Leishmania spp. are sandfly transmitted protozoan parasites that cause a spectrum of diseases in more than 12 million people worldwide. Much research is now focusing on how these parasites adapt to the distinct nutrient environments they encounter in the digestive tract of the sandfly vector and the phagolysosome compartment of mammalian macrophages. While data mining and annotation of the genomes of three Leishmania species has provided an initial inventory of predicted metabolic components and associated pathways, resources for integrating this information into metabolic networks and incorporating data from transcript, protein, and metabolite profiling studies is currently lacking. The development of a reliable, expertly curated, and widely available model of Leishmania metabolic networks is required to facilitate systems analysis, as well as discovery and prioritization of new drug targets for this important human pathogen.Leishmania major (v5.2), based on the annotation published by the Wellcome Trust Sanger Institute. LeishCyc was manually curated to remove errors, correct automated predictions, and add information from the literature. The ongoing curation is based on public sources, literature searches, and our own experimental and bioinformatics studies. In a number of instances we have improved on the original genome annotation, and, in some ambiguous cases, collected relevant information from the literature in order to help clarify gene or protein annotation in the future. All genes in LeishCyc are linked to the corresponding entry in GeneDB (Wellcome Trust Sanger Institute).The LeishCyc database was initially built from the genome sequence of Leishmania major genes, gene products, metabolites, their relationships and biochemical organization into metabolic pathways. LeishCyc provides a systematic approach to organizing the evolving information about Leishmania biochemical networks and is a tool for analysis, interpretation, and visualization of Leishmania Omics data  in the context of metabolic pathways. LeishCyc is the first such database for the Trypanosomatidae family, which includes a number of other important human parasites. Flexible query/visualization capabilities are provided by the Pathway Tools software and its Web interface. The LeishCyc database is made freely available over the Internet .The LeishCyc database describes  Leishmania spp. are sandfly transmitted protozoan parasites (family Trypanosomatidae) and are the etiological agent of leishmaniasis. Leishmaniasis refers to a spectrum of diseases ranging from self-healing cutaneous lesions to debilitating mucocutaneous and lethal visceral infections. It is estimated that more than 12 million people have active leishmaniasis, and 350 million people are at risk, making Leishmania the most important parasitic disease after malaria . No vaccines against leishmaniasis exist; high toxicity and cost of current treatments and the emergence of drug resistant parasite strains point to the urgent need for novel drug targets.Protozoan parasites comprise a highly divergent group of eukaryotes that cause a range of debilitating diseases in humans, including malaria, leishmaniasis, African sleeping sickness, and Chagas' disease. Leishmania metabolism would open new avenues for the development of new drugs, and also lead to a greater understanding of how these parasites adapt to nutrient environments in the sandfly and mammalian hosts. For example, the flagellated promastigote stages of the parasite that develop in the digestive tract of the sandfly vector obtain nutrients from the sugar rich blood meal and plant saps upon which the sandfly feeds [Leishmania species  has provided the first blueprints of the metabolic potential of these parasites [L. major Friedlin strain and make predictions about essential genes and pathway robustness [Leishmania genome cannot yet be assigned a function based on homology searches, and therefore it is likely that in silico models will need to be substantially improved as new metabolic pathways are identified.A detailed understanding of ly feeds . In contly feeds ,3. The rarasites -6. Recenbustness . HoweverLeishmania genomic data is the GeneDB genome resource, established by the Sanger Institute [T. brucei, L. major, and S. pombe, and was later expanded to include curated data for a number of other organisms, including bacteria, fungi, and protozoa [Leishmania community, it does not integrate genomic data into biochemical networks [The major database for nstitute -10, and protozoa ,10. Genenetworks -10. Kyotnetworks ,12. Relenetworks , which inetworks . In contnetworks -18) and networks . MetaCycnetworks ,18. A nunetworks ,19-24.L. major based on the BioCyc ontology. The initial build of LeishCyc was based on the genome sequence of L. major [a) annotation and assignment of additional enzymes; (b) checking, deletion, creation, and modification of existing reactions and pathways; and (c) assignment of evidence codes and literature citations.In this work, we report on the development and use of LeishCyc, the pathway/genome database for L. major  and the L. major Friedlin genome is 32.8 Mb in size, with a karyotype of 36 chromosomes. The genome data (version 5.2) was downloaded from the Sanger Institute public database . The Pathway Tools component of PathoLogic was used to build the initial version of LeishCyc from the genomic data [L. major genome annotation originally provided by Sanger was in the Artemis format, and we used Artemis to convert the annotation file for each chromosome into the GenBank format. The resulting GenBank files were edited to add headers and subsequently the automated trial and build procedure was performed in PathoLogic.The mic data . PathoLoL. major genome contains 8283 genes predicted to encode polypeptides. The Pathway Tools software matched 574 of these genes to MetaCyc reactions based on the presence of an EC number in the gene annotation. Another 267 polypeptides, where no EC number was supplied, were matched to reactions based on their annotated name. The automated build resulted in 841 enzymes predicted for L. major. After the initial build, the list of 'probable enzymes' was constructed. Probable enzymes were gene products predicted to be enzymes but which could not be matched to any particular reaction by PathoLogic. These entries were manually reviewed and assigned to reactions where possible. There were 328 probable enzymes predicted for L. major and 148 were assigned to reactions by manual review.The Extensive manual curation of the database was performed based on literature search, and in-house experimental and bioinformatics studies. This included verification of enzymes and reactions deduced from the original genome annotation, refinements and improvement in the annotation of genes, enzymes, reactions and pathways, assignment of evidence codes, and inclusion of literature citations. At present LeishCyc contains 1027 enzymes and 566 metabolites organized into 704 enzymatic reactions, 37 transport reactions, and 143 metabolic pathways  and related glycolipids, and the assembly of complex phosphoglycans on the cell surface and secreted proteins and glycolipids [Leishmania spp. For example, the pathways for dolichyl-diphosphooligosaccharide and fatty acid biosynthesis were modified to reflect what has been experimentally observed or predicted for Leishmania [Only pathways present in MetaCyc can be automatically incorporated into the pathway database by Pathway Tools . As Metacolipids . These aishmania ,28. In tishmania . We haveLeishmania spp. In some cases, pathways were deleted and replaced with Leishmania-specific pathways. For example, two pathways for phospholipid biosynthesis were present after the initial build (phospholipid biosyntheses I and II). These were replaced with Leishmania-specific pathways for phospholipid biosynthesis (ester phospholipid biosynthesis and ether phospholipid biosynthesis) [After the initial build of LeishCyc, it was necessary to review the pathways and remove false-positive predictions . All patnthesis) ,30. In tnthesis) .L. major promastigotes revealed the presence of several metabolites (i.e. glucitol and glycerol 2-phosphate) for which exogenous sources or biosynthetic enzymes were lacking, indicating the presence of new or unanticipated reactions. Recent analyses of sugar phosphates using high resolution Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometry, identified a novel mannose cyclic phosphate that is the primer for the major intracellular reserve carbohydrate of Leishmania, linear polymers of mannose which we have now termed mannogen [Our own experimental work was used to add and verify some of the information present in LeishCyc. For example, GC-MS analysis of polar metabolites from cultured mannogen ,32. WhilLeishmania spp. [L. major genes encoding each of the mannosyltransferases in this pathway . Sequences that had been characterised in other organisms were used to build HMMs for each gene product. These models were then used to scan predicted L. major proteins to identify the most likely candidate for each individual ALG gene. The functional assignments made based on bioinformatics studies were documented in the annotations with the appropriate evidence codes (see below).Targeted bioinformatics studies were used to aid curation and improve the LeishCyc annotations. For example, the original genomic annotation implied only two enzymes to participate in the pathway 'dolichyl-diphosphooligosaccharide biosynthesis'. Literature review has shown that this pathway is indeed present in nia spp. , and henLeishmania spp. genes have been identified in the literature since the L. major genome was published. As a result, these genes were not accurately annotated in the LeishCyc automated build which relied on the original annotation of the L. major genome project. We used extensive searches and manual reviews of published literature to incorporate additional Leishmania genes, proteins, enzymes, and transporters in LeishCyc. If a gene had been identified in L. major, the published accession number was used to identify the gene in LeishCyc. In some instances, we have judged the quality of the published information and entered the information accordingly. For example, 25 new annotation refinements were proposed for the L. major genome based on weak similarity using BLAST searches [N-acyltransferase' based on the similarity to Cryptococcus neoformans sphingosine N-acyltransferase  although a protein BLAST search of the NCBI non-redundant database returns a list with over a hundred hits with similar or better E-value, including Trypanosoma brucei and Trypanosoma cruzi proteins of unknown function . In such cases, where we believed that further evidence is needed to firmly support the proposed annotation, we have quoted the literature source and the proposed annotation, while retaining the original 'unknown' function associated with the database entry. In cases where it was deemed that computational evidence was sufficiently strong, the new functional annotation was introduced with the appropriate evidence code, as described below.The functions of a number of searches . One of L. major genes, we also identified L. major orthologs of enzymes and transporters that have been characterized in other Leishmania species and trypanosomatid species such as T. brucei and T. cruzi. The L. major orthologs were identified by a systematic Needleman-Wunsch alignment of the given sequence against L. major predicted proteins with a processing pipeline built in-house. The results of Needleman-Wunsch alignment were manually reviewed for