Recent studies have enabled the incorporation of thermodynamics and metabolomics data to improve the predictive capabilities of these approaches. However, an in-depth comparison and evaluation of these methods is lacking. This study presents a thorough analysis of two different in silico methods tested against experimental data (metabolomics and 13C-MFA) for the mesophile Escherichia coli. In particular, a modified version of the recently published matTFA toolbox was created, providing a broader range of physicochemical parameters. Validating against experimental data allowed the determination of the best physicochemical parameters to perform the TFA . An analysis of flux pattern changes in the central carbon metabolism between 13C-MFA and TFA highlighted the limited capabilities of both approaches for elucidating the anaplerotic fluxes. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA. Finally, this study emphasised the need for standardisation in the fluxomics community: novel approaches are frequently released but a thorough comparison with currently accepted methods is not always performed.Metabolic engineering in the post-genomic era is characterised by the development of new methods for metabolomics and fluxomics, supported by the integration of genetic engineering tools and mathematical modelling. Particularly, constraint-based stoichiometric models have been widely studied: (i) flux balance analysis (FBA) ( Biotechnology has benefitted from the development of high throughput methods characterising living systems at different levels (e.g. concerning genes or proteins), allowing the industrial production of chemical commodities. Recently, focus has been placed on determining reaction rates (or metabolic fluxes) in the metabolic network of certain microorganisms, in order to identify bottlenecks hindering their exploitation. Two main approaches are commonly used, termed metabolic flux analysis (MFA) and flux balance analysis (FBA), based on measuring and estimating fluxes, respectively. While the influence of thermodynamics in living systems was accepted several decades ago, its application to study biochemical networks has only recently been enabled. In this sense, a multitude of different approaches constraining well-established modelling methods with thermodynamics has been suggested. However, physicochemical parameters are generally not properly adjusted to the experimental conditions, which might affect their predictive capabilities. In this study, we have explored the reliability of currently available tools by investigating the impact of varying said parameters in the simulation of metabolic fluxes and metabolite concentration values. Additionally, our in-depth analysis allowed us to highlight limitations and potential solutions that should be considered in future studies. Metabolic engineering aims to improve microbial strains by considering comprehensive metabolic pathways in their entirety rather than overexpressing a single gene . To imprC) is assumed, so that the stoichiometric matrix (S) (including the stoichiometric coefficients of metabolites in each reaction of the metabolic network) constrains the set of metabolic fluxes (υ) [This systematic framework exploits information regarding the metabolic state, which comprises the metabolome (complete set of low-molecular-weight metabolites <1.5 kDa)) and the fluxome  [ kDa) anduxes (υ) :dCdt=S×YX/S, equal to the ratio growth rate/substrate uptake rate), maximisation of ATP yield, and minimisation of sum of fluxes, which have been suggested to compete in the regulation of bacterial metabolism [13C-MFA) [13C-MFA is considered to be the gold standard in fluxomics [Two main approaches to solve this equation can be found: (i) flux balance analysis (FBA), normally applied to large models   or (ii) tabolism . Hence, tabolism . In contluxomics . Howeverluxomics ) limit i13C-MFA assume most reactions to be reversible [a priori chosen objective function [13C-MFA they are determined by the MIDs [rG′ and ΔrG′o are the Gibbs free energies of reactions (the latter referring to adjusted standard conditions), Q and keq are the ratio of products to reactant concentrations or activities (the latter at equilibrium) and (J+/J−) is the relative forward-to-backward flux [The set of constraints characterising stoichiometric modelling approaches  is insufversible : in the function ), whereathe MIDs . The fluthe MIDs ) links tard flux .rG′ bounds leads to biased results [YX/S) and simulates metabolomics data [in silico metabolite concentration values [Four main approaches exploiting thermodynamics data can be highlighted: (i) energy balance analysis (EBA), where pre-selecting Δ results , (ii) ne results , (iii) m results , and  are considered, (ii) salinity (S) is not taken into account when calculating parameter A, and (iii) Gibbs free energy values are adjusted for ionic strength (I) using the extended Debye-Hückel equation , where  < 0.1 M .t, I and S) on the predictive capabilities of TFA under mesophilic growth conditions. In order to do so, a modified matTFA was developed by increasing the number of parameters and parameter values that were originally considered [13C-MFA and metabolomics data was performed. In particular, flux pattern changes between in vivo and in silico fluxes in the central carbon metabolism were analysed, with a focus on the anaplerotic reactions. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA.This study was based on determining the impact of varying and adjusting the physicochemical parameters : iJO1366, which has proven to predict phenotypes in a wide range of growth conditions [C with minimal medium and a fixed specific growth rate (μ) of 0.20 h-1. The experimental glucose uptake rate (2.93 mmol gDCW-1 h-1) was used as a constraint, leaving the default lower and upper bounds for transport reactions. Maximisation of the biomass yield was selected as the objective function, and no flux value was forced through the biomass reactions (vbiomass). Directionalities of resulting flux values from TFA were compared on a reaction-by-reaction case against in vivo fluxes from 13C-MFA, for which a mapping and directionality correction step was needed . Analyses were performed using the COBRA toolbox [The original matTFA toolbox uses unique values for t and I , and S it and I , the com toolbox  in MATLAI affects the Gibbs energy of formation, an adjustment from the reference state  . In the (ΔfGj′o)  and othe(ΔfGj′o) ,28 the e < 0.1 M Eq 3). T. TI affe-1/2L1/2 ,32. Mod- < 0.5 M .I, where NH(j) is the number of hydrogen atoms in species j, R is the gas constant, T is the absolute temperature and zj refers to the charge of the species [C, but the lack of measured changes in enthalpy (ΔHo) for all the metabolites prevents from doing so [C to 37°C were assumed to be small, as shown elsewhere [A is normally assumed to be constant [F), vacuum permittivity (ε0), gas constant (R) and Avogadro’s constant (NA)), and the second is the temperature (T in K and t in °C), and salinity (S) dependent functions to calculate the density (ρsw) [sw) [Both formulas include terms correcting the pH and  species . Applyindoing so . Hence, lsewhere . The parconstant or calculconstant ,26, and constant was also  term in  includesty (ρsw) and the rsw) [sw) for seawaA (mol-1/2kg1/2) and B (mol-1/2L1/2) is achieved by assuming 1 kg = 1 L. In this study, an expression for seawater . Since different factor combinations converged into the same set of solutions, tests were characterised at the fluxomics and metabolomics levels by considering either the full set of values, or the subset with an experimental counterpart.Mesophilic growth conditions for inations  were tes13C-MFA flux values (r) was performed, as shown in [Results yielding feasible solutions were also compared against x values  and expex values , respectshown in . In ordeshown in . Finallycurrency [side [pool [The constraining capacity of metabolites is not uniform, and depends on their connectivity in the network ,46. To fcurrency , side [4cy [side or pool [de [pool metabolitG, defined as a pair G = , where the vertices (or nodes) V are the metabolites, and the edges E the reactions connecting them. The stoichiometric matrix was converted into an adjacency matrix using an in-house script . This s6 tests (iJO1366 [-1 h-1), reaching a μ ≈ 0.28 h-1  for all FBA and TFA tests. Overall, 26/64 tests were unsuccessful (no cell growth), and the remaining 38/64 converged into common optimal solutions  by calcI (M) was the top one for all responses except for TFA (full), where it equalized t (°C) at 95.7% and was second to the adjustment method. In all cases, using either default concentrations values for AMP, ADP and ATP , or experimental data made no difference. As a result, tests only differing in this factor showed the same correlations with experimental data (The importance of each factor was assessed by means of decision trees (CART in Minitab 19) . Brieflytal data .r ≈ 0.02, whereas for TFA it varied within the range from 0.90 to 0.95. A reaction-by-reaction comparison of flux directionalities in central metabolism showed inherent differences between 13C-MFA and FBA/TFA, as discussed in the last section of this study. At the metabolomics level, it ranged from 0.08 to 0.18  and degradation during extraction [Regarding the metabolomics level, the 9 non-redundant solutions were subjected to a similar analysis. Likewise, only 46/972 metabolites had a variance among tests greater than zero , out of traction –63. SinccalcDGspecies.m). In addition, Gibbs free energy values are relaxed when no feasible solution is found, so the constraining power of experimental metabolite concentration values is