultant metabolic flux maps have been implemented by the metabolic network management program MetaFluxNet.19 The wild-type maintenance energy requirement was taken as 7.6 mmol/g DCW/h as determined from chemostat experiments.3 Both balance equations for synthesizing the biomass and plasmid in E. coli were considered as putative cellular objectives along with ATP dissipation (ATP + H2O → ADP + H + PI) representing maintenance energy expenditure.
Flux variability analysis
Flux variability analysis is a methodology designed to examine the redundancy of biological systems contributing to their robustness.20 The minimum and maximum flux values of each reaction in the model are sequentially calculated to determine the achievable flux variation satisfying the given optimum phenotype. As such, this approach allows us to identify “active reactions” that could be potentially used in the model to attain the desirable cellular phenotype. Among them, reactions without flux variation or with small range of fluxes are essential for achieving same phenotypic state, whereas more internal flexibility in their fluxes implies the presence of alternative suboptimal pathways.
Results and Discussion
Evaluation of plausible cellular objectives in wild-type and plasmid-bearing E. coli cells
The growth rate was simulated by means of constraint-based flux analysis of genome-scale E. coli model under the conditions given in Table 1. For the wild-type or plasmid-free (P−) cells, simulated growth rate matches well with the experimental measurement (Figure 1). This result is consistent with the earlier finding that wild-type E. coli appears to have evolved toward optimum rate of growth and thus maximizing growth rate (Max growth) in this simulation could adequately reflect their metabolic states and physiological phenotype.4 The simulated growth rate (0.44 h−1) for the P+ cells is, however, noticeably higher than the experimentally observed growth rate (0.29 h−1). As in silico flux simulations represent the optimal growth capability under the given set of constraints, the lower simulated growth rate indicates that the P+ cells may not be growing at its maximum rate, and they could adopt alternative physiological objectives other than optimum growth.
To evaluate the physiological state which best describes the P+ cell metabolic behavior and phenotype, we additionally considered other cellular objectives including (1) maximizing plasmid production rate (Max plasmid) and (2) maximizing maintenance energy expenditure (Max ATPm). For these P+ cell simulations, the predicted oxygen uptake rate and carbon dioxide production rate were compared with chemostat experimental data. Unexpectedly, the predicted rates in both Max growth and Max plasmid cases are ∼50% lower than the experimental values (Figure 2). Only the simulation result for Max ATPm case shows a good agreement with the experimental oxygen uptake and carbon dioxide evolution rates. We further compared the in silico quantified internal fluxes with experimental isotope-based flux values within the central metabolic pathways (Figure 3). Experimentally, a higher proportion of flux into pentose phosphate pathway was observed in the P− cells, whereas P+ cells showed more flux leading into glycolysis and higher fluxes within TCA cycle than the P− cells. The experimental and simulated central metabolic fluxes are summarized in Figure 3. As mentioned earlier, the comparison of intracellular fluxes within the central metabolic pathways reveals that (1) P− cell (Max growth) simulation result is in good agreement with the experimental fluxes, and (2) among three conditions tested for P+ cell simulation cases, only P+ cells (Max ATPm) simulations are consistent with the experimental fluxes.
Variation of internal fluxes
The current genome-scale E. coli model consists of 933 metabolic reactions including biomass and plasmid equations, but not all reactions are actively used to achieve the flux solution space. We conducted flux variability analysis to evaluate the range of possible variation in flux within each reaction, thus identifying the active reaction set. Overall, flux distribution is depicted for the P− cells Max growth (Figure 4a) and P+ cells Max ATPm simulations (Figure 4b). Of the 933 reactions in the model, 318 and 320 reactions were used for the simulation cases of P− cells Max growth and P+ cells Max ATPm, respectively. For the active reactions, highest fluxes are found within the central metabolism, energy metabolism, and transport-related pathways. This is consistent with the findings that E. coli metabolism is characterized by highly uneven distribution of metabolic fluxes, and the overall metabolic activity is dominated by several reactions with high fluxes.21 The detailed examination of these fluxes could shine light on the cellular metabolic state, which would be useful for metabolic engineering.
