Metabolomics, synthetic biology, and microbiome research demand information about organism-scale metabolic networks. The convergence of genome sequencing and computational inference of metabolic networks has enabled great progress toward satisfying that demand by generating metabolic reconstructions from the genomes of thousands of sequenced organisms. Visualization of whole metabolic networks is critical for aiding researchers in understanding, analyzing, and exploiting those reconstructions. We have developed bioinformatics software tools that automatically generate a full metabolic-network diagram for an organism, and that enable searching and analyses of the network. The software generates metabolic-network diagrams for unicellular organisms, for multi-cellular organisms, and for pan-genomes and organism communities. Search tools enable users to find genes, metabolites, enzymes, reactions, and pathways within a diagram. The diagrams are zoomable to enable researchers to study local neighborhoods in detail and to see the big picture. The diagrams also serve as tools for comparison of metabolic networks and for interpreting high-throughput datasets, including transcriptomics, metabolomics, and reaction fluxes computed by metabolic models. These data can be overlaid on the metabolic charts to produce animated zoomable displays of metabolic flux and metabolite abundance. The BioCyc.org website contains whole-network diagrams for more than 18,000 sequenced organisms. The ready availability of organism-specific metabolic network diagrams and associated tools for almost any sequenced organism are useful for researchers working to better understand the metabolism of their organism and to interpret high-throughput datasets in a metabolic context. Synthetic biologists, metabolomics researchers, and microbiome researchers increasingly demand information regarding organism-scale metabolic networks. Conversely, the convergence of genome sequencing with computational methods for metabolic network reconstruction have yielded organism-scale metabolic network information for thousands of sequenced organisms. These networks are large, complex, and highly interconnected, and are therefore challenging for scientists to comprehend. Visualizing metabolic networks accelerates scientific understanding and analysis, and enables scientists to perform numerous network-based analysis operations, such as comparing the networks of one or more organisms, and interpreting omics datasets.We present a rich set of bioinformatics tools that are available within the Pathway Tools (PTools) software for generating and manipulating organism-scale metabolic network diagrams. The simplest versions of these metabolic charts depict the full metabolic network of a unicellular organism. The charts have also recently been extended to depict the different subnetworks that are active in the different cell types of multi-cellular organisms. These charts have also been extended to depict the pan metabolic network computed from a pan-genome and to illustrate the metabolic networks of an organism community. Pathway Tools’ metabolic charts are also used to visualize comparisons of genome-scale metabolic networks and serve as tools for interpreting high-throughput datasets, including transcriptomics data, metabolomics data, and metabolic fluxes computed by metabolic models. These tools have been evolving for several years and have recently been re-engineered for faster operation with higher quality graphics within modern web browsers.The remainder of the Introduction summarizes our past work on PTools metabolic charts including their graphical organization and generation. That past work lays the foundation for the recent enhancements presented in the Results section. The new implementation is JavaScript-based for speed and improved graphics quality. It provides fast semantic zooming whose most detailed level identifies metabolites, genes, enzymes, and pathways. The new diagram gives animated views of omics data with a dynamically controlled color scale.BioCyc.org [PTools ,2 is an oCyc.org .PTools metabolic charts have evolved through multiple generations of improvements ,10,11,12Escherichia coli is at Reference [Each PTools metabolic chart, also known as a cellular overview diagram, is organized according to the cellular architecture of the organism (that architecture is described within the PGDB), depicting the cytosol, extracellular space, and plasma membrane. For Gram-negative bacteria, an additional outer membrane and periplasm are included (see eference ). WithinTransporters and other membrane proteins are drawn on the appropriate membrane, and reactions or proteins located in the periplasm or extracellular space are drawn between or outside the membranes. Lines in the chart depict biochemical reactions, and nodes depict metabolites. Nodes are shape coded, for example, to distinguish amino acids from carbohydrates from tRNAs.BioCyc.org via the command Metabolism→Generate Metabolic Map Poster.Connections between pathways are not shown to keep the diagram from becoming unduly tangled, except insofar as pathways are combined into superpathways that are defined in the PGDB. Using the desktop PTools, the user can interactively add selected connections between metabolites to explore the connectivity of the network. A PDF version of the chart for any organism, which can be printed as a poster, is available at The input required to construct a PTools metabolic chart is the metabolic network of one or more organisms described as one or more PGDBs. Each PGDB can capture the genome, proteome, metabolome, reactome, and metabolic pathways of an organism. PGDBs in turn are created by the PathoLogic module of PTools, which computes a metabolic reconstruction from a user-supplied annotated genome. All metabolic charts in this article were generated from PGDBs obtained from BioCyc. BioCyc PGDBs were generated from GenBank annotations with varying degrees of subsequent manual curation.Most BioCyc metabolic charts are organism-specific in the sense that they include only the pathways, reactions, enzymes, genes, and metabolites present in a single organism’s PGDB. When the chart is regenerated, it automatically includes the latest information from the organism’s PGDB, such as reactions or pathways that curators have deleted or added using the PTools editors .PTools creation of a new diagram follows the following procedure.Query the PGDB to determine the cellular architecture of the organism, meaning what membranes and cellular spaces are presentQuery the PGDB to determine the sets of reactions, proteins, and pathways present in different regions of the diagram, such as the sets of biosynthetic, catabolic, and energy-related pathwaysLay out each individual pathway diagram using PTools pathway layout algorithms Run a layout algorithm that arranges the pathways within each pathway block (such as Amino Acid Biosynthesis)Run a layout algorithm that arranges the pathway blocks relative to one another within the biosynthesis, catabolism, and energy-metabolism regionsLay out the grids of individual reactions in the cytosol, periplasm (if applicable), and extracellular spaceArrange the transporters in the cellular membrane(s)We recently re-engineered the web version of PTools charts to overcome several limitations of the previous implementation. The previous implementation used sets of tiled images at different zoom levels that were generated on the server side. The diagram was slow to zoom  because the tiled images were slow for the web browser to download from the server. Also problematic was the existence of discrete zoom levels for the diagram—the user could not obtain a zoom level in between those pre-specified levels.BioCyc.org.In the new implementation see  the grapTo achieve smooth semantic zooming see , four diTooltips provide further details when the user mouses over a metabolite or a reaction, such as the reaction equation, EC number, enzyme name(s), and containing pathway(s). E. coli metabolic chart highlighting all genes directly regulated by FNR, a transcriptional regulator that mediates the transition from aerobic to anaerobic growth.Search operations are available in the right-sidebar menu to locate genes, metabolites, reactions and pathways of interest within a chart. For example, the user can search for reactions by name, identifier, substring, EC number, enzyme name, evidence code, and by cellular location of the enzyme. In addition, users can search by regulation , or by curation level . The Species Comparison operation highlights all reactions shared or not shared with one or more other selected organisms. Because BioCyc charts are so information-dense, visually picking out all highlighted entities can be difficult. In the web implementation, we offer two solutions. Sliders at the top of the page enable the user to decrease the opacity of non-highlighted portions of the diagram and/or increase the width of highlighted reaction edges relative to non-highlighted edges. Either individually or in combination, these simple adjustments make the highlighted entities stand out visually. Alternatively, the user can request a list of all entities highlighted in a particular operation and then select one to identify with a distinct marker icon.A particular metabolite may appear in multiple different reactions, and a particular reaction may appear in multiple pathways within a chart. In the desktop implementation, right-clicking on a compound node or reaction edge brings up a menu of operations, including navigating to the detail page for that compound, reaction or pathway either in the main display or in a pop-up window, and highlighting the compound, reaction, pathway, or all reactions of the compound everywhere they appear within the diagram. One option in the compound menu is to draw connections from that compound node to other instances of that compound elsewhere in the chart. A control panel enables the user to selectively hide or show subsets of possible connections.A new visualization, currently available only in the downloadable PTools software running in desktop mode, depicts the metabolic chart customized for the metabolic reactions and pathways active in specific cell types. When a PGDB captures a representation of multiple different cell types, each protein can be annotated with the set of cell types in