highest similarities and, if deemed appropriate, the L. major gene encoding the protein was annotated as the predicted ortholog (see below for the explanations of the evidence code assignments). In such cases, the percent sequence identity and/or similarity that the L. major sequence shared with the known homologous sequence was recorded in the LeishCyc annotation entry. For example, the myo-inositol transporter (MIT) has been characterized in L. donovani, but had not been identified L. major. The Needleman-Wunsch alignment of the L. donovani sequence against all L. major peptides identified LmjF24.0680 as the clear candidate for this protein in L. major, and the peptide with the greatest similarity to L. donovani MIT. This gene was originally annotated as 'sugar transporter, putative' in both the original GenBank annotation file and in the GeneDB entry for LmjF24.0680. We manually annotated LmjF24.0680 as the predicted L. major MIT, and assigned the evidence code indicating that the inference was computational. In addition, for every gene in LeishCyc, we have added a link to the corresponding entry in GeneDB which directly connects the entries from the two databases.In addition to identifying published Leishmania spp. or other trypanosomatids. Such genes were identified in LeishCyc, checked as to whether they were linked to the correct reaction(s), and, if not, the respective entries were corrected.Literature searches have identified a number of genes that have been linked to a particular enzyme or transporter in L. major Genome Project annotation file, resulting in the enzyme being linked to incorrect reaction(s). For example, the phosphomannomutase enzyme catalyzes the reaction EC 5.4.2.8 (α-D-mannose 1-phosphate → mannose 6-phosphate), but in the annotation file it was associated with EC 3.1.3.11 and thus was linked to the EC 3.1.3.11 reaction . In the subsequent manual curation, phosphomannomutase was removed from the EC 3.1.3.11 reaction and linked to the EC 5.4.2.8 reaction. In total, we found 7 enzymes to be annotated with the incorrect EC number in the L. major genome file, and we linked these enzymes to the correct reactions.Some enzymes were associated with an incorrect EC number in the L. major genome annotation file, the Pathway Tools software has attempted to link the gene based on matches of the product name to enzyme function. For example, the gene LmjF15.1010 was annotated as glutamate dehydrogenase and was matched to three glutamate dehydrogenase reactions each with a different EC number . The three reactions only differ in the cofactor used:For genes not associated with an EC number in the + + H2O → α-ketoglutarate + ammonia + NADHEC 1.4.1.2: L-glutamate + NAD+ + H2O → α-ketoglutarate + ammonia + NAD(P)HEC 1.4.1.3: L-glutamate + NAD(P)+ + H2O → α-ketoglutarate + ammonia + NADPHEC 1.4.1.4: L-glutamate + NADPL. tarentolae mitochondrial glutamate dehydrogenase [L. tarentolae enzyme uses NAD+ as a cofactor, but also has an NADP+ binding site, and so, in this case, the linkage of LmjF15.1010 to EC 1.4.1.3 was kept, and removed from EC 1.4.1.2 and E.C. 1.4.1.4.LmjF15.1010 is the predicted ortholog of the rogenase . The L. L. major [In certain cases, manual intervention was required to link enzymes to the multiple reactions they catalyze. For example, the enzyme pteridine reductase was associated with EC 1.5.1.33 and was thus automatically linked to only one reaction. However, this enzyme has been shown to catalyze additional reactions in folate and biopterin metabolism in L. major , and we L. major , thus weL. major inositol phosphorylceramide (IPC) synthase gene was recently identified by [L. major genome annotation file. We changed its annotation in LeishCyc to 'inositol phosphorylceramide synthase', manually created a new reaction , and linked the product of the gene to this reaction.For newly discovered enzymes without annotation in the original genome project files, the required enzyme objects were manually linked with the relevant reactions and, if necessary, the reaction in question was created. For example, the ified by . This geL. major transporters  and created 31 transport reactions [see Additional file In addition to metabolic enzymes, a concerted identification and curation of transport reactions was performed. After the automated build, there were 23 transporters identified in LeishCyc, but only 6 transport reactions. Furthermore, many of the identified transporters had not been assigned specific transporter identities (e.g. MIT). Using the literature, we identified a further 26 Leishmania spp. If the supporting evidence was only computational the evidence code 'EV-COMP' was assigned (this type of evidence is shown as a computer icon). If the evidence is supported by a publication, alongside each evidence code there is a link to the supporting publication. The code for curated proteins shows the evidence that supports the association of the protein with its linked reaction . In cases where the L. major ortholog was identified by the LeishCyc curator from similarity to a published sequence, the evidence code assigned was 'EV-COMP-HINF-FN-FROM-SEQ' (human inference of function from sequence), with additional explanations and the percent identity that the L. major sequence shares with the published sequence given. Currently, 208 proteins (including 2 protein complexes), 254 reactions, and 130 pathways have been assigned evidence codes in LeishCyc, and 200 references have been added to the database  data sets within the LeishCyc cellular overview diagram [LeishCyc provides a platform for curation, refinement, and dissemination of information about software . The undsoftware ,38, and software . Furthersoftware ,19-24, w diagram . Three eL. donovani promastigotes to in vitro differentiated (axenic) amastigotes [Figure stigotes , mapped stigotes .L. mexicana MZ 379 promastigotes were cultured in RPMI 1640 medium supplemented with 10% heat-inactivated foetal bovine serum (iFBS) at 27°C. Log phase promastigotes were harvested approximately two days after inoculation of the media. Axenic amastigotes were generated from stationary phase parasites (5–6 days after passage) by adjusting the conditioned media to pH 5.5 with HCl and the addition of iFBS to 20% [In the second example, LeishCyc was used to visualize data from metabolic profiling experiments performed in our group Figure . L. mexiS to 20% ,42. The S to 20% . Figure P. falciparum PlasmoCyc database [[P. falciparum [Chokepoint analysis has been used to prioritize potential drug targets in the database . Chokepodatabase ,44. Pathdatabase . This lidatabase . The TDRatabase [ was usedatabase [. Intereslciparum .Leishmania metabolic pathways from genome annotations and literature sources, and organizes this information into a structured database supported by a well developed, publicly available ontology [Leishmania biochemical networks, as well as tools for analysis, interpretation, and visualization of Leishmania high-throughput ('omics') data in the context of metabolic pathways. We believe that LeishCyc provides an important new resource for analysis and construction of metabolic network models for these parasites, for mapping species- or stage-specific changes in transcript, protein and metabolite levels, and for prioritizing potential drug candidates by metabolic network analysis. LeishCyc advanced search features and Omics Viewer capabilities can be accessed through a standard web browser, and the LeishCyc content is provided based on the Creative Commons license .LeishCyc captures the information about ontology -15,47. LLeishmania infect humans. The genome of L. major was the first to be completely sequenced, and was used as the basis for the initial build of LeishCyc [Leishmania can exhibit distinct trophism for different sandfly species, and induce a spectrum of disease in humans and other mammalian hosts, recent sequencing projects have highlighted a remarkable degree of synteny and conservation across the genomes of three major pathogenic species [Leishmania. The metabolic networks identified in LeishCyc are therefore likely to be relevant to all species of Leishmania. Interestingly, recent studies have suggested that species specific differences in gene transcription or protein expression may underlie some of the differences in biology and disease phenotypes of different Leishmania species [It is believed that 24 species of  species ,48. Only species . As demoLeishmania and other trypanosomatids are unusual in lacking a conventional network of transcriptional factors and most protein encoding genes are constitutively transcribed in all life cycle stages [Leishmania metabolism may be largely regulated by post-translational mechanisms. In particular, it is likely that changes in external nutrients and scavenging pathways, and allosteric regulation of intracellular enzymes may play key roles in regulating metabolic processes [L. mexicana can be mapped onto the LeishCyc metabolic network, providing an important tool for both identifying stage-specific changes in metabolism and assessing the extent to which these changes correlate with transcript or protein levels.Another important feature of LeishCyc is the capacity to overlay metabolite profiling data sets on the predicted metabolic networks. e stages . Consequrocesses . As showLeishmania biochemical reactions, gene products and metabolites into metabolic pathways in a mathematically well defined manner that will serve as the foundation for Leishmania systems studies, including computer-aided reconstructions of metabolic networks. Such a reconstruction of the L. major metabolic network has recently been reported by Papin and colleagues [L. major iAC560 metabolic network reconstruction included 560 genes (6.7% of the genome) and an additional 103 predicted gene associated reactions that were added for proper functioning of the computational model. The latter remain to be experimentally verified. Interestingly, the iAC560 metabolic network reconstruction was only partially successful in predicting a number of experimentally observed properties of Leishmania metabolism, such as minimal amino acid requirements and the potential lethality of single gene deletions [T. brucei, is currently under development [The LeishCyc database organizes the existing knowledge about lleagues . The L. elopment . A colleelopment .LeishCyc is available on the Internet from URL: myo-inositol transporter; iFBS: heat-inactivated foetal bovine serum; GC-MS: gas chromatography-mass spectrometry; TCA: tricarboxylic acid.KEGG: Kyoto Encyclopedia of Genes and Genomes; GPI: glycosylphosphatidylinositol; MIT: Leishmania parasites. MJM was involved in guidance in the development of LeishCyc and, in particular, was the chief Leishmania biology adviser. VAL was responsible for all bioinformatics aspects of the project. MAD and VAL have drafted the initial manuscript. MJM, MAD, JIM, VAL have been involved in revising the manuscript. All authors have read and approved the final manuscript.The LeishCyc project was established by VAL and MJM. MAD performed the main curation work of LeishCyc during the initial development, including manual editing of the database, literature searches, and bioinformatics studies with VAL. JIM was involved in the database curation. DPDS and ECS were involved in metabolite profiling experiments of LeishCyc pathways created or modified after the initial build. Contains a table summarizing LeishCyc pathways created or modified after the initial build.Click here for filePathways removed from LeishCyc after the initial build. Contains a table showing pathways were manually removed because either there was weak evidence for their existence in Leishmania spp. or they were replaced with a Leishmania-specific pathway.Click here for fileTransporters in Leishmania. Transporters and transport reactions identified in LeishCyc. Shown are the enzymes linked to those reactions. Details of transporter synonyms and localization  are also indicated.Click here for fileTime course proteomic experiment shown in LeishCyc OmicsViewer. Colour-coded representation of changes in steady-state protein levels during promastigote differentiation into amastigotes. The data is from the time course experiments of Rosenzweig et al. :590–602), with 2.5 h, 5 h, 10 h, 15 h, 24 h (promastigote), and 144 h (amastigote) time points shown. Changes are shown relative to the 0 h time point (promastigote). Metabolites and proteins are represented by shapes and lines, respectively. Proteins that are decreased are shown in yellow, those increased in red, and those unchanged in blue.Click here for fileLeishCyc chokepoint reactions. Chokepoint reactions were identified for L. major using the Pathway Tools chokepoint identification tool. Shown are the enzymes linked to those reactions. Enzymes are grouped within major pathway categories and those with human orthologs are indicated .Click here for file


