Supporting Information - PNAS...2010/07/29 · Flux-Converging Pattern Analysis. Within the group...

Supporting InformationPark et al. 10.1073/pnas.1003740107SI Materials and MethodsE. coli Genome-Scale Metabolic Model. The genome-scale metabolicmodel describing E. coli metabolism is derived from the publiclyavailable sources (BioSilico, EcoCyc, and KEGG pathway data-bases). The metabolic network of the model incorporates 814metabolites (144 extracellular metabolites and 670 intermediates)and 979 metabolic reactions along with the specific growth ratethat is quantified by a biomass equation derived from the drain ofbiosynthetic precursors (11 intermediates) into E. coli biomasswith their appropriate ratios (1).

Flux Balance Analysis. The stoichiometric relationships amongall metabolites and reactions of the E. coli genome-scale metabol-ic model were balanced under the steady-state hypothesis. Theresultant balanced reaction model is, however, almost always un-derdetermined in calculating the flux distribution due to insuffi-cient measurements and/or constraints. Thus, the unknown fluxeswithin the metabolic reaction network were calculated by linearprogramming-based optimization with an objective function ofmaximizing the growth rate, subject to the constraints pertaining tomass conservation and reaction thermodynamics (2, 3),

∑j∈J

Sijvj ¼ bi; αj ≤ vj ≤ βj; [S1]

where Sij represents the stoichiometric coefficient of metabolite iin reaction j, νj is the flux of reaction j, J is the set of all reactions,and bi is the net transport flux of metabolite i. If this metaboliteis an intermediate, bi would be zero. αj and βj are the lower andupper bounds of the flux of reaction j, respectively. Herein, theflux of any irreversible reaction is considered to be positive: Thenegative flux signifies the reverse direction of the reaction.

Genomic Context Analysis Across Organisms. The availability ofcomplete genome sequences and the advancement of high-throughput technologies have assisted in the prediction of theassociation among proteins: analyses for genomic context andcoexpression of functionally related proteins. By consideringprotein–protein associations on the basis of genomic contextanalysis including a conserved genomic neighborhood, the eventsof gene fusion, and co-occurrence of genes across organisms,significantly related reactions were organized in a group (4). Theconserved neighborhood shows the genes that occur repeatedlyin close proximity to each other on genomes. The gene fusionshows the events forming a hybrid gene from previously separategenes per organism. The co-occurrence shows the presence orthe absence of linked proteins across organisms. This approachbased on the information on the locus of genomic sequences hasa powerful advantage of not being limited by experimental data,such as coexpression and complex regulation data, and can ex-plore protein–protein associations of all genome-sequenced or-ganisms without experimental data.After the assignment of association scores for each predictor of

functional associations of proteins, the final combined scorebetween any pair of proteins was summed up as

S ¼ 1− ∏ið1− SiÞ; [S2]

where Si denotes the score of each predictor i. This combined scoreis usually higher than the individual subscores. After consideringthe criteria ofminimal score from 0.7 to 0.95 to organize the groupsthat are composed of significantly related reactions, we determinedthe minimal score as 0.75 that showed good prediction fidelity with

experimental data. The individual and combined scores to predictprotein–protein associations were calculated and obtained easilyfrom a database of known and predicted protein interactions,STRING 8.0 (4). The database covers 2,483,276 proteins from 630organisms and has seven selectable prediction methods includingthree genomic sequence-based prediction methods, coexpressiondata measured by using microarray analysis, probability of findingthe related proteins within the same pathway on curated databasessuch as KEGG, probability of finding the related proteins withinexperimental data, and text mining that searches for comentioningof gene names in abstract and title. Applying these data except forgenomic context to predict protein–protein associations could leadto an unbalance of score because of the absence of the data forsome genes. Additionally, because these data are condition de-pendent, they are inconsistent with our objective. Thus, we usedthree genomic sequence-based prediction methods to define thegroups of reactions (Tables S1 and S2).We assumed that closely related reactions in a predicted group

