Escherichia coli, achieving highly significant overlap with published cases (hypergeometric p = 4.4e-13). We then validate three novel predicted target-replacer gene pairs in new multicopy suppression experiments. We next go beyond PROPER and develop a network-based approach, GEM-PROPER, that integrates PROPER with genome-scale metabolic modeling to predict promiscuous replacements via alternative metabolic pathways. GEM-PROPER predicts a new indirect replacer (thiG) for an essential enzyme (pdxB) in production of pyridoxal 5’-phosphate (the active form of Vitamin B6), which we validate experimentally via multicopy suppression. We perform a structural analysis of thiG to determine its potential promiscuous active site, which we validate experimentally by inactivating the pertaining residues and showing a loss of replacer activity. Thus, this study is a successful example where a computational investigation leads to a network-based identification of an indirect promiscuous replacement of a key metabolic enzyme, which would have been extremely difficult to identify directly.Recent insights suggest that non-specific and/or promiscuous enzymes are common and active across life. Understanding the role of such enzymes is an important open question in biology. Here we develop a genome-wide method, PROPER, that uses a permissive PSI-BLAST approach to predict promiscuous activities of metabolic genes. Enzyme promiscuity is typically studied experimentally using multicopy suppression, in which over-expression of a promiscuous ‘replacer’ gene rescues lethality caused by inactivation of a ‘target’ gene. We use PROPER to predict multicopy suppression in  E. coli. Notably, we predict and validate several new cases where a ‘replacer’ gene can compensate for the loss of an essential ‘target’ gene through a promiscuous activity. Next, we couple our method with a genome-scale metabolic model, in order to search for ‘replacer’ genes that compensate for essential ‘target’ genes by metabolically bypassing them. We use this network-augmented approach to uncover a novel promiscuous pathway for the production of pyridoxal 5’-phosphate (the active form of Vitamin B6) in E. coli. This study represents an important step in understanding promiscuous functions in bacteria, and is a prime example of a systems-level analysis leading to new biological insight.Many enzymes can perform secondary functions at low affinities or rates, but such ‘promiscuous’ functions have never been predicted on a genome-wide scale. Here, we present the first genome-wide method to predict promiscuous functions of metabolic genes, which we apply to  Enzymes have traditionally been associated with discrete activities . Clear-cexisting promiscuous activities on a genome-wide, network scale. A notable recent effort did probe the global relevance of promiscuous enzyme activities, but the study used ‘as is’ data collected from enzyme databases, which, while having the advantage of being fully experimentally verified, include many non-biologically-relevant instances and exclude many biologically relevant ones , or transport processes . Fatty acid degradation and synthesis processes are known to involve enzymes with many potential specificities depending on only small alterations , 26pdxB thiG supporting Vitamin B6 biosynthesis is based on similarities between a portion of thiG and a portion of pdxS from Staphylococcus haemolyticus, as found in our gene similarity trees. pdxS in Staphylococcus haemolyticus was annotated as such based on high similarity (81% identity over 98% of the genes) with the well-studied pdxS gene in B. subtilis . Notably, our list of indirect replacers for pdxB also included hisH, with the predicted function of pdxT. Thus, hisH is a strong candidate for functionally complimenting the potential pdxS function of thiG. However, pdxS is also present in the genomes of certain organisms in the absence of pdxT, and it has been hypothesized that it might operate in these organism as an ammonium-dependent synthase of P5P, thus bypassing the need for the glutamine amidotransferase subunit pdxT , and revealed a potential overlap of ThiG residues with the PdxS active site: Lys-95, Asn-204, and Glu-97 from the E. coli ThiG homology-model lie within 1.4, 2.2, and 4.9 angstroms respectively from the catalytic residues Lys-81, Asp-24, and Asp-102 in PdxS . The third residue of the proposed active site, Asn-204, was not altered since, as noted, this residue comprises part of the primary ThiG dyad active site. We thus created a mutated form of thiG (thiGmut) with the proposed secondary active site disturbed, but the site for the primary activity of thiG unaffected.To validate the putative secondary triad active site of ThiG , we tested whether inactivation of the predicted active site would eliminate the ability of ThiG to replace PdxB thiGmut overexpression