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Open AcceMethodology articleOptimization based automated curation of metabolic reconstructionsVinay Satish Kumar1, Madhukar S Dasika2 and Costas D Maranas*2
Address: 1Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, University Park, PA 16802, USA and 2Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802, USA

Email: Vinay Satish Kumar - [email protected]; Madhukar S Dasika - [email protected]; Costas D Maranas* - [email protected]

* Corresponding author

AbstractBackground: Currently, there exists tens of different microbial and eukaryotic metabolicreconstructions (e.g., Escherichia coli, Saccharomyces cerevisiae, Bacillus subtilis) with many moreunder development. All of these reconstructions are inherently incomplete with somefunctionalities missing due to the lack of experimental and/or homology information. A keychallenge in the automated generation of genome-scale reconstructions is the elucidation of thesegaps and the subsequent generation of hypotheses to bridge them.

Results: In this work, an optimization based procedure is proposed to identify and eliminatenetwork gaps in these reconstructions. First we identify the metabolites in the metabolic networkreconstruction which cannot be produced under any uptake conditions and subsequently weidentify the reactions from a customized multi-organism database that restores the connectivity ofthese metabolites to the parent network using four mechanisms. This connectivity restoration ishypothesized to take place through four mechanisms: a) reversing the directionality of one or morereactions in the existing model, b) adding reaction from another organism to provide functionalityabsent in the existing model, c) adding external transport mechanisms to allow for importation ofmetabolites in the existing model and d) restore flow by adding intracellular transport reactions inmulti-compartment models. We demonstrate this procedure for the genome- scale reconstructionof Escherichia coli and also Saccharomyces cerevisiae wherein compartmentalization of intra-cellularreactions results in a more complex topology of the metabolic network. We determine that about10% of metabolites in E. coli and 30% of metabolites in S. cerevisiae cannot carry any flux.Interestingly, the dominant flow restoration mechanism is directionality reversals of existingreactions in the respective models.

Conclusion: We have proposed systematic methods to identify and fill gaps in genome-scalemetabolic reconstructions. The identified gaps can be filled both by making modifications in theexisting model and by adding missing reactions by reconciling multi-organism databases of reactionswith existing genome-scale models. Computational results provide a list of hypotheses to bequeried further and tested experimentally.

Published: 20 June 2007

BMC Bioinformatics 2007, 8:212 doi:10.1186/1471-2105-8-212

Received: 14 December 2006Accepted: 20 June 2007

This article is available from: http://www.biomedcentral.com/1471-2105/8/212

© 2007 Satish Kumar et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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BackgroundThe genome of several microorganisms has been com-pletely sequenced and annotated in the past decade [1-4].This information has aided the metabolic reconstructionsof several microbial and eukaryotic organisms usingexperimental evidence and bioinformatics based tech-niques providing single compartment (e.g., Escherichia coli[5]) and multi-compartment models (e.g., Saccharomycescerevisiae [6]). All of these reconstructions are inherentlyincomplete with some functionalities missing due to thelack of experimental and/or homology information.These missing reaction steps may lead to the prediction oferroneous genetic interventions for a targeted overproduc-tion or the elucidation of misleading organizational prin-ciples and properties of the metabolic network. A keychallenge in the automated generation of genome-scalereconstructions is the elucidation of these gaps and thesubsequent generation of hypotheses to bridge them. Thischallenge has already been recognized and a number ofcomputational approaches have been under developmentto resolve these discrepancies [7-11].

Most of the aforementioned efforts are based on the use ofsequence homology to uncover missing genes. Specifi-cally, sequence homology is used to pinpoint genes inrelated species that have significant similarity with anunassigned ORF of the curated microorganism [12].Green et al formalized and further extended this conceptby introducing a method that identified missing enzymesin a metabolic network using sequence homology relatedmetrics within a Bayesian framework [11]. Alternatively,non-homology based reconstructions have been imple-mented by identifying candidate genes by measuring thesimilarity with metrics such as mRNA co expression data[8] and phylogenetic profiles [10] while also taking intoaccount the local structure of the existing partially recon-structed metabolic networks. A recent advancement inthis direction uses multiple types of association evidenceincluding clustering of genes on the chromosome andprotein fusion events in addition to phylogenetic profiles[9]. All methods described above postulate a set of candi-date genes and then evaluate the likelihood that any ofthese candidate genes is present in the microorganism'smetabolic network of interest using a variety of scoringmetrics. In addition to these approaches, various genomiccontext analyses have also been used to identify missingmetabolic genes [7,13-16]. Specifically, a recent studyexploits the availability of highly curated metabolic net-works to hypothesize gene reaction interactions in lesscharacterized organisms [16]. These aforementionedmethods predict missing enzymes in the metabolic net-work by conducting sequence based comparisons ofentire genomes and inferring possible metabolic func-tions across different microorganisms.

Alternatively, a recent systems based computationalapproach identifies the location of missing metabolicfunctions in the E. coli iJR904 model by pinpointing dis-crepancies between in silico model predictions and knownin vivo growth phenotypes [17]. Subsequently, an optimi-zation based algorithm is used to resolve these discrepan-cies by searching for missing metabolic functions from acandidate database of reactions. In this paper instead, wepinpoint metabolites that cannot carry any flux throughthem and subsequently generate hypotheses to restoreconnectivity. To this end, we introduce an optimizationbased procedure (GapFind) to first identify such gaps inboth single and multi-compartment metabolic networksand subsequently using an optimization based procedure(GapFill) restore their connectivity using separate pathol-ogy resolving hypotheses. In contrast to the previousmethods which fill gaps only by identifying missingenzymes [8-11,17] or adding transport reactions [17], wealso explore whether these gaps can be filled by makingintra model modifications. Figure 1 pictorially illustrateshow such gaps arise in metabolic reconstructions andintroduces the definitions proposed in this paper to pre-cisely describe these pathologies.

Gaps in metabolic reconstructions are manifested as (i)metabolites which cannot be produced by any of the reac-tions or imported through any of the available uptakepathways in the model; or (ii) metabolites that are notconsumed by any of the reactions in the network orexported based on any existing secretion pathways. Werefer to these metabolites as root no-production (e.g.,metabolite A) and root no-consumption metabolites (e.g.,metabolite B) respectively. At steady-state conditions noflow can pass through them due to the incomplete con-nectivity with the rest of the network. Clearly, suchpathologies are not physiologically relevant and thus

Characterization of problem metabolites in metabolic net-worksFigure 1Characterization of problem metabolites inmeta-bolic networks. Metabolite A is defined as a root no-pro-duction metabolite because there is no-production or transport mechanism for it in the network. Metabolite C is a downstream no-production metabolite because, despite there being a reaction that produces it, it can carry no flux as A cannot be produced in the network. Equivalently, B and D are defined as root and downstream no-consumption metab-olites.