which it has been observed. We have defined six cell types in the HumanCyc database: endothelial cell, hepatocyte, leukocyte, oocyte, sperm, and type B pancreatic cell. These cell types were selected because protein data for them is available and could be imported from the Bgee database of gene expression patterns . When viClostridioides difficile, Escherichia coli, Helicobacter pylori, Listeria monocytogenes, Mycobacterium tuberculosis, Pseudomonas putida, Salmonella enterica, Shigella flexneri, and Vibrio cholerae.Although most metabolic charts include pathways, reactions and enzymes for a single organism, BioCyc also includes several pan-genome PGDBs. These databases contain the union of all genes, enzymes, reactions, and pathways for all strains of a particular species for which annotated genomes are present in BioCyc. Thus, the metabolic chart for a pan-genome PGDB illustrates the full range of metabolic and transport functionality across members of the species. Pan-genome databases are currently available in BioCyc for nine medically important and well-studied species: A pan-genome PGDB is constructed as follows. A new, empty PGDB for a species is created. We select a so-called “lead PGDB” from the set of available strain-specific PGDBs. It is usually the earliest sequenced, most experimentally characterised, and best annotated strain. All of the lead organism’s replicons, genes, proteins, reactions, and pathways are imported into new the pan-genome PGDB. Thereafter, all remaining strain PGDBs from the chosen set are visited, and each protein-coding gene in that PGDB is checked for orthology with the genes in the pan-genome PGDB. If an ortholog is found, the software records the existence of the ortholog in the gene of the pan-genome PGDB. If no ortholog is found, then the gene is imported from the strain PGDB, along with its proteins and any reactions and pathways associated with that gene that are not yet in the pan-genome PGDB.Pseudomonas putida pan-genome, with both core and unique genes highlighted.Two additional search options are available for pan-genome metabolic charts. Under the web Highlight Gene(s) menu are commands to highlight either pan-genome core genes or pan-genome unique genes. Core genes are those for which orthologs exist in all strains of the species. Thus, this highlight command illustrates the metabolic and transport functionality that is a fundamental characteristic of the species. Unique genes are those that only exist in a single strain. Note that some reactions will be highlighted both as core and unique if they have multiple isozymes, one of which is part of the core genome and another of which is unique to one strain. A new visualization, currently only available in the downloadable PTools software running in desktop mode, is the community overview diagram, which combines the metabolic charts for multiple selected organisms, along with optionally one or more exchanged metabolites, into a single display see . The metThe user must specify the set of exchange metabolites to be included, if any. If particular metabolites are known to be exchanged, they can be specified explicitly, along with which organisms in the community import and export those metabolites. Alternatively, the user can request that the software suggests possible exchange metabolites. Suggestions are based on the presence of influx or efflux transporters for a metabolite, and/or the identification of metabolites that are consumed but not produced in a dead-end metabolite analysis.Most of the same search and highlight operations that are available for BioCyc single-organism metabolic charts have been extended to also support searching and highlighting across all the organisms that make up a community overview. Many of these highlight operations give the user the choice of applying them to all of the organisms in the community or to just one or a subset of them.Combining metabolic charts for multiple organisms into a single diagram facilitates new species-comparison operations. We have added four new highlighting operations: reactions present in all organisms, pathways present in all organisms, reactions unique to a single organism, and pathways unique to a single organism. A pathway is considered present in an organism so long as some variant of it is present. For example, one organism might have a different variant of an arginine degradation pathway than some other organism—for the purposes of this comparison, these are not considered unique pathways.A PTools metabolic chart can be used as a vehicle for metabolism-based interpretation of omics data, such as gene expression or metabolomics data. In this mode of use the chart color codes reactions and metabolites according to omics data values provided in an input file, and enables the user to see which pathways and reactions are more or less active under some set of experimental conditions. The tool automatically maps the omics data range to a user-selected color scale. A data series that consists of multiple time points or conditions can be viewed as an animation. In the web implementation, the control panel to the right of Users can input omics data to this tool in several ways. Data can be uploaded from a tab-delimited file, from a SmartTable, or imported directly from GEO  curated When transcriptomics or proteomics data are displayed, mousing over a reaction (or mousing over a metabolite when metabolomics data are shown) in a chart and clicking the Omics button in the resulting tooltip window generates an “omics-popup” window that graphs the data for the relevant objects over the entire data series. The user can choose whether this data is shown as a bar graph, an X-Y plot, or a heatmap. Omics data can be overlaid onto a community overview diagram, just as for a single-organism diagram. Users specify which of the organisms in the community have available omics datasets and supply the data for each organism in a separate file.N most highly perturbed pathways based on a pathway-perturbation score calculated from the omics data; (3) on a user-specified set of pathways (a Pathway Collage); (4) on a genome-scale regulatory network diagram called the regulatory overview [This tool is part of a full suite of omics analysis and visualization tools available in PTools. In addition to displaying omics data on metabolic charts, data can be viewed (1) on individual pathway diagrams; (2) on a table of the overview ; and (5)PTools supports a variety of other analysis tools, many of which are tightly integrated with metabolic charts, making visualizing analysis results from multiple biological perspectives easy. Tools integrated with metabolic charts include the following:SmartTables  enable uE. coli). The steady state reaction fluxes computed by a model can be painted onto the metabolic chart for that organism, to visualize the activity levels of different portions of the metabolic network under the modeled conditions.MetaFlux  enables A dead-end metabolite analysis tool generates lists of metabolites that are either consumed but not produced, or produced but not consumed by any reaction in an organism’s metabolic network. These metabolites represent either true cellular inputs and outputs, or gaps in the metabolic network corresponding to missing information. The metabolite lists generated by such an analysis can be highlighted on the metabolic chart.A chokepoint analysis tool identifies reactions that are potential drug targets because they represent chokepoints in the metabolic network, such that eliminating them would eliminate the only path to or from a particular metabolite. These reactions can be highlighted on a metabolic chart.The Pathway Collage Viewer  enables The Omics Dashboard  is a novIn this section we compare PTools metabolic charts with those from several other tools: KEGG Mapper , KEGG AtPTools metabolic charts have been developed over many years and have grown from a manually drawn diagram for a single organism to automatically formatted diagrams for more than 18,000 organisms. The charts depict which pathways are active in different cell types and can be used to analyze pan-genomes and organism communities. PTools charts are viewable online and printable as posters. Their myriad search operations enable users to rapidly locate enzymes, pathways, and metabolites of interest, and to compare the metabolic networks of different organisms. PTools metabolic charts are tightly integrated with other modules of PTools including quantitative metabolic models, SmartTables, computation of dead-end metabolites and metabolic choke points, and with Pathway Collages and the Omics Dashboard. A new JavaScript-based implementation of BioCyc charts provides higher-quality graphics and enables real-time semantic zooming of the diagrams and animated overlay of omics data with dynamic control of the color scale.Project name: Pathway Tools.https://brg.ai.sri.com/ptools/.Project home page: Operating systems: Linux, MacOS and Windows.Programming languages: Common Lisp and JavaScript.https://BioCyc.org/download.shtml.License: Pathway Tools is free to academic users, and is available for a fee to commercial users. To obtain the software, see