E. coli can use several parallel sets of alternative catabolic and biosynthetic pathways that perform similar metabolic functions, but each with a varying degree of efficiency in conserving energy.22 The existence of flux variation is an indication of the presence of these alternative pathways attaining same physiological state. Figures 4c and 4d zoom in to examine the flux variation in metabolic reactions related to central metabolism. For the P+ cells (Max ATPm) simulation (Figure 4d), four vertical bars representing reactions with flux variations greater than 3 mM/g DCW/h were observed. These relatively large flux variations indicate the potential involvement of two pairs of alternative pathways, which are subsequently identified as (1) the conversion of fructose-6-phosphate into glyceraldehyde-3-phosphate catalyzed by phosphofructokinase/fructose-bisphosphate aldolase or by fructose 6-phosphate aldolase and (2) the conversion of phosphoenolpyruvate into pyruvate catalyzed by either pyruvate kinase or dihydroxyacetone phosphotransferase. Interestingly, although the pyruvate kinase catalyzed reaction produces ATP, the dihydroxyacetone phosphotransferase-catalyzed reaction does not. The potential activation of the latter alternative pathway is an example of a less energetically efficient metabolic route that can be taken by the cell.
Cellular objectives in plasmid-bearing cells
Although any simulations using a metabolic model can only be considered as an exploratory estimate of reality, they are still useful as tools for the evaluation of hypotheses under a defined environment.23 Conventionally, the extra biosynthetic drain of precursors and energy for plasmid-related DNA replication and protein synthesis is considered as the main factor for the metabolic burden phenomenon.24 Thus, the metabolic flux simulation for the P+ cells was conducted by taking into account a plasmid equation describing the expected biosynthetic drain of nucleotides and energy for plasmid DNA replication. This equation also includes the additional amino acid precursors and energy required for synthesis of the plasmid-encoded antibiotic selection marker protein, β-lactamase. Based on the experimentally measured plasmid level of 0.63 pmol/g DCW/h and the β-lactamase level of 3% of total cell proteins, simulation using the maximum growth rate objective function revealed that this additional drain of biosynthetic precursors and energy for plasmid and protein biosynthesis could not sufficiently describe the observed drop in growth rate (0.44 h−1 simulated versus 0.29 h−1 experimental growth rate). A subsequent attempt to increase the β-lactamase level to 6% further reduces growth marginally by 3.6% (results not shown). Therefore, other unaccounted factors seem to be involved.
It seems conceivable that the plasmid levels or protein synthesis could be underestimated in our simulation. In such case, maximizing plasmid (and protein) production might be more plausible and predictive. However, when the plasmid production rate was maximized while constraining the growth rate to be the experimental value of 0.29 h−1, the predicted O2 and CO2 levels from this simulation turn out to be lower by around 50% compared with the experimental values. The determined intracellular fluxes in the central metabolic pathways are also inconsistent with the experiments. In this simulation, plasmid production increased ∼10-fold to 6.4 pmol/g DCW/h, whereas β-lactamase becomes 30% of total cell proteins. The plasmid level of 6.4 pmol/g DCW/h is equivalent to a plasmid copy number of ∼600, which is an abnormally high value for cells during exponential growth.25 Hence, it is unlikely that the sole biosynthetic drain of precursors and energy could explain the actual physiological state of the P+ cells.
Finally, because plasmid is known to trigger stress responses, which could lead to the increase in the nongrowth-related requirement for maintenance energy, we conducted another simulation by maximizing ATPm, while constraining growth rate and plasmid level to the experimental values (Table 1). Under this simulation condition, all calculated fluxes (O2, CO2, and intracellular central metabolic fluxes) were in good agreement with the experimental observations. The ATPm increased approximately five times from 7.6 mM/g DCW/h to 40.6 mM/g DCW/h. The fivefold increase in ATP production appears reasonable considering that a 2.7-fold increase has been reported for other recombinant cells.26 Hence, a higher metabolic priority toward ATP dissipation is shown to best describe the principal cellular objective driving metabolism within the P+ cells, suggesting that an increased requirement for maintenance energy could contribute significantly to the metabolic burden effect of P+ cells. In a similar study to identify appropriate cellular objective for network operation of the wild-type (P−) E. coli metabolism, Schuetz et al. examined 11 objective functions under various environmental conditions.9 Although they found that no single objective function could describe metabolic states under all conditions tested, reasonably accepted simulation results for nutrient-limited culture condition were achieved by maximizing the yield of ATP (or biomass). This indicates that P− E. coli cells are able to maximally form ATP, which is then economically allocated for synthesizing biomass precursors rather than nongrowth-related energy dissipation observed in P+ cells. It should also be noted that the P+ cells have not been selectively evolved in chemostat culture over many generations. Thus, it is possible that the cellular objective could be functionally fine-tuned and gradually changed toward more efficient growth or energy expenditure through adaptive evolution27 or genetic engineering. For example, we have recently engineered P+ cells to display improved growth rate by targeting a global regulator of central metabolism.17 In such a case, the engineered P+ strains may not be described by maximizing ATP dissipation.