B

DA

C



must be caused by omission and/or errors in the modelreconstruction process. Notably, the lack of flow in rootno-production metabolites and root no-consumptionmetabolites is propagated downstream/upstream respec-tively giving rise to additional metabolites that cannotcarry any flow. We refer to these metabolites that are indi-rectly prevented from carrying flow as downstream no-pro-duction (e.g., metabolite C) metabolites and upstream no-consumption metabolites (e.g., metabolite D) respectively.It is important to note that by restoring connectivity forthe root problem metabolites all upstream/downstreammetabolites are also automatically fixed. We concentrateon resolving only no-production metabolites in the caseof cytosolic metabolites. In the case of non-cytosolic (i.e.,present in internal compartments) metabolites, we iden-tify mechanisms to resolve both no-production and no-consumption metabolites.

For single compartment metabolic networks (where wehave only cytosolic metabolites), we postulate three sepa-rate mechanisms for fixing no-production metabolites(see also Figure 2). We explore whether (i) reversing thedirectionality of existing reactions in the model (Mecha-nism 1), (ii) adding new reactions from a multi-speciesdatabase (e.g., MetaCyc [18]) (Mechanism 2) or finally(iii) allowing for the direct importation of the problemmetabolite restores flow into the no-production metabo-lite (Mechanism 3). For multi-compartment models,(e.g., S. cerevisiae) (Figure 3) we treat gaps in the cytosoldifferently than gaps in compartments (e.g., mitochon-dria, peroxisome etc). For cytosolic no-production metab-olites, in addition to the three connectivity restorationmechanisms proposed for single compartment models,we additionally explore whether they can be fixed by add-ing intracellular transport reactions between compart-ments and the cytosol (Mechanism 4). For non-cytosolicproblem metabolites, present in internal compartments,direct importation from the extracellular space is not pos-sible. Thus, their connectivity to the network is attemptedto be restored based solely on reversing directionalities,adding external reactions or adding transport reactionswith the cytosol. In both single and multi-compartmentmodels, downstream/upstream no-production/consump-tion metabolites are automatically fixed by restoring con-nectivity to their corresponding root no-production/consumption metabolite. Alternatively, we identify con-nectivity restoration mechanisms for downstream prob-lem metabolites in addition to the indirect mechanismsthrough the fixing of root problem metabolites.

The proposed procedures are demonstrated on two widelyused genome-scale metabolic models: E. coli [5] and S.cerevisiae[6]. The resultant connectivity resolving modifi-cations in these models then serve as hypotheses. Specifi-cally, we test if reactions can be reversed in the E. coli

The multi-compartment model of Saccharomyces cerevisiaeFigure 3The multi-compartment model of Saccharomyces cer-evisiae. All compartments interact only with the cytosol. Only the cytosol interacts with the extracellular space.

Connectivity restoration mechanisms for problem metabo-litesFigure 2Connectivity restoration mechanisms for problem metabolites. In (a), reversing the directionality of a reaction restores the connectivity of metabolite (A) to the network. In (b) reactions are added from the external database to the model organism in order to enable production and consump-tion of no-production and no-consumption metabolites respectively. In (c), the production of no-production metabo-lite A is enabled by adding an external uptake pathway, the consumption of no-consumption metabolite B is enabled by adding an external secretion pathway.

Mechanism 1 Mechanism 2

(a) (b)

Mechanism 3

(c)

BA

ext

ext

ext

ABA

B

ModelDatabase ModelDatabase



model (Mechanism 1) using two independent methods.First, we query the EcoCyc database [19] about the revers-ibility of the tested reaction and subsequently we examinethe reaction free energy change ΔG values as approxi-mated by Henry et al [20]. Values of ΔG close to zero areindicative of a reversible reaction because the sign of ΔGwill be sensitive to small concentration changes in the par-ticipating metabolites. Given the limited information(compared to E. coli) available to thermodynamicallycharacterize reactions in S. cerevisiae, we only employ thefirst method of testing for the latter model. We test if reac-tions are reversible by querying the MetaCyc database forcorresponding information; if no such information isavailable, we check if the same reaction is reversible inother organisms.

Evidence for the presence of newly added reactions in themodel is identified by checking for sequence similaritybased on bidirectional BLAST scores searches [21]. Next,we determine whether a particular metabolite has anexternal uptake/secretion route (Mechanism 3) by search-ing for evidence in the open literature. Finally, in the caseof multi-compartment models, we validate added intrac-ellular transport reactions by examining whether metabo-lites with similar structures have known transportreactions in the metabolic network. The developed math-ematical frameworks for identifying and filling gaps arediscussed in the Methods section. The next two sectionsdescribe in detail the results obtained by applying theabove procedures to the two most highly cited genome-scale models of E. coli [5] and Saccharomyces cerevisiae [6].

ResultsE. coliIn this study, we first identify all no-production metabo-lites (both root and downstream) using the (GapFind)formulation using the most recent E. coli genome-scalemodel [5]. All metabolites in the iJR904 model [5] that areidentified as transport metabolites are allowed to enterand leave the cell. All metabolite and reaction abbrevia-tions used in this section are taken from the iJR904 model[5]. Figure 4 summarizes the results obtained by using the(GapFind) formulation on the iJR904 model. As shown inFigure 4, there are 64 no-production metabolites; 28 ofthese metabolites are root and 36 are downstream no-pro-duction metabolites. Of the 64 identified no-productionmetabolites, 31.2% belong to Cofactor and ProstheticGroup Biosynthesis, 25% belong to Alternate CarbonMetabolism, 14% belong to Oxidative phosphorylation,10.9% belong to Cell Envelope Biosynthesis, 7.8% belongto Nucleotide Salvage and the remaining 12.5% are notassigned to any pathway. The presence of so many unbal-anced metabolites is quite surprising given how exten-sively this model has been curated and how widely it isused.

We next proceed with the gap-filling procedure using the(GapFill) formulation. We first identify the metabolitesfor which production mechanisms are established byreversing directionalities of existing reactions in E. coli. Asshown in Figure 4, for 26 out of 64 no-production metab-olites, production pathways are established by reversingdirectionality of existing reactions in E. coli. Also, 19 outof these 26 require a single reaction directionality reversalwhile three (i.e., 3dgulnp, 5prdmbz, adocbip, bbtcoa,ctbtcoa) require the reversal of directionality of two reac-tions while four metabolites (adocbi, dmbzid cbi andpc_EC) require the reversal of three reactions respectively.To ensure that all 26 metabolites are produced in the net-work, (GapFill) identifies that the directionalities of atleast twenty eight reactions have to be reversed. It isimportant to note that the identified reaction directional-ity reversals leading to the establishment of productionroutes for the problematic metabolites are to a large extentunique. Specifically, only two additional reaction reversalare identified when the (GapFill) model is re-solved(using integer cuts) to exhaustively identify all possiblereaction reversals capable of resolving all no-productionmetabolites (See Table 1). These results indicate that theproduction of most of the no-production metabolites canbe enabled by expanding the directionality of existingreactions in E. coli rather than adding new ones.