Phosphates are ubiquitous molecules that enable critical intracellular biochemical reactions. Therefore, cells have elaborate responses to phosphate limitation. Our understanding of long-term transcriptional responses to phosphate limitation is extensive. Contrastingly, a systems-level perspective presenting unifying biochemical concepts to interpret how phosphate balance is critically coupled to (and controls) metabolic information flow is missing. To conceptualize such processes, utilizing yeast metabolic networks we categorize phosphates utilized in metabolism into cycles, sources and sinks. Through this, we identify metabolic reactions leading to putative phosphate sources or sinks. With this conceptualization, we illustrate how mass action driven flux towards sources and sinks enable cells to manage phosphate availability during transient/immediate phosphate limitations. We thereby identify how intracellular phosphate availability will predictably alter specific nodes in carbon metabolism, and determine signature cellular metabolic states. Finally, we identify a need to understand intracellular phosphate pools, in order to address mechanisms of phosphate regulation and restoration. Phosphorus, like other essential chemical elements – carbon, nitrogen, oxygen, and sulfur, is central to life. Inside cells, phosphorus is found in the form of salts and esters of phosphoric acid , and is widely present in a range of macromolecules . PhosphaSaccharomyces cerevisiae. For example, in yeast, the cellular transcriptional response to extended phosphate limitation is mediated by the PHO pathway  synthesis proteins and vacuolar polyphosphatase (Most cells (particularly free-living microbes or sessile organisms) experience fluctuations in available nutrients. Therefore, cells have evolved multiple regulatory mechanisms to sense and adapt to nutrients. In the contexts of phosphate availability, such regulatory responses have been well studied in plants, bacteria, or model eukaryotic cells such as the budding yeast  pathway . This sysphatase , which csphatase , bacterisphatase  and othesphatase .In contrast to our extensive knowledge about regulated gene expression during phosphate starvation, how distinct nodes in cellular metabolism are themselves coupled to phosphate balance is surprisingly not as clear. Effectively, our collective understanding of phosphate demand and utilization, and the role of phosphates in regulating the metabolic state of the cell, remains poor. In this perspective, we first identify metabolic processes that are irrevocably coupled to phosphate balance, and therefore overall cellular metabolic homeostasis. We illustrate how cellular metabolism depends on intracellular phosphate amounts, and can maintain Pi levels, by effectively ‘squeezing’ internal phosphate availability through specific metabolic outputs. We conceptualize phosphates in central metabolism into cycles, sources, and sinks. By defining and distinguishing these roles, it now becomes possible to more systematically contextualize how phosphates will control biochemical information flow in cells, and thereby determine cellular metabolic states.Phosphates are integral components of lipids, nucleic acids, proteins, and sugars. They are present in many energetically costly metabolites, including reducing equivalents in the form of pyridine nucleotides (NADH and NADPH), cellular energy currencies (represented by adenosine triphosphate (ATP), phosphoribosyl phosphate (PRPP), pyrophosphates (PPi), pyridoxal phosphate (PLP)), and signaling molecules like inositol phosphates. Each of these molecules has substantial metabolic roles. Indeed, phosphates are ubiquitous, because of their unique chemistry. They easily ionize (and are retained within cells), yet phosphate bonds are stable, and so phosphates are ideally suited to link nucleotides, function as intermediary metabolites, and serve as energy sources . Under pas long as the total amounts of these metabolites are unchanged. These enclosed ‘phosphate cycles’ use phosphates integrally in their reaction mechanisms. Therefore, although these reactions require phosphates, they can be considered distinct from the metabolic reactions that can immediately affect the total phosphate pools available in the cell, or reactions that must most rapidly change when phosphates become limiting (these are discussed later). Of course, the absolute amounts of these metabolites do change, depending on the metabolic needs of the cell. By first separating out these closed phosphate cycles, we can now conceptualize how other, distinct phosphate utilizing/dependent reactions (which are not part of these phosphate cycles) can be critical for phosphate homeostasis, and consequently regulate overall carbon metabolic flux.Importantly, such instances can be viewed as contained biochemical systems. If there is a fixed amount of phosphates, no new phosphate molecules are required for such a system to continue indefinitely, S. cerevisiae and plants  extreme phosphate starvation, due to a severe or continuing depletion of phosphate in the extracellular environment, or (2) transient limitations in phosphate availability and/or in intracellular Pi levels. Our understanding of transcriptional responses to extreme phosphate starvation is reasonably advanced, at least in model systems like d plants . Here, uIn contrast to severe phosphate starvation, there can also be transient limitations in internal phosphate levels. In such contexts, even before the phosphate-responsive gene-regulatory programs fully come into effect, changes in metabolism can immediately restore intracellular phosphate levels. We illustrate how this can happen, using a hypothetical reaction network . In suchA notable point emerges if such mobilization of metabolic Pi stores by mass-action based processes occur: as we will illustrate subsequently, there will be an accompanying rewiring of overall carbon flow, where reactions that release Pi are favored. This is associated with the accumulation of other central carbon (glucose) derived metabolites. This therefore highlights an underappreciated point of how tightly central carbon metabolism is coupled to phosphate homeostasis. By clearly identifying nodes of metabolism that will change with phosphate availability, we can predictably address how intracellular Pi changes will re-route carbon flux through very specific nodes of carbon metabolism to alter cellular metabolic states.sources of phosphate can now be defined as metabolites which themselves may not contain phosphate/phosphorus, but importantly their synthesis results in phosphate release. These metabolites will therefore restore phosphate pools and balance Pi during transient Pi fluctuations. However, in order to do so, they should satisfy the following criteria; their synthesis should increase in response to phosphate limitation (and be accompanied by Pi release), the metabolic flux towards these molecules should be  high, and they need not always accumulate in the cell. This definition therefore alters the idea of a source from a phosphate-containing molecule, to include molecules that themselves do not contain phosphates, but are made concurrent with Pi release. The metabolic precursors of these sources will be phosphate-containing molecules. As we will exemplify shortly, many metabolic pathway intermediates or ‘end products’ that do not themselves contain phosphates will act as very effective phosphate sources, since Pi will be released during the synthesis of these molecules.Extending beyond closed biochemical reactions where phosphates continuously cycle (discussed in the earlier section), we can now organize phosphate-dependent metabolic reactions into classes that would affect the internal phosphate amounts distinctly. These metabolites can be classified into two groups – phosphate sources and sinks . Here, ssinks of phosphate will be phosphate-containing metabolites, where the synthesis of these metabolites results in the storage of excess Pi. Sinks therefore should satisfy the following criteria; the synthesis of these molecules should decrease in response to phosphate limitation, they should have a slow turnover rate, and should accumulate in abundance.Contrarily, By using such a definition, it becomes clear that a source and a sink need not necessarily be the same molecules, and in fact may often not even be in the same biochemical pathway. However, their respective synthesis must be anti-correlated in the cell, in response to phosphate limitation. This central idea is illustrated in PHO response (which mimics phosphate limitation), results in carbon (glucose) flux rerouted towards trehalose synthesis, and away from the pentose phosphate pathway (PPP) and glycolysis (tps2Δ cells), this decreases the cellular phosphate pools  to idenycolysis . This isycolysis . Furtherte pools . Taken tte pools . In linete pools . Moreovete pools . This suThree other major biosynthetic processes derived from glucose metabolism result in abundant products and also release phosphate. Serine biosynthesis from 3-phosphoglycerate (3PG) occurs in three steps, and the last step releases one Pi molecule. Chorismate synthesis  requires one molecule of erythrose-4-P (E4P) (from the pentose phosphate pathway) and two molecules of phosphoenolpyruvate (PEP), and occurs in seven steps. Here, three molecules of Pi are released . The pre+, inositol pyrophosphates, and polyphosphates (PolyP) are all putative phosphate sinks (and not sources). Is there evidence that is consistent with the plausibility of these metabolites as phosphate sinks? Going by the earlier described criteria of a sink, these metabolites are abundant in cells . Phosphate limitation results in a rapid decrease in both their synthesis and steady-state levels , which mimics phosphate limitation, also revealed reduced de novo nucleotide synthesis. This was not due to reduced amounts of nucleotide biosynthesis enzymes, but instead was governed by mass action in cells . A secone levels . In a res action . Furthers action . Phm8, as action . The rel+ and its intermediate metabolites also become potential phosphate sinks. Although direct estimates of these molecules during phosphate limitation have not been made, we can predict that there will be reduced synthesis of these metabolites, as they utilize nucleotide triphosphates as their phosphate donor, and nucleotide synthesis itself decreases under these conditions. Indeed, consistent with this prediction, during low Pi conditions, pyridine nucleotides, NAD+ and NAD+ intermediates (NMN and NaMN) are broken down by specific nucleotidases, and this will also release phosphate hosphate . Indeed,tabolism .+ molecules as Pi sinks, two relevant points emerge. In an insightful review, Bogan and Brenner summarize that ribonucleoside monophosphates  come from both salvage and de novo synthesis. The 5’-nucleotidases themselves allow the reverse reactions of nucleoside kinases  eration) . These oeration) . These pPHO related transcripts in yeast , we can obtain insights into coordinated process that maintain phosphate levels. In this article, we have conceptualized and categorized phosphates into metabolic cycles, and then sinks and source. This is a first step toward building an integrative understanding of how phosphates control metabolic information flow. Since the metabolic control of phosphate homeostasis depends on central carbon metabolism and vice versa, identifying control-hubs that facilitate cross-talk between these two systems should therefore be an exciting area of future inquiry.