determined above will be closely regulated under the conditionsexamined. Microarray data showed that the genes belong to thesame functional group exampled by transcription units thatshowed similar expression patterns for several experimentalconditions (5). Thus, we applied simultaneous on/off of reactionsas constraints (Con/off) in the same predicted group to an E. coligenome-scale metabolic model. The binary variable, y, is avail-able to indicate the on/off states of the reactions for each group(Eq. S3). The binary variables in each group possess the samevalues and are multiplied to lower and upper bounds of eachreaction (Eqs. S4 and S5). If y = 1 for a group, the metabolicreactions in the same group have the flux capability representedby the lower to upper bounds of the reactions. If y = 0 for thegroup, the metabolic reactions in the same group have no fluxcapability, which is zero:

yðv1Þ ¼ yðv2Þ [S3]

yðv1Þ·v1;min ≤ v1 ≤ yðv1Þ · v1;max [S4]

yðv2Þ·v2;min ≤ v2 ≤ yðv2Þ · v2;max: [S5]y denotes a binary variable, 0 or 1. vj is the flux of reaction j andv1 and v2 belong to the same group. vj,min and vj,max are lower andupper bounds for the flux of reaction j.

Flux-Converging Pattern Analysis. Within the group classified bygenomic context analysis, constraints for flux-converging patternanalysis, which represents a set of stricter constraints, are presentand when added, improve the fidelity of the prediction of themodel. The flux values of closely related reactions metabolizingmetabolites with the same carbon number have good chance ofbecoming similar. In 13C-based flux analysis, the scale of fluxvalues is controlled by the carbon number of the primary me-tabolite excluding cofactors in each reaction. In this regard, thescale of flux values is distributed by splitting or combining thecarbon number of metabolites (Eq. S6). To classify the reactionsbased on flux-converging pattern analysis, the three type ofmetabolites on a branch point in a metabolic pathway, split,combined, and flux-converging metabolite, should be considered(Fig. 1B). A metabolite could be split into different metabolitesor created by combining two metabolites. The upper reactionsfrom a split or combined metabolite have a different carbonnumber compared with the lower reactions with the total carbonnumber unchanged. The reactions in each orange, blue, and

Park et al. www.pnas.org/cgi/content/short/1003740107 1 of 11

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st01.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st02.docwww.pnas.org/cgi/content/short/1003740107

purple circle consist of reactions with metabolites having thesame carbon number and have a good chance of having a similarflux scale. However, the flux scale of some reactions can bedifferent despite having metabolites with the same carbonnumber, because of split fluxes converging into a flux-convergingmetabolite. The flux-converging metabolite is defined as a me-tabolite that sums fluxes originated from a reaction that pro-duces two or more metabolites into parallel pathways (Fig. 1B).These metabolites were identified by examining the networktopology for fluxes that converge downstream after splitting intotwo parallel pathways (Fig. S1).For example, although the reaction in the green circle has the

same carbon number with C3 reactions in the blue circle, the fluxscale of reaction in the green circle should be distinguished fromreactions in the blue circle. In this case, the C6 metabolites dividedinto C3 metabolites but the C3 metabolite in the green circle flowsinto the flux-converging metabolite on the blue circle. Thus, theflux scale of reactions in the blue circle is 2-fold larger than that ofreactions in the orange and green circles (Fig. 1B). These flux-converging metabolites categorize Jy into four types, denoted as JA,JB, JC, and JD, where each subscript indicates the number of flux-converging metabolites passed zero to three times, respectively,for the given flux originated from a carbon source. Analysis of theflux-converging pattern is terminated if the flux goes back to thereaction it has already passed. Three flux-converging metabolites,glyceraldehyde-3-phosphate, pyruvate, and malate, exist in E. colicentral metabolism (Fig. 1). Among them, pyruvate deservesfurther attention as it causes more complex changes of flux dis-tribution, compared with the other two flux-converging metabo-lites; fluxes split from 6-phospho-D-gluconate eventually convergeinto pyruvate, but one of them goes through glyceraldehyde-3-phosphate, which is a flux-converging metabolite. Therefore,subscript E, which specifically indicates that the flux has onceconverged into pyruvate, is placed next to subscripts of J, includingA, B, C, or D. Finally, the reactions that possess identical carbonnumbers that pass the same number of flux-converging metabo-lites and are in the same group from the genomic context analysisbelong to the same flux scale group (Eqs. S6 and S7 and Fig. 1).The term to classify the flux scale of reaction can be defined asfollows:

