Pseudomonas putida is an archetype of such microbes due toits metabolic versatility, stress resistance, amenability to geneticmodifications, and vast potential for environmental and industrial applications.To address both the elucidation of the metabolic wiring in P.putida and its uses in biocatalysis, in particular for the productionof non-growth-related biochemicals, we developed and present here a genome-scaleconstraint-based model of the metabolism of P. putida KT2440.Network reconstruction and flux balance analysis (FBA) enabled definition of thestructure of the metabolic network, identification of knowledge gaps, andpin-pointing of essential metabolic functions, facilitating thereby therefinement of gene annotations. FBA and flux variability analysis were used toanalyze the properties, potential, and limits of the model. These analysesallowed identification, under various conditions, of key features of metabolismsuch as growth yield, resource distribution, network robustness, and geneessentiality. The model was validated with data from continuous cell cultures,high-throughput phenotyping data, 13C-measurement of internal fluxdistributions, and specifically generated knock-out mutants. Auxotrophy wascorrectly predicted in 75% of the cases. These systematic analysesrevealed that the metabolic network structure is the main factor determining theaccuracy of predictions, whereas biomass composition has negligible influence.Finally, we drew on the model to devise metabolic engineering strategies toimprove production of polyhydroxyalkanoates, a class of biotechnologicallyuseful compounds whose synthesis is not coupled to cell survival. The solidlyvalidated model yields valuable insights into genotype–phenotyperelationships and provides a sound framework to explore this versatile bacteriumand to capitalize on its vast biotechnological potential.A cornerstone of biotechnology is the use of microorganisms for the efficientproduction of chemicals and the elimination of harmful waste. Pseudomonasputida, a representative of the industrially relevant pseudomonads. Themodel was initially expanded and validated with substrate utilization data andcarbon-tracking data. Next, the model was used to identify key features ofmetabolism such as growth yield, internal distribution of resources, and networkrobustness. We then used the model to predict novel strategies for theproduction of precursors for bioplastics of medical and industrial relevance.Such an integrated computational and experimental approach can be used to studyits metabolism and to explore the potential of other industrially andenvironmentally important microorganisms.The pseudomonads include a diverse set of bacteria whose metabolic versatilityand genetic plasticity have enabled their survival in a broad range ofenvironments. Many members of this family are able to either degrade toxiccompounds or to efficiently produce high value compounds and are therefore ofinterest for both bioremediation and bulk chemical production. To betterunderstand the growth and metabolism of these bacteria, we developed alarge-scale mathematical model of the metabolism of  Pseudomonas putida is one of the best studied species of themetabolically versatile and ubiquitous genus of the Pseudomonads Pseudomonas putida particularly attractive forbiocatalysis. To date, strains of P. putida have been employed toproduce phenol, cinnamic acid, cis-cis-muconate, p-hydroxybenzoate, p-cuomarate, andmyxochromide P. putida have been employed in a variety of otherbiocatalytic processes, including the resolution ofd/l-phenylglycinamide into d-phenylglycinamide andl-phenylglycine, production of non-proteinogenic l-amino acids,and biochemical oxidation of methylated heteroaromatic compounds for formation ofheteroaromatic monocarboxylic acids http://www.genomesonline.org, http://www.pseudomonas.com),and a series of studies are underway to elucidate specific aspects of their genomicprograms, physiology and behavior under various stresses .P. putida strain KT2440, a workhorse of P.putida research worldwide and a microorganism Generally Recognized asSafe (GRAS certified) P. putida species, and opened avenues for thedevelopment of new biotechnological applications P. putida through this sequencing effort,the relationship between the genotype and the phenotype cannot be predicted simplyfrom cataloguing and assigning gene functions to the genes found in the genome, andconsiderable work is still needed before the genome can be translated into a fullyfunctioning metabolic model of value for predicting cell phenotypes The sequencing of Constraint-based modeling is currently the only approach that enables the modeling ofan organism's metabolic and transport network at genome-scale Through various analysis techniques, constraint-based models can help predictcellular phenotypes given particular environmental conditions. Flux balance analysis(FBA) is one such technique, which relies on the optimization for an objective fluxwhile enforcing mass balance in all modeled reactions to achieve a set of fluxesconsistent with a maximal output of the objective function. When a biomass sink ischosen as the objective in FBA, the output can be correlated with growth, and themodel fluxes become predictive of growth phenotypes However, in all previous applications in which a constraint-based approach was usedto design the production of a biochemical, the studies addressed only the productionof compounds that can be directly coupled to the objective function used in theunderlying FBA problem. The major reason for this is that FBA-based methods predicta zero-valued flux for any reaction not directly contributing to the chosenobjective. Since the production pathways of most high-added value and bulk compoundsoperate in parallel to growth-related metabolism, straightforward application of FBAto these biocatalytic processes fails to be a useful predictor of output. Otherconstraint-based analysis methods, such as Extreme Pathways and Elementary Modesanalysis, are capable of analyzing non-growth related pathways in metabolism, but,due to combinatorial explosion inherent to numerical resolution of these methods,they could not be used so far to predict fluxes or phenotypes at genome-scale forguiding biocatalysis efforts P. putidaand the use of P. putida for the production of non-growth-relatedbiochemicals, we developed and present here a genome-scale reconstruction of themetabolic network of Pseudomonas putida KT2440, the subsequentanalysis of its network properties through constraint-based modeling and a thoroughassessment of the potential and limits of the model. The reconstruction is based onup-to-date genomic, biochemical and physiological knowledge of the bacterium. Themodel accounts for the function of 877 reactions that connect 886 metabolites andbuilds upon a constraint-based modeling framework 13C-measurement of internal fluxes P. putida of polyhydroxyalkanoates, a class ofcompounds whose production consumes resources that would be otherwise used forgrowth. This reconstruction thus provides a modeling framework for the explorationof the metabolic capabilities of P. putida, which will aid indeciphering the complex genotype-phenotype relationships governing its metabolismand will help to broaden the applicability of P. putida strains forbioremediation and biotechnology.To address both the elucidation of the metabolic wiring in P. putida at the genome-scalethrough a process summarized in pre1);(2) a model building stage in which simulations were performed withiJP815pre1 and reactions were added until the model was able togrow in silico on glucose minimal medium(iJP815pre2); and (3) a model completion stage in which BIOLOGsubstrate utilization data was used to guide model expansion and insilico viability on varied substrates. The final reconstruction,named iJP815 following an often used convention We reconstructed the metabolism of in silico on glucose in minimal medium.The remaining gaps identified in the model completion step (Most network gaps (27) were identified during the second round of thereconstruction and were resolved through detailed literature mining, therebyenabling iJP815 to grow ion step  were mosThe iJP815 model includes 289 reactions for which non-zero flux values cannot beobtained under any environmental condition while enforcing the pseudosteady-state assumption (PSSA). We term these reactions“unconditionally blocked” meaning that they are unable tofunction because not all connections could be made with the informationavailable. Three hundred sixty two metabolites that are only involved in thesereactions are classified as “unbalanced metabolites”.Another important subset of model reactions is the “weaklyannotated” set, which means that all the genes assigned to these 57reactions are currently annotated as coding for “putative”or “family” proteins. The relationships between all thesubsets are shown in P. putida genome and to65% (1253) of those currently assigned to the classes‘Metabolism’ (K01100) and ‘MembraneTransport’ (K01310) in the Kyoto Encyclopedia of Genes and Genomes(KEGG) orthology classification The final reconstruction accounts for the function of 815 genes, corresponding to15% of all genes in the P.putida to validate and extend the model. In this assay, P.putida was tested for its ability to oxidize 95 carbon substratesin minimal medium. Of these 95 substrates, P. putida oxidized45. We added 2 other carbon sources to the positive-oxidation group despite a negative BIOLOGresult, since these substrates had been previously shown to be growth substratesin vivo. Forty seven out of the 95 carbon sourcestested were accounted for in iJP815pre2, enabling a comparison ofthese BIOLOG data with FBA simulations of iJP815 grown on insilico minimal medium with the respective compound as sole carbonsource (see A high-throughput BIOLOG phenotypic assay was performed on urce see .pre2) was able tosimulate growth with 14 of the 47 BIOLOG-assayed compounds as sole carbonsources. This version of the reconstruction contained only a few transportreactions, prompting us to identify compounds that could not be utilizedin silico simply due to the lack of a transporter. This wasachieved by allowing the intracellular pool of each compound of interest to beexchanged with environment in silico, and by evaluating theproduction of biomass in each case through FBA simulations. This approachincreased the number of utilizable substances to 34 but also produced sixfalse-positives . These includedthree metabolites involved in central metabolic pathways , anintermediate of the l-histidine metabolism pathway (urocanate), anintermediate of branched amino acids biosynthesis (2-oxobutanoate), and thestorage compound glycogen. This analysis