on the growth of ΔpdxB cells in minimal media, we transformed ΔpdxB cells with plasmids encoding IPTG-inducible copies of thiGmut (ΔpdxB/thiGmut), thiG (ΔpdxB/thiG), pdxB (ΔpdxB/pdxB rescue plasmid positive control), as well as the empty vector (ΔpdxB/empty negative control). To determine the optimal M9 glucose media conditions for growth comparison, we performed a checkerboard dilution assay in deep-well microplates in which we individually assessed the growth of each strain across a matrix of varied IPTG and ammonium nitrate (NH4Cl) concentrations to identify synergistic combinations of inducer and nitrogen source, respectively. The nitrogen source (NH4Cl) was varied because we observed that vitamin B6 is used heavily as a cofactor in enzymes that participate in amino acid metabolism  for all strains grown at the experimentally observed optimum NH4Cl concentration (~3%), across all IPTG concentrations, revealed highly significant differences between growth of the ΔpdxB/pdxB and ΔpdxB/thiG group versus the ΔpdxB/thiGmut and ΔpdxB/empty group after 96 hours (p< = 4.7e-3), but no significant differences within these groups. Importantly, these findings were consistent with subsequent batch culture growth experiments performed using the optimized concentrations of 10 μM IPTG and ~3% NH4Cl in M9 glucose , was found by coupling our promiscuity predictor with a GEM. Finally, we predict and then experimentally validate the promiscuous active site of thiG for this replacing activity, revealing a striking new promiscuous route for the production of an essential nutrient, p5p, in E. coli.Identifying promiscuous gene functions is a fundamental task in biology. Promiscuous functions have been causally associated with the evolution of new gene functions , 31, andWhile sequence similarity-based methods  are used ubiquitously to determine primary gene functions, their ability to call promiscuous functions is unclear. Our method gives a first estimate, as we were able to experimentally validate around 20% of direct target-replacer pairs we could test in the lab (This is 100x higher than expected if guessing target-replacer pairs randomly). It is likely that the number of target-replacer pairs we validated is an underestimate of true promiscuity, as some true replacers might not show during multicopy suppression due to incorrect expression levels , insufficient effects of target knockout, or other confounding factors. Notably, many of our predictions might be correct even though they cannot be directly validated through multicopy suppression . Our comparison to the work of  emphasizE. coli are available , we choE. coli. Without such a systems approach, it would have been extremely difficult to identify thiG as a candidate replacer for pdxB. Thus, this study serves as a successful example where systems biology can provide a roadmap for biological investigation, identifying the most promising targets to then follow up on with more costly and time-consuming experiments.In all, this work constitutes the first ever genome-wide prediction of metabolic gene multicopy suppression, and the first integration of such predictions with a GEM to achieve network-reliant indirect predictions. We begin with an unsupervised, large-scale method to predict enzyme promiscuity, and finally dial in on and then experimentally verifying a key prediction of biological significance in E. coli; (2) using these trees to build a matrix of promiscuous gene functions; and (3) applying this matrix to determine potential promiscuous gene replacers for target genes of interest. In GEM-PROPER, step (3) is replaced by a GEM-based approach, in which we search for promiscuous functions (from step 2) that can rescue in silico growth of a GEM model after knockout of the target gene. Here, we describe these steps in detail:PROPER proceeds in three steps, as outlined in To identify as many promiscuous gene functions as possible, we performed an unsupervised iterative PSI-BLAST based search for distant sequence relationships between genes in E. coli and all other genes in the SEED database. Our method involved five steps: (1) align the current query sequences; (2) cluster the aligned sequences to reduce sampling bias in sequencing; (3) trim aligned representatives to eliminate non-conserved ends; (4) use trimmed alignments in a PSI-BLAST search against the non-redundant protein database in SEED; and finally, (5) keep PSI-BLAST hits that match certain criteria, as outlined below. These hits would be kept for the next round of PSI-BLAST, and the process would continue for three rounds with increasingly more relaxed thresholds for keeping PSI-BLAST hits.The intuition behind this approach was to use iterative trimming to build a compact protein profile that is effective at recruiting distant homologs. These profiles differ from individual protein domains such as some