The validity of the identified reaction directionality revers-als is examined by employing two independent proce-dures as stated above. First we queried the identifiedreaction directionalities in the EcoCyc [19] database. Wefound that eleven out of the identified 30 reactions arelisted as reversible in EcoCyc even though they are treatedas irreversible in the iJR904 [5] model (Table 1). This pro-

Classification of mechanisms of restoring connectivity for no-production metabolites in E. coli using (GapFill)Figure 4Classification of mechanisms of restoring connectiv-ity for no-production metabolites in E. coli using (GapFill). The numbers in the boxes indicate the mode of flow restoration for problem metabolites in E. coli.

No Production Metabolites

(64)

Mechanism 1

(26)

Mechanism 2

(11)

Mechanism 3

(22)

Mechanism (1+2)

(5)

Single reactions reversal

(19)

Three reactions reversed

(4)

E.Coli reactions

added

(1)

Non-E.Coli

reactions added

(2)

Two reactions reversed

(3)

No Production Metabolites

(64)

Mechanism 1

(26)

Mechanism 2

(11)

Mechanism 3

(22)

Mechanism (1+2)

(5)

Single reactions reversal

(19)

Three reactions reversed

(4)

E.Coli reactions

added

(1)

Non-E.Coli

reactions added

(2)

Two reactions reversed

(3)



vides independent verification for allowing reversing thedirectionality of these eleven reactions to be reversedwhen they are used in the context of the E. coli genome-scale model. As shown in Table 1 seven out of the elevenreactions belong to Cofactor and Prosthetic Group Bio-synthesis, while two belong to Alternate Carbon Metabo-lism, one to Cell Envelope Biosynthesis and one is notassigned to any specific pathway. Notably, four of theseeleven reactions which are treated as reversible in EcoCyc[19] (ADOCBLS, ACBIPGT, NNDMBRT and RZ5PP) areinvolved in enabling the production of more than one no-production metabolite. Of the remaining nineteen reac-tions for which the EcoCyc database does not provide pos-itive evidence, the directionality of two reactions isunspecified whereas nine reactions take place in the direc-tion specified in the iJR904 model. There is no informa-tion regarding the remaining eight reactions in the EcoCycdatabase.

As a second method of testing, we used the free energychange values ΔG of the identified reactions as approxi-mated by Henry et al [20]. It should be noted here that ΔG

values are available for only seventeen out of the 30 can-didate reactions. It is likely that reactions that have calcu-lated ΔG values closer to zero are reversible. These ΔGvalues are contrasted against the ΔG of all the reactionspresent in the E. coli iJR904 model according to the proce-dure of Henry et al [20] (see Figure 5). Upon quantifyingthe uncertainty in the approximated ΔG values based onthe procedure by Henry and coworkers most of the iden-tified reactions (fourteen out of seventeen) involve freeenergy ranges that span both negative and positive values(see Figure 6). This indicates that there is a reasonablelikelihood that these fourteen reactions are reversible.Interestingly, five out of these fourteen reactions are alsoindependently deemed as reversible based on the EcoCycdata (Figure 6). Using these two separate tracks of valida-tion we find 35.71% unanimity in the prediction betweenthe two methods.

The second mechanism restores production routes byadding reactions from the database described in the previ-ous section. As shown in Figure 4, eleven out of the 64 no-production metabolites are reconnected by adding reac-

Table 1: Reactions whose directions have to be reversed to restore connectivity of metabolites using mechanism 1.

(GapFill) identified reversible reactions in E. coli

Corresponding metabolite(s) in E. coli which is (are) fixed

Pathway

ADOCBLS rdmbzi, agdpcbi, adocbi, adocbip Cofactor and Prosthetic Group BiosynthesisHETZK 4mhetz Cofactor and Prosthetic Group BiosynthesisHMPK1 4ahmmp Cofactor and Prosthetic Group BiosynthesisSPODM o2- UnassignedDXYLK dxyl Cofactor and Prosthetic Group BiosynthesisACBIPGT adocbi, adocbip, 5prdmbz Cofactor and Prosthetic Group BiosynthesisPGLYCP 2pglyc Alternate Carbon MetabolismNNDMBRT 5prdmbz, dmbzid Cofactor and Prosthetic Group BiosynthesisPEAMNO peamn Alternate Carbon MetabolismALDD19x peamn Alternate Carbon MetabolismCRNt7 crn, gbbtn, ctbt, crncoa*, bbtcoa, ctbtcoa Transport, ExtracellularAP4AH ap4a Nucleotide Salvage Pathways2DGLCNRy 2dhglcn Alternate Carbon MetabolismDKGLCNR2x 2dhglcn, 25dkglcn Alternate Carbon MetabolismBETALDHx betald UnassignedBETALDHy betald UnassignedDKGLCNR1 25dkglcn, 2dhglcn Alternate Carbon MetabolismX5PL3E ap5a, xu5pL, Alternate Carbon MetabolismDKGLCNR2y 25dkglcn Alternate Carbon MetabolismDKGLCNR2x 25dkglcn, 2dhglcn Alternate Carbon Metabolism2DGULRx 2dhguln Alternate Carbon Metabolism2DGULRy 2dhguln Alternate Carbon MetabolismGP4GH gp4g Nucleotide Salvage PathwaysDOGULNR 23doguln, 3dhguln Alternate Carbon MetabolismADOCBIK adocbi Cofactor and Prosthetic Group BiosynthesisKG6PDC 3dgulnp, 3dhguln Alternate Carbon MetabolismRZ5PP dmbzid Cofactor and Prosthetic Group BiosynthesisGPDDA5 g3pi Cell Envelope BiosynthesisGPDDA3 g3ps Cell Envelope Biosynthesis

The reactions in bold have support in the EcoCyc database. The pathways in which these reactions are present and the metabolites whose production they enable are as shown. The metabolites shown in bold are fixed by a combination of mechanisms 1 and 2.



tions from the customized external database. The reac-tions and the corresponding metabolites are shown inFigure 7. (GapFill) identifies that at minimum nine reac-tions from the external database must be added. As seenfrom Figure 7, metabolites tcynt and cyan require theaddition of the same set of five reactions from MetaCyc.Interestingly, two of these reactions L-carnitine dehy-dratase and putative cyanide hydratase are E. coli reactionsthat are present in the MetaCyc database but absent in theiJR904 model. Notably, the reaction putative cyanidehydratase is mentioned in [5] as a possible annotation fora conserved protein which is transcribed by the gene ygiU.For the remaining added reactions, we determine e-valuesobtained by checking for sequence similarity using theBLAST [21] algorithm between the candidate enzymesand the ORFs in the E. coli genome are shown in Table 2.The enzyme with the best bidirectional BLAST score of(1e-21,2e-23) phenylpyruvate decarboxylase, is involvedin enabling the production of four no-production metab-olites (Table 2). An e-value of 1e-21 indicates that only anexpected number of 1e-21alignments with equivalent orbetter bit scores can occur in the database search bychance. The obtained low e-value four enzymes (see Table2) are indicative that these functions may indeed bepresent in E. coli. Since the focus of this study is to providetestable hypotheses and not to conduct a thorough bioin-formatics based analysis of missing enzymes, we believethat BLAST scores are sufficient. Alternatively, more elab-orate scoring matrices based on Bayesian analysis andBLAST searches have been published by Green et al [11].