suggests that the inability ofP. putida to utilize these compounds invivo is likely due to the lack of appropriate transport machinery.The initial working version of the model (iJP815P. putida model (iJP815) grew on 39 of the 51compounds tested in the BIOLOG assay and that concurrently were accounted for inthe model. Of these, 33 were true positives . Themode of utilization of the remaining fourteen in vivo oxidizedcompounds  could not be elucidated. The remaining fortytwo compounds posed true negatives, eight of which were accounted for in thereconstruction. Ten utilized compounds also lack transport reactions, as nothingis known about their translocation into the cell. Nevertheless, this comparisonof in silico growth predictions with BIOLOG substrateutilization data indicates that the core metabolism of P.putida has been properly reconstructed.The final P. putida is able to grow on minimal medium supplementedwith these compounds, we considered the assumption to be justified.A note of caution when comparing the BIOLOG assays with growth predictions isthat this assay evaluates whether an organism is able to oxidize the testedcompound and yield energy from it, which is different from growth. However, asP. putida metabolic network,we discovered a number of genes that appear to have been improperly annotated inbiological databases . Thesemis-annotations arose due to a lack of information at the time of the originalannotation or because knowledge that was available in the literature had beenoverlooked in the original annotation. In a number of other cases, the modelbuilding process has also generated new hypotheses for gene functions. Forinstance, our reconstruction process identified an unlikely gap in thel-lysine degradation pathway of P. putida. Extensiveliterature search and careful reannotation has provided considerable evidencethat the genes PP0382 and PP5257, currently annotated as‘carbon-hydrogen hydrolase family protein’ and‘oxidoreductase, FAD binding’ respectively, most probablycode for a ‘5-aminopentamidase’ and‘l-pipecolate oxidase’, respectively pre2 version this pathway was complete except for one enzymaticactivity, namely the 2-methylisocitrate dehydratase. Analysis of the enzymesflanking this reaction showed that all of the enzymes are encoded by genesimmediately adjacent to the ORF PP2330. Inspection of this region of the genomerevealed that PP2336 is annotated as “aconitate hydratase,putative”, although the flanking genes are responsible for degradationof propanoate. Analysis of PP2330 via BLAST revealed a homology of more than99% over the whole length of the protein with the 2-methylisocitratedehydratase from other bacteria, such as other strains of P.putida , Burkholderia prymatum STM 815,Burkholderia multivorans ATCC 17616, Pseudomonasaeruginosa PA7, and Stenotrophomonas maltophiliaR551-3. Consequently the gene was reannotated to code for this function and thegap in propanoate degradation pathway was thus closed by addition of thecorresponding GPR. In other cases, discrepancies exist between variousdatabases, as in the case of PP5029, which is annotated in KEGG as‘formiminoglutamase’ but in NCBI as‘N-formylglutamate deformylase’. Analysisof network gaps, genomic context and sequence homology provided a strongindication that ‘N-formylglutamatedeformylase’ is the correct annotation. In many other cases thereannotation meant changing the substrate specificity of the enzyme (whichcorresponds to changing the last part of the EC number). These were mainlyidentified by BLASTing the protein against protein sequences of other microbesand, whenever available, cross-checking the BLAST results against primaryresearch publications. The full list of reannotations suggested by thereconstruction process is shown in The reconstruction process systematizes knowledge about the metabolism of anorganism, allowing the identification of errors in, and discrepancies between,various sources of data. A major value of a manual model-building effort is thecareful revision of the current genome annotation, based on literature evidenceencountered during the model building process, BLAST searches, and gap closures.During the reconstruction of the P. putida, a basic property ofthe modeled organism. In silico growth yield on succinate wascalculated by FBA and compared with in vivo growth yieldmeasured in continuous culture in silico yield werelower than the experimental, it would indicate that the network may lackimportant reactions that influence the efficiency of conversion of carbon sourceinto biomass constituents and/or energy. In fact, the calculated insilico yield (0.61gDW⋅gC−1) was higherthan the experimental yield (0.47gDW⋅gC−1), indicatingthat some of the processes reconstructed in the network might be unrealisticallyefficient and/or that P. putida may be diverting resources intoother processes not accounted for in the model. This greater efficiency of thein silico model versus in vivo growth datais also consistent with recent studies that suggest optimal growth is notnecessarily the sole objective (function) of biochemical networks After completing the reconstruction, we assessed whether the model was capable ofpredicting the growth yield of in silico growth yield is influenced not only by thestructure of the metabolic network, but also by other factors including biomasscomposition and the growth-associated and non-growth-associated energymaintenance factors (GAM and NGAM), the values of which represent energy coststo the cell of “living” and “growing”,respectively E. colimodel The P. putida ,its influence is negligible, as increasing or decreasing it twofold alters thegrowth yield by merely 5%. A higher GAM value in P.putida than in E. coli could contribute to thediscrepancy between the experimental measurements and in silicopredictions, but it could not be the only factor unless the E.coli and P. putida values differ more than twofold,which is unlikely.Subsequently, the effects of changes in the GAM on the e tested . It was insilico growth yield. The NGAM growth dependency is influenced bythe rate of carbon source supply, and thus indirectly by the growth rate. If thecarbon intake flux is low , the fraction of energyutilized for maintenance purposes is high and therefore so is the influence ofthe NGAM value on growth yield  Finally, we assessed the effects of changes in the value of NGAM on th yield . Under sin vivo growth yield. It isalso worth mentioning that maintenance values may depend on the carbon sourceused For a high influx of carbon source  the inflP. putida on solesources of three other important elements—Nitrogen (N), Phosphorous(P), and Sulfur (S)—and compared these with published experimentaldata from continuous cultivations in silicousage of basic elements, this analysis can aid in assessing how well the biomassequation, which is equivalent to the E. coli biomass reaction,reproduces the true biomass composition of P. putida. The yieldon nitrogen differs only by 10% between in silicoand in vivo experiments, which suggests that the associatedmetabolic network for nitrogen metabolism is well characterized in the iJP815reconstruction. The yields on phosphorous and sulfur, however, differ by morethan a factor of two between the in vivo and insilico analyses, suggesting that there may be significant differencesbetween the biomass requirements and the metabolic networks of P.putida and E. coli for these components. Thedifferences in yields, however, may be also caused by the change of thein vivo biomass composition, which decreases the fractionof compounds containing the limited element, when compared to the biomasscomposition while the bacterium is grown under carbon-limitation. Such changeswere observed experimentally in P. putida for nitrogen andphosphate limitations P.putida needs to be determined precisely in the future. However, forthe purpose of this work and since the global effect of the biomass compositionon the outcome of the simulations is negligible (as shown above), we consideredthe use of the original biomass equation to be justified.Additionally, we computed the growth yields of P.putida model. The first group of reactions includes members ofincomplete pathways that, with increasing knowledge and further modelrefinement, will gradually become connected to the core. This subset comprises108 reactions (35% of blocked reaction set). The second group ofreactions comprises also members of incomplete pathways, but many of them belongto pathways that are complete but that lack a transport reaction for the initialor final compound. Examples of pathways lacking a transporter are thedegradation of fatty acids and of propanoate.As described above, iJP815 contains 289 unconditionally  blocked reactions , corresponding to 33% of themetabolic network. In previously published genome-scale metabolicreconstructions, the fraction of blocked reactions varies between 10 and 70percent In addition, there could exist compounds whose production is required only incertain environmental conditions, e.g., under solvent stress, and as such arenot included in generic biomass equation. Pathways synthesizing compounds thatare not included in the biomass equation but that likely are conditionallyrequired include the synthesis of thiamine, various porphyrins and terpenoids.In this case, reactions involved exclusively in the production of such compoundswould be blocked if no alternative outlets exist for those pathways. Allowing anon-zero flux through these reactions would require inclusion into biomass ofthe conditional biomass constituents, which in turn would require having variousbiomass equations for various conditions. This level of detail, however, isbeyond the scope of our initial metabolic reconstruction and investigation.The high number of blocked reactions in iJP815 clearly indicates that there arestill vast knowledge deficits in the model and, thus, in the underlyingbiochemical and genomic information. Since a genome-scale metabolic model seeksto incorporate all current knowledge of an organism's metabolism, thesereactions are integral elements of the metabolic reconstruction and of themodeling scaffold, even if they are not able to directly participate in steadystate flux studies. Therefore, the inclusion of these reactions in the modelprovides a framework to pin-point knowledge gaps, to include novel informationas it becomes available and to subsequently study their embedding and functionin the metabolic wiring of the cell.P. putida. We subsequently used the model to probe thenetwork and to ascertain the distribution of internal fluxes and properties suchas network flexibility and redundancy of particular reactions. To this end, wepredicted the distribution of reaction fluxes throughout the central pathways ofcarbon