CDDs in that they capture the conserved arrangement of multiple domains in related protein sequences. The parameters used in this protocol were manually tuned to facilitate inspection of related protein functions in the same tree for expert annotators at SEED. The detailed protocol and parameters are provided in the supplementary materials . For theuncovered region of the query sequence < = 100the query sequence is at least 60% coveredsequence percent identity > = 0.15sequence percent positive match > = 0.30 [This is the percentage of aligned bases with positive scores from the substitution scoring matrix indicating conserved changes ].E. coli variants of the protein. We use MAFFT [As PSI-blast itself can do iterative search, the main difference in our approach was trimming and clustering. By trimming we eliminated non-conserved ends, so the profile is more compact and more effective at recruiting distant homologs during each search. The clustering step keeps only the representative sequences in the profile, thus alleviating some of the sampling bias, i.e., so that the profile is not dominated by se MAFFT  for aligse MAFFT  for treeE. coli that links to other genes with any sequence similarity, which were then candidates for assigning potential (predicted) promiscuous functions to the root gene.This whole procedure provided a tree for each gene in Genes in RAST are annotated with functions, which then (in the case of metabolic genes) link to metabolic reactions. After a few attempts to set distance thresholds in the trees for assigning functions, we found that including all function in the tree as a potential promiscuous function gave optimal results. Therefore, all functions existing in the tree of a root E. coli gene are considered potential promiscuous functions, as are their metabolic reactions. In cases where a gene is promiscuously associated with only one subunit of an enzyme complex, we predicted that entire function is associated with the root gene. We entered these gene-function promiscuous pairings into a matrix for further analysis.To search for direct target-replacer pairs, we identified cases in our matrix in which any of a ‘replacer’ gene’s promiscuously assigned functions is the same as the primary annotated function of a ‘target’ gene of interest.To search for indirect target-replacer pairs, we identified cases in our matrix in which any of a ‘replacer’ gene’s promiscuously assigned functions can metabolically bypass the primary annotated function of a ‘target’ gene of interest. This analysis could only be done for target genes that are conditionally essential in silico, i.e., whose knockout causes in silico death on M9 medium but not on rich medium.Escherichia coli K12 taxon ID 83333.1 as downloaded from SEED [in silico, and the subset of Patrick targets that were also conditionally essential in silico were kept for further analysis. All essentiality tests were done using Flux Balance Analysis testing for a nominal production of biomass [in silico growth was rescued. Cases in which the indirect replacer gene  rescued in silico growth were considered predictions of indirect replacement.The GEM used was a genome-scale metabolic model for rom SEED . Target  biomass . MetabolMulticopy suppression is an established assay that has been described elsewhere  and transformed with ASKA plasmids over-expressing the corresponding predicted replacer gene.llection , which cllection , which cWhen we were developing our assay, we found that knockout colonies usually grew after some amount of time on M9 medium regardless of whether the replacer gene had been added to the plasmid, despite the fact that each of the target strains we tested was previously reported to be non-viable on M9 medium. The previous study by Patrick  had not KanR). Thus we verified correct location of the knockout in each target strain by amplifying and sequencing the area directly flanking the kanamycin insertion, using a kanamycin universal primer and a strain-specific reverse primer located downstream of the knocked out gene. Since the orientation of the kanamycin insertion depends on the orientation of the original knocked out gene, the KanR primer 5’-ATATTGCTGAAGAGCTTGG was used when the original gene had been forward coded and the KanR primer 5’-AATGAACTCCAGGACGAG was used if the original gene had been reverse coded. Correct sequence of the replacer gene was verified by amplifying and sequencing the ASKA plasmid insert .In the KEIO collection each knocked out gene is replaced by the kanamycin resistance gene  containing IPTG. All TR pairs were plated on both M9 with 50μM and 125μM IPTG; TR pairs of particular interest  were plated on 250μM as well. In each TR plating experiment, the empty and frvX negative controls were plated alongside the TR pairs. Plates were wrapped in nylon to avoid dehydration, incubated at 37 and