Platt's 1964 essay on strong inference A half century ago Platt proposed a formal schema for scientific inquiry based, in part, on his assessment of the rapid progress made in molecular biology and theoretical physics in the middle part of the twentieth century. Building on the “simple old-fashioned method of inductive inference that goes back to Francis Bacon” “1. Devising alternative hypotheses;2. Devising a crucial experiment , with alternative possible outcomes, each of which will, as nearly as possible, exclude one or more of the hypotheses;3. Carrying out the experiment so as to get a clean result;1′. Recycling the procedure, making subhypotheses or sequential hypotheses to refine the possibilities that remain; and so on.”Current use of the scientific method ideally applies this logic, but all too often work stagnates at a particular step without completing the cycle. In adopting and effectively applying Platt's steps, hypotheses are systematically disproved and refined, successively moving toward a more complete understanding of nature. Hypotheses are not precious “personal property” to be protected and defended. Instead, successful disproof is the key to progress. Likewise, the goal of publication of an experimental result is to alert the community of progress and invite criticism, alternative explanations, and—what often hurts an investigator's ego—a more rigorous experiment.Platt warns that when alternative hypotheses are not sought, scientific inquiry becomes a “conflict between men, each with his single Ruling Theory.” In that case, “the scientist has no choice but to be either soft-headed or disputatious.”  “discover which DNA sequence changes in a gene can cause disease” and “develop new treatments at the molecular level.” Surely the project was an enormous success, providing not just the sequence itself, but also new technologies for sequencing and associated tasks that have become indispensible parts of the biomedical research toolbox. Yet nearly a decade and a half later, progress on many of the health concerns described in the White House press release proceeds much as it did before, during, and immediately after completion of the Human Genome Project. Thanks in part to information revealed by the Human Genome Project, it is now appreciated that most diseases  involve a complex interplay between many genes and environmental factors. Sequences and sequencing technologies are helping us to see where there are gaps in knowledge and helping to fill in those gaps. The sequence itself neither identifies the gaps nor fills them in.The point is that large-scale sequencing has introduced important new tools—perhaps even revolutionary tools—for biomedical research, while the underlying logical framework for “exploring the unknown” has remained unchanged. Some hype and oversimplification might be expected in promoting a grand technological achievement. But the Human Genome Project truly set a new standard for expectations. With this achievement hailed as an epoch-changing event, what's next? If the epoch has changed, what does that mean for the old-fashioned scientist who is still engaged in careful, cautious hypothesis testing? Why would anyone want to make deliberate progress on a particular biological question when the lab down the hall is getting the attention (and funding) for fully embracing The Next Really Big Thing?Systems biology is one of the names we are calling the next big thing these days. More than just a name, systems biology represents a potential vehicle for systematic application of Platt's principles to biomedical research. The opportunity exists because the need is especially obvious at this particular time. Former NIH director Elias Zerhouni points out that while “discovery in the life sciences is accelerating at an unprecedented rate,” we are now faced with the critical “need to understand complex biological systems” Apparently Platt did not hold much stock in mathematical modeling and simulation: “Equations and measurements are useful when and only when they are related to proof: but proof or disproof comes first and is in fact strongest when it is absolutely convincing without any quantitative measurement.” This is perhaps where Platt's vision needs to be recalibrated for the times. The mechanisms underlying the operation of biological systems—e.g., gene regulatory networks, metabolic networks, signaling networks, and the interoperation of all of the above—cannot be cast in a meaningful way into the simple qualitative framework of an earlier era of molecular biology. Increasingly, describing the operation of the biological systems under current investigation requires invoking computational models to simulate the system. For example, efforts to capture the physiome and construct a virtual human simulation represent the height of ambition of computational biology The fundamental key is to recognize that a computational model, however simple or complex, is a hypothesis, or perhaps a series of hypotheses bundled together into a set of equations or a computer algorithm that best represents how we think a complex systems works. Formulating hypotheses as computational models has at least two advantages when using strong inference to systematically uncover the important mechanisms governing a complex system:Computational/mathematical models are precise. Cartoons and thought models constructed out of words serve useful purposes in textbooks and in discussion sections of articles. However, when qualitative methods (such as drawing boxes and arrows to indicate interactions in a molecular network) are used to describe a hypothesis, that hypothesis can be interpreted many ways, and is therefore difficult to disprove without ambiguity.Computational/mathematical models, as necessarily simplified representations of reality, are sometimes useful but always incomplete. By virtue of their incompleteness, computational models fit naturally into Platt's scheme. Models can remain the precious “personal property” of their inventors and still be subject to disproof and refinement. It is the natural process of mathematical and computational modeling to close the loop between Platt's Step 3 and Step 1.Closing the loop, of course, requires data. After all, “without data, there is nothing to model; and without models, there is no source of deep predictive understanding” In the remainder of this essay we apply strong inference to analyze two long-standing questions in the control and regulation of cardiac energy metabolism: the metabolic stability hypothesis—the hypothesis that the rate of oxidative ATP synthesis in the heart is not influenced by any significant changes in substrate concentrations with changes in rate of ATP hydrolysis—and the phosphocreatine shuttle theory—a loosely organized set of ideas regarding possible roles of creatine and phosphocreatine in transporting ATP hydrolysis potential in the cardiomyocyte. These examples show how significant progress can be made on largely stalled areas of investigation by applying strong inference.31phosphate magnetic resonance spectroscopy (31P-MRS) of the canine myocardium. That study was followed up by Katz et al. 2). The data from the Katz et al. study are reproduced here in 2  are lumped together in one set of figures for ADP (relative to baseline), inorganic phosphate , and CrP/ATP ratio.The landmark metabolic stability hypothesis was formulated based on the observation that the heart maintains relatively stable concentrations of phosphate metabolites over the observed range of cardiac oxygen consumption. This phenomenon was first reported by Neely et al. 2 is discernable from the data, it was concluded that these variables are not responsible for modulating the rate of oxidative ATP synthesis in vivo, and the hypothesis of feedback regulation by ADP and Pi was declared disproven.Although the experiments summarized in The hypothesis that the substrates for oxidative phosphorylation (ADP and Pi) are not the primary regulators of oxidative phosphorylation has been stated by Balaban:“…recent data from intact tissues with high oxidative phosphorylation capacities  indicate that the cytosolic concentration of ADP and Pi do not change significantly with work. These data imply that [a] simple feedback model is not adequate to explain the regulation of energy metabolism in these tissues…” 2+, in which Ca2+ ion stimulates oxidative phosphorylation mainly through activating tricarboxylic acid (TCA) cycle enzymes The insufficiency of feedback regulation has inspired a number of theories to explain the control of oxidative phosphorylation in the heart in vivo. Indeed, several putative explanations of metabolic stability in the heart have been formulated as computational models simulating cardiac energy metabolism. Examples include: feed-forward activation by CaYet, however important it has been in inspiring theory and experiments, the above quotation laying out the hypothesis of metabolic stability was not authored under the philosophy of strong inference. In fact, while we have recast the message as a hypothesis, this and similar statements are presented as conclusions in the original sources. The metabolic stability hypothesis is widely accepted and serious effort has been put into trying to explain it. Yet if the hypothesis is disprovable, then the longer it goes un-disproved, the less it inspires and the more it impedes progress.31P-MRS data on cardiac phosphate metabolites reported in a series of studies by Zhang and coworkers. Here we see that the trend of relatively stable CrP/ATP versus MVO2 observed by Katz et al. 31P-MRS in vivo. The data points in 2 do not correspond to direct measurements. This is because using newer MRS technology that provides a more spatially localized signal than was possible in the Katz et al. study, it has been repeatedly demonstrated that Pi is not detectable in the myocardium at baseline. Since the baseline Pi is not measured, Pi is appropriately reported as ΔPi, the measured increase over baseline . The shaded data points in Also note that in It is possible that the baseline signal identified as Pi by Katz et al. 2, the case for constant Pi is not strong. Leaving the derived variable ADP out of our analysis, what is left from 2. While a line of zero slope passes through this data cloud, these data certainly do not