metabolism by flux variability analysis (FVA), and compared thesimulations to internal fluxes computed from experimentally obtained13C data in P. putidaThe assessment performed as described above by means of high-throughputphenotyping assays, growth experiments and continuous cultivations, has shownthat the model is coherent and that it captures the major metabolic features of13C) measurements are not able to distinguish which glucoseuptake route is being used by P. putida, all the fluxes in the13C experiment and in the FVA simulations were computed assumingthat glucose is taken up directly into the cell. For the precise description ofthe network models used in this comparison  see 13C fluxmeasurement data”).Genome-scale metabolic networks are, in general, algebraically underdetermined13C values fall within the FVAintervals, where intervals were predicted, or both values are close to eachother , when a single value was predicted. As P.putida lacks phosphofructokinase, glucose can be converted topyruvate (the entry metabolite of TCA cycle) via the pentose phosphate (PP) orthe Entner-Doudoroff (ED) pathways. The ED pathway is energetically moreefficient and the 13C measurements indicate that KT2440 uses itpreferentially over the PP pathway. Therefore, the FVA yields locally singleflux values rather than intervals, which reflects the relative rigidity of thispart of the network. In contrast, the energy generating part of the centralmetabolic network (the TCA cycle and its vicinity) exhibits greater flexibility,as illustrated by the broad flux intervals. Firstly, the conversion ofphosphoenylpyruvate into pyruvate can proceed either directly or viaoxaloacetate, although the bacterium appears to use the direct route . Secondly, the conversion of malate to oxaloacetatemay also occur directly or via pyruvate. The 13C flux measurementsindicate that the bacterium uses the indirect route in addition to the directone although, according to the FVA, the indirect route is energetically lessefficient. Interestingly, our model suggests also that the glyoxylate shuntcould be used interchangeably with full TCA-cycle without any penalty on growthyield. However, as the glyoxylate shunt is inactivated in many bacterial speciesvia catabolite repression upon glucose growth P. putida.in silico predictions and13C measurements, there still exist a number of discrepancies.For instance, the 13C-experiments suggest that the bacterium utilizesthe portion of glycolysis between triose-3-phosphate andd-fructose-6-phosphate in the gluconeogenic direction, which is notenergetically optimal and as such is not captured in standard FBA (or FVA)simulations. This illustrates one of the possible pitfalls of FBA, which perdefinition assumes perfect optimality despite the fact that microorganisms mightnot necessarily allocate their resources towards the optimization functionassumed in analysis, and in some cases may not operate optimally at all 13C model vs. iJP815. A thirdgroup of differences revolves around pyruvate and oxaloacetate, whereby thein vivo conversion of malate to oxaloacetate shuttlesthrough a pyruvate intermediate rather than directly converting between the two.The last area where discrepancies exist between in silico and13C data is in the TCA cycle, around which the flux is lower inFVA simulations than in the experiment. This suggests that the insilico energetic requirements for growth  are stilltoo low when compared to in vivo ones, as the main purpose ofthe TCA cycle is energy production.Despite the general agreement between 13C-derivedfluxes fall between FVA intervals for every flux value in the 13Cnetwork. To filter out artifacts, we re-did all FVA computations using thestructure of the network used in the 13C-experiment and found nomajor differences . Gene essentiality was assessed by:(i) identifying for each gene the operability of the reaction(s) dependenton this gene, (ii) removing from the network the reactions renderedinoperative by the deletion of that particular gene, and (iii) determiningthe ability of the model to produce biomass in the same manner as for thereaction essentiality tests. Additionally, we estimated for both carbonsources the smallest possible set of reactions able to sustain insilico growth, in order to estimate the number of reactionsnecessary for biomass synthesis in minimal medium . This setencompasses both all reactions that are essential  and the minimal number of non-essential reactionsthat, together, are able to provide in silico growth , we carried out an owth see. Thesecowth see. This esE. coliThe sets of essential reactions consist of 259 and 274 reactions for glucoseand acetate conditions respectively, constituting 82 and 86 percent of theminimal set. These numbers indicate that most of the crucial metabolicroutes are not duplicated at the level of metabolic network structure. Theset of essential reactions under glucose growth is a subset of that underacetate, suggesting that the growth on glucose is more resistant toperturbations . The reactions belonging exclusively to the acetate minimalset are mostly members of glyconeogenic pathway, with ATP synthase, thereactions constituting the glyoxylate shunt, and acetate transport reactionsbeing the exceptions. The inessentiality of ATP synthase under glucose andessentiality of the glyoxylate shunt under acetate conditions are notsurprising and similar effects have been reported in The reactions belonging to the non-essential part of the minimal set aremostly members of central metabolic pathways , which emphasizes the importance of these pathways for theoperation of the metabolism and is in agreement with observations made inother bacteria in silico essential gene predictions,including 153 and 159 genes under minimal glucose and acetate growthrespectively, in order to determine how gene/pathway redundancy affectsnetwork robustness. These values may seem low when compared to the size ofthe predicted essential reactions sets . However, it must first be noted that eachessential reaction set contains about 25  non gene-associated reactions, and thatelucidating the genes catalyzing these reactions would increasesubstantially the number of in silico essential genes.Further, approximately 20% of each minimal set  consists of essentialreactions that can be catalyzed by two or more isozymes and thus areessential at the metabolic network level but not at the genetic level. Incontrast to non-essential reactions in the minimal set, these reactionsessential at the metabolic network level but not at the genetic level arenot clustered in particular metabolic pathways but are rather spreadthroughout the entire metabolic network. Altogether, these results indicatethat for about 40% of the reactions required to produce biomass,there are alternative at either the genetic or the metabolic network level.The metabolic robustness of an organism may also be provided at the geneticlevel through genes coding for isozymes. Data on gene and reactionessentiality provide insights into this phenomenon. We utilized FBA togenerate a list of This analysis highlights the limitations of possible interventions aimed atreshaping the flux distributions, because these can be applied only toreactions that are not essential . Identification of reactions catalyzedby multiple enzymes shows which reactions may be best avoided when planningmutational strategies as their inactivation may pose additional technicalproblems, by requiring production of multiple knock-outs.To further investigate these conclusions, we determined the flexibility offluxes over particular reactions as a measure of metabolic networkflexibility during biomass production. We found that the variability offluxes is similar under either glucose or acetate growth, but that acetategrowth instills a slightly higher rigidity to the metabolic network (asobserved above). We observed also that the flux of more than a half of thereactions can vary to some degree without influencing biomass output. Wenext analyzed the pathway-distribution of reactions exhibiting variableflux, and found that biosynthetic pathways are in general more rigid  than otherpathways. This rigidity might reflect the essentiality of these pathwaysmodules for the survival of the cell . This comparison was performed onlyfor strains whose knocked-out gene is included in iJP815. Thirty-eight out ofthe 51 strains tested did not grow in silico (insilico but not in vivo), four  are mutated in genes considered non-essential insilico due to “weakly annotated” gene putativelyencoding redundant isozymes. In the case of PP5185 (coding forN-acetylglutamate synthase), its essentiality is removed byPP1346 , which isnot only an isozyme of PP5185 (the N-acetylglutamate synthasefunction) but which also catalyses a reaction (ornithine acetyltransferase) thatproduces N-acetyl-l-glutamate (the product ofN-acetylglutamate synthase) and thus renders the activityof PP5185 redundant. It appears either that this is a mis-annotation or that theenzyme is utilized only under different conditions.Assessment of network models through comparison of n silico .Of the fumC) seems to have two paralogues  coding for isoenzymes of fumarate hydratase, but since the mutant inPP0897 does not grow auxotrophically, they are either non functional ormis-annotated. The enzyme complex that is composed of proteins expressed fromthe genes knocked-out in the two false positives PP4188 and PP 4189 catalyzesthe decarboxylation of α-ketoglutarate to succinyl-CoA in the TCA cycle,concurrently producing succinyl-CoA for anabolic purposes. In the model, thisfunctionality is not needed as this part of the TCA cycle can be circumvented bythe glyoxylate shunt, whereas succinyl-CoA can be produced by reverse operationof succinate-CoA ligase. Restricting this reaction to be irreversible rendersboth genes essential. This altogether suggests that either the succinate-CoAligase is irreversible or the glyoxylate shunt is inactive. The latter solutionis, however, impossible, due to the essentiality of the glyoxylate shunt upongrowth on acetate.In addition, PP0897  are involved in the serinebiosynthesis pathway. We found experimentally that mutants in these genes cangrow on acetate if the medium also contains l-serine. These genes canbe rendered in silico essential by setting glycinehydroxymethyltransferase to operate only unidirectionally from l-serineto glycine. The operation of this enzyme, however, is required for growth of thebacterium on glycine, which is possible; though very slow (results not shown).One of these genes (PP5155) has also a weakly annotated isozyme (PP2335). Wefound out as well that several of the mutants  growin silico on glucose, which we confirmed experimentally(results not shown). Altogether, these experimental