reduced [Thermus thermophilus, a potential non-model metabolic engineering platform [Other limitations refer to the design of the tool itself. This method does not consider other complex phenomena affecting the thermodynamic feasibility of metabolic pathways, such as Mg complexation with metabolites, or compound dissociation into more than two protonated species ,20(as shplatform ), recentplatform .Successful tests converged into 5 solutions at the fluxomics level , which aPageRank scores were calculated, allowing to identify metabolites in the top 50% for which experimental data was available . OverallE. coli, where the former also plays a role as nitrogen donor in the biosynthesis of nucleic acids [+, NADH, CO2, menaquinol-8, menaquinone-8 and D-lactate. All but the latter were classified as side compounds for this study , D-fructose-6-phosphate and glyceraldehyde 3-phosphate (not quantified). Both L-glutamate and 2-oxoglutarate participate in the assimilation of nitrogen in ic acids . The latic acids . Accordiic acids , where tic acids ). In parexcluded ), since E. coli, concentration values for NAD(P)H oscillate along the cell cycle [The impact of the inherent dynamics (cell cycle and cell ageing) has been pointed out as a source of metabolic heterogeneity in clonal microbial populations . In a chll cycle , and ATPll cycle . From a ll cycle . Particull cycle , and nicin vivo and in silico fluxes in the central carbon metabolism were analysed, with a particular focus on the anaplerotic reactions. The ‘anaplerotic node’ , PYK and PPS (between phosphoenolpyruvate and pyruvate), ME1 and ME2   , and fin and PPS , which cin silico flux distributions are the result of optimising the system according to the chosen objective function. Accordingly, when maximising the biomass production (which requires ATP), FBA and TFA promote pathways that reduce wasting ATP in the optimal solution [E. coli grown on glucose has proven that both PPC and PPCK (which constitute a futile cycle) are active and play a role in metabolic regulations [13C-MFA.On the other hand, solution . For insulations . Howeverulations ). In thiulations . FBA/TFAEven though flux pattern changes between predicted and experimentally determined intracellular fluxes were present, TFA offered a reliable prediction of intracellular fluxes . This ovIn addition, the nonlinear dependency of the anaplerotic fluxes on the growth rate has been reported in the literature, limiting the reliability of conclusions from experiments using single dilution rates ,71. Partin vivo fluxomics data (r ≈ 0.9) was high enough to enable the analyses on the impact of varying the physicochemical parameters in the predictive capabilities. Studying flux pattern changes on a reaction-by-reaction basis also allowed to confirm previously reported limitations from both 13C-MFA and FBA/TFA with regards to the anaplerotic node [Consequently, it was assumed that the high correlation coefficient achieved for TFA against tic node ,69,75. TThis study showed that the predictive capabilities of TFA can be potentially improved by using physicochemical parameters closer to the experimental conditions and adequate equations. In addition, we proposed a method based on centrality measures to identify important metabolites allowing to further constrain the TFA. In contrast to previous attempts, our strategy is not limited by the size of the network and is computationally cheap. Therefore, a preliminary TFA could be considered when designing a metabolomics protocol to maximise the constraining power of the experimental concentration values. Overall, our study stressed the necessity of performing an in-depth assessment of available methods in the fluxomics field. For instance, interesting published potential solutions to known problems (e.g. elucidation of the anaplerotic fluxes) should be integrated with the widely used approaches. This should increase the degree of standardisation in the community, allowing to cross-validate novel strategies and improving the reliability of the simulated data.S1 Appendix(DOCX)Click here for additional data file.S1 Dataset(XLSX)Click here for additional data file.S2 Dataset(XLSX)Click here for additional data file.S3 Dataset(XLSX)Click here for additional data file.S4 Dataset(XLSX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.


Campylobacter jejuni, the most frequent cause of food-borne bacterial gastroenteritis, is a fastidious organism when grown in the laboratory. Oxygen is required for growth, despite the presence of the metabolic mechanism for anaerobic respiration. Amino acid auxotrophies are variably reported and energy metabolism can occur through several electron donor/acceptor combinations. Overall, the picture is one of a flexible, but vulnerable metabolism. To understand Campylobacter metabolism, we have constructed a fully curated, metabolic model for the reference organism M1 (our variant is M1cam) and validated it through laboratory experiments. Our results show that M1cam is auxotrophic for methionine, niacinamide, and pantothenate. There are complete biosynthesis pathways for all amino acids except methionine and it can produce energy, but not biomass, in the absence of oxygen. M1cam will grow in DMEM/F-12 defined media but not in the previously published Campylobacter specific defined media tested. Using the model, we identified potential auxotrophies and substrates that may improve growth. With this information, we designed simple defined media containing inorganic salts, the auxotrophic substrates, L-methionine, niacinamide, and pantothenate, pyruvate and additional amino acids L-cysteine, L-serine, and L-glutamine for growth enhancement. Our defined media supports a 1.75-fold higher growth rate than Brucella broth after 48 h at 37°C and sustains the growth of other Campylobacter jejuni strains. This media can be used to design reproducible assays that can help in better understanding the adaptation, stress resistance, and the virulence mechanisms of this pathogen. We have shown that with a well-curated metabolic model it is possible to design a media to grow this fastidious organism. This has implications for the investigation of new Campylobacter species defined through metagenomics, such as C. infans. Campylobacter, the leading cause of acute bacterial gastroenteritis, is Gram-negative, microaerophilic, spiral-shaped, highly motile bacteria , a temperature of 37°C or 42°C, with complex media containing blood, peptone, meat, or yeast extract ; in addition to the ability to utilize O2 as an electron acceptor, nitrate, nitrite, and fumarate have also been described as alternatives. Campylobacter spp. would therefore appear to have the potential to carry out anaerobic respiration  describe the metabolic interactions of an organism with its environment, based on a reaction network ultimately inferred from enzymes encoded by the genome. Their analyses enable an investigation of metabolic behavior of the whole system, rather than individual reactions and pathways, and can be used to identify mechanistic links between cellular genotype and metabolic phenotype.Over the last two decades, GSMs have become a valuable tool to analyze cellular behavior under different biological conditions, to design drug targets, to investigate metabolic interactions in microbial communities, and to design defined growth media reversibility. Such information can usually be obtained from a number of on-line databases including databases such as BioCyc  metabolites, otherwise they are referred to as internal metabolites. Reactions that only involve internal metabolites are therefore internal reactions, while those which involve internal and external metabolites are transport reactions. Although gene annotation with regard to enzymes is usually well-defined, annotation of transporters tends to be less comprehensive. Experimental investigations involving growth on defined media thus proves a useful independent method to infer the presence of transport processes, as well as providing useful data for subsequent analyses of the model.In addition to defining the properties of internal reactions, it is, for all practical purposes, necessary to identify the properties of transport processes, representing the consumption and production of compounds in the assumed environment. Compounds present in the environment are referred to as Despite the fundamental importance of online databases, any reconstruction based solely upon these is likely to exhibit a number of problems, the most common of which are: missing gene-protein-reaction (GPR) associations, inconsistent naming of metabolites, and reaction identifiers, incorrect reaction stoichiometries, and reversibility, which propagates to the draft model. Thus, in order to represent a realistic representation of a given organism, an initial draft model will require refinement and curation by the user. The curation process usually begins with correcting reaction stoichiometries and reversibility to ensure that the model follows the law of mass and energy conservation, followed by checking consistency of identifiers, and identifying missing reactions by “gap-filling.” Such gap-filling may often lead to an updated gene annotation. One area of metabolism that requires special attention is the electron transport chain, to ensure that translocated protons are correctly assigned to their location in the cell or the environment.Usually, large-scale metabolic models such as GSMs, are analyzed using constraint based linear programming (LP) approaches  with experimental validation. In doing so we define new, chemically defined, media compositions that will serve as a basis for further modeling and experimental studies