prove that the relationship underlying these data is a line of zero slope. A line of zero slope becomes a slightly less convincing description when compared to the data of Contrasting that evidence for constant Pi with, for example, the six studies summarized in 2, while Pi increases from somewhere below the minimum detectable concentration at baseline to more than two times the minimum detectable concentration at maximal or near maximal MVO2. Even in the detectable range the Pi measurements suffer from substantial noise, resulting in large uncertainty in ΔPi/CrP. Thus the nature of the relationship between Pi and MVO2 is not clearly revealed due to noise and individual variability in the measurements. Moreover, due to both the low signal-to-noise ratio and the fact that the Pi signal originates from both the cytoplasm and the mitochondrial matrix, absolute Pi concentrations (in mass per unit volume) are not easily estimated from these relative measurements.Synthesizing the available data on phosphate metabolites in the normal heart in vivo shows: CrP/ATP decreases either slightly (perhaps 15%) or not at all with increases in MVOThese data inspire the formulation of an alternative to the metabolic stability hypothesis. Formally, we state the metabolic stability hypothesis as “biochemical feedback is not adequate to explain the regulation of energy metabolism in the heart,” and its alternative, “biochemical feedback is adequate to explain the regulation of energy metabolism in the heart.”These alternative hypotheses are clearly mutually exclusive, satisfying the requirement of Platt's Step 2. In this case, since these hypotheses relate to potential mechanisms underlying data that have already been collected, Platt's Step 3 takes the form of a simulation experiment. Specifically, if an independently validated simulation of energy metabolism in the heart, in which the rate of oxidative phosphorylation is controlled by biochemical feedback, is able to match the available data, then the stability hypothesis will be disproved and the alternative proved. In a recent series of papers we have developed a computer model of cardiac energy metabolism that provides the means to distinguish the hypotheses. Briefly, the model to simulate mitochondrial metabolism and electrophysiology is based on a large number of kinetic and steady-state data from purified mitochondria Integrating this energy metabolism model with a model to simulate oxygen transport in the myocardium, we are able to simulate the experiments summarized in Furthermore, these simulations help resolve an old scientific debate that was never adequately concluded. One of us recalls that twenty years ago the findings of Balaban and colleagues generated extensive and compelling discussions both in the literature and at scientific meetings: “You did not consider alternative hypotheses!”, “The methods are not precise enough to justify your conclusion!”, “How did you calibrate the NMR [nuclear magnetic resonance] spectral signals into concentrations?”, “How do you know that the CK is maintained at equilibrium in the cell so that the ADP concentration can be calculated?”, “What experiment can distinguish feed-back from feed-forward control?” While such questions were debated extensively at poster sessions for years, the critical disproofs that came later were presented in terms that decidedly avoided challenging the status quo.2 are appropriately interpreted as a simple direct disproof. Yet, those observations were presented as consistent with the Balaban data. Specifically, much was made of the fact that the later experiments achieved rate-pressure products (RPP) significantly higher than the earlier studies and that only at the higher values of RPP does the Pi signal become observable. Making this point, one of us is guilty of this sort of equivocation intended to avoid conflict. In discussing our model predictions in comparison to the data on inorganic phosphate, Wu et al. 2. So the emphasized point of agreement is trivial while the crucial point of disagreement is deemphasized.Recall that the metabolic stability hypothesis is formulated on the foundation that both biochemical substrates for oxidative phosphorylation, ADP and Pi, remain essentially constant in the heart. Thus the observations of significant increases in Pi with MVOPutting equivocating statements aside, the experiments of Zhang and colleagues directly contradict the assertion that concentrations of substrates for ATP synthesis do not significantly change in response to changes in ATP hydrolysis rate. By comparing computer simulations to these data, we are able to firmly disprove the associated metabolic stability hypothesis. This outcome is an affirmation of strong inference. The stability hypothesis of Balaban and coworkers has stood for twenty years and inspired deeper investigations into the control of energy metabolism in the heart. Its disproof is an opportunity for further refinement and progress. Furthermore, this disproof does not represent a proof of our computational model. However, the integrated model has been validated on the basis of a comparison of the data in Km values and do not change appreciably with flux? Hochachka showed how intracellular microcompartments could account for “metabolic stability.” The laboratories of Walliman  Ca2+ to be orders of magnitude lower than other charged and uncharged solutes r in the diffusion equations was responsible for the enhanced gradients. These contrasting views of metabolite localization and mobility are mutually exclusive.Hypotheses about the nature of the cellular interior and the properties of water as solvent and metabolites as solutes remain fruitful avenues of investigation. Macroscopic features can hide microscopic properties. For example, measured diffusivities of water and of low molecular weight solutes in gels that are macroscopically a solid, such as a gelatin cube, are slightly reduced compared to diffusivity in pure aqueous solution. From these studies Wang developed a view of proteins as macromolecular strands in an aqueous environment that obstruct random three-dimensional diffusion and so decrease the measured diffusivity by a calculable extent We now consider how strong inference can advance these questions. Two issues are intertwined and need to be separated. First, the descriptions of “the creatine phosphate shuttle” and “intracellular compartments” admit various definitions and interpretations; compartments bounded by membranes are clearly defined. The concepts of the shuttle and compartmentalization have been described qualitatively from the original diagrams in Meyer et al. Vmax in vitro is determined without reverse flux from products and without substantial binding of both products or both reactants) and not consistent with predictions from the obligatory shuttle hypothesis. Thus these experiments apply Platt's strong inference by disproving the obligatory shuttle hypothesis, at least for certain skeletal muscle tissues, and not disproving the facilitated diffusion model.In experiments made specifically to falsify the “obligatory shuttle” or the “facilitated shuttle” hypotheses, NMR polarization transfer methods were used to measure unidirectional fluxes of the CK reaction: CrP→ATP and the reverse 2+-ATPase (SERCA), and elsewhere on muscle structures. Enzyme localization does not mean the metabolites are similarly localized. Because of high diffusivity and concentration, the local concentrations of CrP, Cr, and ATP exceed, by at least an order of magnitude, the binding constants of the enzyme, as discussed by Meyer et al.  is approximately 0.015 mM in isolated cardiac mitochondria and 0.30 mM in suspensions of permeabilized cardiomyocytes Evidence for a more crucial role of a CK-mediated transport system includes observations that the ADP concentration necessary to achieve the half-maximal rate of oxidative phosphorylation  and Michaelis-Menten constant (Km) for ATP for the reaction Cr+ATP→CrP+ADP, assayed in suspensions of purified mitochondria, depend on whether or not there is a net flux through the ANT. Specifically, when mitochondria are synthesizing ATP, the apparent Vmax is increased and the apparent Km for ATP decreased, suggesting that mtCK turns over more readily when ATP is provided from ANT than when it is available only from the bulk solution. The thermodynamic evidence is that under certain conditions when Cr and ADP are available to respiring purified mitochondria, they are able to synthesize CrP in concentrations such that [CrP]·[ADP]/( [Cr]·[ATP]) exceeds the equilibrium mass-action ratio of the CK reaction Cr+ATP→CrP+ADP Saks et al. All of these observations may be explained by the direct-transfer hypothesis There is an obvious unresolved conflict when two labs report opposite results for the same experiment. Either one or both of the results is incorrect. In this case, neither result is entirely clear because it is unknown how oxidative phosphorylation could be viable with the “removal of the mitochondrial outer membrane” since cytochrome c—a necessary redox carrier in the electron transport system—diffuses freely in the intermembrane space. It is possible that the digitonin treatment in these experiments yielded a heterogeneous distribution of partial permeabilization and functional characteristics of mitochondria. Regardless of any possible explanation, from the conflicting results it can only be concluded that the hypothesis that the outer membrane presents a permeability barrier that is responsible for the apparent functional coupling remains without a rigorous attempt at disproof.Km for ATP of approximately 56 µM and 48 µM, respectively. These values—lower than apparent Km values estimated for nonrespiring mitochondria, which are in the range of 100 µM and higher Finally, kinetic experiments on the purified mtCK enzyme This is a simple, clear and unambiguous statement that is phenomenologically consistent with all of the independently reproduced data on functional coupling of mtCK and ANT. What remains is to determine if this statement can be successfully cast in terms of a quantitative hypothesis and associated theoretical/computational model. Attempts so far have not been successful. For example, Vendelin et al. Saks and colleagues promote a hypothesis that “ATP is directly channeled by ANT from matrix into microcompartment (‘gap’) between” ANT and mtCK The subhypothesis that the CK reaction mass-action ratio can be far from equilibrium in the cytoplasm of a cardiomyocyte is commonly proposed as a component of the phosphocreatine shuttle hypothesis −1·(kg tissue)−1 versus values in the range of 25–40 mmol·sec−1·(kg tissue)−1 measured for the nonmitochondrial isoforms in vivo Simulation studies of Saks and Aliev Here we have demonstrated the utility of applying Platt's strong inference to critical questions in cardiac energy metabolism. Regarding the hypothesis of metabolic stability, Platt's rigorous logic provides a framework for disproof and for establishing and testing alternatives. In doing so, we have shown seemingly contradictory data (on metabolic kinetics in purified mitochondria Hence further progress in this field, and in biological systems research in general, will rely on further application of strong inference. Likewise, application of strong inference to complex biological systems requires computational simulation to formulate the hypotheses, to compare hypotheses to data, and to design the experiments to distinguish between alternatives. Biological systems research, strong inference, and computational modeling are constructively and inseparably coupled.