monitored during the next three weeks. Nearly all negative control plates showed some growth phenotype, ranging from very strong  to very weak  pair were grown overnight in LB+CAP, washed and serially diluted in saline (0.9% NaCl). Aliquots (100 ul) of 10ΔglyA, ΔptsI and ΔpabB) was also monitored in liquid culture. Cultures in LB+CAP were washed once in saline and re-suspended at a dilution of 1:100 into M9-glucose-kanamycin-chloramphenicol minimal media supplemented with IPTG (50 μM). Growth measurements were performed in a 96-well plate incubated for 19–24 h at 37°C in a temperature-controlled plate reader with continuous shaking , and OD595 was monitored every 15 min. Each TR pair was loaded into 2 duplicate wells. Growth of the negative controls (empty and frvX plasmids) for each target strain was likewise monitored during every run.Growth of TR pairs that showed exceptionally high growth on the negative control plates  and 25 μg/mL chloramphenicol (ASKA plasmids) selection. Cells were washed in 1x PBS and diluted 1:100 into M9-glucose-kanamycin-chloramphenicol for plate seeding; M9 was prepared without a nitrogen source. A checkerboard matrix was generated in 2mL deep-well, 96-well assay plates by serial dilution of NH4Cl (22.5% w/v maximum concentration) across plate columns and IPTG (500 μM maximum concentration) across plate rows. Wells were uniformly inoculated with cells, and each well contained a final volume of 1.2 mL. Plates were sealed with gas-permeable membranes and grown in a light-protected, microplate incubator shaker at 37°C and 700 RPM; 700 RPM was determined to be equivalent to 300 RPM in a standard incubator shaker. Samples for OD600 measurements were taken at designated timepoints using a SpectraMax M5 microplate multimode plate reader (Molecular Devices), and the gas permeable membrane resealed after each timepoint. 100 μL samples were taken for OD600 measurements to minimize the total volume loss.Overnight cultures of each strain were grown in LB with 30 μg/mL kanamycin (4Cl (w/v) and 10 μM IPTG, in 250 Erlenmeyer flasks. Cultures were grown at 37°C and 300 RPM in an incubator shaker, with samples for OD600 measurements taken at designated timepoints.For batch culture experiments, cells were prepared from overnight cultures as described above. Cells were diluted 1:100 in 30 mL of M9-glucose-kanamycin-chloramphenicol, containing ~3% NHB. bacillus) in complex with pdxT, was downloaded from the pdb database, and the residues of the pdxS active site were identified from the publication  [pdxS units from the multimeric structure were overlaid and were found to be coincident  . Multiplsy.org/; ) based o ID 2htm ). The stng pyMol .hisA/∆hisH and cysM/∆ilvA. Conversely, growth of purE/∆purK, one of the target-replacer pairs predicted by both Patrick and us, was almost entirely inhibited when IPTG concentration was increased to 125uM. These results illustrate that over-expression can also have deleterious effects [frvX caused a decrease of the background seen in the empty plasmid control (see Low (50μM) IPTG concentration was sufficient to induce all of the replacers. Interestingly, increasing the IPTG concentration affected growth sometimes positively and sometimes negatively, depending on the specific strain. Increasing IPTG concentration up to 250μM caused increases in colony size and number, and decreases in incubation times, for  effects . The opttrol see .S1 Text(DOCX)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.S2 FigAll target-replacer pairs predicted by our method were assessed for how often a metabolic target paired with a metabolic replacer, with a non-metabolic replacer, a non-metabolic target with a metabolic replacer, etc. We found that (A) Replacer genes with metabolic primary functions take more metabolic targets than do replacer genes with non-metabolic primary functions; (B) Replacer genes with non-metabolic primary functions take more non-metabolic targets than do replacer genes with metabolic primary functions; and (C) The number of targets replaced by replacer genes with non-metabolic vs. metabolic primary functions is the same.(TIF)Click here for additional data file.S3 FigHistograms are shown of: (A) number of genes represented in each tree; (B) number of unique organisms represented in each tree; (C) number of distinct functions represented in each tree; and (D) number of E. coli metabolic functions present in each tree.(TIF)Click here for additional data file.S4 Fig(TIF)Click here for additional data file.S5 Fig(TIF)Click here for additional data file.S6 Fig(TIF)Click here for additional data file.S7 Fig(A) E. coli thiG is aligned with pdxS, the gene whose function it putatively performs promiscuously. Key residues in both genes are marked, as per the key at the bottom. Two alignments are shown as they came up in BLASTP sequence alignment. (B) The active residues of thiG for its primary function are shown, along with putative active residues for the pdxS function.