CxJy [S6]

x ¼ NC;Rj2

: [S7]

Cx defines the carbon number of a reaction j and Jy defines thenumber of flux-converging metabolites that were passed to arriveat reaction j from a carbon source. The Nc,Rj is total carbonnumber of metabolites excluding cofactors in reaction j. Withthese rational criteria, we classify the reactions in central me-tabolism of E. coli (Fig. 1).Finally, we use constraints for flux scale of related reactions

(Cscale) to incorporate this characteristic subject to each reactiongroup classified from genomic context analysis. If the CxJy ina reaction group is the same (Eq. S8), the Cscale for the pair ofreactions is applied to the model (Table S1). The Cscale is for-mulated by Eq. S9. Each flux is considered by an absolute valueof fluxes to overcome difficulties of calculation caused by thedirectionality and reversibility of reaction and normalized bydividing each flux by the carbon source uptake rate.If

ðCx1J y1 ¼ Cx2J y2Þ [S8]in a group, each group classified by genomic context analysis,

Cscale ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�jvn1j−

jvn1 jþjvn2 j2

�2 þ

�jvn2 j−

jvn1 jþjvn2 j2

�2

2

vuuut≤ δ: [S9]

Each flux is considered by an absolute value of fluxes to overcomedifficulties of calculation caused by the directionality and re-versibility of reaction and normalized by dividing each flux by thecarbon source uptake rate. δ denotes a constant defining the fluxlevel of reactions in a reaction group. v1

n, v2n are normalized flux

of reaction 1, 2 by dividing each reaction by the carbon sourceuptake rate, such as glucose. The value of δ is recommended as0.3. These grouping reaction constraints, Con/off and Cscale, wereapplied to the central metabolism of the E. coli genome-scalemetabolic model including glycolysis, the PP pathway, the TCAcycle, the anaplerotic pathway, and pyruvate metabolism.

Determinants to Recognize the Change of Metabolic Fluxes forEnvironmental/Genetic Perturbations. We cannot determine anexact true flux for any reactions because of alternate optima for anobjective value caused by redundancy of reactions. Thus, weinvestigated the metabolic flux distributions and the change ofmetabolic flux pattern for several perturbations by using fluxvariability analysis (FVA) that calculates minimal and maximalflux values of each reaction for an objective value, in this case, themaximal cell growth rate. These values were compared with thecontrol flux solution space to determine the change of flux so-lution space for each reaction after environmental and geneticperturbations (6–8). Consequently, we suggest simple determi-nants, flux bias (Vavg) and flux capacity (lsol), to effectively rec-ognize the changes of metabolic flux solution space forenvironmental or genetic perturbations as follows:

Vavg ¼ V’max þ V ’min

2[S10]

lsol ¼ V ’max −V ’min: [S11]Vmax′ and Vmin′ denote the maximal and minimal flux values fora reaction on an objective value. lsol denotes the length of theflux solution space that means the difference between the max-imal and minimal flux values for a reaction on an objective value.We could investigate the changes of capacity and bias of fluxsolution space for an objective value with Vavg and lsol for envi-ronmental or genetic perturbations. For an objective value, thebias of flux value for a reaction computed by optimization couldbe examined by the shift of the median (Vavg) between Vmax′ andVmin′ on the flux solution space after environmental or geneticperturbations. The changes of flux capacity could be investigatedby the length of flux solution space (lsol) for an objective valueafter environmental or genetic perturbations. If the Vavg value ofa flux solution space after environmental or genetic perturba-tions is larger than the control Vavg, we assumed that the fluxsolution space was biased toward an increase of flux. The in-creased length of the flux solution space after given perturba-tions reveals that the lsol of the reaction increased. If the lengthof the flux solution space decreases, compared with that of thecontrol flux solution space, there is a better chance that morespecific flux value would exist between maximal and minimal fluxvalues, and the lsol of the reaction decreases. No change of Vavgor lsol for a reaction indicates that the environmental or geneticperturbation has no effect on those properties. These compar-ative tools were applied to the comparative study of simulationresults from FBA with grouping reaction constraints, with dif-ferent 13C experimental sets examining change of carbon sourcesand gene knockouts. Flux values from FBA and 13C-based ex-periments are relative fluxes that were normalized to the re-spective carbon source uptake rates.