Advances in bioinformatic techniques and analyses have led to the availability of genome-scale metabolic reconstructions. The size and complexity of such networks often means that their potential behaviour can only be analysed with constraint-based methods. Whilst requiring minimal experimental data, such methods are unable to give insight into cellular substrate concentrations. Instead, the long-term goal of systems biology is to use kinetic modelling to characterize fully the mechanics of each enzymatic reaction, and to combine such knowledge to predict system behaviour.We describe a method for building a parameterized genome-scale kinetic model of a metabolic network. Simplified linlog kinetics are used and the parameters are extracted from a kinetic model repository. We demonstrate our methodology by applying it to yeast metabolism. The resultant model has 956 metabolic reactions involving 820 metabolites, and, whilst approximative, has considerably broader remit than any existing models of its type. Control analysis is used to identify key steps within the system.http://www.mcisb.org/resources/genomescale/.Our modelling framework may be considered a stepping-stone toward the long-term goal of a fully-parameterized model of yeast metabolism. The model is available in SBML format from the BioModels database (BioModels ID: MODEL1001200000) and at  S. cerevisiae (bakers' yeast) consists of 1761 reactions and 1168 metabolites [Recent advances in genome sequencing techniques and bioinformatic analyses have led to an explosion of systems-wide biological data. In turn, the reconstruction of genome-scale networks for micro-organisms has become possible. Whilst the first stoichiometric models were limited to the central metabolic pathways, later efforts such as iFF708  and iND7abolites .The ability to analyse, interpret and ultimately predict cellular behaviour is a long sought-after goal. The genome sequencing projects are defining the molecular components within the cell, but describing their integrated function will be a challenging task. Ideally, one would like to use enzyme kinetics to characterize fully the mechanics of each reaction, in terms of how changes in metabolite concentrations affect local reaction rates. However, a considerable amount of data and effort is required to parameterize even a small mechanistic model; the determination of such parameters is costly and time-consuming, and moreover much of the required information may be difficult or impossible to determine experimentally. Instead, genome-scale metabolic modelling has relied on constraint-based analysis , which uhttp://sbml.org/) [http://www.ebi.ac.uk/miriam/) [In a previous paper, we presented a method for constructing a kinetic model for a metabolic pathway based only on the knowledge of its stoichiometry . Here, wml.org/) , using Mmiriam/) . Criticahttp://www.comp-sys-bio.org/yeastnet). In all, the resulting consensus network consists of 1857 reactions (of which 1761 are metabolic) involving 2153 chemical species (of which 1168 are metabolites). Species in the model are annotated using both database-dependent  and datg. InChI ) referenSpecies are localized to 15 compartments, including membranes. To limit complexity, we decompartmentalize the model, restricting entities to intra- or extra-cellular space. We also lump together reactions catalyzed by isoenzymes; the resultant model is reduced in size to 1059 reactions, of which 956 are metabolic, involving 1748 species, of which 820 are metabolites (the remaining 938 species are enzymes and enzyme complexes). Estimation of unknown system fluxes are addressed with the use of flux balance analysis (FBA) . FBA allZ, a linear combination of the fluxes vj, that we maximize over all possible steady state fluxes  satisfying certain constraints. In many genome scale metabolic models, a biomass production reaction is defined explicitly that may be taken as a natural form for the objective function. The metabolic reconstruction used here [That is, we define an objective function sed here  lacks sused here .In a previous paper , we defiN).• Network stoichiometry (v*) through the network.• Reference fluxes (x*).• Reference metabolite concentrations (ε) -- changes in reaction rates with effector levels.• Elasticities (th release) [To the stoichiometric model, we append kinetics  from the set of models available from the BioModels database 11release) . As meta1release v*) is found by solving the linear programming problem described in formulation 2 below, by minimizing the distance to these 55 target fluxes (vT):55 reactions in the  genome-scale model have fluxes that are defined in models stored on the BioModels database. Of these, the 21 data specific to yeast are presented in Table BM denotes the subset of j that includes all the reactions with fluxes defined in BioModels. A unique reference flux . We then find the bounds on each reaction flux, subject to the new constraint that the total flux through the network cannot be larger than Z1. The bounds are calculated by solving an optimisation problem for maximizing and minimizing the flux of each reaction iteratively. These limits are set as the new upper and lower bounds for the fluxes. The "centre" for each flux is the mean of the new bounds, as the most representative value of all solutions.A simple FBA formulation is solved, in order to identify the maximum achievable growth rate, al flux. ) may be Z1, as found in the first iteration. In turn, this leads to new bounds and a corresponding centre. Each iteration of the algorithm adds an additional constraint, and the flux is drawn towards the centre of the bounds. After a finite number of iterations, the bounds converge to a single solution, within a specified tolerance.In the second iteration, we place a box around the hull (defining new bounds), before minimizing the distance between the flux of each reaction and the centre value, subject to the constraint that the total network flux cannot exceed The algorithm is explained in detail in a previous paper , which d82 intracellular metabolites' concentrations are defined in various models within BioModels. Of these, the 22 specific to yeast are presented in Table et al. [151 elasticities are calculated from models within BioModels, using symbolic differentiation. For the remaining values, we follow the tendency modelling approach of Visser et al. , wherebyv = k A2 B and hence elasticity An assumption of irreversible mass-action kinetics would lead to reaction rate To produce our genome-scale, kinetic model of yeast metabolism, the above parameters may be combined in a phenomenological rate law such as linlog kinetics:c denotes the compartment volumes. The benefit of this approximation lies in the existence of analytic forms for steady states and their stability matrix [E. coli sugar metabolism [where y matrix , thus avy matrix . In a retabolism .To test the resultant genome-scale model, and to try and indentify key steps in the metabolic network of yeast, we calculate the flux control coefficients for reactions, as defined by metabolic control analysis (MCA). MCA studies how the control of fluxes and intermediate concentrations in a metabolic pathway is distributed among the different enzymes that constitute the pathway. Developed independently by Kacser and Burns  and HeinN) (here = 616). However, once kinetics are taken into account, this number drops drastically to rank(N·diag(v*)·ε) = 205. Reder's method only holds if these two values are identical. Thus, in Methods, we derive again the main results of MCA without relying on such an assumption.Whilst Reder's formula is often used in computational applications, it assumes that a certain matrix is invertible; this may not be true, especially if some reference reaction rates are zero. For example, the number of independent metabolites is often defined solely in terms of stoichiometry as rank have beIn this paper, we present a novel methodology that can be used to create a parameterized, genome-scale kinetic model of the metabolic network of an organism. The methodology is demonstrated by its application on yeast metabolism, through appending existing kinetic submodels from the BioModels database to a stoichiometric model of yeast. The final model has 956 metabolic reactions involving 820 metabolites and, to our knowledge has significantly wider scope than any previous models of comparable type. We demonstrate the usefulness of such a model, by applying the principles of metabolic control analysis to identify key steps within the network.Critically, both the original stoichiometric model, and the kinetic model that constitutes the end-result of the method are available in SBML, using MIRIAM-compliant annotations. Models in BioModels are annotated with computer-readable references such as ChEBI  or InChIhttp://www.mcisb.org/resources/genomescale/.Our methodology clearly has limitations, in that the linlog framework is only valid in a region near the chosen reference state. Moreover, due to the vast lack of information, many of the parameters used in building the model are unknown and must be estimated through techniques such as flux balance analysis. Nonetheless, our modelling framework is a necessary stepping stone at creation of a genome-scale kinetic model, and may thus be considered the first step in the deductive-inductive 'cycle of knowledge' crucial for systems biology . We havex = x* corresponds to a steady state - i.e. N v* = 0, where v* = v(x*). Writing N = diag(c)-1·N and Let us return to Equation (3), a generalized description of the temporal evolution of a metabolic network in differential equation format. Let us also assume that the reference state x = 0 now corresponds to the steady state. Linearizing about this steady statewhere ε' is the n × m unscaled elasticity matrix.where N ε') = m0 <m and the system defined above will display moiety conservations - certain metabolites can be expressed as linear combinations of other metabolites in the system. Note that the number of independent metabolites is not given simply by rank(N), as is generally (and erroneously) suggested; rather the local dynamics of the system must also be taken into account via the elasticity matrix. The conservations may be removed through matrix decomposition, using a m × m0 link matrix L that relates the complete vector of internal metabolites to the vector of independent metabolites [A = N ε' and letting Ar denote a m0 × m matrix composed of linearly independent rows of A, the corresponding link matrix is defined as +' denotes the Moore-Penrose pseudoinverse [A = L·Ar.In general, the rank, and noting that the rows of m0 × m0 matrix (Nr·ε'. L) is invertible through introduction of the link matrix L.where the jHaving transformed the system, we add a small perturbation to reaction δ is our perturbation; ej denotes the jth standard basis vector and the notation Nr, j is used to denote the jth column of Nr. The new steady state resulting from this perturbation is given bywhere Using Equation (9), we may resolve the definition of  flux control and concentration control coefficients asandr' is defined as the independent rows of N, leading to r = r' (i.e. if rank(N ε') = rank(N)), then L = L' and the two results are equivalent.respectively. If we compare our expressions to those given in Reder , we see N ε') < rank(N), as is the case for our model (rank(N ε') = 205, whilst rank(N) = 616). From Equations (10) and (11), one may trivially deduce the summation and connectivity theorems.As such, we may see that we have extended Reder's work to encompass the possibility that rank(Equation (10) may be used to calculate flux control coefficients for our genome-scale model. These parameters may also be defined in their more usual scaled formThe indices and variables appearing throughout the paper are defined in Table KS performed the calculations. KS and ES drafted the manuscript. All authors conceived the methodology and read and approved the final manuscript.Genome-scale model for yeast. Compressed ZIP file (220 KB) containing the model in SBML format.Click here for fileReference fluxes. Excel spreadsheet  containing the reference flux for all reactions, as estimated by application of the algorithm [lgorithm .Click here for fileControl over glucose transport. Excel spreadsheet  containing flux control coefficients for all reactions for control over glucose transport.Click here for fileControl over biomass production. Excel spreadsheet  containing flux control coefficients for all reactions for control over biomass production.Click here for file


