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
The stoichiometric relationships among the metabolites and the reactions of the E. coli genome-scale metabolic model were balanced under the pseudo-steady state assumption. The balanced reaction model was almost always underdetermined in calculations of the flux distribution due to insufficient measurements of the extracellular fluxes. Thus, the unknown fluxes within the metabolic reaction network were calculated by linear programming-based optimization using an objective function that maximized the growth rate, subject to constraints pertaining to mass conservation and reaction thermodynamics [33], This optimization problem can be mathematically formulated as follows:
(1)
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
The algorithm introduced in this study, FVSEOF with GR constraints, starts with formulation of GR constraints, which are based on the genomic context and flux-converging pattern analyses (Figure 1). Briefly, genomic context and flux-converging pattern analyses aim at grouping functionally related reactions. Such functionally related reactions were constrained to be on or off simultaneously (Figure 1) [28]. First, reactions were grouped using STRING database that performs genomic context analysis, including conserved neighborhood, gene fusion, and co-occurrence [28, 29]. Simultaneous on/off constraint (C
on/off
) can be described as follows:
(4)
(5)
where y( v
1
) and y( v
2
) indicate binary variables (on or off) of a certain reaction 1 and 2, respectively.
Each reaction is then given a C
x
J
y
index, determined by flux-converging pattern analysis. C
x
and J
y
denote the total number of carbon atoms in metabolites that participate in each reaction and the number of passing flux-converging metabolites, respectively. Here, it should be noted that cofactors were not considered because the flux scales are controlled by the carbon number of primary metabolites, not cofactors, according to 13C-based flux analysis [28]. For J
y
, the flux-converging metabolites indicate metabolites at which two pathways split by another metabolite converge. J
y
has four types, including J
A
J
B
J
C
, and J
D
, depending on the characteristics of flux-converging metabolites. Subscript of J
y
denotes the passing number of flux-converging metabolites, counting zero, one, two, or three times for the flux coming from a carbon source. In some cases, the subscript E is placed next to the subscripts of A, B, C, or D to indicate the fluxes derived from pyruvate, which causes more complex changes in flux distributions. The values of C
x
J
y
for each reaction were assigned based on possible flux routes reaching from glucose, and are partitioned by a slash. Based on this analysis, another constraint C
scale
, indicating the flux scale of a reaction, can be given to the metabolic reactions. First, terms used to describe the flux scale of the reaction are as follows:
where indicates the carbon number involved in a reaction j 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.
If reaction 1 and 2 were predicted to be in the same functional unit according to the genomic context analysis, and their and are equivalent, C
scale
is applied to these two reactions, which is defined as follows:
(8)
where vn
1
and vn
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 () and theoretical maximum () 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:
Min/Max = or
(9)
(10)
(12)
(13)
(14)
where indicates the initial or minimal point of the flux value constrained for the target bioproduct, while 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 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: () [23]. The is an additional constraint provided during this stage of the constraints-based flux analysis; it starts with the initial value plus one nth of the difference between the and , and is increased to a value adjacent to 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]:
(15)
(16)
The and 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).