Synechococcus sp. PCC 7002, a cyanobacterium with large potential to produce renewable biofuels. We use regularized flux balance analysis to observe flux response between conditions across photosynthesis and energy metabolism. We then incorporate principal-component analysis, k-means clustering, and LASSO regularization to reduce dimensionality and extract key cross-omic features. Our results suggest that combining metabolic modeling with machine learning elucidates mechanisms used by cyanobacteria to cope with fluctuations in light intensity and salinity that cannot be detected using transcriptomics alone. Furthermore, GSMMs introduce critical mechanistic details that improve the performance of omic-based machine learning methods.Machine learning has recently emerged as a promising tool for inferring multi-omic relationships in biological systems. At the same time, genome-scale metabolic models (GSMMs) can be integrated with such multi-omic data to refine phenotypic predictions. In this work, we use a multi-omic machine learning pipeline to analyze a GSMM of   •Synechococcus sp. PCC 7002 is presentedA pipeline for metabolic modeling in •Metabolic fluxes display clear differences in pathway activity across conditions•Omic-informed GSMMs provide critical mechanistic details within machine learning•Combining GSMM and machine learning improves methods based on transcriptomics alone Metabolic Engineering; In Silico Biology; Artificial Intelligence; Bioengineering In the field of systems biology, several approaches have been proposed to capture the enormous complexity of biological systems by utilizing mathematical modeling and computational methods, with the goal of amalgamating the information required to build and refine predictive models. The challenges presented by such an undertaking are numerous and persistent owing to the size, format, scale, and variation of the disparate data types. Among these, metabolism is currently the only biological layer that can be modeled genome-wide . ConstraIn recent years, genome-scale metabolic models (GSMMs) have been integrated with multiple data types, including omics, codon usage, enzyme costs, and limited resource availability . This seCyanobacteria is a phylum of oxygenic, phototrophic microalgae that need to adapt to constant fluctuations in temperature, salinity, light intensity (or irradiance), and nutrient availability, among other factors , primarily through maximizing their growth rates  has been utilized to estimate internal metabolic fluxes more accurately in nditions . Similar2 mutant . Such moSynechococcus genus, a comparative analysis of slow- and fast-growing strains in terms of their active reactions under phototrophic conditions has been proposed to better inform their development into production hosts , primarily by maximizing their growth rates  in various environmental conditions.k-means clustering for flux data are included in As highlighted above, our goal is to reconnect metabolism to growth and other cellular objectives using a data-driven multi-view approach that yields biologically reasonable predictions. The results of PCA and Synechococcus GSMM, and we employed a regularized FBA to obtain condition-specific flux distributions  was higher than the control condition . The biomass is likely to be higher at OD 0.4 than OD 0.7 due to adjustment of the photon constraint, which allowed for more transmission of light at lower OD. Apart from the dark anoxic and low O2 conditions, all fluxes through photosystem II were negligible, but the fluxes through photosystem I were still maintained (0.058 mmol gDW−1 h−1 in the high light intensity condition as opposed to 0.016 mmol gDW−1 h−1 in the control).As shown in −1 h−1). When photosystem II was set as the secondary objective, the highest fluxes through the photosystem II reaction were given by the phosphate limitation, mixotrophic, and low salinity conditions (0.016 mmol gDW−1 h−1).When photosystem I was set as the secondary objective, a low amount of flux through ATP maintenance reaction was retained in phosphate-limited, heat shock, and low salinity conditions  (−1 h−1 compared with 0.053 mmol gDW−1 h−1). Although the fluxes through photosystem II were disrupted, the fluxes through photosystem I were still maintained (0.058 mmol gDW−1 h−1 in the high light intensity condition as opposed to 0.016 mmol gDW−1 h−1 in the control). Heat shock resulted in no fluxes through any of the four reactions within all three objective pairs. It was previously reported that transcript levels for genes encoding photosystem I decreased slightly in cells grown at high salinity and remained constant at low salinity (m−2 s−1) . This wasalinity . On the salinity .It can be argued that analyzing single-omic data alone has limited relevance in the context of metabolic processes, as it does not capture the full complexity of the phenotype in relation to environmental variability. The hybrid approach proposed in this work connects transcriptomic and fluxomic data using a data-driven multi-view approach that supports machine learning algorithms to yield more accurate predictions . Conside∘C and oxidative stress in plot (a), and high light intensity, phosphate limitation, mixotrophic, and low salinity conditions in plots (b) and (c).The PCA indicates the proportion of variance exhibited by fluxes in the first two dimensions for each objective pair. For all three pairs of objectives in ∘C, and high salinity. Once again, sulfate and iron limitation were the highest in the second dimension, along with phosphate limitation, nitrogen limitation, dark anoxic/oxic, and the last phase of the batch growth (OD 5.0).When considering only the gene transcript data A, the coWhen using a combined dataset of both gene transcripts and fluxes  in k=6. The full list of members of each cluster is reported in the For the flux data  was used to select a subset of the input variables by minimizing the number of nonzero coefficients. It employs L1 regularization, which penalizes the sum of absolute values of all the coefficients; this sets the coefficients of unnecessary or recursive features equal to zero, resulting in a sparser matrix , as well as the growth-limiting conditions such as nitrogen limitation  demonstrated the importance of the tricarboxylic acid (TCA) cycle in the generation of energy for biomass accumulation. To illustrate this, a comparison of flux values between the nitrogen-limited and urea-supplemented growth conditions is provided in mitation A. This smitation  where thmitation .Synechocystis sp. PCC 6803, folate is synthesized from chorismate and is known to be important for cellular processes such as DNA replication, repair, and methylation, in addition to being a vital precursor for the biosynthesis of certain amino acids, co-factors, nucleotides, and tRNAs  suggest that fluxes can help to gain more biological insights into machine learning analyses. As a different, unrelated set of genes displayed a strong correlation with the growth rate, it is evident that analyzing both transcriptomic and fluxomic data provides a more complete picture of cyanobacterial metabolism than single-omic analyses. In particular, the role of metal transport pathways in cyanobacteria was significant because they are highly relevant in the context of photosynthesis. The detection of latent, biologically significant patterns and adaptive mechanisms to fluctuations in light intensity and salinity elucidates the maintenance of metabolic efficiency at the cellular level, as well as the attainment of multiple cellular objectives.in silico when developing the optimal production host, or to analyze multi-omic outputs (both independently and in combination with other omic data). In this regard, the use of transcriptomic data to characterize fluxomic predictions elucidates many of the unique mechanisms employed by Synechococcus sp. PCC 7002 when adapting to changes in light intensity, salinity, and other conditions. In the case of cyanobacteria, we also emphasize the importance of assessing model inputs in accordance with specific growth conditions before conducting FBA. These contribute to the organism's underlying objective of maintaining metabolic efficiency for phototrophic growth and light-dependent photosynthesis. As a result of predicting and classifying metabolic profiles in various growth conditions, our approach sheds light on the cross-omic mechanisms of its adaptation process, which enables survival across a wide range of environments and stress conditions.Algal engineering supplemented with data from multi-omic studies can contribute to informing the scale-up of these processes. Such multi-omic data are sensitive enough to detect the effect of stress on metabolism. Metabolic engineers could apply this pipeline to test more strategies Synechococcus sp. PCC 7002 cultures was not available. Hence, the photon uptake constraints were approximated using DCW and photon consumption based on the availability of light. Likewise, the setting of nutrient uptake rates was approximated based on data provided by in vivo experiments rather than measured directly.The availability of exact measurements for the various growth conditions could yield more precise flux predictions. For example, in our case, the exact photon absorbance of the Furthermore, in this study we adopted linear transformations and linear methods, where possible. This was with the goal of maximizing the biological interpretability of the predictions, using quadratic terms for regularization only. However, different dimensionality reduction or clustering methods could be implemented, e.g., to elucidate any further non-linear relationship among the omic elements.Finally, there is further potential for other types of omic data to be integrated into the model . It is expected that integrating further omic datasets, i.e., further data views in our multi-view machine learning setting, could produce even more detailed insights into metabolic adaptations, or better support existing findings derived from transcriptomic and fluxomic data.c.angione@tees.ac.uk.Dr. Claudio Angione, email: The study did not generate new unique reagents or other materials.https://github.com/Angione-Lab/Synechococcus7002-metabolic-modelling.The complete source code of our pipeline is freely available on GitHub at The RNA-seq data integrated into the model were from transcriptomic datasets uploaded by All methods used in this study can be found in the accompanying