of this organism.The aim of this study is to explore Campylobacter jejuni M1cam (https://www.ncbi.nlm.nih.gov/nuccore/CP012149). Genes were predicted and annotated, and used to construct a strain specific Pathway/Genome database (PGDB) for Campylobacter jejuni M1cam. This was used as the basis for the model which was structured in a modular fashion as described by Poolman et al. , as described by Thiele et al. , nitrogen (N), phosphorus (P), and sulfur (S), iron (Fe), sodium (Na), oxygen (O), proton (H), and charge. Metabolites with unknown atomic compositions or generic compounds and reactions involved with such metabolites were replaced, where possible, by balanced reactions with known atomic composition of metabolites. For example, reactions involved with generic compounds  were replaced with specific metabolites and the stoichiometric coefficient balanced on both sides of the reaction. Reactions involved with non-metabolic species  were excluded from the model. Similarly, reactions were corrected for reversibility so that the model is not able to generate energy (in the form of ATP and NAD(P)H) in absence of a mass flux through the system. Thus, the model is ensured to follow the laws of mass and energy conservation, and is free from stoichiometric inconsistencies  flux values (including transporters), subject to the constraints: Nv = 0 (steady-state assumption), vi..j = bi..j defines flux in biomass transporters, as described in section 2.1.2, vk..l defines fluxes in the reactions importing media components, as described in section 2.1.2, vATPase = A defines flux in a hypothetical ATPase reaction in order to account for a growth and non-growth associated maintenance cost and vOtx ≤ Otxmax defines a maximum microaerophilic O2 consumption rate. A was assigned a value of 16 mmol/g DW/hr   set to zero, one at a time. Failure to obtain a solution was taken as demonstrating auxotrophy with respect to the component whose transporter was thus constrained.Substrate auxotrophies were determined, using the model, by repeatedly attempting to solve Equation (1) with individual media transporters (Campylobacter spp. was successfully cultured in the DMEM/F-12 medium (section 2.4), the initial model could not account for the production of all biomass components from these nutrients. These components were identified by modifying Equation (1) to account for the production of a single biomass component, sequentially. Additional reactions were then identified by their presence in other Campylobacter spp. specific biochemical databases in Biocyc and KEGG, literature surveys, and with reference to BLAST  was modified to represent Brucella broth was purchased from Sigma-Aldrich  and Brucella agar from BD . Gibco Dulbecco's Modified Eagle Medium/Nutrient Mixture F-12 (DMEM/F-12) media with no added phenol red, was purchased from Thermo Fisher Scientific . All chemicals were of commercial analytical grade and obtained from Sigma-Aldrich. All solutions, except amino acids and vitamins, were made every week, sterile filtered , and kept at −4°C until needed. Amino acids and vitamins were prepared immediately before use.Campylobacter jejuni M1 has a published genome sequence .The other 7 strains, selected from different clades, according to Champion et al.  and Stab2 [v/v], 5% CO2 [v/v], 85% N2 [v/v]), using an anaerobic cabinet and gas supply , on Brucella broth agar plates, for 48 h at 37°C, except those tested in the Department of Veterinary Medicine, Cambridge University, which were grown at 42°C using a gas mix of hydrogen , also using an anaerobic cabinet and gas supply .All strains were grown under microaerophilic conditions  OD600 of approximately 0.004 in Brucella broth, incubated with shaking (180 rpm) using the same temperature and gas supply indicated previously, to an OD600nm of 0.6 (approximately 2.8 × 109 CFU/ml). Cultures with OD600 different to 0.6 were standardized to that value using sterile PBS. After 20 h, 1.7 mL of this culture was collected, washed twice and resuspended in 1.7 mL of sterile PBS. Each one of the media tested in our study was inoculated in triplicate at 1% (100 μL in 10 mL of media), using Campylobacter jejuni washed cells. Cultures were then incubated microaerobically for 48 h with shaking (180 rpm), under the same temperature and gas conditions stated above, and growth was assessed daily, measuring OD600 in triplicate of each of the technical replicates, using a plate reader . For this purpose, cultures were sampled in a class II cabinet and returned immediately to the anaerobic cabinet. All experiments performed in this study were repeated three times, each time using a new starting culture, prepared from glycerol stock, and with freshly made simple defined media.All Campylobacter jejuni M1cam genomic DNA for WGS was extracted using Maxwell® RSC Cultured Cells DNA Kit. DNA extracts were converted into a Nextera library for sequencing on an Illumina NextSeq 500 platform and genomes were assembled using Velvet de-novo genomic assembler and then subjected to multi-locus sequence typing (MLST).To confirm the identity of the experimental organisms, typical cellular morphology was checked using x1000 bright field microscopy of carbol fuchsin stained cultures and whole genome sequencing (WGS) was performed on selected isolates. Campylobacter jejuni M1cam  to confirm auxotrophy of the compounds tested. If no growth was obtained, experiments were repeated, to confirm results.Campylobacter jejuni M1cam in the defined media given by Guccione et al. ] and adjusted to pH 7 using 1M NaOH or 1M HCl solutions. To maintain sterility, work was carried out in a class II microbiological safety cabinet, and 10 mL of media was filtered into each of the four 50 mL sterile cell culture flasks , closed with their filter caps and kept at 37°C until inoculation. Maintaining media at 37°C until inoculation proved to be very important to obtain reproducible results. Finally, in order to compare our results with previously published defined media, we also tested growth of e et al.  and Alaze et al. .Campylobacter jejuni M1cam PGDB comprised of 228 pathways with a total 1,366 reactions, including 22 transport reactions, and 1,009 compounds. There were 291 reactions without any assigned gene and were inferred from pathway prediction algorithm. This also included reactions that were essential for biomass productions in the model. There were also genes that encoded metabolic enzymes but were not associated with reactions. The reason for the missing GPR association was mainly: (i) information necessary to attribute a particular reaction to specific gene was missing in the annotated file (ii) though the gene product had been annotated it was not detected by the Pathologic software. Reactions, particularly those inferred as essential for biomass production, without any gene association were revisited to establish GPR relation (see 2.1.1) where possible. https://data.quadram.ac.uk/dipali.singh/CJM1cam_DB/.The automatically generated The curated model consists of 994 reactions. The number is less than that of the initial draft model generated from the PGDB due to removal of reactions involved with non-metabolic species and those of unknown atomic composition, as described in 2.1.3. 76% of reactions in the model have gene associations, 6% are spontaneous, while the remainder are inferred by the gap filling algorithm or added after careful curation. The model includes 115 transporters, 968 internal metabolites and 93 external metabolites, summarized in 4 and CO2 were among the excreted by-products. The model is able to account for ATP generation under anaerobic conditions through oxidative phosphorylation, using nitrate or fumarate electron acceptors. However, it is not able to generate biomass in the absence of O2.The solution to Equation (1), with DMEM/F-12 media, has a total of 326 reactions, including transporters. There are 165 essential for biomass production: removal of any one of these results in Equation (1) having no feasible solution. The solution has no net import flux of amino acids, leucine, arginine, histidine, valine, asparagine, phenylalanine, alanine, threonine, tyrosine, tryptophan, and lysine . There was, however, notable net import of pyruvate, as a carbon source, and the amino acids, aspartate, serine, glutamine, and proline; Acetate, succinate, NHmethionine, pantothenate and niacinamide  were identified as auxotrophic. The pathways for the de-novo biosynthesis of these metabolites were absent in the PGDB and thus the model. These included homoserine O-succinyltransferase and methionine synthase from the methionine biosynthesis pathway, 3-methyl-2-oxobutanoate hydroxymethyltrasferase, pantothenate synthetase, and 2-oxopantoate reductase from the pantothenate biosynthesis pathway, and nicotinate-nucleotide diphosphorylase and quinolinate synthetase from the niacinamide biosynthesis pathway.Out of the 33 organic substrates tested in the model, 30 substrates were identified as non-essential. The remaining three substrates, The model analysis suggests that growth can be supported with a medium containing only pyruvate, methionine, pantothenate, and niacinamide . Furthermore, the fact that aspartate, serine, glutamine, and proline were imported in excess, relative to that required by the biomass composition, suggests that the presence of these compounds in the media would enhance growth.C. jejuni M1cam. The removal of methionine, pantothenate and niacinamide from the DMEM/F-12 media , pantothenate, and niacinamide  supported growth of 12 media  resultedAs part of the media development, the concentration of sodium pyruvate, as a carbon source, was increased from 0.5 to 10 mM. In addition, the