http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/pnas.201003740SI.pdf?targetid=nameddest=SF1http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st01.docwww.pnas.org/cgi/content/short/1003740107

Formulation of Flux Balance Analysis with Grouping Reaction Con-straints. Max/Min ZðvÞSubject to ∑

j∈JSijvj ¼ bi ∀i ∈ I

li ≤∑j∈J

Sijvj ≤ ui ∀j ∈ J

vbiomass ¼ Zopt·0:95

vj;min ≤ vj ≤ vj;max ∀i ∈ E

vj,max = 1,000 mmol·g DCW−1·h−1

vj,min = −1,000 mmol·g DCW−1·h−1

vuptakecarbon = 10 mmol·g DCW−1·h−1.

Simultaneous on/off constraint (Con/off)

yðv1Þ ¼ yðv2Þ

yðv1Þ· v1;min ≤ v1 ≤ yðv1Þ· v1;max

yðv2Þ· v2;min ≤ v2 ≤ yðv2Þ· v2;max:Flux scale constraint (Cscale)

Cx Jy

x ¼ NC;Rj2

:

If ðCx1Jy1 ¼ Cx2 Jy2Þ is in a functional group,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�jvn1j−

jvn1 jþjvn2 j2

�2 þ

�jvn2 j−

jvn1 jþjvn2 j2

�2

2

vuuut≤ δ;

I, J = set of metabolites and reactions, respectively,E = set of extracellular metabolites,v, vj = flux vector and the flux of reaction j, respectively,Z(v) = objective function,Zopt = optimal growth rate,Sij = stoichiometric coefficient of metabolite i in reaction j,bi = net transport flux of metabolite i,li, ui = lower and upper bound for the net transport flux of

metabolite i, respectively,vj,min, vj,max = lower and upper bound for the flux of reaction j,

respectively,vuptakecarbon = carbon source uptake rate,

y(v1), y(v2) = binary variables of reaction 1, 2,Cx = carbon number of a reaction j,Jy = number of flux-converging metabolites that were passed

to arrive at reaction j from a carbon source,Nc,Rj = total number of carbon of primary metabolites ex-

cluding cofactors in reaction j,vn1, v

n2 = normalized flux of reaction 1, 2 by dividing each

reaction by the carbon source uptake rate, such asglucose,

δ = constant defining the flux level of reactions in a functionalgroup.

The unknown fluxes within the metabolic reaction networkwere calculated by mixed integer nonlinear programming(MINLP)-based optimization using CPLEX and DICOPT solverwith an objective function of maximizing the growth rate, subjectto the constraints including functionally grouping constraints,mass conservation, and reaction thermodynamics.

Formulation of Euclidean Distance Between Predictions and Exper-imental Fluxes. Max/Min DNSubject to ∑

j∈JSijvj ¼ b i ∀i∈ I

li ≤∑j∈J

Sijvj ≤ ui ∀j∈ J

vbiomass ¼ Zopt·0:95

vj;min ≤ vj ≤ vj;max ∀i∈E

vj,max = 1,000 mmol·g DCW−1·h−1,

vj,min = −1,000 mmol·g DCW−1·h−1,vuptakecarbon = 10 mmol·g DW

−1·h−1,

DN ¼�∑n

JðV comp;Nj −V exp;Nj Þ2

�12

,

I, J = set of metabolites and reactions, respectively,E = set of extracellular metabolites,v, vj = flux vector and the flux of reaction j, respectively,Zopt = optimal growth rate,Sij = stoichiometric coefficient of metabolite i in reaction j,bi = net transport flux of metabolite i,li, ui = lower and upper bounds for the net transport flux of

metabolite i, respectively,vj,min, vj,max = lower and upper bound for the flux of reaction j,

respectively,vuptakecarbon = carbon source uptake rate,DN = Euclidean distance between predictions and experi-

mental fluxes normalized by carbon source uptakerate,

V comp;Nj ;Vexp;Nj = normalized computational and experimental

fluxes.