Escherichia coli, iAF1260) and large  genome-scale metabolic models. EFMviz is open-source and integrated into COBRA Toolbox. The analysis workflows used for the two use cases are detailed in the two tutorials provided with EFMviz along with the data used in this study.Elementary Flux Modes (EFMs) are a tool for constraint-based modeling and metabolic network analysis. However, systematic and automated visualization of EFMs, capable of integrating various data types is still a challenge. In this study, we developed an extension for the widely adopted COBRA Toolbox, EFMviz, for analysis and graphical visualization of EFMs as networks of reactions, metabolites and genes. The analysis workflow offers a platform for EFM visualization to improve EFM interpretability by connecting COBRA toolbox with the network analysis and visualization software Cytoscape. The biological applicability of EFMviz is demonstrated in two use cases on medium ( Cellular metabolism is comprised of many parallel chemical interactions. Metabolic reactions consume or produce compounds in the cell. Proteins catalyzing these metabolic reactions are called enzymes and the conversion rate of metabolic reactions is termed metabolic flux. Metabolic reactions are concatenated into metabolic pathways which can act simultaneously in the cellular environment, forming highly connected, complex networks. In the past two decades, novel experimental technologies have resulted in an explosion of “omics” data for various organisms which, together with computational advancements, has enabled the construction of large genome-scale metabolic networks. Integration of omics data in such networks opens new avenues to understanding cellular processes in greater detail .Escherichia coli, which contains merely 110 reactions [29 [A method that has been used to comprehensively study pathways in metabolic networks is Elementary Flux Mode (EFM) analysis . EFMs preactions . In humaions [29 ,15. Therions [29 ,21,22,23ions [29 .yield analysis and EFM enrichment, (2) compare EFMs using preserved visual arrangement and subsystem occurrence, (3) assess overlap between EFMs (backbone identification) and (4) construct advanced visualizations including omics data mapping on reactions and molecules. We demonstrate the applicability of EFMviz using two genome-scale models: (1) a medium-sized, E. coli model  ), such aeference ) and (2)eference ). The anefmImport, efmFilter, efmYieldAnalysis, efmEnrichmentAnalysis, efmSubmodelExtractionAsSBML, efmSubsystemsExtraction and efmBackboneExtraction. Additionally, a tutorial accompanies each use case which walks the user through all the steps necessary to not only reproduce results from this study but also to adapt other EFMs of interest. This section describes each component of the workflow in detail  and EFM enrichment (in Use Case 2) B.The concept of “yield analysis” was first introduced by Song and Ramkrishna  as a metStatistical enrichment analysis enables identifying EFMs characterizing a biological condition. Rezola et al.  used a mUsing the above mentioned criteria, we highlight how an EFM can be selected for further analysis through visualization; for instance, EFM with minimum yield or maximum yield or the most significantly enriched EFM.Once an EFM was selected, the reactions in this EFM were identified using the model that was previously imported. All the remaining reactions were removed from the model, along with any unconnected genes and metabolites, thereby creating a “submodel” Ci. This + and H2O, the visualized network can be difficult to interpret due to their participation in numerous reactions. In such cases, these metabolites can be removed from visualization during submodel creation. In the present work, the EFMs without ubiquitous metabolites have been visualized and are described in Results, and the corresponding networks with ubiquitous metabolites are provided in the Cytoscape is an open-source tool commonly used for visualization and analysis of biological networks. It not only enables data visualization and advanced network analysis, but also network extension with other types of molecular data, all within a single framework. Additional functionality can be accessed through various apps that can easily be installed within the Cytoscape GUI. Cy3sbml  is one sE. coli) and Recon 2.2 (human).This section describes two biological applications of EFMviz on two different models, iAF1260  and lowest yields (84 EFMs) were identified. EFM 18 and the shortest EFM with lowest yield (EFM 885) were selected for visualization. A submodel corresponding to each of the selected EFMs was generated without ubiquitous metabolites and visualized in Cytoscape  compared to only 3.43 gDW−1 h−1 in As mentioned earlier, this workflow can be applied to several EFMs at a time. A useful feature for visualizing and understanding multiple networks is having the shared nodes at the same position across networks. Such a preserved arrangement facilitates visual comparison by highlighting the differences between EFMs immediately. Using the utility of Copycat Layout in Cytoscape, the node positions of The second use case demonstrates EFMviz using lactate-releasing EFMs and EFM enrichment as a means of studying Warburg effect .The publicly available RNA sequencing data from the TCGA breast cancer project was used for this analysis . Using tFor this analysis, the human reconstruction, Recon 2.2, was used. The COBRA model contains 1675 genes, 5324 metabolites and 7785 reactions.EX_glc(e)_b, (see EX_lac_L(e)_f were retained for further analysis. Statistical enrichment analysis was performed using differential gene expression to understand metabolic differences in the EFMs which describe processes involving glucose uptake and lactate release. EFM enrichment analysis resulted in 17 filtered EFMs that were significant _b, see  were loaWe further probed into “subsystem occurrence”, i.e., the distribution of reactions across subsystems, to understand the differences in the processes among the significantly enriched EFMs. The reactions in all of the 17 significantly enriched EFMs belonged to a total of 37 subsystems and were predominantly involved in transport, central carbon metabolism, fatty acid metabolism and nucleotide interconversion . About 1backbone as reactions that are present in a large number (80–90%) of EFMs. A visual comparison of such a backbone, from different proportions of EFMs, reveals the most commonly occurring reactions and gives an indication of the underlying conserved structure. Through this added functionality, the backbone reactions present in 65% and 25% of EFMs were extracted from the EFMs from E. coli  relative reaction fluxes (in Use Cases 1) and (b) differential expression of genes (in Use Case 2). Nevertheless, other molecular data, such as metabolomics, proteomics and C13 fluxes, can also be mapped effortlessly.In addition, the approach presented here facilitates both the automation of network operations in Cytoscape and the exploration of large EFMs. Due to yFiles libraries being available only in the Cytoscape application, layout application was performed using the GUI. Nevertheless, automation of network manipulation minimizes both user effort and time, thereby accelerating EFM investigation. EFMviz also allows simultaneous exploration of multiple EFMs within a single Cytoscape session. Every EFM imported into MATLAB can be visualized using EFMviz. However, trying to navigate through and understand several networks simultaneously, even 10–15, can be very difficult to comprehend. Therefore, it is highly recommended to apply a series of filtering criteria (as demonstrated in the use cases) in order to select the EFM(s) most relevant for the research question under study. EFMviz is currently limited to the MATLAB implementation of COBRA toolbox, but an EFMviz extension for COBRApy (Python) is planned to support a broader community.Apart from the advanced visualizations and data mapping, EFMviz offers various strategies for both selecting relevant EFMs and comparing EFMs. Thus, the standardized integrative workflow presented here marks an important step forward for EFM analysis. It is important to note that the visualization aspect of EFMviz is not limited to EFMs. In principle, one can visualize any set of reactions, such as (a) a subsystem, (b) a solution of a flux balance analysis (c) or any flux vector, to name a few. Combining metabolic networks with multi omics data, such an integrated visualization approach will serve as an extremely useful tool for characterizing cellular metabolism. Utilizing the powerful, open-source Cytoscape platform not only allows network visualization and data mapping, but also opens new avenues for EFM extension with other molecular components. Taken together, we demonstrate that with effective visualization of the metabolic networks, the proposed workflow can allow for a comprehensive understanding of the biological processes under investigation.


K-Ras in cancer cells involves both glucose and glutamine utilization sustaining enhanced, unrestricted growth. The development of effective anti-cancer treatments targeting metabolism may be facilitated by the identification and rational combinatorial targeting of metabolic pathways.Rewiring of metabolism induced by oncogenic We performed mass spectrometric metabolomics analysis in vitro and in vivo experiments to evaluate the efficacy of drugs and identify metabolic connectivity.K-Ras-mutant lung and colon cancer cells exhibit a distinct metabolic rewiring, the latter being more dependent on respiration. Combined treatment with the glutaminase inhibitor CB-839 and the PI3K/aldolase inhibitor NVP-BKM120 more consistently reduces cell growth of tumor xenografts. Maximal growth inhibition correlates with the disruption of redox homeostasis, involving loss of reduced glutathione regeneration, redox cofactors, and a decreased connectivity among metabolites primarily involved in nucleic acid metabolism.We show that Our findings open the way to develop metabolic connectivity profiling as a tool for a selective strategy of combined drug repositioning in precision oncology. A metabolic rewiring in which glucose is converted to lactate, while glutamine-derived α-ketoglutarate (Akg) enters the tricarboxylic acid cycle (TCA)—undergoing partial reductive carboxylation to citrate —characteK-Ras, which is mutated in approximately 35% of lung adenocarcinomas and 45% of colorectal cancers. K-Ras activation increases tumorigenicity, promotes environmental adaptation and acquisition of drug resistance, resulting in poor prognosis Gln) tracers in the different metabolites  are present in many pathways. Thus, their presence within a list of differentially regulated metabolites is sufficient to enrich for that pathway. Metabolic flux analysis allows to estimate intracellular metabolic fluxes , or BKM120 (50 mg/kg)  . Network, 1 . NetUsing the Cytoscape plugin MCODE, we could extract locally dense modules of connected metabolites from the whole A549 and HCT116 connectomes , and amino sugar metabolism Figs. A–B, sugg13C6]Glc and [U-13C6]Gln in A549 and HCT116 cells treated with both drugs  and PPP (M5-Ru5P) coming from U-1C6-Glc, o13C5]Gln and [15N]Gln stable isotopes  also uses glutamine as an amino group donor to glucose-6-phosphate, to produce glucosamine-6-phosphate. Hexosamine biosynthesis requires a coordinated utilization of glucose and glutamine, leading to glycosylation of signal transduction components regulating cell growth and proliferation . A549 cen = 28 genes) mainly participate in metabolic processes, such as organic acid, carboxylic acid, fatty acid, pyruvate, propionate, acetate, and acetyl-CoA metabolisms  involved in the redox metabolism according to the KEGG database. Among these metabolites, 14 (plus NAD+ and NADH) are common to both cell lines, 10 (plus NAD+) showing a congruent change in concentration in both A549 and HCT116 cells  with metabolites involved in other pathways (Figure Sras mutational activation, since we observe the strongest effect in A375 melanoma cells, which have two wild type ras genes. In-depth metabolic analysis is therefore required to rationalize the results of the drug treatments and to develop rational guidelines for effective combinatorial drug protocols.Concurrent drug perturbation of glucose and glutamine utilization pathways severely reduces the growth of A549 and HCT116 xenografts and cell lines. This result is consistent with the major role that glucose and glutamine play in supporting cellular proliferation. However, results reported in Figure SOur systems metabolomics analysis shows that the metabolic unbalance originated by the combinatorial drug treatment affecting both glucose utilization and glutamine metabolism may be so significant that the tumor is unable to maintain the redox homeostasis, consistently with the proposed crucial role of redox control for cancer cell growth , 45, 46.Additional file 1. Supplementary Materials.Additional file 2.Additional file 3.Additional file 4.