Metabolic uncoupling and futile cycles in plasmid-bearing cells
Maintenance energy can be defined as energy expended on functions not directly growth-related.28 This broad definition of ATPm can include the additional energy expenditure or dissipation related to metabolic uncoupling and futile cycles. As the consequence of having a limited pool of cellular resources, any extra drain for maintenance activities will invariantly reduce the allocation of resources for growth or proliferation.29 Metabolic uncoupling refers to the inefficient coupling between energy generation and consumption and leads to the inability to generate maximum amount of theoretical energy. Conversely, futile cycles occur when two enzymes interconvert substrates in opposing directions at the same time.28 The typical net reaction is ATP hydrolysis resulting in energy loss.
Induction of futile cycle in E. coli was shown to stimulate oxygen consumption, reduce growth yield on glucose, and increase excretion of fermentation products including acetate.30 Notably, higher acetate and oxygen uptake rates of the P+ cells over the P− cells are also observed in the experimental data (Figure 2), indicating that the futile cycles could indeed be active in the P+ cells. The loss of energy from metabolic uncoupling and futile cycles could be accounted for by an increase in maintenance energy requirement. Although the basis for the proposed higher maintenance energy requirement remains unclear, the presence of plasmids is known to perturb the bacterial global regulatory network.17, 31 It appears likely that some plasmid-induced regulatory changes upregulate innately inactive metabolic enzymes in recombinant cells, which could in turn lead to futile cycles or other energetically inefficient pathways. Using chemostat cultures, an increased requirement for ATP of 2.7-fold in recombinant protein-expressing P+ E. coli over the P− cells with a corresponding decrease in maximum specific growth rate from 0.75 to 0.5 h−1 was reported.26 This increase in ATP requirements was attributed to an increase in RNA turnover and protein degradation. It is interesting to also note that the sole presence of plasmids has been reported to lead to higher expression of heat-shock proteins,12 many of which are proteases and chaperones. The upregulated heat-shock proteins in P+ cells and their associated protein degradation and refolding activities could further promote energy expenditure, hence contributing to increased maintenance energy requirement.
Although metabolic fluxes for wild-type E. coli can be readily determined with the objective function of maximizing growth rate by constraint-based flux analysis, we show that maximizing ATPm expenditure provides a more fitting description of the underlying physiological driving force that presumably directs overall metabolism and cellular phenotype of P+ E. coli. That implies that cellular resources in P+ cells are being expended on functions not directly growth-related. At the same time, in silico analysis also suggests that the metabolism of P+ cells could be less energetically efficient. Although the source of increase in maintenance energy requirement remains unclear, it could be related to inefficient energy metabolism and heat-shock responses. On an added note, flux analyses of P+ cells in comparison with P− cells, both using the maximum growth objective function, indicates that P+ cells have not reached their optimal growth capacity. This suggests that, phenotypically, further improvement in growth rate is potentially achievable through adaptive evolution or metabolic engineering. Although constraint-based metabolic flux analysis is already a well-established modeling technique, this work demonstrates the need to conscientiously identify and select an appropriate cellular objective for accurate simulation studies of recombinant organisms relevant to biotechnological applications.
The financial support of the Agency for Science, Technology and Research (A*STAR) is gratefully acknowledged. The authors also wish to express gratitude to Drs. May May Lee, Pang See Jye, Raymond Lee, and Chailian Lee for their proficient support and Dr. Rudiyanto Gunawan for his valuable review and suggestions.