The connectivity restoration for five out of the sixty no-production metabolites requires the combination ofMechanisms 1 and 2 (see Figure 4). Specifically, for two ofthese metabolites (peamn and g3pi), in addition torequiring the reversal of directionality of existing reactionsin the iJR904 model (see Table 1) additional reactions

need to be added from MetaCyc to enable their produc-tion. Interestingly for metabolite 3dhguln the added reac-tion L-xylulose kinase is present in EcoCyc but absent inthe iJR904 model [5].

The production of the remaining twenty two no-produc-tion metabolites (Figure 4) is possible only by the uptakeof the corresponding metabolite from outside the cell.Four of these twenty four metabolites (dms, dmso, tmaand tmao) even though they have an extracellular compo-nent in the iJR904 model, there are no correspondingreactions which explicitly allow transport into the cell(i.e., no reactions of the form metabolite A [e] --> A [c]).Due to their presence as extracellular components, it isreasonable to assume that the corresponding transportreactions may also be present. For the remaining twentymetabolites, the validity of adding uptake routes is testedby searching for corresponding evidence in literature.While no direct evidence was retrieved for the existence ofuptake reactions for any of these sixteen metabolites,there exists evidence that trans-acontitate is formed spon-taneously from cis-acontitate which is an intermediate inthe citric acid cycle [22,23]. Note that all the hypothesesgenerated to fill gaps are available in an additional file[see Additional File 1]. In the next section we describe theresults obtained by applying the (GapFill) and the (Gap-Find) procedures to the genome-scale model of Saccharo-myces cerevisiae [6].

S. cerevisiaeIn this study, we first identify the no-production metabo-lites using the modified form of (GapFind) for multi-com-partment models in the Saccharomyces cerevisiae iND750model [6]. All metabolite and reaction abbreviations usedin this section are taken from the iND750 model [6]. Fig-ure 8 shows the distribution of no-production metabo-lites across the different compartments in theSaccharomyces cerevisiae iND750 model. As shown in Fig-ure 8(A), a majority of the problem metabolites are in thecytosol, the mitochondria and the peroxisome. Surpris-ingly, Figure 8(B) reveals that none of the metabolites ineither the peroxisome or the golgi apparatus are accessi-ble. On the other hand, all the metabolites in the endo-plasmic reticulum are connected. Also, as shown in Figure9, there are a number of common problem metabolitesbetween the cytosol and the inner compartments. Nota-bly, as shown in the figure, more than 25% of the problemmetabolites in the mitochondria also cannot be producedin the cytosol. This suggests that identifying productionpathways for cytosolic no-production metabolites mayautomatically fix some of the corresponding downstreamproblem metabolites in the inner compartments. Takingthis into account, we restore flow through problemmetabolites in two steps: First we identify productionmechanisms for cytosolic no-production metabolites.

ΔG values for (GapFill) identified reversible reactions in E. coliFigure 5ΔG values for (GapFill) identified reversible reactions in E. coli. Contrasting ΔG values between reactions found under Mechanism 1 and reactions in the iJR904 E. coli model on a log scale

1

10

100

1000

-13

-12.

1-1

1.2

-10.

3-9

.4-8

.5-7

.6-6

.7-5

.8-4

.9 -4-3

.1-2

.2-1

.3-0

.4 0.5

ΔG Values (kcal/mol)

Nu

mb

er o

f re

acti

on

s

E coli reactions Model identified reversible reactions




Range of ΔG values for (GapFill) identified reversible reactionsFigure 6Range of ΔG values for (GapFill) identified reversible reactions. The abbreviations of the reactions are as shown on the horizontal lines. EcoCyc reversible reactions are those which have evidence in EcoCyc regarding their reversible nature, while EcoCyc irreversible reactions correspond to those that do not have any such evidence in EcoCyc.

`` (Reversible)

EcoCyc (Irreversible)

EcoCyc

EcoCyc

-25 -20 -15 -10 -5 0 5 10

G P DDA5

G P DDA3

NNDMBRT

DXYLK

HMP K1

KG 6P DC

DO G ULNR

RZ5 P P

P G LYCP

2 DG LCNRx

2 DG LCNRy

2DG ULRx

2 DG ULRy

DKG LCNR2 x

DKG LCNR2 y

LP LIP A5

X5P L3E

-25 -20 -15 -10 -5 0 5 10

G P DDA5

G P DDA3

NNDMBRT

DXYLK

HMP K1

KG 6P DC

DO G ULNR

RZ5 P P

P G LYCP

2 DG LCNRx

2 DG LCNRy

2DG ULRx

2 DG ULRy

DKG LCNR2 x

DKG LCNR2 y

LP LIP A5

X5P L3E

Table 2: BLAST scores of added reactions in E. coli

Reactions E Value Best hit in E. coli Organism

formiminoglutamate hydrolase 9e-13,3e-17 arginase/agmatinase/formimionoglutamate hydrolase Bacillus subtilisHistidase 3.8, 0.003 Putative formate acetyltransferase 3 Bacillus subtilisimidazolone-5-propionate hydrolase 0.007,3e-07 guanine deaminase Bacillus subtilisinositol-1-phosphate synthase no similarity hypothetical protein EcolE_01002634 Mycobacterium tuberculosisphenylalanine ammonia lyase 8.6, 3e-04 Ornithine/acetylornithine aminotransferase Arabidopsis thalianaphenylpyruvate decarboxylase 1e-21,2e-23 acetolactate synthase isozyme III Thauera aromaticaUrocanase 0.006, 3e-07 hypothetical protein Z4243 Bacillus subtilisL-carnitine dehydratase ------------ ------------ E. coliputative cyanide hydratase ------------ ------------ E. coli

Candidate reactions from the MetaCyc database (along with BLAST scores) added to enable production of no-production metabolites in E. coli.


Subsequently, the identified additions/modifications thatfix cytosolic no-production metabolites are appended tothe original network and the problem metabolites in theremaining compartments are identified using (GapFill)for each compartment separately.

Figure 10 shows the distribution of the production mech-anisms identified by (GapFill) to enable production ofcytosolic no-production metabolites. As shown, a major-ity, i.e., 14 metabolites are fixed by adding transport reac-tions from other compartments to the cytosol. Also 14metabolites are fixed by adding missing reactions fromthe MetaCyc database and 19 metabolites are fixed byreversing the directionalities of existing reactions in theSaccharomyces cerevisiae model. Interestingly, 33 no-pro-duction metabolites are fixed by more than one of theabove mechanisms. Finally, since (GapFill) does not iden-tify production mechanisms for any of the remaining fif-teen no-production metabolites, we enable theirproduction by enabling transport reactions for them fromthe environment. As shown in Figure 10, productionpathways for seven peroxisomal and seventeen mitochon-drial metabolites are automatically identified by fixingcytosolic no-production metabolites. Thus, identifyingproduction pathways for cytosolic metabolites restoresconnectivity to 24 out of the 199 non-cytosolic problemmetabolites.

