Flux variability scanning based on enforced objective flux for identifying gene amplification targets

E. coli genome-scale metabolic model

EcoMBEL979 was used throughout this study [30], which is a slightly modified version of the genome-scale E. coli metabolic network model, i JR904 [31]. EcoMBEL979 contains 814 metabolites (144 extracellular metabolites and 670 intermediates) and 979 metabolic reactions, along with a biomass equation derived from the E. coli biomass composition [32].

Constraints-based flux analysis

where S _ij represents the stoichiometric coefficient for metabolite i in reaction j ν _j is the flux of reaction j J is the set of all reactions, and b _i is the net transport flux of metabolite i. If this metabolite is an intermediate, b _i is equal to zero. α _j and β _j are the lower and upper bounds of the flux of reaction j, respectively. Herein, the flux of any irreversible reaction is considered to be positive; a negative flux indicates the reverse direction of a reaction.

Grouping reaction (GR) constraints based on the genomic context and flux-converging pattern analyses

where y( v ₁ ) and y( v ₂ ) indicate binary variables (on or off) of a certain reaction 1 and 2, respectively.

where $C_{\mathit{xj}}$ indicates the carbon number involved in a reaction j$J_{\mathit{yj}}$ the number of the passing of the flux through the flux-converging metabolite near reaction j, and N _C,Rj the total number of carbon of primary metabolites without cofactors in reaction j.

where v ⁿ ₁ and v ⁿ ₂ are the normalized flux of reaction 1 and 2, obtained by dividing each reaction flux by the carbon source uptake rate, such as glucose. δ is the constant defining the flux level of reactions in this functional unit; the value of δ is recommended as 0.3.

Flux variability scanning based on enforced objective flux (FVSEOF) with grouping reaction (GR) constraints

Once grouping reaction constraints are defined, FVSEOF with GR constraints is subsequently performed as follows (Figure 2). First, the initial or theoretical minimum ($v_{targetproduct}^{\mathit{initial}}$) and theoretical maximum ($v_{targetproduct}^{\mathit{max}}$) of the target product formation rates were calculated; these were implemented by setting the objective function as minimizing and maximizing the target product formation rate using constraints-based flux analysis with GR constraints. This can be formulated as follows:

where $v_{targetproduct}^{\mathit{initial}}$ indicates the initial or minimal point of the flux value constrained for the target bioproduct, while $v_{targetproduct}^{\mathit{max}}$ indicates the maximal flux value for the bioproduct. l _i and u _i are the lower and upper bound for the net transport flux of metabolite i, respectively, and $v_{\mathit{carbon}}^{\mathit{uptake}}$ is the carbon source uptake rate.

Second, the cell growth rate, Z( v _biomass ), was maximized while gradually increasing the target product formation rate from its initial (or minimal) flux value to its near theoretical maximum: $v_{targetproduct}^{\mathit{enforced}}=v_{targetproduct}^{\mathit{initial}}+\frac{k}{n}\left(v_{targetproduct}^{\mathit{max}}-v_{targetproduct}^{\mathit{initial}}\right)$$K=\left\{k|k=1,2,\cdots ,n-1\right\}$ ($n\ge 10$) [23]. The $v_{targetproduct}^{\mathit{enforced}}$ is an additional constraint provided during this stage of the constraints-based flux analysis; it starts with the initial value $v_{targetproduct}^{\mathit{initial}}$ plus one n^th of the difference between the $v_{targetproduct}^{\mathit{max}}$ and $v_{targetproduct}^{\mathit{initial}}$, and is increased to a value adjacent to $v_{targetproduct}^{\mathit{max}}$ in k steps.

Third, FVA was carried out with GR constraints by maximizing or minimizing the fluxes of all intracellular reactions, Z( v _{intracellular reaction} ), with additional constraints: the enforced production rate of the target bioproduct, which varied from its initial to maximum values in 10 steps, and 95% optimal cell growth rate, v _biomass = 0.95 · Z( v _biomass ) ^opt , for each step. The attainable flux ranges of intracellular reactions for each step were subsequently subjected to the targeting criteria introduced in the following section.