Gene expression and protein abundance data of cells or tissues belonging to healthy and diseased individuals can be integrated and mapped onto genome-scale metabolic networks to produce patient-derived models. As the number of available and newly developed genome-scale metabolic models increases, new methods are needed to objectively analyze large sets of models and to identify the determinants of metabolic heterogeneity. We developed a distance-based workflow that combines consensus machine learning and metabolic modeling techniques and used it to apply pattern recognition algorithms to collections of genome-scale metabolic models, both microbial and human. Model composition, network topology and flux distribution provide complementary aspects of metabolic heterogeneity in patient-specific genome-scale models of skeletal muscle. Using consensus clustering analysis we identified the metabolic processes involved in the individual responses to endurance training in older adults. •Distance metrics express heterogeneity between genome-scale metabolic models•Flux distribution and network topology are the main components of metabolic distance•Machine learning algorithms are applicable to sets of genome-scale metabolic models•We model individual responses to endurance training in older adults High-throughput techniques enable the analysis of complex biological systems at multiple levels, including genome, transcriptome, proteome, and metabolome. Integration of multi-omics data is often focused on dimensionality reduction and feature selection for classification tasks. Genome-scale metabolic models are extensive maps of the network of biochemical reactions taking place in a particular cell, tissue or organism. Each reaction is associated with the respective enzyme and gene, enabling the mapping of transcriptomics and proteomics data and providing a structure for the system-level interpretation of multi-omics datasets. The result of this process is a personalized model that gives a snapshot of the metabolic status of an individual. Analyzing these complex models, for example, to detect differences between individuals, is cumbersome. We applied consensus clustering to a set of data-driven models to monitor the progression of a lifestyle intervention in a cohort of older adults. Genome-scale metabolic models are maps of the metabolic network that function as structures for the integration of molecular data, such as transcriptomics and proteomics. We developed a method for the analysis of large sets of data-driven models, using different distance metrics to quantify model similarity. Consensus analysis is then used to reach a single metabolic distance. The method was applied to model the individual variability in the responses to endurance training in a cohort of older adults. Methods to identify clinically relevant subgroups of individuals who respond similarly to the same treatment and estimate their future outcome for a given treatment would be relevant both in research and for clinical practice, for example, to study the heterogeneous pace of aging observed in different individuals,,,,,,Genome-scale metabolic models (GSMMs) take a third, alternative approach: they mathematically reproduce the network of metabolic reactions happening inside an organism or tissue and can be used to simulate the response to specific environmental conditions, such as the availability of nutrients. The activity of each reaction in the model can be linked to experimental data, such as levels of gene expression and protein abundance, making such models a combination of data-driven and physiology-driven methods and interesting platforms for the system-level integration of multi-omics datasets.,Machine learning (ML) algorithms are able to identify patterns in very large datasets, relying on distance metrics to quantify similarity between different data points.We identified several different similarity metrics for model composition, network topology, and flux distribution and compared their properties by applying them to two large GSMMs sets: the AGORA set,GSMMs are complex data structures with three main features: they are databases of metabolic genes and the associated metabolites and biochemical reactions which were experimentally found or predicted to be present in a certain tissues or organisms; they are mathematical representations of the topology of the metabolic network; and they are used to simulate how the metabolism of a tissue or organism adapts to a particular environment or condition by limiting with upper and lower bounds the metabolic fluxes through exchange reactions with the external medium.Starting from the idea of Euclidean distance between data points as a similarity measure in ML, we asked how this concept could be expanded and applied to GSMMs. In this context, distance can be thought of as a proxy for functional similarities between the metabolisms of two organisms. As an example, let us consider Bacilli and Clostridia, two families of sporulating bacteria belonging to the same phylum (Firmicutes). What distinguishes them is the fact that the former is aerobic, and the latter is not.de facto standard to measure similarity between genome-scale models.,,One way to quantify their similarity is by measuring the proportion of biochemical reactions they have in common. This information is summarized by the Jaccard metric. We computed the pairwise Jaccard distance between hundreds of bacterial models belonging to the Bacilli (n = 197) and Clostridia (n = 131) families, which were included in the AGORA model set. The results are visualized in We hypothesized that the heterogeneity within each of these three complementary components contributed to the “total” model heterogeneity and defined a different distance metric for each of them: the Jaccard metric was used to compute the overlap between the reaction lists of a pair of models; A graph kernel, i.e., a function to compute similarity between network topologies, was used to obtain a similarity score between metabolic networks. Pearson's correlation coefficient was instead used as similarity score between normalized flux distribution vectors as a metric of similarity between constraint-based models. The flux distributions are obtained averaging 1,000 random samples of the solution space of each model, then the flux through each reaction is normalized by subtracting the mean and dividing by the standard deviation of each reaction. A more detailed discussion of these metrics can be found in the Experimental Procedures section. To compare the properties of these metrics, we computed the pairwise distances for the models in the AGORA and PD-GSM datasets for each of the three different distance metrics. To test our hypothesis, we then looked at the correlation between the resulting pairwise symmetric distance matrices. The clustered distance matrices for each of the three metrics are shown in The modest correlation between network structure, described by the first two metrics, and the flux correlation metric  can be eTo test if the observations we made regarding distance between microbial models are valid also for human metabolic models, we studied the distances in a subset of the PD-GSMM set, containing 100 patient-derived models of skin and liver metabolism.The correlation between the metrics  is lowerGiven the low correlation between flux correlation and the other two metrics, flux distribution similarity should be viewed as a separate and complementary component of metabolic heterogeneity. Nevertheless, when we applied this metric to the PD-GSMM set, the two classes overlapped significantly. From an ML perspective, the flux correlation metric could not discriminate between the two classes. A classifier algorithm trained using this similarity metric would have worse performance than one trained using the Jaccard metric. For these reasons we decided to use only the Jaccard metric as a measure of metabolic heterogeneity for the remainder of this study.The publication of large GSMM collections, such as AGORA for gut microbiota models and PD-GSM for individualized human cancer models, showed the need for new scalable methods of analysis that can be applied to large model sets. We were interested in the concept of distance between individualized models and whether it could be applied to obtain biologically relevant insights about a set of GSMMs. Once we established the properties of distance metrics in GSMMs, we developed a distance-based workflow for the characterization of heterogeneity in metabolic models sets that, through the combination of ML and constraint-based metabolic modeling techniques, such as FBA,n is the number of models in the set. Each of the three metrics gives a different view of the heterogeneity present in a given model set. A consensus clustering approach is used to reconcile these differences and give a more comprehensive and robust view of metabolic heterogeneity: agglomerative hierarchical clustering is applied separately to each of the three distance matrices, then a consensus algorithm is applied to find an agreement between the three label vectors. For this task, we considered three consensus algorithms: the cluster-based similarity partitioning algorithm, the hyper graph partitioning algorithm, and the meta-clustering algorithm.The distance between each pair of models is computed using three different metrics: Jaccard distance, graph kernel and flux correlation, resulting in three square distance matrices of size The label predicted by the consensus clustering algorithm is used to investigate the differences in the flux distributions of the models between the clusters. A flux distribution matrix is created, merging the flux distribution vectors obtained via averaging 1,000 random samples of the solution space of the models. The flux matrix is then normalized, by subtracting the mean for each flux and dividing by its standard deviation. Using the Kruskal-Wallis test,Skeletal muscle plays an important role during the aging process, not only in maintaining the ability to perform activities of daily living, but also because it increases resilience against stressors and adverse events, such as traumatic injuries and diseases.Nutritional and physical activity interventions are currently the only possible treatments to slow muscle wasting in older adults. Nevertheless, aging individuals express a large variation of health outcomes, due to causes ranging from genetic differences to socioeconomic and behavioral factors,,We developed an original set of 24 patient-derived GSMMs from longitudinal gene expression data of skeletal muscle of 12 older adults (84 ± 1 years old), before and after an intervention consisting of 12 weeks of resistance training. Although previous studies have investigated the metabolism of skeletal muscle using GSMMs,The observation that AT models are on average somewhat larger than UT models , suggestWe applied our distance-based workflow to visualize the relationships between the models in the skeletal muscle model set and to perform a cluster analysis. The first step was to compute the Jaccard distance between each pair of models. The pairwise distance matrix was clustered with hierarchical clustering, and presented as a heatmap in Health is not a single immutable state but rather can be defined as a set of dynamic processes at different points in time that together form a health trajectory.The ability to model the health trajectories of different individuals over time to understand the differences in their responses to the same interventions and how their present condition affects future health would have a large impact not only on basic biomedical research, but also in clinical practice. Previous examples include modeling the progression of biological treatment in a “health space,” whose axis represent biological processes, such as oxidative stress, inflammation, and metabolism.The different directions and magnitudes of these shifts in the metabolic space reveal the heterogeneity of the individual response to the training program. The results of consensus clustering are visualized as colored shapes. Three main responses can be observed: individuals 4, 6, and 10 show a limited shift and remain in cluster 1 (orange) with mostly UT models even after the training is finished. UT model no. 5 starts as an outlier, but clusters together with UT models at the end of the intervention and was included in this group. Individuals 1, 2, 3, and 12 remain in the blue cluster, which includes mostly AT individuals, but also show a limited shift during the training. Conversely, individuals 7, 8, 9, and 11, who were starting from the orange cluster on the right, show the largest shift during the training intervention, clustering with other AT models in the blue cluster after