Obtaining quantitative predictions for cellular metabolic activities requires the identification and modeling of the physicochemical constraints that are relevant at physiological growth conditions. Molecular crowding in a cell's cytoplasm is one such potential constraint, as it limits the solvent capacity available to metabolic enzymes.E. coli cells when they are shifted from low to high growth rates. The switch is characterized by a change in effective optimization strategy, the excretion of acetate at high growth rates, and a global reorganization of E. coli metabolic fluxes, the latter being partially confirmed by flux measurements of central metabolic reactions.Using a recently introduced flux balance modeling framework (FBAwMC) here we demonstrate that this constraint determines a metabolic switch in E. coli cells operating at high metabolic rates and for the activation of a metabolic switch when they are shifted from low to high growth rates. The relevance of this constraint in the context of both the aerobic ethanol excretion seen in fast growing yeast cells (Crabtree effect) and the aerobic glycolysis observed in rapidly dividing cancer cells (Warburg effect) should be addressed in the future.These results implicate the solvent capacity as an important physiological constraint acting on  Understanding an organism's metabolism at a system level requires knowledge of the physicochemical constraints limiting its metabolic capabilities under different growth conditions, and the genetic regulatory mechanisms that ultimately allow it to adapt to a changing environment. In some cases there is an obvious connection between an environmental change and the regulatory mechanisms responding to it, an example being a switch from aerobic to anaerobic growth . HoweverE. coli cells growing in a mixture of carbon sources  Fig. .E. coli MG1655 metabolic network that takes into account this constraint referred to as 'flux balance analysis with molecular crowding' (FBAwMC) -glucose . Cells were grown in a continuous growth mode at 5 different dilution rates  in a Labfors bioreactor . The growth of the bacterial culture was regularly monitored at A600nm to document steady state, as described in Additional file The 4, 2 mM DTT and 0.1 mM EDTA, and then disrupted in a sonicator by 3 sonication cycles of 30 sec each. The cell debris was removed by centrifugation and the resulting cell extract (supernatant) was immediately used for enzyme assays or stored at -20°C. All subsequent steps were carried out on ice. Supernatants of the samples were used for quantitative assaying of endogenous enzyme activities by continuous spectrophotometric rate determination at 30°C in a thermostatically controlled spectrophotometer (Cary 500) with 1-cm light path, as described in the Additional file For determining metabolic enzyme activities from three separate experiments, the cell pellets  were first resuspended and washed in 100 mM Tris-HCl (pH 7.0) sonication buffer containing 20 mM KCl, 5 mM MnSO13C tracer enrichment in multiple intermediary metabolites of glycolysis, glycogen synthesis, tricarboxylic acid cycle and their intracellular products from -D-glucose, as described in detail in Additional file For flux analysis, biomass (from ~100 ml culture) and supernatant samples were collected at all five dilution rates. These samples were immediately flash frozen in liquid nitrogen and stored at -80°C until further analysis. Flux rates were determined using a tracer-substrate based GC-MS and NMR metabolome mapping platform. The analyses included determining positional g for 5 min at 4°C, followed by flash-freezing of pellets with liquid nitrogen. Cell pellets were stored at -80°C until further use. RNA was isolated from the frozen cell pellets using Masterpure RNA isolation kit  and RNA samples were processed for transcriptome analysis using E. coli Affymetrix microarray chips, as described previously [At all five dilution rates, 10–20 ml of the cell culture was collected, mixed with 10% (v/v) of ice cold stop-solution (5% water-saturated phenol in absolute ethanol), and cell pellets were obtained by centrifugation at 4,500 × eviously . Dchip mAV, MAM, and A-LB developed the theoretical framework and AV implemented it. QKB and LGB performed the experiments, with the exception of the microarray experiments that were performed at the Boston University Microarray Center. JE and ZB-J analyzed the microarray data. AV and ZNO guided and coordinated the project. AV, QKB, ZB-J, LGB, and ZNO prepared the manuscript. All authors have read and approved the final version of the manuscript.E. coli metabolic reactions and biomass vectorClick here for fileMeasured enzyme activity values for various intracellular enzymes of the central carbon metabolismClick here for fileDchip Microarray analysis of biomass samples from all five dilution/growth ratesClick here for fileE. coli metabolismImpact of the solvent capacity constraint on Click here for filein silico of E. coli metabolism during growth on glucose-limited mediumFlux predictions for 710 reactions in the Click here for fileList of all genes along with their 'b'-numbers showing similar expression profile with query genes.Click here for file


Microbial hosts offer a number of unique advantages when used as production systems for both native and heterologous small-molecules. These advantages include high selectivity and benign environmental impact; however, a principal drawback is low yield and/or productivity, which limits economic viability. Therefore a major challenge in developing a microbial production system is to maximize formation of a specific product while sustaining cell growth. Tools to rationally reconfigure microbial metabolism for these potentially conflicting objectives remain limited. Exhaustively exploring combinations of genetic modifications is both experimentally and computationally inefficient, and can become intractable when multiple gene deletions or insertions need to be considered. Alternatively, the search for desirable gene modifications may be solved heuristically as an evolutionary optimization problem. In this study, we combine a genetic algorithm and elementary mode analysis to develop an optimization framework for evolving metabolic networks with energetically favorable pathways for production of both biomass and a compound of interest.E. coli central metabolism revealed two clusters of EMs with respect to their ΔGp°. For proof of principle testing, the algorithm was applied to ethanol and lycopene production in E. coli. The algorithm was used to optimize product formation, biomass formation, and product and biomass formation simultaneously. Predicted knockouts often matched those that have previously been implemented experimentally for improved product formation. The performance of a multi-objective genetic algorithm showed that it is better to couple the two objectives in a single objective genetic algorithm.Utilization of thermodynamically-weighted elementary modes for flux reconstruction of E. coli. The designed algorithm can be applied to any small-scale model of cellular metabolism theoretically utilizing any substrate and applied towards the production of any product.A computationally tractable framework is presented for the redesign of metabolic networks for maximal product formation combining elementary mode analysis , pathway thermodynamics, and a genetic algorithm to optimize the production of two industrially-relevant products, ethanol and lycopene, from  Microorganisms are increasingly utilized to synthesize a variety of products -3, inclu13C-labeling based metabolic flux analysis (13C-MFA) [Currently, there exists a variety of methods for studying metabolic networks in both quantitative and qualitative manners: flux balance analysis (FBA) -31, 13C-13C-MFA) , metabol13C-MFA) , element13C-MFA) , extreme13C-MFA) , cyberne13C-MFA) ,37, and 13C-MFA) -40. Many13C-MFA) , regulat13C-MFA) , OptKnoc13C-MFA) , OptStra13C-MFA) , OptReg 13C-MFA) , and Opt13C-MFA) . All six13C-MFA) , other e13C-MFA) . In addistrictly from the wild-type organism's metabolic network topology, utilizing thermodynamics.Genetic algorithms (GAs) have been classically utilized as a search method for optimization of objective functions that are discontinuous, non-differentiable, stochastic, or highly non-linear. As the name implies, the underlying theory behind GAs is based on Darwinian evolution. GAs seek to evolve a population of potential solutions by crossover and mutation, and through multiple generations, the entire population will eventually "evolve" towards a global optimum (a "fitness score"). They have been used to some extent in modeling biological systems  and are any metabolic state achievable by the cell's stoichiometry. The algorithmic complexity of this problem has not been studied in detail and has therefore been classified as at least an NP-hard  problem [E. coli that are efficient at producing biomass from glucose [Corynebacterium glutamicum [Lactobacillus rhamnosus growing on medium containing mixed substrates [E. coli, mediated by a thermodynamic analysis of the EMs [An elementary mode (EM) is a non-decomposable set of reactions (encoded by a set of genes) that leads to a functional metabolic pathway. EMA is a method of enumeration of all of the EMs of a metabolic network. As such, an EMA presents a convex analysis problem from computational geometry, in which the extreme rays of the polyhedral cone (as defined by stoichiometry and reversibility) are the EMs of the metabolic network. As a result, an EM represents a single functional pathway within overall cellular metabolism, a linear combination of a cell's EMs can be used to describe  problem . Empiric glucose  and etha glucose . In two utamicum , and to bstrates . EMA has the EMs .E. coli. We addressed issues of computation speed by coupling the EMA model with a GA to efficiently explore genotypic space. This algorithm presents a combination of a variety of traits that have been explored previously by themselves: 1) it is based solely on reaction stoichiometry and network topology, independent of any experimental flux measurements ; 2) by the utilization of a GA, it contains an efficient search method arriving at a solution within minutes on a single-processor notebook system; 3) by the utilization of a GA, it arrives at an optimal solution in a computationally tractable amount of time; and 4) it contains the option to use a multi-objective genetic algorithm (MOGA), only utilized very recently in analysis of metabolic networks, but still within the context of FBA [In this study, an algorithm based on EMA, pathway thermodynamics, and a GA has been constructed with the goal of redesigning a metabolic network towards maximally producing compounds of interest while simultaneously sustaining high biomass formation. This algorithm was applied to producing ethanol and heterologous lycopene through t of FBA .Gp°). Next, the yields of biomass and product on substrate are calculated and the strain's corresponding fitness is evaluated. This fitness, a reflection of the cellular phenotype, is then used by the GA to enrich the population of potential solutions to those that have a higher fitness value. This process is repeated until one of the GA's stopping criteria is met.The framework is schematically shown in Figure Escherichia coli using a previously published model as a template [1 and the theoretical yield of lycopene on glucose is 0.316 g g1. There are 14 (0.04%) EMs that produce the theoretical yield of ethanol on glucose , while there is only one EM (0.002%) that produces the theoretical yield of lycopene on glucose . EMA was conducted on a notebook equipped with an Intel® Core™ 2 Duo T9300 CPU running at 2.50 GHz, 4.0 GB memory, and a 32-bit version of Microsoft Windows Vista™ Ultimate. The computation time required to enumerate the entire set of EMs was 8.04 s ± 0.27 s (n = 10) and 12.30 s ± 0.24 s (n = 10), for the ethanol and lycopene models, respectively. More detailed information of both models can be found in Additional File Additional File As test cases, two small-scale stoichiometric models were