(TIF)Click here for additional data file.S8 FigMultiple alignments are shown.(TIF)Click here for additional data file.S9 FigThe residues in thiG that we predict can perform the pdxS function show a high degree of conservation, as shown in the plot. This was generated from the output of ConSurf, set with default settings except for a maximum cutoff of 70% homology in the sequences to be aligned (higher cutoffs led to less resolution in distinguishing how conserved the key residues are versus their neighbors).(TIF)Click here for additional data file.S10 Fig(DOCX)Click here for additional data file.S11 FigResults analogous to those shown in Fig 5 of the main text are shown, but at the 48 hour timepoint (instead of 96 hours as shown in the main text). (A) Ranksum test across all IPTG concentrations in the microwell plate experiment . (B) Results of a separate batch culture experiment, with 5–8 replicates per group, which show the same trend of the microwell plates from subfigure A. P-values are from t-tests across replicates of each strain grown in identical condition . #OD600 values in (A) were measured using 100uL of culture, where 300uL of culture would be the equivalent of a normal 1mL cuvette.(DOCX)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.


To overcome these limitations, fermentation engineering should merge with systems metabolic engineering. Modern fermentation engineers need to adopt new metabolic flux analysis tools that integrate kinetics, hydrodynamics, and 13C-proteomics, to reveal the dynamic physiologies of the microbial host under large bioreactor conditions. Based on metabolic analyses, fermentation engineers may employ rational pathway modifications, synthetic biology circuits, and bioreactor control algorithms to optimize large-scale biofuel production.Metabolic engineering has developed microbial cell factories that can convert renewable carbon sources into biofuels. Current molecular biology tools can efficiently alter enzyme levels to redirect carbon fluxes toward biofuel production, but low product yield and titer in large bioreactors prevent the fulfillment of cheap biofuels. There are three major roadblocks preventing economical biofuel production. First, carbon fluxes from the substrate dissipate into a complex metabolic network. Besides the desired product, microbial hosts direct carbon flux to synthesize biomass, overflow metabolites, and heterologous enzymes. Second, microbial hosts need to oxidize a large portion of the substrate to generate both ATP and NAD(P)H to power biofuel synthesis. High cell maintenance, triggered by the metabolic burdens from genetic modifications, can significantly affect the ATP supply. Thereby, fermentation of advanced biofuels (such as biodiesel and hydrocarbons) often requires aerobic respiration to resolve the ATP shortage. Third, mass transfer limitations in large bioreactors create heterogeneous growth conditions and micro-environmental fluctuations (such as suboptimal O The desired biosynthetic pathway for advanced biofuels often requires multiple enzymatic steps. Current molecular biology techniques can effectively alter enzyme levels to increase the flux toward biofuel synthesis. Common strategies include choice of plasmids and its copy numbers, promoter engineering, codon optimization, synthetic scaffolds, directed evolution/modification of key enzymes, improvement of ribosome binding sites, and knockout/knockdown of competitive pathways   , the poor mixing/aeration can cause temperature and pH fluctuations, O2 limitations, substrate/product inhibitions, and accumulations of wastes (such as acetate)  are used for fermentation, gas-liquid mass transfer resistances pose another serious challenge as the gaseous substrates must diffuse across the gas-liquid interface . This has been reported to cause increased production of waste products, such as formate, lactate, and succinate  is used to directly measure enzymatic reaction rates. Compared to other omics studies, 13C-MFA can provide insights into cell's physiology during large-scale fermentations. 