the end of the treatment.Since this study is based on publicly available data, we do not have any information about the physiological status or lifestyle of these individuals , neither at baseline nor in response to the intervention. Thus we can only speculate whether the three different responses that we detected are correlated with the baseline fitness of the individual and to actual improvements in their condition after the intervention. For this reason, we will compare the models both according to the ground truth  and to the predicted classes , inspecting the reaction content and average flux distribution of the models in each of the two groups.In the last step of the workflow, we use a statistical test  to analyze the differences between flux distributions across groups of models and identify the metabolic processes associated with a certain class of models. We applied this step both to the ground truth label  and to the label predicted by the consensus clustering .www.vmh.life/#nutrition). The statistical test is used to screen for reactions whose activity differs between the groups, using a p value of 0.05 as threshold. In total, we identified 147 reactions whose activity significantly differed between AT and UT models, and 238 significant reactions when comparing models of consensus clusters 0 and 1. The full list of significant reactions and associated p values, for both cases, is available in The Kruskal-Wallis test is applied to a normalized flux distribution matrix obtained by random sampling of the solution space of each model in the set. All the exchange reactions of the models were constrained with input flux values that reproduce the nutritional intake of an average European diet , is organized and integrated, enabling the interpretation of the results in terms of the resulting system-level metabolic phenotype. The resulting individualized model is a snapshot of the status of the metabolic network of an individual in a particular condition that combines a metabolic knowledge base and experimental data. When ML algorithms are applied to these novel data structures and a pattern is detected, the relevant models can be further interrogated to generate and test hypotheses, going beyond mere correlations and toward mechanistic insights.To harmonize these two approaches, we used distance between GSMMs as a proxy for metabolic similarity. Our initial hypothesis considered three different aspects of a GSMM, and assigned to each of them a different metric, to describe different but complementary components of metabolic distance. When we compared these three metrics—Jaccard distance, graph kernel similarity, and correlation between flux distributions—we found that the first two were very highly correlated, while the flux similarity metric had a medium to low correlation with the other two metrics. This observation made us reject the initial hypothesis in favor of a two-components interpretation of metabolic heterogeneity: a static component, which is the structure of the metabolic network, described by the Jaccard metric, and a dynamic one, which is the flux distribution.Nevertheless, our proposed metric for flux distribution similarity, flux distribution correlation, was found to lack the resolution power to sufficiently separate the model classes and to be successfully used in ML applications. The problem of defining a suitable metric for flux similarity is still open. The solution space of the flux distribution is constrained by the topology of the metabolic network in combination with bounds set on particular reactions in the network. For example, lower and upper bounds on transport fluxes are used to incorporate information on medium composition and implement physiological conditions. We expect the metric based on flux correlation to be strongly dependent on these boundaries. Unknown variation and uncertainty in these boundaries can make the flux correlation metric less reliable. This could potentially explain why flux correlation performed worse than the other two metrics, when considering the separation of the classes, in both benchmark model sets.Comparing the normalized fluxes between AT and UT models, we were able to extract a metabolic signature consistent with the effects of resistance training A. Fatty The results of the comparison between models of the two groups identified via consensus clustering B shows tIn this study we investigated the concept of distance between patient-derived models comparing the properties of different distance metrics. We identified flux distribution and network topology/composition as the two complementary aspects of metabolic heterogeneity and developed a distance-based workflow that combines the ability of patient-derived metabolic models to provide previous knowledge of the structure of metabolic networks and a context for the integration and interpretation of omics data with the scalability and the pattern recognition capabilities of ML.By applying this workflow to a set of patient-derived genome-scale models of aging muscle metabolism before and after a 12-week endurance training program, we identified subgroups of individuals expressing heterogeneous responses to the intervention. The fatty acids oxidation, kynurenine, and beta-alanine pathways were identified as differentially active between the two groups. Increased activity of these pathways in response to training explains the benefits of physical activity on metabolic and mental health during aging. We believe that the application of ML algorithms to sets of physiology-based computational models parametrized with individual molecular data will contribute significantly to the advancement of personalized medicine in the near future.a.cabbia@tue.nl)Andrea Cabbia . For each reaction r in the parent model, if r is also included in the contextualized model, the rth position of the vector will be 1, else it will be 0.Graph kernel functions were used to compute similarity scores between pairs of networks. Kernels are non-linear functions that map the data samples to a different dimensional space, known as the Hilbert space, usually with a higher dimensionality than the starting one. In this new space, the distance of samples represents their similarity. The exact coordinates in the Hilbert space, but rather their distance, is found by simply computing their inner products, an operation that is often computationally cheaper than the explicit computation of the new coordinates.Kernel methods have been applied to heterogeneous types of data, such as biological sequence data,Two main approaches can be considered to compute the similarity between pairs of constraint-based metabolic models, defined as: the first consists in comparing the functionality of two models, for example, comparing their ability to utilize different carbon sources or the minimal nutrient combinations predicted from the structure of the metabolic network.We hypothesized that, since each of these three different aspects of a GSMM encapsulates different aspects of metabolic heterogeneity, they would need different definitions of distance. Two recently published large model sets of microbial and human cancer metabolism, the AGORA model set,GSE28422. Gene expression data were measured with microarray technology (platform HG U133 Plus 2.0). Older participants  included 6 men and 6 women. All subjects participated in 12 weeks of progressive resistance training consisting of bilateral knee extensions with 3 × 10 reps at 70% of 1-RM, and 3 days/week for a total of 36 training sessions. Vastus lateralis biopsies were obtained in conjunction with the first and last training session. We refer to the former as UT status, and to the latter as AT status. From this dataset we developed 24 patient-derived GSMMs, two for each subject, respectively, for the UT and AT status.The workflow described in the section above was applied to a set of metabolic models that was developed for this study. This model set describes the skeletal muscle metabolism of 12 older individuals, and was created from longitudinal gene expression data, collected before and after a resistance training program of 12 weeks. The gene expression dataset from which the skeletal muscle metabolism models were developed was collected during a study on the acute and long-term effects of resistance training on skeletal muscle gene expression in older adultsSeveral different methods for the integration of multi-omics data in GSMMs have been reviewed in Opdam et al.We used the CobraPy


Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology. Metabolism comprises the biochemical reactions that convert nutrients into biomolecules and energy to sustain cellular functions. Advances in high-throughput screening technologies have enabled the quantitative characterization of metabolites, proteins and nucleic acids at the genome-scale, revealing previously unknown links between metabolism and many other cellular processes. For example, gene regulation . The notion of a metabolic pathway is typically employed to organize sets of related reactions into functionally cohesive subsystems. Thus, lipid pathways, for example, are traditionally studied as distinct subsystems from amino acid or aerobic respiration pathways. Although conveniently descriptive, such The complexity of metabolism has prompted the development of a myriad of methods to analyse its connectivity  is satisfied by an infinite number of flux vectors. A number of methods aim at probing the geometry of such flux solution space. For example, Elementary Flux Modes  as a solution to the optimization problem:The most widespread method for genome-scale modeling is Flux Balance Analysis (FBA), which selects a vector of metabolic fluxes J(v) is chosen to describe the physiology of a particular organism under study. In microbes, biomass production is the most common choice for the objective function, in which J(v) = cT·v, i.e., the rate of biomass production is assumed to be a linear combination of specific biosynthetic fluxes, defined by the positive vector of weights c. There are many dedicated FBA software packages . From a metabolite-centric perspective one can build a graph where the nodes are metabolites and the edges corresponds to reactions between them . Conversely, from a reaction-centric perspective we can construct graphs with reactions as nodes and edges describing the sharing of metabolites as reactants or products , or weighted/unweighted (where the elements Aij can have weights encoding different properties). Such modeling choices can strongly influence the conclusions drawn from network analyses  are directly computed from the stoichiometric matrix S and a flux vector obtained with FBA. Different mass flow graphs can be then computed for FBA solutions corresponding to specific environmental conditions. Thanks to the flux weighting, mass flow graphs avoid the need to prune pool metabolites, a common limitation of reaction graphs (Gerlee et al., E. coli metabolism in various growth media (Beguerisse-D́ıaz et al., where the sum acts on all the metabolites that are produced by agt gene involved in glyoxylate breakdown (Pagliarini et al., Flux-graph integration has also provided opportunities to explore centrality scores for quantifying essentiality of reactions and metabolites . One exaA number of other works have sought to define new, metabolism-specific, centrality scores that can reveal new information on the topology of metabolic networks. For example, Koschützki et al.  built a Recent discoveries have led to a renewed interest in the interplay of metabolism with other layers of the cellular machinery (Chubukov et al., When used in isolation, both FBA and network science can be insufficient to understand changes in metabolic connectivity triggered by physiological or environmental perturbations. Here we argue that the use of flux-weighted graphs  allows fAnother promising application domain is industrial biotechnology (de Lorenzo et al., Further developments at the interface of FBA and network science offer a novel way to explore the impact of perturbations on metabolic connectivity. The flexibility of FBA allows for the modeling of metabolic perturbations of various kinds, including changes in growth conditions, deletion of metabolic genes or the action of enzyme inhibitors, whereas the application of network-theoretical tools can bring a broadened understanding of emergent properties of the overall system. This flexibility offers promising potential to deploy network science tools across a range of questions in basic science, biomedicine, and industrial biotechnology.VD and DO conceived the study. All authors contributed to writing the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling editor declared a past co-authorship with one of the author, DO.