results assisted us inimproving the accuracy of the model.The false positive PP4782 is involved in thiamine biosynthesis. This cofactor isnot included in the biomass, which is why the gene is not Albeit limited to a relatively small mutant set, this analysis shows that whileconstraint-based models are not always able to predict exact flux values, theyare very useful in the identification of essential reactions and, through theGPRs, the genes responsible for their catalysis. This enables identification ofvulnerable points in the metabolic network.in silico PHA production would decrease thegrowth. Consequently, in classic optimization-based approaches , noPHA production would be predicted while optimizing for growth yield. The aim wasthus to increase the available pool of the main precursor ofPHAs—Acetyl Coenzyme A (AcCoA). This approach was based on theobservation that inactivation of isocitrate lyase (ICL) enhances the productionof PHAs in P. putida due to increased availability of AcCoAthat is not consumed by ICL To illustrate the utility of a genome-scale model for metabolic engineering, weused iJP815 to predict possible improvements to an industrially relevantprocess; namely, the production of polyhydroxyalkanoates (PHAs) fromnon-alkanoic substrates for biomedical purposes Two main methods were employed to model a cellular pooling of AcCoA. The firstwas the maximization of AcCoA production by pyruvate dehydrogenase (PDH). In thesecond, an auxiliary reaction was introduced that consumed AcCoA  and that would represent thepooling of AcCoA , insets.in silico mutants, we allowed the OptKnockprocedure to block a maximum of two reactions, which corresponds,experimentally, to the creation of a double mutant. To avoid lethal insilico strains, the minimal growth yield was limited to a valueranging between 0.83 and 6.67gDW⋅molC−1,corresponding to about 5 and 40 percent of maximum growth yield, respectively.To create the Six mutational strategies suggested by this approach are presented in pgl/PP1023) and periplasmatic glucose dehydrogenase(gcd/PP1444), would produce 29% more AcCoA thanthe wild type growing on glucose as a carbon source (tpiA/PP4715). As the mutant fortpiA was generated in this work, we tested whether it is ableto grow on the predicted carbon source (d-fructose), but the observedgrowth was very weak . This suggests that growth might be too inhibited by this strategy for itto be of great use.One promising hypothesis (strategy 2) generated by the AcCoA production methodpredicted that a double-mutant devoid of 6-phosphogluconolactonase(n source . As we aprpD/PP2338) andcitrate synthase (gltA/PP4194), and supplying P.putida with valine. Using this strategy, AcCoA pooling couldtheoretically reach 21.9mmol⋅gDW−1⋅h−1,but at a severe expense in bacterial growth (P. putida (One strategy suggested by the AcCoA pooling method (strategy 4) called forknocking out 2-methylcitrate dehydratase  that can be overcome only through extensive studies infunctional genomics.Firstly, the high number of blocked reactions and the mismatches with the BIOLOG datashow that there are still many areas of the metabolism that require thoroughexploration. The genes encoding transport-related are particularly relevant, as formost of them, neither the translocated compound nor the mechanism of translocationis known. Furthermore, it should be highlighted that the genome still has 1635 genesannotated as “hypothetical” or “conservedhypothetical”, more than 800 genes annotated as putative, and over 800 forwhich the functional annotation gives no information beyond the protein family name.It is thus likely that a fraction of the hypothetical and non-specifically annotatedgenes in the current in silico flux spacethrough FBA and FVA and obtained distribution spaces roughly consistent with thoseexperimentally determined via 13C- flux analysis, these approaches areinherently limited as they assume growth as a sole metabolic objective and ignoreany effects not explicitly represented in a constraint-based metabolic model. It hasbeen shown that FBA using objective functions other than growth can improvepredictive accuracy under certain conditions L. plantarum these factors may lead to false predictions.Secondly, although we carefully constrained the in silico flux space is generally larger than the truein vivo flux space of the metabolic network. This, in turn, mayinfluence the robustness of the metabolic network and the essentiality of somereactions and genes. The lack of regulatory information and of the geneticinteractions involved is likely to be one of the causes for faulty predictions ofthe viability of mutant strains. Adding this information will be an important stepin the further development and improvement of the accuracy of the reconstruction.Thirdly, the reconstruction includes causal relationships between genes and reactionsvia gene-protein-relationships (GPRs) but it lacks explicit information regardinggene regulation. The regulation of gene expression causes that there are many genesin the cell that are expressed only under certain growth conditions. Therefore, theFourthly, although our analyses indicated that growth yield is relatively insensitiveto changes in biomass composition, these analyses also suggest that factors otherthan the structure of the metabolic network play an important role in defining therelationship between the growth yield and environmental conditions. The predictionof the exact growth yield requires the precise measurement of maintenance values,which may vary substantially from one condition to the other P. putida provides agood opportunity for incorporating kinetic information into a genome-scale model asthere are various kinetic models available and under development for small circuitsin P. putidaTo enhance the usefulness and predictiveness of the model, several avenues could befollowed in the future. Firstly, additional constraints can be overlaid on thenetwork to reduce the space of possibilities and increase the accuracy ofpredictions. In addition to specific knowledge of particular enzymatic or transportprocesses, such constraints are best based on high-throughput experimental evidencesuch as transcriptomic and proteomic data, which are instrumental in expandinggenotype-phenotype relationships in the context of genome-scale metabolic modelsP.putida community , focus willbe put on these low-knowledge areas for future experimental endeavors. We anticipatethat this model will be of valuable assistance to those efforts.Experimental validation of a genome-scale model is an iterative process that isperformed continuously as a model is refined and improved through novel informationand validation rounds. In this work, we have globally validated iJP815 as well asspecific parts thereof by using both up-to-date publicly available data and datagenerated in our lab, but there will be always parts of the model that includeblocked reactions and pathways that will require further, specific validation. Asmore knowledge becomes available from the joint efforts of the large in silico analysis ofpolyhydroxyalkanoate production, we show how central metabolic precursors of acompound of interest not directly coupled to the organism's growth functionmight be increased via modification of global flux patterns. Furthermore, as thespecies Pseudomonas putida encompasses strains with a wide range ofmetabolic features and numerous isolates with unique phenotypes, the reconstructionpresented provides a basic scaffold upon which future models of other P.putida strains can be built with the addition or subtraction ofstrain-specific metabolic pathways. Due to its applicability across the numerousP. putida strains iJP815 provides a sound basis for many futurestudies towards the elucidation of habitat-specific features, bioremediationapplications and metabolic engineering strategies with members of this ubiquitous,metabolically versatile and fascinating genus.The metabolic reconstruction, the subsequent mathematical computation and theexperimental validation reported here provide a sound framework to explore themetabolic capabilities of this versatile bacterium, thereby yielding valuableinsights into the genotype-phenotype relationships governing its metabolism andcontributing to our ability to exploit the biotechnological potential ofpseudomonads. By providing the means to examine all aspects of metabolism, aniterative modeling process can generate logical hypotheses and identify conditions thatwould reconcile disagreements between experimental observations and simulationresults. Through a detailed P. putida model we present was built using aconstraint-based (CB) approach. A constraint-based model consists of a genomewide stoichiometric reconstruction of metabolism and a set of constraints on thefluxes of reactions in the system The In addition to the reactions, the model includes a set of genes tied via Booleanlogic to reactions that their protein products catalyze, which allows foraccurate discrimination of the effects of genetic perturbations such asknockouts The second part of the CB-model, namely the constraints, constitutes a set ofrules that narrow down the interval within which the flux of particular reactionmust lie. These constraints rest upon physico-biological knowledge. One of them,the information regarding reaction directionality, has already been mentionedabove. Another constraint that is widely applied in biological systems is thePseudo-Steady-State Assumption (PSSA) S is the stoichiometric matrix containing reaction stoichiometryinformation, v is a vector of all reaction fluxes in the system, vmin and vmax represent minimum and maximum constraints on reactionfluxes, respectively, and Tc is a vector containing coefficients for each flux that is to bemaximized  is a primary method for analysis ofconstraint-based models. Generally, a constraint based model of metabolismrepresents an underdetermined system, i.e., one in which a range of fluxdistributions are mathematically possible. FBA narrows the fluxpossibilities by determining a point in closed flux space that maximizes acertain linear combination of fluxes. FBA optimization yields an optimal value for the objective along with a fluxvalue for every reaction belonging to the metabolic network. Commonly, FBAis used to predict maximal growth or metabolite production yields. Cellgrowth is simulated by the flux over a special ‘Biomass’reaction that consumes precursors of cellular components  and produces a virtual unit of cell biomass.Maximization of this flux is usually set as the FBA objective. Thisprocedure assumes that organisms have been shaped by the evolution towardsgrowth maximization, an assumption that has been validated under a varietyof conditions Metabolic networks