Fermentation. Batch cultures were carried out using the M9 me-dium containing 20 g/L of glucose or 10 g/L of acetate at 37 °C. TheM9 medium contains per liter: Na2HPO4, 33.9 g; KH2PO4, 15 g;NH4Cl, 5 g; NaCl, 2.5 g; 1 M MgSO4, 2 mL; 1 M CaCl2, 0.1 mL.Na(CH3COO)·3H2O was added to give the final concentration of10 g/L for acetate fermentation. Seed cultures for aerobic fer-mentation were prepared by transferring 500 μL of 10-mL over-night cultures prepared in Luria–Bertani (LB) medium into250-mL Erlenmeyer flasks containing 50 mLM9medium and cul-tured at 37 °C with 250 rpm. Cultured cells were used to inoculatethe fermenter containing 2 L ofM9medium. Batch fermentationswere carried out in a 6.6-L Bioflo 3000 fermenter (New BrunswickScientific). The pH was controlled at 6.8 by automatic feeding ofNH4OH or HCl. The dissolved oxygen concentration for fullaerobic conditions was maintained >40% of air saturation bysupplying air at 1 vvm (air volume/working volume/minute) and byautomatically controlling the agitation speed up to 1,000 rpm.

Analytical Procedures. Cell growth wasmonitored bymeasuring theabsorbance at 600 nm (OD600) using an Ultrospec3000 spectro-photometer (Pharmacia Biotech). Cell concentration defined asgram dry cell weight (gDCW) per liter was calculated from thepredetermined standard curve relating the OD600 to dry weight(1 OD600 = 0.34 gDCW/L). Glucose concentration was measuredusing a glucose analyzer (model 2700 STAT; Yellow Springs In-strument). The concentrations of glucose and organic acids weredetermined by HPLC (ProStar 210; Varian) equipped with UV/visible-light (ProStar 320; Varian) and refractive index (ShodexRI-71) detectors. A MetaCarb 87H column (300 × 7.8 mm; Var-ian) was eluted isocratically with 0.01 N H2SO4 at 60 °C at a flowrate of 0.4 mL/min.

1. Neidhardt FC, Curtiss R (1996) Escherichia coli and Salmonella: Cellular and MolecularBiology (ASM, Washington, DC).

2. Stephanopoulos GN, Aristidou AA, Nielsen J (1998) Metabolic Engineering (Academic,San Diego).


www.pnas.org/cgi/content/short/1003740107

3. Lee SY, Papoutsakis ET (1999) Metabolic Engineering (Marcel Dekker, New York).4. Jensen LJ, et al. (2009) STRING 8—a global view on proteins and their func-

tional interactions in 630 organisms. Nucleic Acids Res 37 (Database issue):D412–D416.

5. Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO (2004) Integrating high-throughput and computational data elucidates bacterial networks. Nature 429:92–96.

6. Bushell ME, et al. (2006) The use of genome scale metabolic flux variability analysis forprocess feed formulation based on an investigation of the effects of the zwf mutation

on antibiotic production in Streptomyces coelicolor. Enzyme Microb Technol 39:1347–1353.

7. Khannapho C, et al. (2008) Selection of objective function in genome scale fluxbalance analysis for process feed development in antibiotic production. Metab Eng10:227–233.

8. Puchałka J, et al. (2008) Genome-scale reconstruction and analysis of the Pseudomonasputida KT2440 metabolic network facilitates applications in biotechnology. PLoSComput Biol 4:e1000210.

Fig. S1. The scheme of flux-converging metabolites. The flux-converging metabolites correspond to metabolites where two split reactions combine, such asglyceraldehyde-3-phosphate, which converges fluxes split by fructose-bisphosphate aldolase.

1. Al Zaid Siddiquee K, Arauzo-Bravo MJ, Shimizu K (2004) Metabolic flux analysis of pykF gene knockout Escherichia coli based on 13C-labeling experiments together with measurementsof enzyme activities and intracellular metabolite concentrations. Appl Microbiol Biotechnol 63:407–417.