13C-MFA uses metabolic reaction stoichiometry and carbon-labeling experiments to precisely estimate metabolite turnover rates   during E. coli fermentation. Recently, proteomic analysis of 13C-peptide labeling has also been developed to assist metabolic flux analysis of heterogeneous microbial systems . Sauer group proposed a “reporter protein”-based 13C-MFA may integrate with microbial kinetics to reveal the changes of cell metabolism throughout its cultivation process. For example, Sauer group have utilized such a dynamic 13C-MFA approach in a fed-batch fermentation to monitor the dynamic changes in intracellular fluxes during the different growth stages. Their results revealed that a riboflavin-producing bacterium's physiology shifted from an overflow metabolism to an exclusively maintenance metabolism at the late fermentation stage  are more promising biofuels than biodiesel/hydrocarbons, as alcohol synthesis pathways are less dependent on the ATP supply and alcohol fermentation can be conducted under anaerobic conditions. Production of biodiesel and hydrocarbon require large amounts of ATP, and their processes are usually restricted to aerobic conditions and their productivities are highly sensitive to the P/O ratio  is naturally tolerant to alcohols and acetate, and it is a robust workhorse for industrial alcohol fermentations. However, the energy metabolism of yeast has a lower net ATP production as additional ATP is consumed during the transport of equivalents of NADH from the cytoplasm into the mitochondria . E. coli has already been engineered to produce higher alcohols, biodiesels and other hydrocarbons that demand large amounts of energy molecules. Another promising chassis is microalgae . Although most studies emphasize their photoautotrophic features, photomixotrophic fermentation has two great advantages for industrial use. (1) Photo-fermentations of organic substrates (sugars) can reach high carbon yields of both biofuel and biomass due to mixotrophic CO2 fixation and light energy harvesting to generate ATP and NADPH .Second, the loss of carbon yield due to ATP/NAD(P)H limitations is often severe in engineered microbial hosts. Therefore, modern fermentation engineering should focus on reducing the metabolic burden and enhancing the prosperity of the energy metabolism. There are several effective strategies to improve NAD(P)H and ATP availability. (1) Adding nutrient sources (such as yeast extract) into cell culture; (2) overexpressing NADH dehydrogenase to enhance the respiration efficiency , and construct sensor-regulator systems to improve cell productivity in industrial bioreactors. Fermentation engineers should have a comprehensive understanding of both the macroscopic  and microscopic (intracellular fluxes) parameters, and thus fill the gaps between laboratory studies and industrial applications. “Scale-down” experiments  with metabolic flux analysis can be routinely used to diagnose the engineered metabolism, verify synthetic biology circuits, and design optimal fermentation strategies Figure . Most imThe 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.


Constraint-based reconstruction and analysis (COBRA) is used for modeling genome-scale metabolic networks (MNs). In a COBRA model, extreme pathways (ExPas) are the edges of its conical solution space, which is formed by all viable steady-state flux distributions. ExPa analysis has been successfully applied to MNs to reveal their phenotypic capabilities and properties. Recently, the COBRA framework has been extended to transcriptional regulatory networks (TRNs) and transcriptional and translational networks (TTNs), so efforts are needed to determine whether ExPa analysis is also effective on these two types of networks.In this paper, the ExPas resulting from the COBRA models of E.coli's MN, TRN and TTN were horizontally compared from 5 aspects: (1) Total number and the ratio of their amount to reaction amount; (2) Length distribution; (3) Reaction participation; (4) Correlated reaction sets (CoSets); (5) interconnectivity degree. Significant discrepancies in above properties were observed during the comparison, which reveals the biological natures of different biological processes. Besides, by demonstrating the application of ExPa analysis on E.coli, we provide a practical guidance of an improved approach to compute ExPas on COBRA models of TRNs.ExPas of E.coli's MN, TRN and TTN have different properties, which are strongly connected with various biological natures of biochemical networks, such as topological structure, specificity and redundancy. Our study shows that ExPas are biologically meaningful on the newborn models and suggests the effectiveness of ExPa analysis on them. Many large-scale biological networks, including metabolic networks (MNs) , signaliEscherichia coli [Sacchoromryces cerevisiae [Helicobacter pylori [Haemophilus influenzae [Methylobacterium extroguens [All the possible phenotypes, i.e. the flux distributions of feasible steady states, of a constraint-based biochemical model form a high-dimensional cone. Network-based pathways such as Extreme Pathways (ExPas)  are defihia coli -19, Saccrevisiae ,21, Helir pylori ,23, Haemfluenzae ,24 and Mtroguens . Besidestroguens  and the E.coli transcriptional regulatory network (TRN) [E.coli transcriptional and translational network (TTN) [E.coli TRN, MN and TTN. In the comparison, differences between biological processes were observed from multiple perspectives, including network structure, reaction participation, specificity and redundancy. The