of living organisms are usually considerablyunderdetermined It is often the case that cells do not operate perfectly optimally when FBAsimulations are compared to real data. Therefore, a variant of the FVAapproach called suboptimal FVA OptKnock is an approach for identification of mutations that selectively increaseproduction of a certain compound of interest, assuming that the mutant wouldoptimize for the same quantity as the wild type  In order to enable the choice of the carbon source(s) the original OptKnockprocedure was modified as follows:A virtual reaction, with limited flux, was created that sourced thevirtual compound “vcarbon”“vcarbon” into therespective carbon source was added to the model. The stoichiometryof this virtual reaction corresponded to the number of carbon atomsin the carbon source, e.g.:For each carbon source a virtual irreversible reaction that convertedthe compound vcarbon → d-glucose.6 jv) a binaryvariable (jz) defining its activity wascreated and following constraint was added to the model:jv ≤jvmax·jz,where the jvmax was set tovalue high enough, so that the whole “vcarbon”could be consumed by each reaction.For each of those reactions  approach, by modifying original FBA LP problem. For every non-blocked andnon-essential reaction a binary variable was added that reflects the activity ofthe reaction. When the binary variable takes value of 1 the correspondingreaction is virtually unlimited .When the variable is set to 0 the corresponding reaction is blocked (non-zeroflux is impossible). This was achieved by adding a following set of equations tothe original LP problem:Pseudomonas putida KT2440 were various biologicaldatabases. Most of the information came from the Kyoto Encyclopedia of Genes andGenomes (KEGG) P.putida contained in these two databases is mainly based on thepublished genome annotation of the bacterium P. putida was collected from KEGG and PGD. Reactionssupported by sufficient evidence and with specific enough functional annotationswere incorporated into the model. For every accepted reaction its reversibilitywas assessed basing on assignments in KEGG pathways as well as information fromBRENDA database. For reactions with inconsistent assignments a decision aboutreversibility was made basing on analysis of the reaction as well as itsreversibility in other organisms. Hereby, a first version of the metabolic modelwas created (iJP815pre1).The main sources of information regarding the composition of the metabolicnetwork of in silico on glucose was tested. Successful insilico growth indicates that every chemical compound belonging tothe biomass equation can be synthesized from present sources, using thereactions contained in the model. Since the exact cellular composition ofP. putida is not known, the composition of E.coli biomass was used as an approximation. This test was performed byrunning FBA with production of each biomass constituent set as the objective. Ifa compound could not be synthesized, the gaps in the pathway leading to it wereidentified manually and a search was performed for reactions that could fill thegaps. If this approach was unsuccessful, gaps were filled with reactions fromthe E. coli model. This yielded the second version of thereconstruction (iJP815pre2).The next step involved assessing whether the reconstructed metabolic network isable to produce energy from glucose. This was achieved by running FBA with ATPproduction set as the objective function. Subsequently, the ability of the modelto grow in silico simulations for growthon those compounds. It was assumed that the ability to grow insilico on the particular compound as the sole carbon sourceapproximates the in vivo utilization. For those compounds thatdid not show in silico growth, a literature search wasperformed in order to identify possible pathways of utilization. The results ofthis search, in the form of reactions and GPRs, were added to the model. Theoutcome was the final version of the model (iJP815).The third round of reconstruction consisted of two sub-steps. First, thecompounds for which transport proteins exist were identified and appropriatereactions added. Second, the results of BIOLOG carbon-source utilizationexperiments were compared with Growth yields on sources of basic elements  were compared withexperimental values obtained by Duetz et al. http://www.lifewizz.com). The optimizations were computed by free, open source, solvers from the COIN-OR family or by the lp_solve ver. 5.5 (http://lpsolve.sourceforge.net/5.5/) software package. Allcomputations were performed on a Personal Computer with a Intel Core 2 2.40 GHzCPU and 2GB of RAM.The model was created and maintained using ToBiN  or SOC-medium  or minimal medium 2SO4 – 20 g,CaCl2 – 0.01 g, FeSO4×7H2O– 0.01 g, H2Odist ad 1000 ml; the potassiumand sodium salts were dissolved separately and subsequently mixed with otherdissolved salts; pH was set to 7.0 by adding 10 mM NaOH) with differentcompounds as the sole carbon source.seudomonas putida KT2440 was tested for its ability toutilize various carbon sources using BIOLOG GN2 Microplates PIf not stated differently, cells were grown on agar plates overnight in30°C.P. putida were created using an invitro transposition system  5-transposase and Tn5-Transposome that, in theabsence of magnesium ions, builds a stable synaptic complex, which can betransmitted into the cell via electroporation. To render Pseudomonasputida KT2440 electrocompetent, cells were grown in 50 ml ofEM-medium to OD600 of 0.6 to 1.0 and subsequently cooled on icefor 15 minutes. The cells were centrifuged  and washedtwice with H2Odist. The cells were washed twice in 0.3M cold solution of sucrose and resuspended in 0.5 to 1.0 ml of 0.3 M sucrosesolution. The electrocompetent cell were used for transformation byelectroporation with Gene Pulser  using the EZ:TN<Kan-2> Tnp Transposome. 20–40 µl of cellswas mixed with 1–2 µl of DNA in ice-cooled cuvette. Theelectroporation setting were 25 µF, 200 Ω, and 1.7 or 2.5for the gap size 0.1 and 0.2 cm, respectively. After two hours of incubationin SOC-medium, transformants were selected on EM agar plates with 60µg/ml of kanamycin. Selection of auxotrophic mutants was performedon minimal medium with acetate as the sole carbon source, by replica-platingP. putida KT2440::Tn5(Kanr) strains on theminimal and EM media.The mutants of P. putida KT2440::Tn5(Kanr)mutants were genotyped by enrichment of either flanking sequences oftransposon insertions using PCR 5′-GCAATGTAACATCAGAGATTTTGAG-3′)primer complementary to the end of Tn5-element and the arbitrary primer ARB1(5′-GGCCACGCGTCGACTAGTACNNNNNNNNNNGATAT-3′)were used. A 1 µl of supernatant from a P. putidaKT2440 lysate was used as the DNA-template. The PCR-reaction was performedin following mixture  under followingconditions: (i) 5 m at 95°C, (ii) 30×, (iii)30×. In the second round of amplification a 5µl of product of the first PCR-reaction was used as theDNA-template, together with the primers TnINT Rev (5′-GAGACACAATTCATCGATGGTTAGTG-3′) andARB-2 (5′-GGCCACGCGTCGACTAGTAC-3′). Thereaction conditions were following: 30×. ThePCR-products were purified with “QIAquick- spin PCR PurificationKit”  according tomanufacturer's instructions. Subsequently, the sequencing procedurewas performed. 200–500 µg of dsDNA in normal sequencingvectors  with 10 pmol of primer (TnINT Rev) and 6µl of “Big Dye Terminator v. 2.0 Ready ReactionMix” were mixed in total volume of 10 µl. The conditionsof the reaction were following: 25×. After the cyclesequencing the remaining dNTP were removed using “Dye Ex SpinKit”  according tomanufacturer's instructions. To the purified product 50µl sterile MiliQ-H2O was added and the DNA wasprecipitated wit 250 µl Ethanol (100% v/v) for 30 minat 16000×g in the room temperature. The supernatant was removedand the pellet washed with 250 µl of ethanol (100%v/v), precipitated again by centrifugation and dried in vacuum-centrifuge. All the DNA-pellets were stored in−20°C in 20 µl Hi-Di Formamide (PE Biosystems)until sequencing. The sequencing was performed with ABI PRISM 377 sequencerP. putida KT2440 genome sequence.The auxotrophic Figure S1Influence of biomass composition on the growth yield. Each bar represents abiomass with the fraction of one compound modified.(0.18 MB TIF)Click here for additional data file.Figure S2DW−1⋅h−1(B) influence when the glucose is supplied with rate 10mmol⋅gDW−1⋅h−1.Influence of maintenance values on the growth yield. (A) influence when theglucose is supplied with the rate of 2.2mmol⋅g(1.07 MB TIF)Click here for additional data file.Figure S313C measurements is used.Predictions of the fluxes in the central metabolism when the networkstructure assumed by the authors of the (1.97 MB TIF)Click here for additional data file.Figure S4Influence of biomass composition on the prediction of internal fluxes. (A)results obtained from Optimal FVA (B) results obtained from suboptimal FVA.(0.63 MB TIF)Click here for additional data file.Figure S5Analysis of variability of particular reactions. Comparison of sizes ofparticular variability groups in various conditions.(0.29 MB TIF)Click here for additional data file.Figure S6Flux Coupling Finder, comparison of numbers of coupled reaction sets withrespect to their size.(0.67 MB TIF)Click here for additional data file.Table S1Comparison of metabolic reconstruction created up to date(0.07 MB DOC)Click here for additional data file.Table S2BIOLOG assay details(0.02 MB XLS)Click here for additional data file.Table S3Distribution of variable reactions among pathways(0.05 MB DOC)Click here for additional data file.Table S4In silico growth results of the mutant strains(0.05 MB DOC)Click here for additional data file.Table S5Assembly of various properties of the reactions belonging to iJP815(0.36 MB XLS)Click here for additional data file.Text S1Supplementary methods(0.11 MB DOC)Click here for additional data file.Text S2Supplementary results(0.05 MB DOC)Click here for additional data file.Text S3Publications that contributed to the iJP815 reconstruction process(0.02 MB DOC)Click here for additional data file.