FVSEOF with GR constraints was calculated using mixed integer nonlinear programming with the DICOPT solver, subject to the constraints including GR constraints, mass conservation and reaction thermodynamics.

Flux bias, its slope and flux capacity as targeting criteria

Flux bias (V _avg ), its slope (q _slope ) and flux capacity (l _sol ) were employed as targeting criteria for the initial set of gene amplification targets predicted from FVSEOF with GR constraints (Figure 2 and 3). Among them, V _avg and l _sol were determined as follows in order to effectively investigate the changes of flux variabilities for genetic perturbations [28]:

$V_{\mathit{avg}}=\frac{V_{\mathit{max}}^{\text{'}}+V_{\mathit{min}}^{\text{'}}}{2}$

(15)

$l_{\mathit{sol}}=V_{\mathit{max}}^{\text{'}}-V_{\mathit{min}}^{\text{'}}$

(16)

The ${V^{\prime }}_{\mathit{max}}$and ${V^{\prime }}_{\mathit{min}}$indicate the maximal and minimal flux values for a reaction under the given condition. The l _sol indicates the difference between the maximal and minimal flux values for a reaction. q _slope was calculated using linear regression of the flux values for a reaction towards the gradually maximized product formation rate.

Bacterial strains and plasmids

The E. coli strains used in this study are listed in the Additional file 1. The XQ52 strain, a putrescine producer, was used as a base strain [34]. E. coli TOP10 was used for gene cloning studies. The plasmid p15SpeC containing a strong tac promoter was used as an expression vector. The plasmid p15SpeC was constructed from the pTac15K plasmid by cloning the speC gene (encoding ornithine decarboxylase in the putrescine biosynthetic pathway) into the site between the EcoRI and SacI restriction enzyme sites of pTac15K. The plasmid contained a kanamycin resistance selective marker. Cells were grown in Luria–Bertani (LB) broth or on plates containing appropriate antibiotics at 37°C for the construction of strains and plasmids. Antibiotics were added at following concentrations: 50 μg/mL ampicillin, 25 μg/mL kanamycin, and 35 μg/mL chloramphenicol.

The plasmids used in this study are listed in the Additional file 1. Polymerase chain reaction (PCR) primers for the gene cloning studies conducted here are listed in the Additional file 2. Pfu DNA polymerase was purchased from Solgent (Daejeon, Korea). Restriction enzymes and T4 DNA ligase were obtained from New England Biolabs (Ipswich, MA) and Roche (Mannheim, Germany), respectively. The genomic DNA of E. coli W3110 was amplified to overexpress the target genes using the Pfu polymerase and PCR primers (Additional file 2). The PCR product was then digested with SacI and XbaI, and ligated into p15SpeC at the same restriction sites downstream of the tac promoter .

Fermentation

Batch cultivation was conducted at 37°C in a 6.6 L jar fermentor (Bioflo 3000; New Brunswick Scientific Co., Edison, NJ) containing 2 L R/2 medium supplemented with 10 g/L glucose and 3 g/L (NH₄)₂SO₄. The R/2 medium (pH 6.8) contained (per liter): 2 g (NH₄)₂HPO₄, 6.75 g KH₂PO₄, 0.85 g citric acid, and 0.7 g MgSO₄·7H₂O. In addition, 5 mL/L of a trace metal stock solution [35] was added. The trace metal solution contained per liter of 5 M HCl: 10 g FeSO₄·7H₂O, 2.25 g ZnSO₄·7H₂O, 1 g CuSO₄·5H₂O, 0.5 g MnSO₄·5H₂O, 0.23 g Na₂B₄O₇·10H₂O, 2 g CaCl₂·2H₂O, and 0.1 g (NH₄)₆Mo₇O₂₄. One milliliter of the overnight culture was transferred into a 300 mL Erlenmeyer flask containing 50 mL of the R/2 medium at 37°C and spun at 220 rpm in a shaking incubator (JEIOTech. Co. SI-900R). After obtaining an initial OD₆₀₀ of 0.3, the seed cultures (200 mL) were introduced into the bioreactor for batch cultivation. The culture pH was maintained at 6.8 by the addition of 6 M KOH. The dissolved oxygen concentration was maintained at 20% air saturation by automatically adjusting the agitation speed. Under the comparable batch culture conditions, the single gene-overexpressing strains based on the E. coli XQ52 strain harboring p15SpeC, denoted as XQ52 (p15SpeC), with each target gene were tested by flask cultivation in duplicate using R/2 medium supplemented with 10 g/L glucose at 37 °C.