Aspergillus niger is an important industrial organism for citric acid fermentation; one of the most efficient biotechnological processes. Previously we introduced a dynamic model that captures this process in the industrially relevant batch fermentation setting, providing a more accurate predictive platform to guide targeted engineering. In this article we exploit this dynamic modelling framework, coupled with a robust genetic algorithm for the in silico evolution of A. niger organic acid production, to provide solutions to complex evolutionary goals involving a multiplicity of targets and beyond the reach of simple Boolean gene deletions. We base this work on the latest metabolic models of the parent citric acid producing strain ATCC1015 dedicated to organic acid production with the required exhaustive genomic coverage needed to perform exploratory in silico evolution.The fungus With the use of our informed evolutionary framework, we demonstrate targeted changes that induce a complete switch of acid output from citric to numerous different commercially valuable target organic acids including succinic acid. We highlight the key changes in flux patterns that occur in each case, suggesting potentially valuable targets for engineering. We also show that optimum acid productivity is achieved through a balance of organic acid and biomass production, requiring finely tuned flux constraints that give a growth rate optimal for productivity.This study shows how a genome-scale metabolic model can be integrated with dynamic modelling and metaheuristic algorithms to provide solutions to complex metabolic engineering goals of industrial importance. This framework for in silico guided engineering, based on the dynamic batch growth relevant to industrial processes, offers considerable potential for future endeavours focused on the engineering of organisms to produce valuable products. Aspergillus niger to secrete organic acids and enzymes has led to it becoming an established industrial organism, and is currently the chief global source of citric acid. The species belongs to the group known as the Aspergilli, which encompasses over 300 species, including the pathogenic A. fumigatus, the feed-contaminating A. flavus, the model organism A. nidulans, as well as A. oryzae and A. niger, both used industrially. In recent years, the Aspergilli have been subject to major advances in systems biology approaches  weAspergillus niger or A. niger in the title, obtained from Web of Science. The full text was searched if available through the University of York Library or open access. The abstract was searched if the full text could not be accessed, and the title was searched if the abstract was unavailable. Reactions were searched for evidence in each record by using an exhaustive list of search terms for each compound. To increase specificity, common compounds were not searched . Compound search terms were compiled from the following databases: KEGG, MMCD, HMD, PubChem, ChEBI, PDB-CCD, 3DMET, NIKKAJI, KNApSAcK, LIPIDMAPS, and LipidBank. To increase specificity, search terms less than three characters were not included. The percentage of reaction compounds found of those searched and number of search hits were recorded and used to rank the results. Reactions with 60% or more compounds found were manually checked for evidence in records with search hits. Reactions with evidence were added to the model.Reactions from the list of KEGG reactions that were not found in the previous model were searched for evidence in an exhaustive body of literature using a custom-built automated text search approach in Python. The body of literature contained all records with d-galactofuranose based on literature evidence [d-galactofuranose was set to 0.133. UDP-alpha-d-galactofuranose is a new compound in iDU1756 and produced by isomerisation of UDP-galactose, a new reaction in iDU1756. This new reaction is essential to biomass production, to produce the galactoglucomannan component of the cell wall, and therefore is a new growth target in iDU1756. Some errors were found in reactions from iHL1210, and corrections were made either to reaction species  was designed. The flux bounds of the reactions in the iDU1756 model were subjected to evolution, with evolutionary pressure to maximise the rate of production of a given organic acid. Each flux bound represented a gene, with the lower bounds being on chromosome 1 and the upper bounds on chromosome 2. The wild-type genes were set as the original flux bounds. The GA was initiated with a population of 500 wild-type individuals, which were subjected to a cycle of fitness evaluation, elimination, selection, recombination, and mutation for a fixed number of generations averaging at 30,000 and ranging from 10,000 to 50,000 depending on the evolutionary goal Fig. .Fig. 8ScThe fitness of new individuals was evaluated by estimating the rate of production of the target acid based on dynamic modelling of organic acid fermentation  with theEstimates were calculated for the target acid yield and time of substrate depletion. Growth occurs in two phases; growth phase 1 (phosphate storage), and growth phase 2 (proton production). The boundary is defined by the time The target acid yield was estimated according toThe time of substrate depletion was estimated according toThe equations for A simplification was made by only applying the mutant flux bounds to growth phase 2, and using wild-type flux bounds in growth phase 1. This assumed that mutations become active at time To evolve production of organic acids not produced by the wild-type, adaptations to the fitness function were required. In such cases, the fitness evaluated to zero in wild-type individuals, preventing evolutionary progress. To fix this, fitness was evaluated as the sum of the estimated rates of proton production and target acid production, with different weights given to each. To ensure stronger evolutionary pressure towards production of the target acid over proton production, a higher weight was given to target acid production. The fitness function was adapted toThe adapted fitness function was applied in evolution of succinic, lactic, malic, acetic, and gluconic production, since none of these organic acids are produced by the wild-type at initial pH 2. The original fitness function was applied in evolution of citric acid production, which occurs in the wild-type.Each generation, 5% of the population  were eliminated. The individuals in the population were ranked based on fitness, and the eliminated individuals were randomly drawn from the bottom 50%. Therefore, individuals with fitness in the bottom 50% had an equal chance of elimination, and individuals with fitness in the top 50% were safe from elimination. This enabled individuals with lower fitness to enter the population with some chance of reproduction, before being eliminated. This was found to be beneficial as some individuals with higher fitness have mutations that individually decrease fitness yet increase fitness when combined.To fill the 5% population gap caused by elimination, new individuals were created. Each new individual was created from two parents, so to fill a 5% gap required a 10% selection . The selection was split across three sources, and did not include any individuals marked for elimination or already selected. 1%  were drawn randomly from across the population. 2%  were drawn from wild-types. The remaining 7%  were drawn randomly from individuals with fitness in the bottom 50%. The percentage from across the population was set such that individuals with fitness in the top 50% reproduced at a sufficiently low rate to prevent their otherwise rapid dominance of the gene pool. This minimised the risk of trapping the evolution on a single solution, allowing distinct solutions to evolve. The percentage from wild-types was set such that a sufficient population of wild-type genes was maintained in the gene pool, allowing the complementation of non-beneficial mutations by recombination. Although the initial population was completely wild-type, the wild-type genes were eventually lost from the gene pool unless re-introduced during the selection stage.A new individual was created by recombination of the genes of its two selected parents. Recombination was designed such that most genes were inherited from one parent and a few from the other parent, according to the recombination rate. The recombination rate was set to 0.04, therefore on average 96% of genes were inherited from one parent and 4% from the other parent. The dominant parent was randomly chosen from the two parents.Once a new individual was created through recombination of its two parents, its genes were subjected to mutation according to the mutation rate. The mutation rate was set to 0.02, and genes were mutated in a random order. Some genes were protected from mutation, including those corresponding to biomass reactions, the maintenance ATP reaction, and transport reactions. A gene was mutated by adding a small positive or negative value to the flux bound, determined by the Laplace function. Wild-type flux values were used as starting points for mutation in the case of wild-type genes. Mutant genes were mutated from the current mutant flux bound. No flux bounds were allowed to mutate below the original lower bound or above the original upper bound, which prevented irreversible reactions from being made reversible. The location parameter of the Laplace function, Output was generated from in silico evolution by logging new individuals that satisfied certain conditions upon fitness evaluation. If the target acid was not produced by the wild-type, any individual that evolved production of the target acid was recorded. In the case of evolution of citric acid production, individuals with fitness greater than the current highest fitness or with fitness greater than 110% of the wild-type fitness were recorded. The flux bounds of recorded individuals were compared with the wild-type to identify mutations. Mutations with no phenotypic effect were filtered out by only recording mutations if the mutant flux was equal to the mutant flux bound.Solutions were obtained from the output by selecting recorded individuals with a fitness > 95% of the highest fitness. These solutions were then processed to discard mutations that have a minimal effect. The fitness was re-evaluated upon complementation of a mutation with the wild-type while retaining other mutations. If the fitness decreased by > 5% of the current solution fitness, the mutation was retained, otherwise discarded. This filtered out background from the solutions, leaving only the mutations that contribute significantly to the overall solution fitness. The frequency of each mutation was calculated from the filtered solutions, by counting the occurrences of corresponding reaction indices in the mutations of each solution, and dividing by the number of solutions. The information was used to identify mutation hotspots and inform target prediction.Additional file 1. The file provides the Additional Tables S1–S14.Additional file 2. The iDU1756 model presented as a spreadsheet.Additional file 3. The iDU1756 model in SBML format.Additional file 4. A detailed complete comparison of the models iDU1756 and iJB1325.Additional file 5: Table S15. Index numbers of mutations and corresponding reactions and mutation effects.Additional file 6. The file provides the additional Figures S1–S15.Additional file 7. Full derivation of the fitness function used for in silico evolution of organic acid production.