Starting with this set we subsequently extract a minimal set of fluxes that must actively be forced through genetic manipulations  to ensure that all fluxes in the network are consistent with the overproduction objective. We demonstrate our OptForce framework for succinate production in Escherichia coli using the most recent in silico E. coli model, iAF1260. The method not only recapitulates existing engineering strategies but also reveals non-intuitive ones that boost succinate production by performing coordinated changes on pathways distant from the last steps of succinate synthesis.Computational procedures for predicting metabolic interventions leading to the overproduction of biochemicals in microbial strains are widely in use. However, these methods rely on surrogate biological objectives  and do not make use of flux measurements often available for the wild-type strain. In this work, we introduce the OptForce procedure that identifies all possible engineering interventions by classifying reactions in the metabolic model depending upon whether their flux values must increase, decrease or become equal to zero to meet a pre-specified overproduction target. We hierarchically apply this classification rule for pairs, triples, quadruples, etc. of reactions. This leads to the identification of a sufficient and non-redundant set of fluxes that  Escherichia coli. The results described in this paper not only uncover existing strain designs for succinate production but also elucidate new ones that can be experimentally explored.Over the past few years, there has been an unprecedented increase in the use of microorganisms for the production of biofuels, industrial chemicals and pharmaceutical precursors. In this regard, biotechnologists are confronted with the challenge to efficiently convert biomass and other renewable resources into useful biochemicals. With the advent of organism-specific mathematical models of metabolism, scientists have used computations to identify genetic modifications that maximize the yield of a desired product. In this paper, we introduce OptForce, an algorithm that identifies all possible metabolic interventions that lead to the overproduction of a biochemical of interest. Unlike existing techniques, OptForce does not rely on the maximization of a fitness function to predict metabolic fluxes. Instead, OptForce contrasts the metabolic flux patterns observed in an initial strain and a strain overproducing the chemical at the target yield. The essence of this procedure is the identification of all coordinated reaction modifications that force the network towards the overproduction target. We used OptForce to predict metabolic interventions for succinate overproduction in  An overarching challenge for metabolic engineers is to optimize the conversion of biomass and other renewable resources into useful metabolic products through fermentation and other biological conversions E. coli. So far, computational strain design procedures have been applied for a variety of metabolic engineering projects including the overproduction of lactic acid E. coliSaccharomyces cerevisiaeGeobacter sulfurreducensFlux balance analysis (FBA) has emerged as an important framework The use of computational tools operating on metabolic reconstructions to identify strain modifications is becoming commonplace. Nevertheless, a number of shortcomings plague all existing approaches. All are sequential in nature generating a single engineering strategy per run thus requiring multiple restarts to generate a set of candidate list of alternatives  that is dwarfed by the myriads of engineering possibilities afforded by genome-scale models spanning thousands of reactions. Furthermore, in the absence of kinetic descriptions OptKnock and other methods rely on the maximization of surrogate biological fitness functions (e.g. maximization of biomass yield target) or multiple desired overproduction targets  must depart away from the range of values allowed to span in the wild-type strain in response to an overproduction target. This maximal range of flux variability for the wild-type strain can be elucidated by iteratively maximizing and minimizing each flux Contrasting the flux ranges for the (wild-type) metabolic network against the ones consistent with the overproduction target(s) provides the cornerstone of OptForce. U whereas the ones that must decrease (see L. Fluxes of reactions with overlapping ranges (see either one or the other reaction flux (but not necessarily both) must increase  encompass all the necessary reaction flux changes that MUST take place in the wild-type metabolic network for the desired overproduction. Appendix B in We refer to reaction fluxes that must increase see  in the fease see  as MUSTLnges see  between nges see . Non-oveincrease  or decreincrease  in valueorks see . As befoThe next step of OptForce is to identify how the collective set of changes (encoded within the MUST sets) can be imparted on the wild-type metabolic network with the minimal number of direct interventions . The identified MUST sets encode Boolean choices regarding which fluxes (or combinations thereof) must change in value. Upon the incorporation of these constraints, an optimization formulation is proposed  gene to the iAF1260 model of E. coli. Note that the abbreviations and directionalities of reactions adhere to the iAF1260 metabolic model definitions.In this section, we benchmark the OptForce framework by identifying metabolic interventions that lead to the overproduction of succinate using the latest genome-scale metabolic model for U and MUSTL sets of reactions whose fluxes must depart the original ranges. Note that because all members of set MUSTL involve fluxes set to zero we re-designate them as MUSTX to signify that they all correspond to reaction eliminations. Not surprisingly, the transport reaction directing succinate out of the cytosol (SUCCt3rpp) was classified into the MUSTU whereas transport reactions for competing by-products such as ethanol , acetate (ACtex), formate (FORtex) and acetaldehyde  were completely blocked . In addition, a number of reactions from hisitidine  and methionine metabolism  were also set to zero. Note that these reactions are essential for amino acid biosynthesis and are fully coupled to growth. Therefore, the drain of carbon flux from the pentose phosphate pathway towards histidine and methionine synthesis is prevented thus halting the production of biomass.U and MUSTL involve primarily intuitive negations of by-products formation, sets MUSTUU, MUSTUL and MUSTLL allude to more complex flux re-allocations (see UU set the increase in the flux for reaction phosphoenolpyruvate carboxylase (PPC) can only be compensated by the simultaneous increase in the flux of five TCA cycle reactions . This implies that at least one of two possible avenues for succinate production must be increased under anaerobic conditions (see E. coli by deactivating the iclR repressor (to activate the glyoxylate bypass) under anaerobic conditions by While results for MUSTions see . For exaions see . SpecifiUU, MUSTUL and MUSTLL into a single graph , down-regulations (MUSTLLL) or combinations thereof (MUSTUUL and MUSTULL). ackA and pta in strain SBS990MG constructed for succinate synthesis LLL, MUSTUUU, MUSTUUL and MUSTULL can also be distilled into a minimal set of modifications . This suggested that additional reactions that participate in higher-order (unexplored) MUST sets were required to guarantee the target yield for succinate. Upon allowing reactions absent from the MUST sets to become members of the FORCE set the imposed target for succinate production was met. The identified minimal set of forced modifications  belonging to competing pathways. The ethanol transport reactions (ALCD2x and ETOHt2rpp) do not have to be completely eliminated but rather lowered in value to 3 mmol/gDW.hr from a wild-type flux value of 19 mmol/gDW.hr.Despite the differences in the MUST sets between cases 1 and 2 the corresponding FORCE sets of reactions were identical. Up-regulations for PPC, CS, MALS, ICL and ACONTa and down regulations for reactions along the pathways leading to competing by-products were required for the 98% succinate yield case. Even though the membership of the FORCE set is the same the corresponding required levels of up or down-regulation are slightly different. E. coli from Lactococcus lactisRhizobium etliPyruvate carboxylase (PYC) has been overexpressed in U set whereas the transport reaction for acetaldehyde is classified as MUSTL. The required increase in the flux for ATP is due to the ATP consuming pyruvate carboxylase. Unlike cases 1 and 2, the synthesis route for by-products (formate and acetyl-CoA) consuming pyruvate through the pyruvate formate lyase (PFL), alcohol dehydrogenase (ALCD2x) and formate dehydrogenase (FDH5pp) reactions are completely shut off to afford a complete conversion of pyruvate to OAA. This suggests that the presence of PYC provides an alternative route to PPC whereby OAA can be replenished either by increasing the flux through PPC or PYC. This is in agreement with the experimental findings by Ka-Yiu San and coworkers The FORCE set of engineering interventions for this scenario is contrasted against cases 1 and 2 and is shown in E. coli reveal that the needed interventions results remain the same upon requiring the production of a small amount of biomass but change significantly upon the addition of a key reaction to the model.In this paper, an optimization-based methodology called OptForce was introduced for predicting all possible metabolic modifications that could guarantee, subject to the model stoichiometry and conditions, a pre-specified overproduction level of a desired biochemical. The results for succinate overproduction in Sorghum vulgare and Actinobacillus succinogenes in E. coli not only increases the yield of succinate but also reduces the secretion of acetate E. coli mutant NZN111 by decreasing the activity for pyruvate formate lyase (PFL) and lactate dehydrogenase et al.adhE and ackA-pta coding for acetaldehyde dehydrogenase (ACALD) reduces the formation of by-products ethanol, acetate and acetaldehyde as suggested by OptForce.Many of the suggested interventions recapitulate existing strain redesign strategies for succinate synthesis. For example, experimental evidence suggests that the overexpression of PPC from citZ gene from Bacillus subtillis that encodes citrate synthase increased the activity through the TCA cycle towards isocitrate and 2-ketoglutarate E. coli strain SBS550MG, an increase in the yield of succinate was not observed The up-regulation of citrate synthase (CS), aconitase (ACONTa/b) and reactions from the glycolytic pathway (PGK and TPI) are engineering strategies suggested by OptForce that to the best of our knowledge have not yet been implemented for succinate production. Heterologous overexpression of the The genetic interventions predicted by OptForce underscore the importance of up-regulating key fluxes along the succinate pathway in addition to the knockouts for by-products. Existing strain optimization procedures . The incorporation of metabolic flux information about the wild-type network allows for a sharper elucidation of engineering interventions. The engineering interventions predicted by OptForce depend on the available flux measurements for the initial strain. OptForce can be modified to predict globally