Analytical procedures

Cell growth was estimated by measuring the optical density at 600 nm (OD₆₀₀) using an Ultrospec 3000 spectrophotometer (Amersham Biosciences, Uppsala, Sweden). Glucose concentrations were measured using a glucose analyzer (model 2700 STAT; Yellow Springs Instrument, Yellow Springs, OH, USA). The concentrations of glucose and organic acids were determined by high-performance liquid chromatography (ProStar 210; Varian, Palo Alto, CA) equipped with UV/visible light (ProStar 320; Varian, Palo Alto, CA) and refractive index (Shodex RI-71, Tokyo, Japan) detectors. A MetaCarb 87H column (300 by 7.8 mm; Varian) was eluted isocratically with 0.01 NH₂SO₄ at 60°C at a flow rate of 0.4 mL/min.

The putrescine concentration was determined by derivatizing putrescine with o- phthaldialdehyde (OPA; Sigma, St. Louis, MO), and the o- phthaldialdehyde derivative was detected by high-performance liquid chromatography (1100 Series HPLC, Agilent Technologies, Palo Alto, CA) with UV detection, as described previously [34]. The OPA derivatization reagent was prepared as described previously [34, 36, 37]. Following the addition of the OPA reagent, the mixture was filtered through a 0.2 mm PVDF syringe filter (Whatman, Maidstone, UK), and the filtrate was immediately injected into the HPLC. A SUPELCO C18 column (cat# 504955; 5μm, 150 mm x 4.6 mm) was operated at 25°C with a 0.8 mL/min mobile phase flow rate. The mobile phase consisted of solution A (55% methanol in 0.1 M sodium acetate, pH 7.2) and solution B (methanol). The following gradient was applied (values given in vol%): 1–6 min, 100% A; 6–10 min, linear gradient of B from 0% to 30%; 10–15 min, linear gradient of B from 30% to 50%; 15–19 min, linear gradient of B from 50% to 100%; 19–23 min, 100% B; 23–25 min, linear gradient of B from 100% to 30%; 25–28 min, linear gradient of B from 30% to 0% [34]. The derivatized putrescine was detected at a wavelength of 230 nm using a variable wavelength detector (G1314A, Agilent Technologies).

FVSEOF with GR constraints

Functionally related reactions can be grouped by genomic context and flux-converging pattern analyses [28]. Several reactions appeared to be related with one another based on genomic context analysis of conserved neighborhoods, gene fusions, and co-occurrence [28, 29]. Flux-converging pattern analysis narrows the range of plausible flux values for metabolic reactions by examining the number of carbon atoms in metabolites that participate in reactions and the converging patterns of fluxes from a carbon source [28]. By controlling the simultaneous on/off activity (C _on/off ) and flux scale (C _scale ) of the metabolic reactions, based on FBA with GR constraints, the flux distributions in gene knockout mutants were accurately predicted [28]. In this study, the GR constraints were further applied to reactions related to the biosynthesis of a target chemical to improve the model accuracy (Figure 1 and the Additional file 3).

FVSEOF with GR constraints was implemented as follows (Figure 2). First, the theoretical minimal and maximal flux values for the target product formation were calculated using constraints-based flux analysis by minimizing and maximizing the target product formation rate with GR constraints. Second, again with GR constraints, the cell growth rate was maximized while gradually increasing the constraint value for the target product formation rate (our objective function which is artificially enforced) from a minimal to a theoretical maximum, as calculated from the first step. Finally, FVA was conducted by maximizing and minimizing the fluxes of all intracellular reactions under additional constraints, including GR constraints, the enforced production rate of the target chemical varied from a minimal to a maximal value, and a 95% optimal growth rate constraint for each step. The attainable flux ranges for the intracellular reactions were calculated under the imposed constraints for each of the three steps.