Connectivity restoration mechanisms for the remainingproblem metabolites in the inner compartments are next

identified using (GapFill). Figure 11 shows in detail thegenerated hypotheses to enable production of the remain-ing problem metabolites in non-cytosolic compartments.As shown a majority of the metabolites are fixed by revers-ing directionalities of existing reactions in the Saccharomy-ces cerevisiae model. Also, as shown in Figure 11, a largenumber of metabolites are fixed adding missing reactionsfrom the MetaCyc database. However, it should also benoted that (GapFill) cannot identify production mecha-nisms for about 17.5% of all metabolites in the innercompartments. This means that none of these metabolitescan be fixed by adding missing reactions from the Meta-Cyc database, reversing the directionalities of existingreactions in the model or adding intracellular transportreactions between the cytosol and the other compart-ments. Resolving these remaining inconsistencies wouldrequire currently absent functionalities and/or metabo-lites in the multi-species reaction database.

As an example, we examine in detail the results obtainedfor the golgi apparatus. As shown in Figure 12(A), (Gap-Find) identifies that the lack of flow in the root no-pro-duction metabolite, macchitppdol, results in fifteendownstream problem metabolites. (GapFill) does notidentify a production mechanism for macchitppdolwhich would automatically enable production of theremaining fifteen metabolites. Instead, it fixes ten of thesixteen no-production metabolites by adding a reactionwhich is downstream of macchitppdol as shown in Figure

Problem metabolites identified by (GapFind) in the Saccharo-myces cerevisiae iND750 modelFigure 8Problem metabolites identified by (GapFind) in the Saccharomyces cerevisiae iND750 model. 8A) shows the number of problem metabolites in each of the compart-ments. 8B) shows the percentage of metabolites in each of the compartments that are disconnected.

A)

B)

E. reticulumPeroxisome

Golgi

Mitochondria

Vacuole

Nucleus

100% 30%

0%80%100%

34.5%16.5%

Cytosol

E. reticulumPeroxisome

Golgi

Mitochondria

Vacuole

Nucleus

100% 30%

0%80%100%

34.5%16.5%

Cytosol

Distribution of blocked metabolites across compartments

0

20

40

60

80

100

cytosol peroxisome mitochondria nucleus golgi vacuole e. reticulum

Compartment

Nu

mb

er o

f b

lock

ed

met

abo

lites

Restoration of flow by adding missing reactions in E. coliFigure 7Restoration of flow by adding missing reactions in E. coli. Mapping between the reactions (left hand side) added by (GapFill) for E. coli through mechanism 2 and the metabolites (right hand side) whose connectivity they (partially) serve to restore.

Imidazoone-5- propionate hydrolase

crn

pac

pacald

phaccoa

tcynt

cyan

peamn

inost

g3pi

cenchddd

cinnm

phenylalanine ammonia lyase

Inositol-1-phosphate synthase

Phenylpyruvate decarboxylase

Formiminoglutamate hydrolase

Urocanase

Histidase

L-carnitine dehydratase

Putative cyanide hydratase

gbbtn

crncoa

ctbt

Imidazoone-5- propionate hydrolase

crn

pac

pacald

phaccoa

tcynt

cyan

peamn

inost

g3pi

cenchddd

cinnm





Urocanase

Histidase



gbbtn

crncoa

ctbt

crn

pac

pacald

phaccoa

tcynt

cyan

peamn

inost

g3pi

cenchddd

cinnm





Urocanase

Histidase



gbbtn

crncoa

ctbt

pac

pacald

phaccoa

tcynt

cyan

peamn

inost

g3pi

cenchddd

cinnm





Urocanase

Histidase



gbbtn

crncoa

ctbt



12(B). Interestingly, the enzyme guanylate kinase that cat-alyzes the added reaction is present in the cytosol where itcatalyzes the same reaction. This information alludes tothe possible presence of this activity in the golgi appara-tus.

As shown in Figures 10 and 11, 144 (108 exclusively byreversing directionalities and 36 by a combination ofreversing directionalities and other mechanisms) (36.7%)of the problem metabolites across all compartments arefixed by reversing the directionalities of 33 reactions in theSaccharomyces cerevisiae model. Ten out of the 33 reactionsare reversible in other organisms according to informa-tion in the MetaCyc [18] database, four of them are alwaysirreversible, seven have unspecified directionality in other

organisms and twelve do not even have any informationabout the presence or absence of the correspondingenzyme in MetaCyc. Interestingly reversing the direction-alies of FAO80p, a reaction that oxidizes Octanoyl-CoA aspart of the fatty acid degradation pathway in the peroxi-some, and FA80tp, a reaction that transports octanoateinto the peroxisome from the cytosol, fixes 83% of allproblem metabolites in the peroxisome. Notably,FAO80p is treated as reversible in other organisms in Met-aCyc. A detailed list of hypotheses generated through(GapFill) are provided in the supplementary material [seeAdditional File 2].

Fifteen reactions are added to the existing Saccharomycescerevisiae model to enable the production of 47 problemmetabolites (43 exclusively by adding reactions and 4 bya combination of adding missing reactions and othermechanisms). Of these, 18 are cytosolic metabolites (Fig-ure 10) and 29 are non-cytosolic metabolites (Figure 11))metabolites the model. Table 3 shows the e-valuesobtained by checking for sequence similarity between thecandidate enzymes and the ORF's in the Saccharomyces cer-evisiae genome by performing the bidirectional BLASTanalysis. As shown, eight of these enzymes have e-valuesless than 10-13 in both the forward and reverse directions.This is indicative that these candidate enzymes and thecorresponding best hits in Saccharomyces cerevisiaegenome are orthologs and not paralogs [24]. Notably,four of these eight enzymes that fix non cytosolic metab-olites are already present in the Saccharomyces cerevisiaegenome as cytosolic reactions. This means that, in addi-tion to identifying missing reactions in the metabolic net-work, (GapFill) predicts potential activities of existingenzymes across compartments in the model and hence, itcould be used effectively to aid in deciphering additionalpotential locations for activities of existing enzymes in agenome-scale metabolic reconstruction.

The production of the 65 (33 exclusively and 32 in com-bination with other mechanisms) problem metabolites inthe Saccharomyces cerevisiae model is enabled by adding 22intracellular transport reactions between the cytosol andthe remaining compartments (Figures 10 and 11). The 43cytosolic problem metabolites are fixed atleast partially(Figure 10) by adding 5 transport reactions from the othercompartments; specifically three transport reactionsbetween mitochondria and the cytosol (transporting themetabolites acACP, ACP, and malACP) and two transportreaction between the peroxisome and the cytosol (ttccoa,hexccoa transport). Examination of the prevalent trans-port mechanisms in the Saccharomyces cerevisiae modelreveals that eight different fatty-acyl carrier protein groupscan be transported between the cytosol and the mitochon-dria. Taking into consideration the structural similaritybetween different acyl carrier proteins, we can hypothe-

Common problem metabolites between the cytosol and the inner compartmentsFigure 9Common problem metabolites between the cytosol and the inner compartments. The numbers show the common problem metabolites between the cytosol and the remaining compartments.

mitochondria

peroxisome reticulum

golgi vacuole

0

02

0

421

cytosol

5454

00

551616

1414

7474

70

mitochondria

peroxisome reticulum

golgi vacuole

0

02

0

421

cytosol

5454

00

551616

1414

7474

70

(GapFill)-cytosolFigure 10(GapFill)-cytosol. Production mechanisms identified by (GapFill) for cytosolic no-production metabolites. As shown, this results in the automatic fixing of seven peroxisomal and seventeen mitochondrial metabolites.