valid metabolic interventions by utilizing biological objectives (i.e. maximization of biomass) when sufficient metabolic flux data are not available. Furthermore, the procedure can hierarchically be applied at intermediate stages of a metabolic engineering project by re-calculating the set of engineering interventions as new flux data for (multiple) mutant strains become available. The restriction of minimality in the calculated FORCE set can be relaxed allowing for the exploration of less parsimonious engineering interventions. For example, we studied the case for identifying additional interventions after retaining the best eight out of the ten interventions originally identified by the OptForce method (for cases 1 and 2). However, we found that even after allowing seven additional interventions (i.e. K = 15), the resulting FORCE set was not sufficient to increase the yield to more than 80% of the theoretical maximum. In addition, reactions that cannot  be directly manipulated can be excluded from consideration during the derivation of the FORCE set. It is to be noted that the OptForce procedure provides targets for genetic manipulations at the metabolic flux level. The lack of a completely quantitative mapping between gene expression and flux levels implies that multiple rounds of experimental strain modifications may be needed to translate the FORCE set of reaction fluxes to the required gene expression levels. An algorithmic implementation of the procedure is available as supplementary material (see supporting information - Text S1Appendix A: Computing flux variability for the wild-type and overproducing networks(0.09 MB DOC)Click here for additional data file.Text S2Appendix B: Bilevel formulation for the identification of MUST sets(0.05 MB DOC)Click here for additional data file.Text S3Appendix C: Bilevel formulation for the identifying the FORCE set(0.07 MB DOC)Click here for additional data file.Text S4Results for MUST considered four-at-a-time (quadruples)(0.12 MB DOC)Click here for additional data file.Text S5Prototype Implementation for the OptForce Algorithm(0.06 MB DOC)Click here for additional data file.Figure S1Minimal set of network modifications for reaction quadruples.(2.08 MB TIF)Click here for additional data file.Figure S2U and MUSTL sets. Figure S2b and S2c shows the network of interacting reactions and the minimal set of network modification for the doubles and triples, respectively, identified for case 2.MUST set of reactions for 98% yield of succinate. Figure S2a shows the list of reactions in the MUST(3.34 MB TIF)Click here for additional data file.


When analyzing complex biological systems, a major objective is localization of function – assessing how much each element contributes to the execution of specific tasks. To establish causal relationships, knockout and perturbation studies are commonly executed. The vast majority of studies perturb a single element at a time, yet one may hypothesize that in non-trivial biological systems single-perturbations will fail to reveal the functional organization of the system, owing to interactions and redundancies.in-silico model of Saccharomyces cerevisiae metabolism. We find that single-perturbations analysis misses at least 33% of the genes that contribute significantly to the growth potential of this organism, though the essential genes it does find are responsible for most of the growth potential. But when assigning gene contributions for individual metabolic functions, the picture arising from single-perturbations is severely lacking and a multiple-perturbations approach turns out to be essential.We address this fundamental gap between theory and practice by quantifying how misleading the picture arising from classical single-perturbation analysis is, compared with the full multiple-perturbations picture. To this end we use a combination of a novel approach for quantitative, rigorous multiple-knockouts analysis based on the Shapley value from game theory, with an established The multiple-perturbations investigation yields a significantly richer and more biologically plausible functional annotation of the genes comprising the metabolic network of the yeast. A central objective of the analysis of complex systems is localization of function, that is, determining which task is executed by each element or, more precisely, assessing how much each element contributes to the execution of specific tasks. For example, one can ask, for a given cell, which gene-products are responsible for energy metabolism, and which are involved in cell cycle and cell fate decisions. Many of the analysis techniques that are aimed at identifying the functional role of elements in biological systems, such as gene expression microarrays, are based on studying correlations in the data. However, establishing causal relationships in the data is not possible using purely correlational measures ,2 withouin-silico multiple-knockouts study of the robustness of the yeast's metabolic network [in-silico studies on the robustness against double and multiple knockouts  does, lesion it and observe the functional consequences. A classical example is studying the effects of systematic deletions of genes on an organism's viability, with the resulting causal categorization of essential genes -6. These network , 74% of s e.g., ,9)..in-silicSuch considerations and findings suggest that understanding even moderately-complex biological systems requires the use of multiple concurrent perturbations. On the other hand, the vast majority of gene knockout studies employ only single knockouts. How detrimental is this gap? To what extent can we rely on the large body of observations that have been made using single knockout studies in biology?synthetic lethal) or damaging. In fact, a large scale experiment looking for such gene pairs in S. cerevisiae [Helicobacter pylori metabolic genes using in-silico models [The first obvious step toward addressing this question lies in double knockout perturbations. As the simplest conceivable genetic interaction is that of full overlap or redundancy , one can set out to experimentally test the phenotype of all double concurrent perturbations, in search of gene pairs whose deletion is lethal , a multin-silico model of the metabolism of S. cerevisiae, and enumerated synthetic lethal pairs and larger lethal groups termed essential sets. In this paper, we start by estimating the extent of multiple-lethality phenomena in S. cerevisiae using the same model, in a manner analogous to the experimental results cited. While useful in its own sake, we will see that this brute force approach leads to serious technical and conceptual scaling problems. Tackling these difficulties, we utilize a novel approach for quantitative rigorous multiple-knockouts analysis, the Multiple-perturbations Shapley value Analysis , a methodology introduced at [Travelling down this path of thought, the next obvious step is to experimentally test triple knockouts, and then quadruple and more. As these experiments are difficult and costly, the key question is whether these multiple-knockouts data will enhance our understanding of the system, and if so – to what extent. In a previous work , we haveduced at . This meduced at -17.The MSA utilizes perturbation (or knockout) experiments for assigning each element of a system a numerical contribution score  to a specific given task. Given such contributions we can address questions regarding the functional role of elements, the identification of submodules in the system, the quantification of localization/distribution of specific tasks, etc. The MSA is the first method providing a unique, axiomatically correct and scalable attribution of contributions to the system's elements, in the context of multiple-perturbations experiments. It was previously applied to brain networks, genetic networks and artificial neurocontrollers -20. Usinin-silico constraint-based modelling approach of [Our first jab at the question of the necessity of multiple perturbations is an obvious one. We wish to estimate the extent of multiple-lethality phenomena in similar lines to the experiments of Tong et al. , that syroach of .in-silico Flux Balance Analysis (FBA) model of [S. cerevisiae under single knockouts of all genes included in the model, finding 101 essential genes comprising 16% of the 619 genes involved in the metabolic network modelled (see Methods). Limited only by computing power, we have proceeded to measure the viability of the yeast in the model under all double knockouts of non-essential genes, and under random samples of triple and quadruple knockouts. Figure We have used the model of  to prediNote the good agreement of the model statistics with the experimental data for the single and double knockouts: For knockout depths 1 and 2, the predicted lethal frequencies are 13% and 28%, respectively, lower than the empirical frequencies, a fairly small bias that might stem from the inherent optimism of the FBA predictions. Similarly, the statistics of three and four concurrent knockout experiments probably bound the expected true experimental frequencies from below, and probably not tightly so.increasing number of lethal interactions that we should aim to find. On the other hand, their frequency among all potential gene combinations is decreasing, because the number of such potential combinations grows even faster. Thus, even the switch to in-silico simulations, while accelerating the process over in-vivo experiments by many orders of magnitude, cannot provide a brute force complete answer to the multiple-perturbations problem. The second problem is a conceptual issue. Given the results of Figure Both experimental and model data suggest that some important knowledge can be mined only from the multiple-perturbations experiments. Unfortunately, Figure More specifically, as we use more concurrent perturbations two main problems potentially hinder the execution of the multiple-perturbations analysis: (a) without prior knowledge about the groups of elements involved in important interactions, the analysis requires the collection of an exponentially large (in the number of elements) set of costly multiple-knockouts experiments; and (b) it necessitates an accepted definition of importance for the analysis of the resulting large data set. In the following, we utilize the Multiple-perturbations Shapley value Analysis (MSA) method (see Methods) to overcome these issues.Applying multiple concurrent perturbations to the metabolic network, we utilize MSA to assess the increase in information gained in the process. MSA, explained in more detail under Methods below, tackles the problem of quantifying the relative contributions of system elements  to a given task. The contribution