Criteria for selecting gene amplification targets

Initial simulation results for FVSEOF with GR constraints were filtered based on rational criteria in an effort to select only the most effective amplification targets. The most important criterion was to identify gene amplification targets, the fluxes of which increased with the flux directed toward the target chemical. This procedure was implemented with quantitative values of q _slope V _avg , and l _sol (Figures 2 and 3). The flux bias (V _avg ) and flux capacity (l _sol ) indicate an average value for the maximal and minimal flux values and the length of the attainable flux ranges for a reaction, respectively [28]. Finally, the gene amplification candidates were evaluated by calculating the slope (q _slope ) of the V _avg flux for each metabolic reaction using linear regression analysis (Figure 2). Changes in the patterns of the reaction fluxes in response to incrementally increasing fluxes toward a target product were categorized into nine types based on combinations of positive and negative changes in V _avg and l _sol in order to facilitate the identification of amplification targets (Figure 3). Types 1, 2, and 3 displayed positive correlations with the amplification candidates for the production of a target chemical; types 4, 5, and 6 displayed negative correlations with the amplification candidates. Finally, types 7, 8, and 9 displayed no clear correlations with the production of a target chemical, based on V _avg (Figure 3). The reaction sets that were positively correlated (type 1, 2, and 3) were initially selected as amplification candidates.

Reaction sets belonging to type 1, 2 and 3, showing positive correlations with the enforced fluxes toward a target chemical, can then be further divided into strongly and weakly positive reactions (Figure 3 and Additional file 4). This step also allows narrowing down the candidates of gene amplification targets. The strongly positive reactions display a continuously increasing V _avg and a positive q _slope in response to the enhanced production of a target chemical, whereas weakly positive reactions show the same pattern, except for the presence of a partially negative q _slope (Additional file 4). Certainly, strongly positive reactions deserve primary attention as potential gene amplification targets.

The potential gene amplification candidates were prioritized by considering the l _sol value, which indicates the length between the maximal and minimal flux values of a metabolic reaction. Among the reactions that were positively correlated with the desired product, reactions with smaller values of l _sol received higher priorities because these reactions were more likely to display the predicted flux values than reactions with larger values of l _sol . A final list of gene amplification targets obtained from the above procedure was then selected based on biological knowledge.

Implementation of FVSEOF with GR constraints for shikimic acid production in E. coli

FVSEOF with GR constraints was employed to identify gene amplification targets for the enhanced production of an important aromatic chemical shikimic acid in E. coli (Figure 2). Shikimic acid is a key metabolic intermediate in the aromatic amino acid biosynthetic pathway. Shikimic acid and its derivatives are industrially important starting compounds for the production of several chemicals, such as phenols, herbicides, antibacterial agents, and the neuramidase inhibitor Tamiflu used for the treatment of influenza infections [38, 39]. FVSEOF with GR constraints predicted that 11 reaction fluxes in the glycolysis (glk and pps), pentose phosphate pathway ( rpi, talAB, and tktAB), and the shikimic acid biosynthetic pathway ( aroB aroD aroE aroF aroG, and aroH) were potential amplification targets. The amplification of aroB aroD aroE aroF aroG aroH talAB tktA glk, and pps genes [38–46], which are the amplification targets predicted by FVSEOF with GR constraints, was previously reported to enhance the production of shikimic acid. The previous FSEOF method without FVA and GR constraints could not identify pps gene as an amplification target. FSEOF results without FVA and GR constraints did not show notable fluxes among metabolic reactions controlled by the pps gene in response to the enforced shikimic acid production rate; however, the FVSEOF method with GR constraints correctly predicted the pps gene as one of the amplification targets beneficial for the accumulation of phosphoenolpyruvate, an important precursor for the production of shikimic acid from pyruvate. This consistency partly demonstrated the power of utilizing FVA and GR constraints for predicting reliable amplification targets by FSEOF. In practice, the overexpression of phosphoenolpyruvate synthase encoded by the pps gene also increased the yield of precursors for the production of shikimic acid [43, 45]. Thus, this strategy enabled the successful identification of gene amplification targets for the enhanced production of a primary metabolite, shikimic acid, in E. coli, in accordance with previous literature reports.