concentrations of auxotrophic substrates, niacinamide and pantothenate, were optimized to 33.1 and 9.4 μM, respectively . The inoThus, four simple defined media compositions were defined, where all four included the auxotrophic substrates, methionine, pantothenate, and niacinamide along with pyruvate as a carbon source, and with different combinations of non-essential but growth-improving organic substrates, presented in Campylobacter jejuni M1cam. Although each of MM1 and MM2 had a similar effect on growth of Campylobacter jejuni M1cam, MM1 was selected as final defined media, as it had a higher starting pH and required less NaOH to reach pH 7.The best results, in terms of growth, were obtained when cysteine, serine, and glutamine or glutamate where present  S containing amino acids, methionine, and cysteine.The modeling and experimental results presented here, indicate that k et al. . On the Campylobacter jejuni M1cam is the derivative of the human isolate Campylobacter jejuni M1 and is epidemiologically related to poultry strains  cluster lies in the hypervariable region  and pyruvate as the carbon source, contains amino acids cysteine, serine, and glutamate/glutamine. The latter amino acids, though not essential for growth, had a significant growth promoting effect on Campylobacter jejuni M1cam under our experimental condition. Similar, reports have been shown for strains 81176 and NCTC11168 where substrates, though not essential, had to be added to improve growth (Alazzam et al., Campylobacter. Although pyruvate transporters have not been identified, pyruvate has been shown to be used as an exogenous carbon source when present in growth medium (Mendz et al., C. jejuni M1cam. It should be noted that the media designed in this study was optimized to maximize the growth of C. jejuni M1cam. Further tests will be needed to optimize the growth of other strains, however it is clear that the designed media MM1 can support the growth of a variety of strains under different conditions.Our media, apart from Campylobacter jejuni M1Cam, we have built and analyzed a strain specific genome-scale model of this organism. The analysis allowed us to identify specific auxotrophies, as well as compounds which are preferentially consumed, and this allowed us to develop a new media suitable for the study of M1Cam and other Campylobacter spp. strains. The model analysis also replicated the apparently paradoxical, but widely reported observation, that although Campylobacter spp. can operate the electron transport chain in the absence of oxygen, oxygen is nonetheless essential for growth. Experimentally confirming all aspects of our model results, in particular the generation of metabolic by-products in the media, was beyond the scope of the current contribution. However, we believe the experimental and modeling results we have presented here, when taken together, provide a solid foundation upon which to build further investigations of Campylobacter jejuni M1cam and related organisms.By adopting a systems-biology approach and using a newly annotated genome of https://data.quadram.ac.uk/dipali.singh/CJM1cam_MM/, https://data.quadram.ac.uk/dipali.singh/CJM1cam_DB/. Additionally, Pathway/Genome database generated in this study is available from Pathway Tool Registry.The datasets generated for this study can be found in the NT and DS designed and supervised research plans with input from JW. DS constructed the biochemical database and genome-scale metabolic model. NT performed experiments for minimal media design with input from BP. LC performed gene predictions and annotations. ES and FN tested minimal media designed in this work in other strains. BD performed sequence analysis. MP and DS analyzed GSM and together with NT wrote the paper with revision from JW. All authors contributed to the article and approved the submitted version.SequenceAnalysis.co.uk and was paid to perform this work. The remaining 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.LC is the director of


Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes. Our findings point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the constraints imposed by the network structure at steady state. Since reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering.Biological networks across scales exhibit hierarchical organization that may constrain network function. Yet, understanding how these hierarchies arise due to the operational constraint of the networks and whether they impose limits to molecular phenotypes remains elusive. Here we show that metabolic networks include a hierarchy of reactions based on a natural flux ordering that holds for every steady state. We find that the hierarchy of reactions is reflected in experimental measurements of transcript, protein and flux levels of  E. coli, which we call the flux order relation. Specifically, we identify pairs of reactions in which one reaction always carries a higher flux than the other at steady state. Hence, the flux order relation creates a hierarchical organization of metabolism. We show that the flux order relation is reflected in experimental data sets of fluxes, gene expression, protein levels, and enzyme catalytic constants. Our results point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the flux order relation.Metabolism results from the activity of thousands of biochemical reactions, which create, transform and recycle all chemicals, i.e., metabolites, required by life. Metabolic reactions depend on enzymes—proteins acting as biological catalyzers—to proceed, which effectively links metabolism to other layers in the organization of cellular physiology, such as transcription and translation. These reactions do not operate in isolation but interact in a metabolic network due to the metabolites they share. The joint action of the reactions imposes constraints on the reaction fluxes denoting rates of conversion between metabolites. Here, we identify one such constraint imposed by the metabolic network of  Hierarchical organization has been recognized as a salient feature of biological networks, spanning from the molecular to the ecosystem scale –6. BioloMoreover, hierarchies that rely on pairwise relationships between components often consider operational principles in conjunction with the network structure. For instance, mass-balance and steady state constraints also induce hierarchies based on asymmetric, pairwise relations among reactions . One sucE. coli Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors investigate the broad field that biological networks across scales exhibit hierarchical organization that may constrain network function. They find that metabolic networks show a hierarchy of reactions based on a natural flux ordering that holds for every steady state, even reflected in experimental measurements of transcript, protein and flux levels of Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes.This is nice and well documented here both by the formal analysis as well as the public experimental data used for validation of these findings and a nice analysis.Comments:--What should be discussed somewhat more is the direct implications of the results and possible explanations:Certainly, there is some input from resource partitioning and there is fine-tuning of enzyme levels in E. coli and of course it has to respect the constraints imposed by the network structure at steady state.However, all this may even more be the result of other more general factors, in particular the evolution of enzyme networks or just the result of fitness optimization, in particular as E.coli is metabolically so active and broad.--I agree that reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, however, it would be good if the authors can show a nice concrete example on how the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering, for instance in plants.Again, there is no doubt that you can do metabolic engineering by constraint-based modelling, but it would be good if the authors can clarify how then the insight in the natural flux ordering presents then a handle to do something novel which is not already obvious from e.g. calculating the flux modes according to standard techniques.Reviewer #2: In their manuscript "flux-based hierarchical organization ..." the authors propose a new method for computing a hierarchy among metabolic reactions.Employing the framework of steady-state fluxes obtained via LP from genome-scale metabolic models, the criterion for ranking reactions is flux ordering. The authors compare the resulting hierarchy with categories derived from metabolic pathways, with flux measurements and with regulatory information.I find the manuscript suitable for PLOS CB. However, I have a few concerns and comments, which the authors should address.(1) From my perspective the literature around the hierarchical organization of metabolic systems  should be cited on a broader level. For example in  the distribution of gene attributes across hierarchical levels has been studied . Also, as the authors point out in the introduction, the hierarchical organization of metabolic systems can be assessed on the level of metabolites, as well as on the level of reactions. Examples for the former, which the authors may consider to cite are: , . Regarding the comparison with transcriptional regulation, I regard the findings from  to be highly relevant. The authors should compare their results with the 'determined' and 'non-determined' categories from this paper.(2) I was surprised that the authors do not discuss the fact that metabolic fluxes follow a power-law distribution . Doesn't this already imply a hierarchical organization?