results indicate that ExPa analysis can be extended to biochemical systems of TRN and TTN, which helps researchers to further understand the corresponding biological systems. Besides an improved method was introduced to simplify the calculation and interpretation of ExPas on TRN models [Recently, there emerged two COBRA models of biochemical systems with different types: rk (TRN)  and E.cork (TTN) . What shN models , which cE.coli MN and TTN is computationally intractable. Fortunately ExPa calculation will be much more manageable if a MN or a TTN is divided into smaller sub-networks. Therefore, we chose the sub-networks with relatively complete and independent functions as the representatives of their belonging biologic systems. For the E.coli MN, two sub-networks were chosen: (1) Amino acid, Carbohydrate and Lipid metabolism (sACL) and (2) Membrane and Murein metabolism (sMM). For E.coli TTN, the two sub-networks were: (1) transcription (sTC) and (2) translation (sTL).Firstly, we calculated extreme pathways of the three biological networks mentioned above. Since the number of ExPas grows exponentially with a networks' complexity , the enuThen ExPa analysis was performed on each network/subnetwork and the properties from different aspects were obtained, including the total number of ExPas, the number-based ratio of ExPa to reaction, ExPa length distribution, reaction participation distribution, correlated reaction sets (CoSets), and the inter-connectivity of ExPas. Finally, a horizontal comparison on the properties was made among the five networks/subnetworks.E.coli TRN model which were stumbled through ExPa analysis are also reported in this section. This findings illustrate that ExPa analysis is capable of directing model refinement.Moreover, some incompleteness and incorrectness in the E.coli TRN model was published by Gianchandani et al. in 2009 [Materials and Methods). The final TRN model contains 1009 components, 1106 internal regulatory reactions, and 1009 exchange reactions each corresponding to a component. All the extracellular metabolites were considered as inputs and all protein products were considered as outputs. There were 1599 ExPas, of which 9 were biologically infeasible because they employed conflicting input fluxes, and thus they were excluded from the ExPa set used in analysis.The  in 2009 . It cont 2009 [R*. The TRNE.coli TRN, 16 reactions do not participate in any ExPa; namely they are never used to form a transcriptional state of the network. These unused reactions were categorized into two types as listed in Table In NOT_BirA (absence of protein BirA). However, no regulatory rule corresponds to the presence or absence of BirA, and therefore, the initial steps are unknown. As a result, the internal reactions using NOT_BirA  and the corresponding exchange reactions  will never be initiated. Furthermore, proteins BirA and the gene products of b0774, b0775, b0776 and b0778 do not participate in any other reaction except those in Table E.coli TRN model and necessitate further refinement.Reactions in Table b1814 can be divided by simple logical transformation into 6 rules, of which 3 contradict with each other  are listed in Table The length of an ExPa equals to the number of reactions that participate in it . Figure E.coli TRN represent transcriptional regulatory rules rather than real biochemical reactions as in MN and TTN, and thus the ExPa length in TRN depicts the number of regulatory rules used for expressing certain genes. A regulatory rule describes how environmental stimuli affect transcriptional factors, which in turn affect downstream target genes. Therefore, the ExPa in TRN is reasonably shorter as the biological network has a relatively flat hierarchical structure [The length distributions of ExPas corresponding to those biological processes are very diverse. The longest ExPas consists 51, 82 32 and 109 reactions in sACL, sMM, sTC and STL, respectively, which is much longer than that in TRN (21). Reactions in tructure . The resThe reaction participation rate (RPR) is defined as the percentage of ExPas in which a given reaction participates . Figure Here the top 10 internal reactions with the highest RPRs of each process are sorted in a descending order Table . SeveralCRP_noGLC_1 and Crp_1 relate to the regulation rules of the transcription factor (TCF) C-reactive protein (CRP). Other high rank reactions Fis_1, Lrp_1, Fnr_1, and NOT_ArcA_1 relate to the regulation rules of the TCFs Fis, Lrp, Fnr and ArcA, respectively. In E.coli, the above TCFs belong to the seven global regulators that control most of the regulated genes [NOT_Cra_1 is relevant to the regulation rules of the TCF Cra, a pleiotropic regulatory protein that controls carbon and energy fluxes in enteric bacteria [NOT_PdhR_1 concerns the regulation rules of PdhR, a TCF that controls the respiratory electron