19 NPM’s fixed by reversing

directionalities

15 NPM’s fixed by

enabling uptake

33 NPM’s fixed by

more than one

mechanism

Mitochondria

Peroxisome

Golgi

0 NPM’s

16 NPM’s E. reticulum

Nucleus27 NPM’s

Vacuole

3 NPM’s

14 NPM’s fixed by

adding transport rxns

14 NPM’s fixed

by adding rxns

75 58

78 71

19 NPM’s fixed by reversing

directionalities

15 NPM’s fixed by

enabling uptake

33 NPM’s fixed by

more than one

mechanism

Mitochondria

Peroxisome

Golgi

0 NPM’s

16 NPM’s E. reticulum

Nucleus27 NPM’s

Vacuole

3 NPM’s

14 NPM’s fixed by

adding transport rxns

14 NPM’s fixed

by adding rxns

75 58

78 71



size that the three added intracellular transport reactionsbetween the cytosol and the mitochondria transportingACP, malACP and acACP are likely to be present in theSaccharomyces cerevisiae model. Also, because there areseven reactions that transport metabolites with CoenzymeA groups from the cytosol to the peroxisome, it is reason-able to hypothesize that the transport reactions transport-ing ttccoa and hexccoa between the peroxisome and thecytosol may indeed be present. Moving to the mitochon-dria, fifteen transport reactions added between the cytosoland the mitochondria serve to atleast partially (takinginto account metabolites fixed by more that one mecha-nism) fix 16 problem mitochondrial metabolites. Two ofthese transport reactions serve to transport gdp and gtpbetween the cytosol and the mitochondria. Also, the threeproblem metabolites in the vacuole are fixed by addingtransport reactions to transport adp and atp from thecytosol and the vacuole. Finally the production of fifteencytosolic metabolites is enabled by uptaking them directlyfrom the extracellular space. We found no evidence in theliterature to support or contradict these uptake mecha-nisms.

Discussion and conclusionIn this paper, we introduced two optimization based pro-cedures, (GapFind) and (GapFill), to identify and fill gapsin genome-scale metabolic reconstructions. This wasachieved by pinpointing metabolites can cannot be pro-duced or consumed in the network using (GapFind) andthen using (GapFill) to generate hypotheses that restoredflow through these metabolites. These procedures weredemonstrated on the single compartment model of E. coliand the multi-compartment model of Saccharomyces cere-visiae[6]. When applied to the single compartment modelof E. coli, the (GapFind) procedure identified that about10.4% of all metabolites were disjoint from the rest ofmetabolism. Flow through a majority of these metaboliteswas restored by reversing directionalities of existing reac-tions in the E. coli model. As many as 40% of them couldnot be fixed by any of the postulated mechanisms insteadrequiring their free uptake from the extracellular space.Flow through the remaining metabolites was restored byeither exclusively adding missing reactions from MetaCycor a combination of reversing directionalities of existingreactions in the model and adding missing reactions.

(GapFill)-inner compartmentsFigure 11(GapFill)-inner compartments. Generated hypotheses identified by (GapFill) to fix problem metabolites in the inner com-partments.

Compartment

Mec

han

ism

Adding missing reactions

Reversing directionalities

Adding transport reactions

Adding external reactions +



+Adding external reactions

Not fixed

Peroxisome MitochondriaGolgi Nucleus Vacuole

1 10 7 11 0

67 0 14 8 0

0 0 16 0 3

0

0

0

0

0

0

7

1

0

0

19

0

0

0

6

0

0

0

3

Reversing directionalities+

Adding transport reactions2

Fixed by fixing cytosolic problem

metabolites7 170 0 0

Compartment

Mec

han

ism

Adding missing reactions



Adding external reactions +



+Adding external reactions

Not fixed

Peroxisome MitochondriaGolgi Nucleus Vacuole

1 10 7 11 0

67 0 14 8 0

0 0 16 0 3

0

0

0

0

0

0

7

1

0

0

19

0

0

0

6

0

0

0

3

Reversing directionalities+

Adding transport reactions2

Fixed by fixing cytosolic problem

metabolites7 170 0 0




The metabolic map of the Golgi apparatusFigure 12The metabolic map of the Golgi apparatus. (GapFind) identifies sixteen no-production metabolites, ten of which are resolved by (GapFill) by adding one reaction to the existing metabolic network as shown. The metabolites colored orange are not fixed, the ones colored dark green are fixed and the ones colored light green are cytosolic metabolites.

A)

B)


Interestingly, for almost 50% of the reactions identified asreversible by (GapFill) had supporting evidence in theinformation obtained from the EcoCyc database. In thecase of the multi-compartment model of Saccharomycescerevisiae, (GapFind) identified that approximately 30%of all metabolites in the model were disconnected. Flowthrough 22% of them was restored by adding intracellulartransport reactions in the model. Connectivity in theremaining 78% of the metabolites was restored by a com-bination of the mechanisms discussed in the case of E.coli. This left approximately 17.5% of all metabolites inthe Saccharomyces cerevisiae model whose connectivity res-toration cannot be accomplished though the postulatedmechanisms.

For both models we found that a substantial percentage ofthe metabolites are disconnected from metabolism andcannot carry any flux. Despite these gaps in silico growthpredictions using models of E. coli and S. cerevisiae are typ-ically in good agreement with in vivo results [6,25]. This isprimarily due to the fact that none of the identified gapsare in the well characterized central metabolism pathwaysand thus have no effect on growth prediction results.However, we anticipate that in de novo metabolic recon-structions of less well curated microorganisms using soft-ware applications such as the hole filler algorithm in thePathway Tools software [26] gaps in central parts ofmetabolism are likely to be present leading to erroneousin silico predictions. We believe that for such automatedreconstructions of less well studied microorganisms theutility of (GapFind) and (GapFill) will be even more pro-

nounced. We have already applied some of these conceptsin the reconstruction of the metabolic model of Myco-plasma genitalium currently underway in our group.