(3) How do the authors motivate their choice of iJO1366 as the genome-scale metabolic model? Wouldn't the more recent model iML1515 from  been a more plausible choice?(4) In Section 2.2 the authors study the distribution of pathways across the hierarchical levels. Maybe I missed this point, but shouldn't these percentages be compared to a null model of shuffled macrosystem labels, in order to eliminate (level and system) size effects?(5) I have not understood the argument in Section 2.5.1 regarding the potential artifcact due to the empirical focus of flux data on the metabolic core. Wouldn't the appropriate test for this be to evaluate the flux order graph obtained from the E. coli 'metabolic core model' from ?(6) Given the scope of comparisons in Sections 2.5.2, I would recommend a correction for multiple testing for the p-values reported here.(7) I might have misunderstood the analysis strategy of the authors here, but when they say 'a reaction is connected to another by a directional edge if it carries a greater of equal flux in any steady state', do they mean 'any steady state compatible with the minimum flux through the biomass reaction' or do they literally mean any vertex of the flux polytope? I suppose it is the former. In this case, however, the results will depend strongly on the choice of this minimal flux to be 95 percent of the maximally feasible biomass production rate . If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  and your responses to reviewer comments. If eligible, we will contact you to opt in or out[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Christoph KaletaAssociate EditorPLOS Computational BiologyJason PapinEditor-in-ChiefPLOS Computational Biology***********************ploscompbiol@plos.org immediately:A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact [LINK]Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors revised their manuscript thoroughly, one question remains:"as discussed in Section 2.7, the difference is that essential reactions which are also flux-ordered affect flux through the biomass reaction in a continuous manner, while essential reactions which are not flux-ordered affect biomass production in a binary  manner. Hence, identifying essential reactions which are flux-ordered with the biomass reaction could allow fine tuning of reaction flux to control biomass production."This is fair enough, but please discuss why not identifying the essential reactions just by looking at those modes which drop out if an enzyme is inhibited does not do a similar good job . I would even think that this method is simpler and allows easy to quantify the more important enzymes (as blocking these inhibits a higher number of modes).--So as mentioned already regarding the previous version of the manuscript, please make still a bit clearer, best by looking at this remaining comment, why and where your approach is preferable to classical elementary mode analysis and what you really gain by using this more complex method of yours.Reviewer #2: The revised version of the manuscript "Flux-based hierarchical organization of Escherichia coli's metabolic network" (PCOMPBIOL-D-19-01496R1) is, from my perspective, a substantial improvement.I agree with their assessment that the results of Shlomi et al. (2007) cannot be directly compared with their findings.Regarding the work by Almaas et al. (2004), I believe that the manuscript would benefit from a short comment on power-law flux distributions .Regarding the choice of the E. coli model, I found the authors' response to my question perfectly convincing.I still disagree with the authors' statement that "empirical p-values" do not require a correction for multiple testing. If I consider all groups of flux-ordered reaction pairs assessed here as an individual hypothesis, I would argue that a large set of hypotheses has been tested (and hence a multiple-testing correction would be required). However, this decision is the responsibility of the authors (they explain quite clearly what they are doing).The point about the dependence of the results on the choice of the minimal flux has been addressed properly by the authors, as have been the other (mostly minor) remarks I had.Summarizing, I have no objection against acceptance of the manuscript .**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Computational Biologydata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: Yes**********what does this mean?). 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Methylocella silvestris is a facultative aerobic methanotrophic bacterium which uses not only methane, but also other alkanes such as ethane and propane, as carbon and energy sources. Its high metabolic versatility, together with the availability of tools for its genetic engineering, make it a very promising platform for metabolic engineering and industrial biotechnology using natural gas as substrate.M. silvestris is presented. The model has been used to predict the ability of M. silvestris to grow on 12 different substrates, the growth phenotype of two deletion mutants (ΔICL and ΔMS), and biomass yield on methane and ethanol. The model, together with phenotypic characterization of the deletion mutants, revealed that M. silvestris uses the glyoxylate shuttle for the assimilation of C1 and C2 substrates, which is unique in contrast to published reports of other methanotrophs. Two alternative pathways for propane metabolism have been identified and validated experimentally using enzyme activity tests and constructing a deletion mutant (Δ1641), which enabled the identification of acetol as one of the intermediates of propane assimilation via 2-propanol. The model was also used to integrate proteomic data and to identify key enzymes responsible for the adaptation of M. silvestris to different substrates.The first Genome Scale Metabolic Model for M. silvestris, such as its use of the glyoxylate shuttle for the assimilation of one and two carbon compounds and the existence of two parallel metabolic pathways for propane assimilation. This model, together with the fact that tools for its genetic engineering already exist, paves the way for the use of M. silvestris as a platform for metabolic engineering and industrial exploitation of methanotrophs.The model has been used to elucidate key metabolic features of  The draMethylocella model and those in 2 previously reconstructed models of type II methanotrophs (Methylocystis hirsuta and Methylocystis parvus) [Figure  parvus) , 16, as Methylocella silvestris is provided as Additional file Methylocella silvestris contains those catalyzed by the enzymes isocitrate lyase  and malate synthase , which form the glyoxylate shunt, allowing the use of ethanol and acetate as sole carbon sources. Other type II methanotrophs such as Methylocystis sp. SB2 and Methylocystis hirsuta [Methylocella silvestris) and have very low specific growth rates . The roMethylocella silvestris and absent in both of the Methylocystis species considered, we predicted 6-phosphogluconate and its derivatives 6-phosphogluconate-1–5-lactone and 2-keto-3-deoxy-6-phosphogluconate, which are involved in the Entner-Doutdoroff pathway. Other specific metabolites are 4-hydroxy-2-oxovalerate and 2-keto-4-pentenoate, which are linked to the presence of a 2-keto-4-pentenoate hydratase .Among the metabolites specific to Methylocella, compared to other methanotrophs, is characterized by its metabolic versatility and the high variety of substrates on which it can grow. In particular, its use of alkanes such as ethane and propane [ propane  is of grMethylocella silvestris . The predicted metabolic fluxes are 0.78 and 0.71 mmol h−1 g-DW−1 for ICL and MS. Enzymatic activities are reported in nmol min−1 mg-Protein−1. Thus, to compare the predicted metabolic fluxes with the results of enzyme activity tests, we need to transform grams of dry weight into milligrams of protein. Assuming that half of the total biomass corresponds to proteins, the predicted in-vivo activities of these enzymes are equivalent to 26 and 24 nmol min−1 mg-Protein−1. The predicted activity of ICL is close to the measured activity (26 versus 23 nmol min−1 mg-Protein−1), whilst the measured activity of MS is one order higher than the minimal activity necessary to support the observed growth rate (424 versus 24 nmol min−1 mg-Protein−1).In order to confirm the activity of these enzymes, enzyme assays were carried out with extracts of acetate grown tris see . The meaM. silvestris were constructed  and “PrMO2” (yielding 2-propanol). Even if some cross activity is possible, the reaction “PrMO” has been annotated as catalyzed by the enzyme PrMO, while the reaction “PrMO2” has been annotated as catalyzed by the enzyme sMMO. Both monooxygenation reactions are coupled to the consumption of an oxygen molecule and the oxidation of an NADH equivalent. bstrates . Growth M. silvestris contains eight genes predicted to encode NAD(P)-dependent alcohol dehydrogenases (ADHs), as well as a pyrroloquinoline quinone (PQQ)-containing methanol dehydrogenase (Msil_0471) and a PQQ-containing ADH with 73% identity to xoxF from Methylobacterium extorquens (Msil_1587). For modelling purposes, it is essential to elucidate if the oxidation of 1-propanol and 2-propanol, to propanal and acetone respectively, is coupled to NAD(P)H generation, or coupled to transfer of electrons to PQQ, which are further transferred to cytochrome-c, with proton extrusion [The genome of xtrusion . OxidatiMethylocella silvestris can grow on both acetone and propanal (the oxidation products of 2-propanol and 1-propanol). The genome revealed the presence of genes encoding a putative pathway from propanal to methylmalonyl-CoA, composed of four reactions with two putative enzymes for