Fig. S2. Distributions of flux values calculated from FBA with grouping reaction constraints in wild-type E. coli and pykF knockout mutant strains based on therandom sampling of glucose uptake rate, using a deterministic algorithm inside GAMS. One thousand flux values for each reaction were generated using 1,000sampling flux values taken from the normal distribution of glucose uptake rate with the mean values of 1.23 and 1.15 mmol·g DCW−1·h−1, which were de-termined by experiments for wild-type E. coli and pykF knockout mutant strains, respectively, having an SD of 1 (1). The calculated flux values of particularinterest are shown. The color gradient and squares indicate the values of Vavg. The red lines indicate that the fluxes show the increment determined by flux bias(Vavg), compared with control fluxes. The blue lines indicate the opposite. Thickness of the lines denotes flux capacities (lsol) after environmental perturbation,compared with control fluxes; three types of thickness were used to indicate the changes in flux capacity. The thickest line indicates the increased flux capacity,the thinnest line the decreased flux capacity, and the medium thickness line refers to no changes in flux capacity. Each graph represents the distributions offlux values from FBA with grouping reaction constraints in E. coli wild type (black circle) and pykF knockout mutant (red circle). The x axis in each graphindicates the relative flux (%) that is normalized to the carbon source uptake rate. The y axis in each graph indicates the relative frequency that is normalizedby the total number of events. The dotted line embedded in each graph indicates the average of distributed fluxes.



Fig. S3. Comparison of 13C-based flux values to those calculated from FBA with or without grouping reaction constraints in wild-type E. coli and zwf knockoutmutant strains on glucose minimal medium under aerobic conditions and flux distribution changes for zwf knockout in E. coli central metabolism (1). The colorgradient and squares indicate the values of Vavg. The red lines indicate that the fluxes show the increment determined by flux bias (Vavg), compared withcontrol fluxes, which were from E. coli wild type aerobically grown in glucose minimal medium. The blue lines indicate the opposite. Thickness of the linesdenotes flux capacities (lsol) after environmental perturbation, compared with control fluxes; three types of thickness were used to indicate the changes in fluxcapacity. The thickest line indicates the increased flux capacity, the thinnest line the decreased flux capacity, and the medium thickness line refers to nochanges in flux capacity. Each graph represents the 13C-based fluxes and solution spaces of each flux predicted with or without grouping reaction constraintsfor wild type and zwf mutant. The y axis in each graph indicates the relative flux (%) that is normalized to the carbon source uptake rate. The 13C-based fluxesare represented in (I) wild type and (II) zwf mutant. The fluxes predicted by FBA without grouping reaction constraints are represented in (III) wild type and(IV) zwf mutant. The fluxes predicted by FBA with grouping reaction constraints are represented in (V) wild type and (VI) zwf mutant. The bars in eachembedded graph denote the range between the maximal and minimal values of each reaction computed from FVA. The graph for succinyl-CoA synthetase is

Legend continued on following page



1. Zhao J, Baba T, Mori H, Shimizu K (2004) Effect of zwf gene knockout on the metabolism of Escherichia coli grown on glucose or acetate. Metab Eng 6:164–174.2. Zhao J, Baba T, Mori H, Shimizu K (2004) Global metabolic response of Escherichia coli to gnd or zwf gene-knockout, based on 13C-labeling experiments and the measurement of

enzyme activities. Appl Microbiol Biotechnol 64:91–98.

not shown because its flux values were outside the range of biologically feasible values in the case of FBA without grouping reaction constraints. In the case ofreversible reaction, the fluxes corresponding to the direction represented in the pathway were considered. The 13C-based fluxes were evaluated with 95%confidence limits obtained from statistical analysis (1, 2).



Fig. S4. Comparison of 13C-based flux values to those calculated from FBA with or without grouping reaction constraints in wild-type E. coli and ppc knockoutmutant strains on glucose minimal medium under aerobic conditions and flux distribution changes for ppc knockout in E. coli central metabolism (1). All symbolsand methods are equivalent to those in Fig. S3. The 13C-based fluxes were evaluated with 90% confidence limits obtained from statistical analysis (1, 2).