Implementation of FVSEOF with GR constraints for enhanced putrescine production in E. coli

The general applicability of FVSEOF with GR constraints was examined by applying the method to putrescine production in E. coli. Putrescine (1,4-diaminobutane) is an important industrial precursor for the synthesis of polymers, pharmaceuticals, surfactants, and certain additives [34]. We confirmed the validity of the newly predicted gene amplification targets by comparison with the genes engineered in the previously reported putrescine-producing E. coli XQ52 (p15SpeC) strain [34]. FVSEOF with GR constraints predicted potential gene amplification targets among the reactions involved in glycolysis (eno pgm, gapA, fbaAB, tpiA, pgk, pykAF, and glk), TCA cycle ( icd acnA acnB, and gltA), putrescine biosynthesis ( gdhA argA argB, argC, argD, argE, speC, and speF), and other pathways ( ackA and ppc). The predicted amplification targets ( argB, argC, argD, argE, speC, and speF) involved in the putrescine biosynthetic pathway were consistent with the mutations introduced in the E. coli XQ52 (p15SpeC) strain, as described in the previous report [34].

The genes predicted to be relevant to the putrescine biosynthetic pathway were expected based on the pathway knowledge, and were intuitively obvious; hence, we focused on the effects associated with amplifying the predicted gene targets involved in other metabolic pathways in order to more rigorously validate FVSEOF with GR constraints. Accordingly, each of the predicted amplification targets was examined one by one by amplifying the gene dosage in the E. coli XQ52 (p15SpeC) strain (see Methods). Among these genes, the glk, acnA, acnB, ackA, and ppc gene, five out of the sixteen target genes, were found to attain increased putrescine yield when they were individually amplified in the E. coli XQ52 (p15SpeC) strain (Additional file 5). These strains, initially examined using flask cultivation, were further validated by batch cultivation at 37°C under aerobic condition (Figure 4 and see the Additional files 1 and 2). The recombinant E. coli XQ52 (p15SpeC) strain additionally expressing the glk, acnA, acnB, ackA, and ppc genes resulted in the production of 2.23, 1.90, 1.89, 2.04, and 2.06 g/L of putrescine, respectively, which are 20.5 % more than that (1.68 g/L) produced by the control strain on average (Figure 4). The yields of putrescine obtained with these strains were 0.223, 0.190, 0.189, 0.204, and 0.206 g putrescine per g glucose, which are again higher than that (0.168 g putrescine per g glucose) obtained with the control strain. Thus, FVSEOF with GR constraints could be successfully used to identify non-obvious gene amplification targets that enhance the production of putrescine in E. coli.

Other gene amplification targets identified by FVSEOF with GR constraints, which did not affect putrescine production in flask cultivation, also deserve discussion. These false-positive hits are most likely involved in biological processes that were not accurately captured in the genome-scale metabolic model. These ineffective genes, including eno pgm gapA fbaAB tpiA pgk, and pykAF genes in glycolysis, and icd and gltA genes in TCA cycle might have been associated with transcriptional and translational regulations because the direct correlation between gene expressions and the metabolic fluxes was not observed. The fact that some of obvious gene amplification targets, such as icd gene responsible for biosynthesis of α-ketoglutarate, seem to be resistant to gene manipulations indicates that other biological variables may affect the effects of the gene amplifications. Potential variables include the plasmid copy number, gene dosage, optimal gene expression, and the gene expression method, either plasmid-based overexpression or chromosomal integration [47]. Although we improved the accuracy of the predicted gene targets by imposing GR constraints, these factors should be carefully considered in any implementation of the FVSEOF method with GR constraints [48].