each of them , which confirmed its relation to propane utilization. More interestingly, when growing on propane, the Δ1641 strain started accumulating acetol in its growth medium . The mutant strain also lost its ability to grow on 2-propanol and acetone, which confirms the involvement of Msil_1641 in the downstream degradation pathway of acetone. Based on the evidence alone (and its annotation by RAST as a NAD associated oxidoreductase), it was assumed that Msil_1641 catalyzes the oxidation of acetol to 2-oxopropanal with concomitant NADH production. The oxidation of acetone to acetol was proposed to be catalyzed by two putative cytochrome P450 oxidoreductases represented in the genome (Msil_0731 and Msil_1926). Similar enzymes have shown to catalyze this reaction in rabbit [The genome annotation did not reveal all the enzymes catalyzing the reactions involved in the downstream metabolism of acetone. Both 2-propanol and acetone accumulated in the culture broth, during growth on propane, which suggests a kinetic bottleneck downstream of acetone. The RAST annotation shows the presence of three putative hydroxyacylglutathione hydrolases  and three putative lactoylglutathione lyases . These reactions would allow the transformation of 2-oxopropanal into lactate, which could be further metabolized via its transformation into pyruvate by a putative lactate dehydrogenase present in the genome . However, the enzymes involved in the transformation of acetone to 2-oxopropanal remain to be elucidated. Proteomics has revealed strong overexpression of the gene Msil_1641, induced by propane. This gene has been annotated as a glucose-methanol-choline oxidoreductase, which does not suggest any specific association with propane degradation, therefore its role in M. silvestris, one of them, via 1-propanol, transforms propane into methylmalonyl-CoA, while a second pathway, via 2-propanol, transforms propane into lactate. Both pathways co-exist simultaneously and the metabolic flux going through each of them depends on the ratio between 1-propanol and 2-propanol produced by PrMO and sMMO [−1 and specific production rates of 2-propanol, acetone and acetol of respectively: 0.188, 0.075 and 0.152 mmol h−1 g-DW−1. This rate of 0.152 mmol h−1 g-DW−1 was assumed to be equal to the rate of acetol oxidation to 2-oxopropanal in the wild type.There are two alternative pathways for propane degradation in and sMMO . Deletio−1, produced 2-propanol and acetone at 0.189 and 0.073 mmol h−1 g-DW−1 respectively (with no acetol accumulation in the medium). These experimental values, as well as the acetol oxidation rate of 0.153 mmol h−1 g-DW−1, inferred from the behaviour of Δ1641, were imposed as constraints in the metabolic model. Propane uptake rate was minimized, leading to a prediction of 0.67 mmol h−1 g-DW−1. This corresponds to a biomass yield on propane equal to 25 g-DW mol−1, which is very close to the experimental yield measured for the wild type of 24 ± 2 g-DW mol−1 [The wild type, which showed a growth rate on propane of 0.0174 ± 0.0002 hMethylocella silvestris have been obtained for growth on methane, succinate and propane [Proteomic data for  propane . The proThe reconstructed model was used to calculate correlation coefficients between the predicted metabolic fluxes in each to the three experimental conditions and the enzyme abundances. This allows to identify metabolic reactions whose predicted fluxes correlate with the abundances of the enzymes catalyzing them . Using the terminology of Metabolic Control Analysis (MCA) , some enp values were obtained for each of the metabolic enzymes detected in the proteome. The p-vales were corrected for multiple testing and a false discovery rate of 0.05 was set as a cutoff. Nine proteins passed this threshold, among them the three subunits of PrMO, which are expressed only in presence of propane. Two other enzymes were expressed only under growth on propane, those were the previously discussed oxidoreductase coded by the gene Msil_1641, and the methylmalonyl-CoA mutase coded by Msil_3785. The identified enzymes included also two enzymes of the serine cycle, namely phosphoenolpyruvate carboxylase (Msil_1718) and serine-glyoxylate aminotransferase (Msil_1714), which show their highest expression levels during growth on methane. 3-oxoacyl-synthase (Msil_2205) and inorganic pyrophosphatase (Msil_1025) showed their highest expression and metabolic flux during growth on succinate, followed by growth on propane and methane.These enzymes are responsible for the transcriptional adaptation of the cell to different carbon sources. Model predictions were carried out by setting specific growth rates to their experimental values and minimizing the carbon source uptake rate. In the case of propane, the fluxes in the pathway via lactate (discussed in the previous section), were also constrained to their experimental values. Pearson correlation coefficients and p value resulting from the correlation. Figure Figure Methylocella. The model captures the metabolic versatility of the strain and is able to reflect its ability to grow on a broad range of substrates as well as to predict quantitatively its biomass yields on methane and ethanol. The model also predicts the phenotypes of two deletion mutants, ΔICL and ΔMS, and could explain the reliance of M. silvestris on the glyoxylate shunt for growth on C1 substrates. This feature makes M. silvestris different from other type II methanotrophs and should be taken in account for the design of future metabolic engineering strategies. Regarding the ability of M. silvestris to grow on propane, two alternative pathways have been identified. Experimental evidence suggests that both pathways operate in parallel. One of the pathways proceeds through methylmalonyl-CoA while the other proceeds through lactate. The existence of 2 independent pathways for propane assimilation makes M. silvestris a potential platform to synthesize compounds using propane as a carbon and energy source. For example, the deletion of lactate dehydrogenase can be expected to disrupt the second pathway and to result in lactate accumulation, while energy and biomass could still be obtained via the first pathway. Alternatively, the second pathway could be disrupted downstream of methylmalonyl-CoA and its metabolic flux deviated to compounds having methylmalonyl-CoA as precursor, while the cell could still use the pathway via lactate to obtain energy and biomass precursors.In this work we present the first GSMM of an organism of the genus Methylocella silvestris BL2 was obtained from the Joint Genome Institute (JGI) (DSM 15510). After annotation with RAST [The genome of ith RAST  a draft ith RAST . The genJGI) DSM 510. Afteith RAST . The genhttps://github.com/SergioBordel/ModelsMethanotrophsThe reconstructed GSMM in SBML format (Methylocella.xml), together with tab separated files containing metabolites (Methylocella_metabolites.txt) and reactions (Methylocella_reactions.txt) and a file containing the top connected metabolites in the model (MethylocellaMets.txt), as well as the RAST annotation in Excel format (Methylocella.xls), can be downloaded from 2 (6 mM), phenylhydrazine HCl (4 mM) L-Cysteine HCl (12 mM) protein (50—200 µg) and was initiated with DL-isocitrate  (8 mM). Increase in absorbance at 324 nm, due to the accumulation of glyoxylate phenylhydrazone, was recorded against reactions containing water instead of isocitrate. After a lag of approximately 1–2 min, the reaction was linear for at least 10 min. Rates were calculated using ε324 for glyoxylate phenylhydrazone of 1.7 × 104 M−1 cm−1. Malate synthase was assayed by following the decrease in absorbance at 232 nm due to the breakage of the acetyl-CoA thio-ester bond in the presence of glyoxylate. Reactions (1 ml) contained Tris buffer pH 8.0 , MgCl2 (3.4 mM), acetyl-CoA  (0.05 mM) and protein (100 µg). Absorbance was measured for 5 min before and after addition of glyoxylate . Without substrate, change in absorbance was less than 0.0008 min−1. Rates were calculated using ε232 for acetyl-CoA of 4.5 × 103 M−1 cm−1. Alcohol dehydrogenase (experiments on propane) was assayed as previously described [Isocitrate lyase and malate synthase (experiments on acetate) were assayed following the method of Dixon and Kornberg , adaptedum salt)  mM. IncrUnmarked deletion mutants of isocitrate lysase, malate synthase and Msil_1641 were constructed by double homologous recombination, followed by removal of the antibiotic cassette, as previously described . UpstreaMethylocella silvestris BL2 and the three marker-free deletion mutants, were grown in 120 ml serum vials, sealed with rubber stoppers, on dilute nitrate mineral salts medium (DNMS) as previously described [escribed . For culescribed , 10 min) and 3 μl of the supernatant injected into an Agilent 7890A gas chromatograph fitted with an HP-PLOT Q column . Biomass was calculated from optical density (OD540), measured with a Shimadzu UV-1800 spectrophotometer, based on the conversion factor 1 OD ml unit = 0.25 mg dry weight. Methane was measured using a Porapak Q column (Supelco).Methane, ethanol and biomass concentrations were monitored over time and the yields were calculating by plotting the produced biomass versus the consumed substrate and obtaining the slope (before reaching limitation by nitrogen). Methane was added to cultures by injection through the rubber stopper to a headspace concentration of 10% v/v, and monitored by gas chromatography (GC) . The iniAdditional file 1: FS1. List of unique reactions and unique metabolites in the model of M. Sylvestris.Additional file 2: FS2. Gene annotation obtained using RAST.Additional file 3: FS3. Equivalence between gene annotations.