constructed of ethanol- or lycopene-producing template , the dete EM 0.00% that prGf°) of metabolites included in the two models were calculated using group contribution theory [Gr°) , rather than physiological conditions. Consequently, it is quite likely these estimates deviate slightly from experimentally determined values. In this study, we used these estimates as first-order approximations to derive the Gibbs energy changes across metabolic pathways (ΔGp°) as defined by the EMs. Histograms of ΔGr° and ΔGp° values . Interestingly, the skewness of both distributions is different: the ethanol model has a negative skewness of 4.54 kcal mol1 while the lycopene model has a slight positive skewness of 0.42 kcal mol1. This indicates a change in distribution to slightly more energetically favorable reactions with respect to the ethanol model. The mean values for ΔGp° are much more negative at 111.87 kcal mol1 and 88.72 kcal mol1 for the ethanol and lycopene models, respectively. Interestingly, the ethanol model contains relatively few  thermodynamically infeasible EMs (having ΔGp° > 0), while the lycopene model contains both a higher number of thermodynamically infeasible EMs in both number (1487) and percentage (3.49%). This exemplifies the nature of a host engineered to produce a compound it does not normally produce, showing that a variety of the pathways are not evolved.Standard Gibbs energies of formation  [Gp < 0) [Gp° values should offer qualitatively correct and quantitatively reasonable estimates of the thermodynamic favorability of metabolic pathways. The change in Gibbs free energy across an entire pathway (an EM) is much more likely to be negative than the change in Gibbs free energy across individual reactions within the pathway as shown in Figure Gp° estimates to identify thermodynamically favorable reaction routes and enrich the mutant organism with these favored routes towards product and biomass production.Previous analyses have shown that most metabolic reactions are near equilibrium (|ΔGr|≈ 0) ; whereas[Gp < 0) , consistSp°) and the weighting factor of its contribution to the overall flux state in both a wild-type E. coli strain and a strain engineered for polyhydroxybutyrate production [Sp° values was then compared to flux values reported in literature and showed a strong correlation (R2 = 0.85). In an analogous manner, we utilized Gibbs free energies for flux determination similar to previous efforts [As stated previously, cellular metabolism (a flux vector) can be represented as a linear combination of the cell's EMs. It has been demonstrated previously that there exists a strong correlation between the standard change in entropy across an EM  using both equal-weighting of the EMs and thermodynamic weighting of the EMs were compared to fluxes calculated by FBA . The two cases were: aerobic production of ethanol (a native compound) and aerobic production of lycopene (a heterologous compound), both in In this case study, equal weighting of the EMs and weighting the EMs based on their corresponding Gibbs free energies led to fitness values of 1.000 for ethanol production (the fitness function described in Eq. 5) requiring 13 and 11 reaction removals, respectively. This indicates that ethanol production at the theoretical yield is thermodynamically feasible. The fitness values for the coupled ethanol and biomass production fitness function were similar, though not identical: 0.266  and 0.241 (thermodynamic weighting). The individual yields of ethanol and biomass were slightly different, with the ethanol fractional yield being higher in both cases. This highlights a potential advantage of utilizing a MOGA: the array of solutions will display a range of organism phenotypes that include: 1) high-producing, slow-growing, 2) low-producing, fast-growing, and 3) moderate-producing, moderate-growing. In most of the cases investigated here, a coupled fitness function (Eq. 7) leads to organisms generated by the third case. However, the potential in using a MOGA is the ability to choose what type of organism the researcher would like to construct based on ease of construction or process economics. As can be seen in Figure E. coli is grown anaerobically [E. coli, namely, that it is mainly produced anaerobically. Also for the majority of the cases, reactions for the pyruvate oxidase (coded by poxB) and phosphate acetyltransferase (coded by pta) were identified for removal, consistent with what has been previously reported for improving ethanol production from glucose through E. coli [frdABCD), malate dehydrogenase (coded by sfcA and maeB), or lactate dehydrogenase (ldhA), all also identified by the pervious study as a near optimal producing genotype.Whenever ethanol was being optimized (either by itself or with biomass), reactions for either NADH dehydrogenase I/ATP synthase (OPM1) or NADH dehydrogenase II  were removed. Both NADH dehydrogenase I and II are involved in driving electron flow, while NADH dehydrogenase I is driven by oxygen. NADH dehydrogenase II uses NADH exclusively and is repressed when obically . The res E. coli . DependiE. coli (the acetic acid pathway) and the lactic acid pathway are chosen for removal over other secreted weak acid metabolites . It is therefore likely that the removal of other fermentative pathways would improve flux to the ethanologenic pathway. Taken together, the general results across many of the fitness functions suggest removal of certain fermentative and anapleurotic pathways improves cellular phenotype.All of the solutions generated strains with between 16 and 24 EMs (over a three order of magnitude reduction in EMs); the different fitness functions produced mutant genomes that shared a number of similarities. Across many of the solutions, reactions in oxidative phosphorylation (as previously described) were removed. Many of the fermentative acid pathways were also removed (most notably for acetate and lactate production), which would limit the formation of undesired byproducts. Relative few reactions in glycolysis, the TCA cycle, and the PPP were removed in the different weighting schemes. It is also interesting to note that the main fermentative pathway preferred by E. coli. The frdA and ndh knockouts were also identified by an EMA-based algorithm and implemented in the laboratory to improve ethanol production [nuo and atp operons were neglected in the previous model because the model was restricted to anaerobic action, therefore as stated previously, the algorithm here correctly identifies these as knockout targets . However, the nuo knockout increases glucose uptake and ethanol production, while decreasing acetate, succinate, lactate, and formate formation in an anaerobic chemostat with complex medium supplemented with glucose [As stated, many of the knockouts identified by the algorithm presented here have been reported in oduction . The nuo glucose . While t glucose ,62, multE. coli metabolic network was optimized for lycopene production. Lycopene is a C40 carotenoid natural product with antioxidant properties. Much work has been devoted to engineering lycopene biosynthesis in E. coli [Next, the  E. coli -72, due  E. coli .Using the same approach as in the ethanol case study, the results were slightly different here. In general, the solutions generated strains with more EMs (between 18 and 174), perhaps due to the fact that the number of EMs in the parent network was nearly 30% larger for this model. First, the thermodynamically-weighted cases often converged to lower values than the equal-weighted cases when lycopene yield was included in the fitness function. Second, the fitness value for both the product yield and biomass yield optimization cases were suboptimal (less than one). While this was the case for biomass production in the ethanol model, it was not the case for product formation. This is likely due to the fact that the ethanol model had 14 EMs capable of producing the theoretical yield of product on glucose, while the lycopene model only had 1 EM that produced the theoretical yield. This genotype resulted in 36 reaction removals, which is well above the number of reaction removals found in the optimal solutions presented in Table E. coli [gdhA, cyoA, gpmAB/yjtC, ppc, glyA, eno, and aceE), two of which are not included in the model used here as they pertain to amino acid metabolic pathways (gdhA and glyA). Of the other five, all were identified in some capacity by our model when optimizing for lycopene or lycopene and biomass, some of them in multiple cases. Of these computationally identified knockouts, numerous single-, double-, and triple-knockout strains were constructed in the laboratory and showed improved lycopene-producing phenotypes.A pioneering study on applying computational methods  for driving metabolic engineering studies focused on lycopene production from glucose minimal medium through E. coli . The sinfdhF knockout  improved specific lycopene production by 4%. Combining these two knockouts with a gdhA knockout  resulted in the best triple knockout strain, improving specific lycopene production by 37% [nuo knockout improved specific lycopene production by 45%  in complex medium supplemented with glucose. The other knockouts identified in this case have either not been reported with respect to improving lycopene production, or are lethal to the cell (as is the case with pgk). The aceE knockout was identified by MoMA simulations and implemented in the laboratory, improving specific lycopene production by 9% in minimal medium supplemented with glucose [pykAF double-knockout improved specific lycopene production three-fold (from approximately 5 to 15 mg gDCW-1) in complex medium [ΔgdhA ΔaceE ΔfdhF triple knockout strain resulted in a lycopene yield of 2.15 mg g glucose-1 [E. coli strongly supports the validity of the algorithm developed here.The n by 37% . The nuo glucose . The pykx medium . While mlucose-1 , less thGiven the dual objective nature of the system in question (product yield and biomass yield), it would be logical to also assess the performance of a multi-objective genetic algorithm (MOGA). MOGA maximizes/minimizes a vector of objective functions  rather than a scalar objective, as was the case for the GA. As a result, there is no single, unique solution to this problem. Instead of identifying a single solution, a MOGA aims to identify a set of solutions in which an improvement in one objective requires a decrease in the other. Each solution is considered to be a non-inferior solution and the entire set of non-inferior solutions is referred to as the Pareto optima. The MOGA invoked here uses a controlled elitist genetic algorithm, a variant of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II).The multi-objective version of the algorithm was tested on the ethanol model, with both equal- and thermodynamic-weighting of the EMs. In each case, of the entire final population, only a small fraction of the individuals (<10%) had non-inferior solutions. In the case for equal-weighting of the EMs, the best individuals had fitness values of 0.3475 and 0.4375 , which has a product of 0.1520 and is much lower than the value of approximately 0.25 found in the solution of the single-objective GA with the coupled fitness function (Eq. 7). Similarly, while thermodynamically-weighting the EMs, the best individual in the Pareto optima had fitness values of 0.6885 and 0.2112 and a product of 0.1454, also much lower than the value of approximately 0.26 found in the solution of the single-objective GA with the coupled fitness function. As stated previously, an advantage of the MOGA is that it allows the user to "choose" whether to pursue constructing a strain predicted to have slightly lower growth rate but higher product yield versus a strain predicted to have a slightly higher growth rate but lower product yield  [Though MOGAs have not been used for optimizing the structure of metabolic networks, there has been a recently reported example of using one for optimizing an industrial bioprocess (penicillin V production from sogenum) . In partE. coli metabolic network for maximal production of two industrially-relevant products, ethanol and lycopene. Our results show that E. coli metabolism can be re-tailored quite efficiently for optimal or near-optimal production of a product of interest (ethanol or lycopene were examples here), biomass, or coupled