Clearly, the role of (GapFill) is to simply pinpoint anumber of hypotheses which need to subsequently betested. Using the basic set of our validation test we wereable to relatively confidently validate or invalidateapproximately 53% of the reversal of directionality ofreactions that were predicted by (GapFill). An increase inexperimental data, such as more information regardingΔG values of reactions, which would help determine moreaccurately the thermodynamic feasibilities of transforma-tions, will help increase this percentage. Also, use ofrecently developed computational procedures whichcombines available ΔG values with heuristic rules to elu-cidate thermodynamic constraints in genome-scale mod-els [27] may also further sharpen the elucidation ofcorrectness of the generated hypotheses. Furthermore,moving beyond the bidirectional BLAST hits that we usedto validate newly added reactions in this study, the likeli-hood of the presence of the added enzymes can be moreaccurately assessed by using previously developed costfunctions [8-10]. Also, by adopting concepts first pro-posed by Reed and co-workers [17], the gap-filled modelcan further be refined by contrasting in silico predictions ofgrowth phenotypes with experimental observations. Aninherent limitation of (GapFill) is the reliance on a candi-date database of reactions. One could envision extending(GapFill) to consider hypothetical reactions in the spiritof the methods proposed by Hatzimanikatis and cowork-

Table 3: BLAST scores of added reactions in S. cerevisiae

Reactions E Value Reaction in S. cerevisiae Organism

methionine γ-lyase 1e-58,1e-68 Cystathionine gamma-lyase Pseudomonas putida2-hydroxyglutarate synthase(no gene identified yet)

---------- --------------- E. coli

2-oxoglutarate reductase/phosphoglycerate dehydrogenase

2e-14, 3e-18 3-phosphoglycerate dehydrogenase Bacillus subtilis

deoxyribose-phosphate aldolase 7.7, 0.006 Phosphatidylinositol 3-kinase TOR2 Mycoplasma pneumoniaeD-lactate dehydrogenase 2, 3e-04 Protein of unknown function E. coliL-tryptophan aminotransferase no information no information Enterobacter cloacaeMethylglyoxal synthase 1.5, 0.001 carbamyl phosphate synthetase E. coliphenylpyruvate decarboxylase 3E-35, 1e-39 Chain A, Pyruvate Decarboyxlase Azoarcus sp. EbN1tagatose-1,6-bisphosphate aldolase 2 1e-12, 1e-16 Fructose 1,6-bisphosphate aldolase E. colitryptophan 2-monooxygenase 2.2, 5e-05 orf:PZA105 E. coli5,10-methylenetetrahydrofolate reductase(present in the cytosol)

1E-38, 2e-42 Isozyme of methylenetetrahydrofolate reductase

E. coli

adenine phosphoribosyltransferase(present in cytosol)

2E-25, 1e-29 Adenine phosphoribosyltransferase E. coli

guanylate kinase(present in cytosol) 9E-38, 7e-42 Guanylate kinase E. coliputative NAD+ kinase(present in cytosol) 2E-27, 6e-28 ATP-NADH kinase E. coliadenylate kinase(present in cytosol and mitochondria)

7E-51, 5e-55 Adenylate kinase E. coli

Candidate reactions from the MetaCyc database (along with BLAST scores) added to enable production of no-production metabolites in S. cerevisiae.



ers [28]. In conclusion, here, we introduced a systematicprocedure to identify and fill gaps in metabolic recon-structions. As seen by the results obtained, these proce-dures can be used to curate existing metabolicreconstructions. In the future, we plan to deploy thesemethods during the generation phase of metabolic recon-structions of less curated microorganisms.

Methods(GapFind): Identification of no-production metabolitesFirst we describe a straightforward procedure to identifyroot no-production metabolites in the metabolic networkunder steady-state conditions. Under steady-state condi-tions, metabolite balances for a metabolic network com-prised of M metabolic reactions and N metabolites yield:

where bi is a parameter which signifies if metabolite i isuptaken (bi is negative) or secreted (bi is positive), vj is theflux in reaction j of the metabolic network, Sij is the stoi-chiometric coefficient of metabolite i in reaction j. Ametabolite i is inferred to be a root no-production metab-olite by simply scanning the ith column of the matrix con-taining the Sij elements and examining whether there existany positive entries (for irreversible reactions) or non-zero(for reversible reactions) signifying production/uptaketerms. If no such entries are present then there is neither adirect production nor importation route for the testedmetabolite implying that it forms the root node of a no-production branch (see Figure 1a). Note that root no-con-sumption metabolites can be identified in the metabolicnetwork by scanning the stoichiometric matrix andemploying a procedure symmetric to the one that identi-fies root no-production metabolites.

In single compartment models, the identification ofdownstream no-production metabolites cannot beaccomplished by simply inspecting the entries of the Sijmatrix. Instead, an optimization procedure is proposed topinpoint downstream no-production metabolites. It isassumed that for all cytosolic metabolites a consumptionterm is assured because of the diluting effect of cell divi-sion acting as a metabolite sink, consumption by non-DNA controlled reactions, participation in macromolecu-lar processes absent from the model involved in proteinand DNA formation or simply export based on simple dif-fusion through the cell membrane. To incorporate thisassumption, constraint (1) is rewritten as

The identification of the no-production metabolite set NP(a subset of N) requires first the introduction of binaryvariables xnp

i and wij which are defined as:

Given a parent metabolic network consisting of a reactionset M and a set N of metabolites, the solution of the fol-lowing optimization formulation (GapFind) identifies alldownstream no-production metabolites in addition tothe root no-production metabolites:

s.t

Sijvj ≥ εwij ∀ i ∈ N, j|(Sij > 0 and j ∈ IR) (4)

Sijvj ≤ Mwij ∀ i ∈ N, j|(Sij > 0 and j ∈ IR) (5)

Sijvj ≥ ε - M(1 - wij) ∀ i ∈ N, j|(Sij ≠ 0 and j ∈ R)(6)

Sij"vj ≥ Mwij ∀ i ∈ N, j|(Sij ≠ 0 and j ∈ R) (7)

LBj ≤ vj ≤ UBj, j ∈ Model (9)

xnpi ∈ {0, 1}, ∀i

wij ∈ {0, 1}, ∀i, j

{j' ∈ M|(Sij > 0 and j ∈ IR) or (Sij ≠ 0 and j ∈ R)}

In (GapFind), sets R and IR comprise of reversible andirreversible reactions in the model respectively. Con-straints (4) and (5) ensure that for each irreversible reac-tion that produces the metabolite i, the binary variable wijassumes a value of one only if the reaction producesatleast ε units of metabolite i (i.e., Sijvj ≥ 0). Similarly, con-straints (6) and (7) ensure that for each reversible reactionin which the metabolite i participates, the binary variablewij assumes a value of one only if the reaction produces εunits of metabolite i. Constraint (8) then ensures that

S v b i Nij j ij M

= ∀ =∈∑ 1... (1)

S v i Nij jj M

≥ ∀ =∈∑ 0 1... (2)

xinp

i =1

0

if metabolite can be produced in the network

otherwwise

if reaction that produces metabolite in t

⎧⎨⎩

=wj i

ij1 hhe metabolic network is active

otherwise0⎧⎨⎩

Maximize xnpi

i

( ) ( )∑ GapFind (3)

w x i Nijnp

ij

≥ ∀ ∈∑’

(8)

S v i Nij jj

∑ ≥ ∀ ∈0 (10)



metabolite i must have at least one production route if xnpi

= 1 by requiring a minimum of that atleast for one reac-tion j that can produce metabolite i, the value of a wij = 1consequently implying that atleast ε units of the metabo-lite i is produced. Constraint (9) restricts the fluxes in thereactions present in the model organism between prede-termined upper and lower bounds, UBj and LBj (LBj = 0 forirreversible reactions). The net positive balance assump-tion which led to (2) is incorporated in constraint (10).Finally the objective function (3) maximizes the sum ofthe binary variables xnp

i over all metabolites ensuring theidentification of all metabolites that have at least one pro-duction route given a set of available substrates. There-fore, if at the optimal solution xnp

i is equal to zero thenmetabolite i is a no-production metabolite thus belongingto set NP. By using this procedure, all no-productionmetabolites are identified. Metabolites identified previ-ously as root no-production are subsequently subtractedfrom the list to yield only the downstream no-productionmetabolites.