Significant efforts have been made in building large-scale kinetic models of cellular metabolism in the past two decades. However, most kinetic models published to date, remain focused around central carbon pathways or are built around ad hoc reduced models without clear justification on their derivation and usage. Systematic algorithms exist for reducing genome-scale metabolic reconstructions to build thermodynamically feasible and consistently reduced stoichiometric models. However, it is important to study how network complexity affects conclusions derived from large-scale kinetic models built around consistently reduced models before we can apply them to study biological systems.Escherichia Coli genome-scale metabolic reconstruction systematically to build three stoichiometric models of different size. Since the reduced models are expansions around the core subsystems for which the reduction was performed, the models are nested. We present a method for scaling up the flux profile and the concentration vector reference steady-states from the smallest model to the larger ones, whilst preserving maximum equivalency. Populations of kinetic models, preserving similarity in kinetic parameters, were built around the reference steady-states and their metabolic sensitivity coefficients (MSCs) were computed. The MSCs were sensitive to the model complexity. We proposed a metric for measuring the sensitivity of MSCs to these structural changes.We reduced the iJO1366 We proposed for the first time a workflow for scaling up the size of kinetic models while preserving equivalency between the kinetic models. Using this workflow, we demonstrate that model complexity in terms of networks size has significant impact on sensitivity characteristics of kinetic models. Therefore, it is essential to account for the effects of network complexity when constructing kinetic models. The presented metric for measuring MSC sensitivity to structural changes can guide modelers and experimentalists in improving model quality and guide synthetic biology and metabolic engineering. Our proposed workflow enables the testing of the suitability of a kinetic model for answering certain study-specific questions. We argue that the model-based metabolic design targets that are common across models of different size are of higher confidence, while those that are different could be the objective of investigations for model improvement.The online version contains supplementary material available at 10.1186/s12859-021-04066-y. Kinetic models of cellular metabolism can provide comprehensive understanding on the dynamics of the cell and its response to environmental changes and perturbations. In depth understanding of cellular metabolism can allow metabolic engineers to tailor cells according to sought specifications and objectives. This could enable the design of cell factories where flux is directed towards the production of biofuels, pharmaceuticals or other specialty chemicals. To be useful though, a kinetic model should represent the dynamics of the cell accurately enough to provide the required study-specific knowledge . To dateWith larger and better quality kinetic models, the mathematical representations become increasingly complex. Furthermore, the parameter sensitivities of systems biology models are in general “sloppy” . We haveIt is important to preserve certain level of detail in a metabolic model in order for its predictions to be realistic. The model needs to include important carbon fluxes from the central carbon up to the biomass building blocks, which also includes the synthetic pathway of interest that we would like to engineer. The fact that energy and redox are used by the synthetic pathway of interest makes it important that we account for “all” the reactions and subsystems that carry significant energy and redox fluxes, such as a detailed tricarboxylic acid (TCA) cycle and electron transport chains (ETCs). Keeping such level of detail is essential in order to avoid making false conclusions from kinetic models.However, nowadays algorithms for reducing GEMs in a more systematic and complete manner are starting to emerge , 12–15. E. coli iJO1366 GEM to three different models, namely D1, D2 and D3, encompassing 271, 307 and 327 enzymatic reactions and 160, 188 and 197 metabolites, respectively. The thermodynamic formulation of the stoichiometric models allowed integration of fluxomics and metabolomics data for aerobically grown E. coli  from the iJO1366 GEM [. [E. coli. Reduced stoichiometric models D1, D2 and D3 inter-connect the pairs of subsystems with up to one, two and three reactions, respectively  around 6 GEM [. . D corre6 GEM [.  and captd-fructose (HEX7) and d-fructose 6-phosphate phosphatase (F6PP), that connect d-glucose with d-fructose 6-phosphate via d-fructose. D2 also includes the maltodextrin system which connects the d-glucose to d-glucose 1-phophate via the maltodextrin phosphorylase and maltodextrin glucosidase reactions. In D2, dihydroxyacetone phosphate can react to methyglyoxal, which in turn can react to d-Lactate, providing increased connectivity between glycolysis and the pyruvate node. Additionally, pyruvate can react to 2-succinyl-5-enolpyruvyl-6-hydroxy-3-cyclohexene-1-carboxylate, which can react to form 2-oxoglutarate, thus connecting the TCA cycle with the pyruvate metabolism. D2 also includes three different ways to connect with two reactions from fumarate to l-aspartate, which—via argininosuccinate, adenylsuccinate and adenylosuccinate—further link the TCA cycle with the ETC. The adenylate kinase (ADK3), nucleoside-diphosphate kinase (NDPK1) and nucleoside-triphosphatase (NTP3) enzymes provide D2 model with additional flexibility in the system’s energy metabolism.The additional reactions in D2 include xylose isomerase (XYLI2), hexokinase d-lactate and l-lactate. Methylglyoxal is a hub metabolite that provides connectivity between upper glycolysis to the pyruvate node. The pyruvate and phosphoenolpyruvate nodes are connected to the TCA cycle via chorismate. Fruthermore, the glutamine and glutamate synthases provide additional flexibility in allowing conversion between l-glutamate and l-glutamine. In D3 the presence of AMP nucleosidase (AMPN) provides an additional connection between the PPP and the ETC. However, the expansion from D1 to D2 resulted in more central carbon metabolites that change in connectivity . To preserve equivalency across the kinetic models, it was desirable that the flux profile and the concentration vector steady-states in D2 and D3 resemble the ones selected in D1. The nested nature of the core models generated with redGEM eased the transferability of steady-states across models, allowing us to preserve similar values for fluxes and concentrations for the overlapping reactions of the three models.. [We connected the core models to the biomass building blocks (BBBs), as defined by Neidhart et al. , via lum. . A lumpeWe studied the lumped reactions in D1–3 and observed that 103 were common between the models Fig. D. D1, D2d-Alanine (DALAtex) that deviates by 8%  formulation that imposes similarity between the representative steady-states of the models (Methods). The D2 fluxes of central carbon reactions are within below one percent deviation from the reference flux of D1  of μ were ranked for D1–3 based on their absolute means across stable models. The models were compared pairwise in increasing order of size  to assess the impact of systematic network expansion on MSCs , phosphofructokinase (PFK) and ATP maintenance (ATPM) are the most consistent in terms of sign and magnitude when comparing D1 with D2 Fig. A. PyruvaWe then compared top cellular growth FCCs in D2 and D3, which are in great sign and magnitude agreement  were mostly from the central carbon metabolism Fig. . The reans Figs. . ACS is ns Figs. .Fig. 4E.l-Lactate dehydrogenase (l-LACD2), as cofactors ubiquinone-8 and ubiquinol-8 partake in both reactions. Interestingly, periplasmic glucose dehydrogen (GLCDpp), where ubiquinone-8 and ubiquinol-8 also participate, has a high DI as well. GLCDpp possibly causes its neighbouring reactions gluconokinase (GNK) and d-gluconate transport (GLCNt2rpp) to have high DIs too, due to stoichiometric coupling. These observations suggest that alterations in flux split ratios around important branching points—caused by network expansion—could result into higher DIs in reactions at their vicinities.We repeated the above analysis for D2 and D3, where we analogously compute the DIs for the 307 common enzymatic reactions (Methods). Similar observations were made for the reactions having low DIs (0–25 percentile) as most were located in central carbon metabolism, within the subsystems around which reduction was performed  when comparing D2 and D3  cover the essential biomass precursor metabolites according to Neidhart as we focused primarily on cellular growth control and, (2) that we capture the ETC essential to account for redox potentials.d-fructose 6-phosphate when expanding from D1 to D2 appeared to significantly affect growth control patterns  that gave a numerical indication on the consistency of the FCCs with respect to a reaction. Most of the reactions around central carbon metabolism, carrying a higher carbon flux, appeared to have lower DIs. Flux control for reactions with larger fluxes were more robust, particularly if the number of connecting reactions did not change between models for the metabolites participating in the reaction. The larger DIs were noted in the ETC and peripheral reactions. Nevertheless, the consistency in the control patterns of network regions that carry larger carbon flux was consistent across the reduced models when the DI was low, suggesting that their MSC-based predictions are independent of the network complexity. Thus, the DI can be used to study the structural robustness of a kinetic model.We could argue that the larger the kinetic model is, the more confident and robust the metabolic engineering decisions derived from the model are. However, using our methodology, a modeler can use the DI as an indicator of structural robustness of the system to assess the confidence and quality of the model’s metabolic engineering predictions. In this context we suggest that the experimental design should first target the steps that are consistently better