product and biomass. As discussed, many of the gene knockouts identified by the algorithm to improve production formation have been tested experimentally  and have been shown to improve product formation rates.This article presents the development and application of a computationally tractable framework which combines elementary mode analysis, pathway thermodynamics, and a genetic algorithm. The framework was then used to efficiently redesign the within the context of the overall cellular network.It has been shown that the contribution of an individual EM to overall cellular metabolism can be estimated from its pathway thermodynamics . It has Generally speaking, equal-weighting of the EMs was shown as a proof-of-principle demonstration of the algorithm. At the same time, this was used as a reference to determine whether certain gene knockouts were predicted under both weighting schemes. Ideally, a significant fraction of the gene knockouts identified would be consistent between equal and thermodynamic weighting of the modes. As a result, the incorporation of thermodynamic calculations was an integral part of this algorithm providing for more accurate flux distributions .17 in silico organisms. With the genetic algorithm, the simulations here converged when evaluating only 2,500 in silico organisms .The utilization of a GA to search the solution space enables the identification of an optimal genotype in a computationally tractable amount of time. The number of reaction removals required to meet these predicted optimal values are well above what is computationally feasible through exhaustive searching. For example, even ten reaction removals  would require evaluating 2.74 × 10E. coli allowed for simultaneous utilization of pentoses and hexoses in batch culture [Metabolic and genetic networks are highly connected with significant regulation across scales, even for microbial systems. A clear disadvantage of the model and algorithm presented, as well as most of stoichiometric modeling, is the lack of integrated regulatory information. Because these models are used to study steady-state behavior, the dynamic regulation of these systems is neglected. There have been efforts to reconstruct genome-scale transcriptional and translational (TR-TR) networks and transcriptional regulatory networks (TRNs) ,75; howe culture . This shE. coli model of 110 reactions (28 of which were reversible) using any combination of glucose, succinate, glycerol, and acetate contained 507,632 EMs [E. coli, minimal medium with a single carbon-source is often used such that many of the reactions in E. coli metabolism would not acquire flux. Therefore, the engineering of high-flux pathways , as represented in this small-scale model, would have more impact on product formation. Very recently, the concept of elementary flux patterns was introduced, where an elementary flux pattern is defined as a set of reactions within a subsystem of a larger network that represents the basic routes of each steady-state flux of the larger network through the sub-network [K-shortest EMs within a genome-scale metabolic network utilizing integer linear programming [A potential limitation of this method is the utilization of EMA, which is computationally intensive and currently cannot be applied to genome-scale metabolic networks. As cited previously, the computation time of EMA algorithms grows approximately quadratically with respect to the number of EMs and the number of EMs grows exponentially with respect to network size. For example, an ,632 EMs . However-network . They argramming . The algE. coli stoichiometric models utilized in this study were based on one previously developed [Zymomonas mobilis; this reaction is not native to E. coli and was therefore also removed.The two small-scale eveloped . BrieflyE. coli) previously used to support heterologous carotenoid production [dxs and ispCDEFGH) held the stoichiometry: glyceraldehyde-3-phosphate + pyruvate + 2 NADPH + ATP → dimethylallyl diphosphate (DMAPP) + CO2 + 2 NADP+ + ADP. The second reaction was for the reversible isomerization of DMAPP and isopentyl diphosphate (IPP), encoded by idi. The third reaction held the stoichiometry 4 IPP → geranylgeranyl diphosphate (GGPP) and is encoded by ispA and crtE. The last reaction was for lycopene biosynthesis and held the stoichiometry 2 GGPP + 8 NADPH → lycopene + 8 NADP+, and is encoded by crtBI. To avoid the inclusion of a specific transport reaction, lycopene was not balanced in this reaction; however, it was taken into account for thermodynamic calculations. The final model included three more metabolites and four more reactions than the ethanol model.For the lycopene case study, the ethanol model previously described served as a basis with four additional reactions added. Lycopene biosynthesis was introduced into the model and coupled to the non-mevalonate pathway .Elementary mode analysis (EMA) was undertaken utilizing the bit pattern tree method . DevelopGf° of metabolites by decomposing a single molecular structure into a subset of smaller functional groups, each individually contributing to overall ΔGf° values. The ΔGr° is then known as a result of the known stoichiometry of the reaction in question. Although currency metabolites were not included in the stoichiometric model, they were accounted for in the Gibbs free energy calculations to ensure consistency with reported data. All of the metabolites used in the stoichiometric models utilized here had corresponding ΔGf° values reported recently [The group contribution method of Mavrovouniotis was used in this study to estimate the standard Gibbs free energy of reaction for all of the model reactions . Brieflyrecently .E. coli due to the organism's biochemical knowledge and sequenced genome [n therefore represents a single individual in the GA population.Chromosomal representation of the metabolic genotype for passing to the genetic algorithm is binary in nature where a "1" indicates the reaction is included in the individual and "0" indicates that the reaction is not present. For simplicity's sake, a one-to-one association between reactions in the network and genes in the GA's population was assumed. This one-to-one association decreases computation time by utilizing fewer variables for optimization. This one-to-one association does not present a significant problem experimentally, for the gene-associations with the enzymes catalyzing the reactions are well-known for d genome -91. A biInitialization of a population is a critical step for determining the success of the algorithm to find the global optimum. An initial population of fifty individuals containing between two and six knockouts was seeded to the algorithm (using MATLAB's "randerr" function). This was arrived at empirically as randomly seeding individuals with approximately 50% 0's resulted in mostly non-viable strains and did not allow for the GA to reach the optimal solution. Next, each individual in the population is evaluated and given a fitness score. A previous study on using GAs to optimize genotypic space for succinate, glycerol, and vanillin production used product flux determined by optimization (FBA and MoMA) as a scoring function . As stat-6) which was always between 50 and 100 generations.Genetic algorithms use crossover of the chromosomes  and mutation (change a "0" to "1" and vice-versa with a specified frequency) to evolve the solution population. The implementation here was interfaced with The MathWorks™ MATLAB software and its Genetic Algorithm & Direct Search Toolbox. For crossover, mutation, and selection of individuals, two-point, uniform, and tournament-based methods were used, respectively. These parameters were not optimized in this study. As stated, the population size was chosen as fifty individuals, with five of the top performing individuals automatically passed to the next generation of the GA. The selection function used in the GA was either roulette- or tournament-based. The GA always terminated as a result of being below the tolerance  reactions that were determined to either 1) reduce maximal product yield to zero, or 2) reduce maximal biomass yield to zero . This reduced the genotypic space from 60 to 49 variables in the ethanol case study and 64 to 52 variables in the lycopene case study.M, with a weighting-vector, c. Here, n is the number of EMs.For the ethanol and lycopene case-studies, three fitness functions were examined utilizing both equal-weighting of the EMs as well as thermodynamically-weighted EMs. The flux vector can be recreated by taking the linear algebra inner-product of the EM matrix, c, is determined. For the equal-weighting method:The differences in the two methods are in how the weighting vector, Gp° values must be calculated from the ΔGr° values:For the case in which the EMs are weighted by thermodynamic calculations, the Δc, is calculated with the following relationship:Next, because it was previously determined that there existed a logarithmic relationship between the weighting factor of a particular EM and its contribution to the overall flux distribution with the change in entropy of the pathway, the weighting factor vector, T represents for temperature, which was taken to be 310.15K . To satisfy the constraint that the sum of the weighting vector must be equal to unity, the weighting vector is then divided by the sum of the weighting vectors.Here, the both a product and biomass on a particular substrate is impossible. Equation 5 was used to optimize a network structure for yield of product, P, on a substrate, S .Three different fitness functions with different goals were examined. The fitness functions corresponding to Eq. 5, Eq. 6, and Eq. 7 are all non-dimensionalized to unity by dividing by the theoretical product of biomass yields on substrate. However, achieving the theoretical yield of X) yield on substrate:Equation 6 was used to optimize for the biomass  . This waS is the stoichiometric matrix as described as previously and v is the flux vector.Here, z = cTvMaximize: c is a row vector containing weighting factors for individual fluxes on the objective function, z. For FBA calculations, this objective is solely the biomass reaction flux. ai and bi are the lower and upper bounds, respectively, of each flux as determined by either thermodynamics or experimental measurements.In this optimization framework, The MOGA invoked the same crossover, mutation, and selection algorithms as in the single-objective GA. Here, 200 individuals were used per population and the initial population was seeded randomly using between two and six removed reactions. The MOGA was run on the ethanol model using both equal-weighted and thermodynamic-weighted EMs subject to the two following fitness functions (those from Eq. 5 and Eq. 6):The computation time for these MOGA simulations was much greater than the single-objective GA simulations, as expected. These simulations generally terminated after approximately 48 hours running on the same computer system described above.Gf°: standard change in Gibbs free energy of formation; ΔGp°: standard change in Gibbs free energy across a pathway/EM; ΔGr°: standard change in Gibbs free energy across a reaction; ΔSp°: standard change in entropy across a pathway/EM; EM: elementary mode; EMA: elementary mode analysis; FBA: flux balance analysis; GA: genetic algorithm; MFA: metabolic flux analysis; MOGA: multi-objective genetic algorithm; MoMA: minimization of metabolic adjustment; NSGA-II: non-dominated sorting genetic algorithm-II; ROOM: regulatory on/off minimization; TRN: transcriptional regulatory network; TR-TR: transcriptional and translational.ΔBAB conceived of the study, participated in its design, performed simulations, and helped draft the manuscript. HS calculated thermodynamic values. KL conceived of the study, participated in its design, and helped draft the manuscript. BAP participated in the study's design and helped draft the manuscript. All authors read and approved the final manuscript.Ethanol model information. A table describing the ethanol model containing reaction number, abbreviation, stoichiometry, as well as corresponding gene names and enzymes.Click here for fileLycopene model information. A table describing the lycopene model containing reaction number, abbreviation, stoichiometry, as well as corresponding gene names and enzymes.Click here for file