The (GapFind) procedure is slightly modified for multi-compartment models. As shown in Figure 3, cytosolicmetabolites can be drained out into the extracellular spacewhile non-cytosolic metabolites can only be transportedout into the cytosol. This implies that for metabolitespresent in compartments the production term mustmatch exactly the consumption term (see constraint (12))as they cannot freely drain into the extracellular space.This implies that the balance constraint (10) in (GapFind)is replaced by the following two constraints in multi-com-partment models.

Note that a GAMS implementation of (GapFind) is avail-able as an additional file [see Additional file 3].

(GapFill): Gap resolution based on minimal metabolic model modificationsUpon the identification of all no-production metabolitesin the model the next step involves filling these gaps usingminimally the three mechanisms described earlier. Wefirst explore whether reaction directionality reversal and/or addition of reactions from Metacyc [18] absent fromthe original model links the problem metabolite with thepresent substrates. This is accomplished by using a data-base of candidate reactions consisting of (i) all reactionsin the original model with their directionalities reversedand (ii) reactions from a curated version of the MetaCycdatabase including allowable transport mechanism

entries between compartments (in the case of multi-com-partment models). It should be noted here that all thereactions in the MetaCyc database are treated as reversiblein the model. These reactions define set Database com-prised of candidate reactions while set Model is composedof the original genome-scale model reactions. It should benoted that if none of the above two/three mechanisms iscapable of connecting the cytosolic no-production metab-olite in single/multi-compartment models then an uptakereaction is arbitrarily added to the model to restore con-nectivity. However, if a non-cytosolic metabolite (in thecase of multi-compartment models) present in an innercompartment cannot be fixed by any of the above mecha-nisms it is flagged as unfixable given the employed mech-anisms.

In addition to the binary variable wij defined previously,the proposed (GapFill) formulation relies on the binaryvariables yj defined as follows:

For the case of single compartment models, the task ofidentifying the minimal set of additional reactions thatenable the production of a no-production metabolite i* isposed as the following mixed integer linear programmingproblem (GapFill).

s.t

Si*jvj ≥ δ - M(1 - wi*j) ∀ j|(Sij ≠ 0) (14)

Si*jvj ≤ Mwi*j ∀ j|(Sij ≠ 0) (15)

LBj ≤ vj ≤ UBj, ∀ j ∈ Model (18)

LBj·yj ≤ vj ≤ UBj·yj, ∀ j ∈ Database (19)

wij ∈ {0, 1}, ∀i, j

yj ∈ {0, 1}, ∀ j ∈ Database

{j' ∈ M | (Sij ≠ 0)}

S v i cytosolij jj

≥ ∀ ∈∑ 0 (11)

S v i cytosolij jj

∑ = ∀ ∉0 (12)

yj

j =1 if reaction from the external database is added to thhe parent network

otherwise0⎧⎨⎩

Minimize y jj Database∈

∑ ( )GapFill (13)

wi jj

∗ ≥∑ 1 (16)

S v i Nij jj

≥ ∀ ∈∑ 0 (17)



In (GapFill), the objective function (13) minimizes thenumber of added reactions from the Database so as torestore flow through metabolite i*. Constraints (14) and(15) are identical to (6) and (7). Constraint (16) ensuresthat these additions are subject to a minimum of δ unitsfor the no-production metabolite i* being produced. Con-straint set (17), as in (GapFind), allows for the free drainof all cytosolic metabolites while bounds on reactionspresent in the Model are imposed by constraint set (18).Constraint set (19) ensures that only those reactions fromthe Database that have non zero flow are added to themodel. This formulation restores flow through no-pro-duction metabolites in single compartment models. Formulti-compartment models, the (GapFill) formulation ismodified. First gaps in the cytosol are filled using themechanisms described earlier for single compartmentmodels. Specifically, the (GapFill) formulation is modi-fied by replacing constraint (17) with constraints (11) and(12) reflecting the fact that no net production term can beimposed for metabolites present with compartments inca-pable of communicating directly with the extracellularspace. The solution of formulation (GapFill) once foreach no-production metabolite i* identifies one mecha-nism at a time for resolving connectivity problems in themodel. It should be noted that through the use of integercuts [29] multiple hypotheses can be generated to resolvethese connectivity problems. In this study, we evaluate themerit of generated hypotheses and subsequently choosethe most probable one using the following three criteriasequentially a) The added hypotheses should not havecycles: since the MetaCyc database consists of multiplecopies of the same reaction (which are present in differentorganisms), there is a proclivity to fix metabolites by add-ing two copies of the same reaction in opposite directions(since all reactions in the MetaCyc database are consid-ered reversible) thereby forming a cycle, b) We choose thehypotheses which enables production of the problemmetabolite with the least number of modifications and c)We choose a hypotheses that has higher probability ofbeing accurate based on our validation metrics (e.g., if tworeactions are added, we choose the one with the betterblast score). Note that a GAMS implementation of (Gap-Fill) is available as an additional file [see Additional file4].

Authors' contributionsCDM conceived the study. VSK, MSD and CDM providedthe mathematical formulations for (GapFind) and (Gap-Fill). VSK implemented (GapFind) and (GapFill). VSK,MSD and CDM drafted the manuscript. All authors readand approved the final version of the manuscript.

Additional material

AcknowledgementsThe authors would like to thank Dr. Anthony Burgard and Dr. Priti Pharkya for valuable discussions which provided insights into the problem. The authors gratefully acknowledge funding from the DOE grant (DE-FG03 01ER25499).

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Additional file 1Testable hypotheses for E. coli. The abbreviations used are from the E. coli iJR904 model.Click here for file[http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S1.xls]

Additional file 2Testable hypotheses for S. cerevisiae. The abbreviations used are from the S. cerevisiae iND750 model.Click here for file[http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S2.xls]

Additional file 3(GapFind). The (GapFind) formulation in the GAMS modeling lan-guage.Click here for file[http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S3.gms]

Additional file 4(GapFill). The (GapFill) formulation in the GAMS modeling language.Click here for file[http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S4.gms]


http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S1.xls

http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S2.xls

http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S3.gms

http://www.biomedcentral.com/content/supplementary/1471-2105-8-212-S4.gms















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