targets across different sized models. Next, we should focus on identifying to what reactions the model predictions are more sensitive to in the larger models, allowing the identification of changes that are responsible for the redistribution of control across the system. Such investigation will serve as a focused analysis for modeling and experiments – understanding which new reactions and pathways, when added during size increase, impact the control distribution in the reference pathways can provide a great insight on how structural changes in a biological network change its function, beyond single enzyme over/down-regulation.Failing to preserve certain level of model complexity when constructing kinetic models can result in erroneous conclusions. Model reduction – whether ad hoc or systematic – is a necessary step when constructing kinetic models and could result in false predictions if not done appropriately. To our knowledge, we propose for the first time a workflow for systematically constructing large-scale kinetic models and tailor their size to match the requirements of the studied biological system. We suggested the deviation index as a metric that highlights differences across model MSCs and serves as an indicator in testing kinetic model size adequacy. The nested nature of the reduced models enabled the maintenance of maximum equivalence between the steady-states and kinetic parameters of the populations of kinetic models. This allowed us to assess the impact of model size on the MSC-based conclusions. We showed that despite consistent model reduction and preserving model equivalency, control coefficients can be significantly affected by network size. However, our method can be used to study and assess the adequacy of models based on control coefficients. As systematic model reduction algorithms gain momentum in the field, we hope to pave a path towards building more robust and transferable kinetic models for the community. Classical statistical model assessment tools could be additional avenues to explore when studying structural robustness of models.E. coli iJO1366 genome-scale model. The lumpGEM algorithm was used to generate lumped reactions for the biosynthesis of biomass building blocks (BBBs) for these models. We used thermodynamic-based variability analysis (TVA) [We developed a workflow for building consistently reduced kinetic models from a genome-scale metabolic model Fig. . We usedis (TVA)  to studyE. coli iJO1366 genome-scale model was reduced, with aerobic minimal media, glucose as the sole carbon source, and the selected starting subsystems corresponding to central carbon metabolism . We incorporated all the reactions that use metabolites of the quinone/quinol pools  as the electron transport chain subsystem in order to account for the energy metabolism of the system. redGEM allows the user to define a degree of connection, D, to define the level of connectivity of the core. D is an input parameter of the redGEM and lumpGEM. D corresponds to the number of reaction required to connect the pairs of metabolites between starting subsystems, as defined in [The stoichiometry of the core networks was defined with the redGEM algorithm, which reduces systematically genome-scale model reconstructions of metabolism . The E. fined in . For thefined in  was usedE. coli iJO1366 and in our reduced model. However, these metabolites, unless they are highly polar or very large, are subject to passive diffusive transport through the cell membrane. Therefore, we explicitly added transport reactions for these metabolites that operate at least at basal level (10−6 mmol/(gDW*h)).For some of intracellular metabolites, a corresponding transport reaction has not been biochemically characterized and does not appear in the https://github.com/EPFL-LCSB/redgem.redGEM and lumpGEM algorithms , 12 haveE. coli physiology as in our previous study [FBA in mid-lower glycolysis operates towards catabolism .Magnesium and phosphate transporters are both set towards uptake , 25.Acetate kinase (ACKr) and phospho-transacetylase (PTAr) operate towards acetate production, as acetate is a by-products .Succinyl-CoA synthetase (SUCOAS) operates towards producing succinate .Polyphosphate kinases  are set towards the polyphosphate polymerization .As we model the same aerobically grown us study , we makeThese directionality assumptions were made in agreement with the modeled physiology. Nevertheless, our workflow could be applied to other physiologies and under other directionality assumptions.E. coli under aerobic conditions and minimal media was integrated in our models. The MILP formulation of the thermodynamics-based flux analysis was used to implement these data into D1, D2 and D3. Since the models were used to build kinetic models, it was undesirable for reactions to be at thermodynamic equilibrium, which would result in them having equal backward and forward fluxes. We imposed MILP constraints to ensure that the thermodynamic displacement, Γ [ ≈ 1. This constraint ensures that we do not have reactions that have net fluxes equal to zero in our system.The available fluxomics and metabolomics data for the optimal growth of ement, Γ , 31, 36,https://github.com/EPFL-LCSB/matTFA and https://github.com/EPFL-LCSB/pytfa.Software used for performing thermodynamic-based flux analysis and TVA has been published  and is aWe sampled the flux space of D1 in order to characterize the solution space without violating physiological, thermodynamic and directionality constraints. The convexity of the solution space enabled us to efficiently sample using the Artificial-Centering Hit-and-Run sampler in the COBRA Toolbox , 38. We ubrxn,i and Flbrxn,i respectively, into D2. Consequently, we use an MILP formulation to minimize the number of violations of flux boundaries that we are trying to impose. For each intracellular reaction that is shared between the two models we create a binary variable zrxn, i so that when it is equal to 1, the constraints that we impose become inactive. We add for each of these reactions the following constraints:UB and LB are the upper and lower bounds of the net fluxes NF of the reactions. We minimize the sum of the binaries, zrxn, i, in order to have minimal violation of the flux constraints:In order to make the comparison of the models equitable, we wanted to maintain most similar steady-states between the models. For instance, for D2 we would like the flux vector to be the equal possible to the one from D1. Topological differences in the models make it impossible to have numerically exactly the same flux distribution in larger model for the same reactions. Hence, we take the representative flux from D1 and apply it with percentage relaxation with upper and lower bounds, FMinimize:Subject to:zrxn, i). After applying the constraints that are not violating model boundaries of D2, we proceed to sampling the solution space. We selected a sample based on mean PCA as with the representative flux of D1. We then implied in a similar manner the concentration profile from D1 into D2 with a 1% relaxation and sampled the concentration space for this flux profile. We repeat this procedure when scaling up the flux and concentration steady-states from D2 into D3.We implied a 1% relaxation to apply and test how many flux constraints we can impose without violation  derived from the summation theorem to quantify the discrepancies in control patterns of a flux between two different models. We define DI as:m enzymes of our system. However, if we perform this computation of DI for all the enzymes m, except the enzymatic reactions added to the system by a model expansion, we can obtain a deviation from zero. This happens if these enzymatic reactions that were added to the system by the expansion exhibit control over the flux v being studied. Hence, if the DI value is not zero for a model expansion, this could suggest that some of the added reactions are important in terms of control to the system.The value of DI will be zero due the summation theory of MCA if we sum over all Additional file 1. MATLAB models of D1, D2 and D3. Models used for obtaining thermodynamically feasible steady-states for constructing populations of kinetic models. Software for reading models is available on GitHub: https://github.com/EPFL-LCSB/matTFA.Additional file 2. Fluxomics and metabolomics experimental data incorporated in the model for optimally grown E. coli. Table with the flux boundaries in mmol/gDW/h and the concentration boundaries in log(mM) that were applied as constraints to the D1-3 TFA models based on the experimental data reported by McCloskey et al. Additional file 3. Thermodynamics-based variability analysis of models. Spreadsheet with the list of metabolites and reactions inside the models with variability analysis of flux and metabolite concentrations. The lumped reactions generated with the redGEM and lumpGEM algorithms begin with LMPD. Reactions added to the E. coli iJO1366 for passive diffusive transport start with TransFlux. The rest of the reactions come from E. coli iJO1366.Additional file 4. Document with additional figures, details about methods and further analysis carried out in this study. Thermodynamic-based variability analysis was performed to study the feasible ranges of metabolic flux across central carbon reactions for D1-3 models. Flux control coefficients for other reactions were analyzed to see how they are affected by model complexity. Mathematical formulations of the kinetic mechanisms describing the reactions in the kinetic models are also provided.Additional file 5. Flux and concentration steady states. Spreadsheet providing metabolic flux and concentration reference steady-states across the models with a comparative study of these steady states between pairs of models. Additional file 6. Analysis of absolute deviations in means of flux control coefficients for the entire systems. The mean flux control coefficient v and the horizontal to the enzymes p. A large deviation indicates a discrepancy in the prediction of the model for that given control coefficient Additional file 7. Kinetic mechanism allocation. Reaction mechanisms assigned for the reactions of D1, D2 and D3 models. The assigned reaction mechanisms in this file refer to the kinetic mechanisms for which a mathematical description is given in Additional file 4.