1. Peng L, Arauzo-Bravo MJ, Shimizu K (2004) Metabolic flux analysis for a ppc mutant Escherichia coli based on 13C-labelling experiments together with enzyme activity assays andintracellular metabolite measurements. FEMS Microbiol Lett 235:17–23.

2. Yang C, Hua Q, Baba T, Mori H, Shimizu K (2003) Analysis of Escherichia coli anaplerotic metabolism and its regulation mechanisms from the metabolic responses to altered dilutionrates and phosphoenolpyruvate carboxykinase knockout. Biotechnol Bioeng 84:129–144.


http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/pnas.201003740SI.pdf?targetid=nameddest=SF3www.pnas.org/cgi/content/short/1003740107

Fig. S5. Comparison of 13C-based flux values to those calculated from FBA with or without grouping reaction constraints in wild-type E. coli and sucAknockout mutant strains on glucose minimal medium under aerobic conditions and flux distribution changes for sucA knockout in E. coli central metabolism(1). All symbols and methods are equivalent to those in Fig. S3. The 13C-based fluxes were evaluated with 90% confidence limits obtained from statisticalanalysis (1).

1. Li M, Ho PY, Yao S, Shimizu K (2006) Effect of sucA or sucC gene knockout on the metabolism in Escherichia coli based on gene expressions, enzyme activities, intracellular metaboliteconcentrations and metabolic fluxes by 13C-labeling experiments. Biochem Eng J 30:286–296.



Fig. S6. Comparison of the changes in the 13C-based flux ranges represented by error bars to those calculated from FBA with or without grouping reactionconstraints in wild-type E. coli and (A) gnd and (B) zwf knockout mutants on glucose minimal medium under aerobic conditions. Each graph represents the 13C-based fluxes with error bars (1) and solution spaces of each flux predicted with or without grouping reaction constraints for wild type and mutants. The y axisin each graph indicates the relative flux (%) that is normalized to the carbon source uptake rate. The 13C-based fluxes are represented in (I) wild type and (II)mutant. The fluxes predicted by FBA without grouping reaction constraints are represented in (III) wild type and (IV) mutant. The fluxes predicted by FBA withgrouping reaction constraints are represented in (V) wild type and (VI) mutant. The bars in each embedded graph denote the range between the maximal andminimal values of each reaction. The 13C-based fluxes were evaluated with 95% confidence limits obtained from statistical analysis (1).

1. Zhao J, Baba T, Mori H, Shimizu K (2004) Global metabolic response of Escherichia coli to gnd or zwf gene-knockout, based on 13C-labeling experiments and the measurement ofenzyme activities. Appl Microbiol Biotechnol 64:91–98.



Fig. S7. Comparison of 13C-based flux values to those calculated from FBA with or without grouping reaction constraints and flux distribution changes in wild-type E. coli for shift of carbon sources from glucose to acetate under aerobic conditions and flux distribution changes for shift of carbon sources from glucoseto acetate in E. coli central metabolism (1). All symbols and methods are equivalent to those in Fig. S3. The 13C-based fluxes were evaluated with 90% con-fidence limits obtained from statistical analysis (1, 2).

1. Zhao J, Baba T, Mori H, Shimizu K (2004) Effect of zwf gene knockout on the metabolism of Escherichia coli grown on glucose or acetate. Metab Eng 6:164–174.2. Zhao J, Shimizu K (2003) Metabolic flux analysis of Escherichia coli K12 grown on 13C-labeled acetate and glucose using GC-MS and powerful flux calculation method. J Biotechnol 101:

101–117.



Fig. S8. Fermentation profiles of E. coli wild type under aerobic conditions using (A) glucose and (B) acetate as a carbon source. Symbols in A and B are asfollows: ○, dry cell weight; ●, glucose; and ■, acetate.

Other Supporting Information Files

Table S1 (DOC)Table S2 (DOC)Table S3 (DOC)

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st01.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st02.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st02.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st02.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st03.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st03.dochttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003740107/-/DCSupplemental/st03.docwww.pnas.org/cgi/content/short/1003740107

Date post:	09-Feb-2021
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

Supporting Information - PNAS...2010/07/29 · Flux-Converging Pattern Analysis. Within the group...

Documents