is computed by measuring the effect of removing an element  not only in the fully functional system – as is done in classic single knockouts, but also after already removing one or more other elements. Thus, interactions between elements can be revealed. This basic idea was already employed, e.g., to identify synthetic lethal gene pairs  – but MSin-silico measure of the potential of growth of the organism.Initially, we use the classic biomass production as the objective function in the FBA modelling. The biomass production target has proved successful in predicting experimental results in wild-type strains and mutants in several organisms -26. It iS. cerevisiae model, for the task of maximal growth. The distribution spans several orders of magnitude, which is to be expected: in accordance with the intuitive notion of importance discussed in the Introduction, the MSA attaches only small contribution values to redundant elements, as their contribution is marginal as long as the element buffering their function is intact. Importantly, however, it does attach non-zero contributions to them, in contrast to what might be expected from single knockout studies.Figure To compare the picture of function localization arising from a single perturbations analysis with that of the full MSA, we track 3 measures: (a) The number of genes involved in the task . Yet, this analysis completely misses a large number (one third) of functionally relevant elements whose contribution, though small, is non-negligible and depends on the status of other elements. In the individual metabolic subtasks, the picture portrayed by single-perturbations analysis is significantly lacking, and in some of these subtasks the single perturbation analysis reveals only 20% of the contributing genes, which together account for only 40% of the total CV mass. The general growth task hence appears simpler than many of the subtasks producing biomass constituents. This is likely because it is a logical AND combination of the subtasks . This translates to an abundance of lethal elements in the general growth task, leaving relatively little mass (in the contribution sense) to the intricate interactions and nonlethal elements.in-silico the experimental paradigm recently introduced in-vivo, of performing a set of multiple knockouts  and assessing the amount of lethal interactions that is uncovered. Remarkably, the model's results for the single and double knockouts concord fairly well with the in-vivo results. The triple and quadruple model experiments confirm the trends observed in the lower-dimensional interactions – that is, as the dimension (size) of the interaction increases, the frequency of lethal interactions decreases and their absolute number increases by about an order of magnitude. However, we find that this approach cannot be extended in practice, even by using in-silico models, because of two main reasons: First, it is computationally intractable, and second, and perhaps more important, it is not clear how the results obtained can actually be transcribed to measures of system size or complexity, or to yield a more useful functional gene annotation. We hence turn to a more rigorous, systematic approach. Using the MSA to quantitatively identify the significant genes and their contribution to the different metabolic tasks, we are able to characterize the functional profile of the genes in the system in both the single and multiple knockouts cases. Indeed, the multiple-knockouts analysis is shown to give a description which is both richer and conforms better with basic biological knowledge than the single knockout analysis.We began our investigation by mimicking 5 perturbation experiments already gives a fairly accurate function localization picture for some tasks, in a system with 600 elements. Depending on the complexity of the analyzed system, knockout depths from k = 4 and up to k = 10 are needed. Given that current in-vivo experimental studies already perform tens of thousands of single perturbations [in-vivo multiple-perturbations analysis of large metabolic pathways, and perhaps even whole cellular systems, will become feasible in the foreseeable future.In our multiple-knockouts study of the yeast metabolism, a batch of 10One should note that the genes that require multiple knockouts to unravel their functional contributions are not of marginal importance and are of considerable biological significance, as already shown in previous studies:  have proSummarizing our findings, this paper shows two fundamental results. First, in response to our basic research question, we show, for the yeast's metabolic network, that the conventionally used single knockout analysis provides only a very partial picture of function localization. Second, we show that the current experimental paradigm for probing the system's higher-order lethal interactions is both practically and conceptually limited. In turn, we demonstrate the essential value of a rigorous multiple-knockouts analysis method for accurately estimating the network's effective significant size. Moreover, the identification of the significant elements might even guide the experimental search for lethal interactions in the future, and make it more efficient. The current study of functional genomics in biological systems is just the beginning of an important endeavor, and much remains to be done. Furthermore, the multi-perturbation approach presented here is not necessarily limited to perturbations at the gene level. One potentially important extension is to the study of complex, combinatorial gene regulation programs, to elucidate the relative role of the different transcriptions factors and their binding sites on a given gene promoter. First steps in this direction have been recently taken by . OverallS. cerevisiae [in-silico models [N metabolic reactions involving M metabolites in an M × N matrix S. It then solves the following linear programming problem:Genome sequencing and annotation have enabled the reconstruction of genome-scale metabolic networks. We use constraint-based models of revisiae . These mrevisiae ,32 is a o models ,24, inclo models ,28,33,34v is the (unknown) vector of fluxes through the reactions. The constraints enforce a steady-state mass balance, and additional lower and upper bounds  are placed on some of the fluxes to enforce all irreversible reactions to have flux in the correct direction, limit environmentally available nutrients etc. At least one vi flux must be bounded from above in order to avoid diverging solutions, and because this is biologically meaningful, for example, due to limitation of substrate uptake. The constant vector c determines the optimization target. Here, we use different objective functions to enable the measurement of different functions or tasks, i.e., different aspects of metabolism. Specifically, we consider optimal production of biomass, and optimal production of particular biomass constituents. For the optimal biomass production in the yeast's case, FBA seeks the maximal production of a linear combination of biomass constituents, including 20 amino acids, 9 nucleotides, 8 lipids, phospholipids, fatty acids and sterols, and 4 carbohydrates, and sulfate (which is available from the environment). The weights for the linear combination were determined in [where mined in . We had n elements (genes) you can end up with 2n numbers. Even restriction to double perturbations solely yields ~n2 results. This data set must be concisely summarized to be of any use. A basic summary should give each gene a contribution score, quantifying its importance to the successful performance of the task. This process can be repeated for different tasks, yielding a soft annotation vector for each gene, across the tasks, denoting to which tasks does it contribute in a significant manner. Another important consideration in looking for such a one-dimensional summary is scalability -these contribution values (CV) should be computable given a very partial data set, as the entire set of 2n experiments can hardly ever be accomplished in reality. The MSA [Assume you can measure the system's performance at some task , and that you can introduce multiple perturbations to the system before measuring performance. This is the essence of knockout studies . Obviously, for a system of  The MSA  addresseN = {1, ..., n} elements, performing a defined task. Suppose we measure the performance of the system at this task under all possible multiple perturbations, i.e., we have a performance score v(S), for every subset S ⊆ N designating the unperturbed elements. Let the marginal contribution of element i to a group S, with i ∉ S, beTo understand the MSA, examine a system of i ∈ N as defined by the Shapley Value [The contribution of element ey Value   is the set of elements preceding i in the ordering R. The Shapley value is the unique fair division of the total performance gap v(N) - v(∅) among the different elements [where elements , i.e.v(S) can represent the performance after some transformations. For example, if one assumes a multiplicative effects model, it is reasonable to use a logarithm transform . While k perturbations contribution value (kp-CV), which is a generalization of the CV concept, defined asImportant to our work is the concept of R(i) is the position of element i in the permutation R, i.e. i is in one of the last k positions. For k = n this reduces to the contribution value, while for k = 1 it is the result of the single-perturbation measurements. The kp-CV has a simple intuitive meaning; it measures the importance of elements when only k-limited knockout experiments  are applied to the system. The kp-CV, computed with k = 1 enables one to assign contribution values to the elements and quantify their importance even using single-perturbations solely.where 5 – 106 perturbation experiments to estimate the contributions of the genes, obtaining very small estimation errors. Unless explicitly marked, standard deviations of presented results are not shown, to reduce clutter.We utilize MSA to analyze the computational model of the yeast's metabolic network. The elements perturbed are the genes coding for enzymes catalyzing the metabolic pathways. Perturbations are defined as complete knockouts of genes. The network's performance is the optimal solution found using FBA. As directed by the MSA method, we sampled random orderings of the elements, then sequentially perturbed them in this order, and measured the performance after each consecutive perturbation. The MSA gives statistical error estimates that allow one to stop sampling when the accuracy of results is satisfactory . These eDD ran the simulations and carried out the data analysis. All authors contributed to the final manuscript.