transport system in E.coli. Its regulation target, the pyruvate dehydrogenase (PDH) multienzyme complex, plays a key role in the metabolic interconnection between glycolysis and the citric acid cycle [In TRN, the two most active reactions ed genes . The reabacteria ,30. The id cycle .ASPTA. It transfers oxoglutarate and aspartate to corresponding ketoacid, which are indispensable in glyoxylate cycle, an anabolic metabolic pathway occurring in E. coli [ASAD which is the second step in the biosynthesis of amino acids in prokaryotes, fungi, and some higher plants. ASAD forms an early branch point in the metabolic pathway producing lysine, methionine, leucine and isoleucine from aspartate as well as diaminopimelate which plays an essential role in bacterial cell wall formation [asd (encoding ASAD) is lethal to the organism as demonstrated by experiments with Legionella pneumophila, Salmonella typhimurium, and Streptococcus mutans, which indicates that ASAD may also be an essential reaction in the metabolism of E.coli [ASPK, which is the commitment step in the pathway to the synthesis of lysine, methionine, threonine and isoleucine.In sACL, the most active reaction is  E. coli . The secormation . Deletiof E.coli . AnotherACCOAC is most active. It is a rate-determining step in the fatty acid synthetic pathway and may play a pivotal role in regulating fatty acid oxidation [MCOATA transfers Malonyl CoA to acyl-carrier proteins (ACPs). The product Malonyl ACP provides malonyl groups for biosynthesis of fatty acid and polyketide. On the other hand, Malonyl CoA, the substrate of MCOATA, is a highly-regulated molecule in fatty acid synthesis as it inhibits the rate-limiting step in beta-oxidation of fatty acids [MCOATA affects the consistency of Malonyl CoA and guarantees the biosynthesis of fatty acid.In sMM, the reaction xidation . The secty acids . Flux chIn sTC, all the top reactions relate to the formation of the transcription elongation complex, an extremely complicated and highly regulated molecular machine that can sense signals coming from numerous regulatory protein factors, as well as those encoded in the DNA sequence. They are the basis of transcription elongation, because transcription can run smoothly and continuously only depending on their precise work.IF2_RECHARG, Rib_30_ini_FORM and Rib_70_DISS are used by all ExPas. IF2_RECHARG recharges the initiation factor 2 (IF2) with GTP and Rib_30_ini_FORM produces 30S translation initiation complex which consists of 30S subunit, IF1, IF2-GTP and IF3. In bacteria, the correct mRNA starting site and the reading frame are selected when, with the help of IF1, IF2 and IF3, the initiation codon is decoded in the peptidyl site of the 30S ribosomal subunit by the anticodon fMet-tRNAfMet. Furthermore, Rib_30_ini_FORM is also proved to be the intermediate step in the formation of 70S initiation complex (70SIC) which regulates translation initiation, the rate-limiting step in protein synthesis [Rib_70_DISS dissociates 70S ribosomes to 30S ribosomal subunit/IF1/IF3 complex (rib_30_IF1_IF3) and 50S ribosomal subunit (rib_50_inact). This is an essential step before a ribosome can participate in a new round of translation since the initiation complex for protein synthesis involves a 30S subunit. The dissociation of 70S ribosomes contributes to the efficiency and sustainability of protein synthesis [In sTL, the reactions ynthesis . The othynthesis .Reportedly, RPRs help to find important reactions in MN . Our resA correlated reaction set (CoSet) comprises reactions that always participate in the same ExPa set in a given network ; namely A CoSet can be transformed to a graph by treating each reaction as a node and adding an edge between two reactions that involve a common substance. In a certain CoSet, some member reactions are topologically connected while others are not. The correlationship of the second type of reactions often indicates a transcriptional coregulation by the corresponding genes  while thCoSets were calculated for each biological network/sub-network about which several features, including the adjacent ratio, were stretched and shown in Table 2O, ATP and NADP commonly seen in various biochemical reactions. In order to further elucidate the difference in crosstalk between ExPa pairs, all the exchange reactions in the four sub-networks were sorted in a descending order depending on RPR and the top 20% ExPa pairs were neglected in the subsequent crosstalk analysis.Crosstalk analysis was first raised to illustrate the relationship between multiple inputs or outputs of a signaling pathway . The whoE.coli TTN and TRN are more deterministic than those in MN. Reportedly, a large number of genes are regulated by only a few independent regulatory rules in E.coli TRN [E.coli TTN have only one coding gene in the genome [As shown in Figure coli TRN , and thee genome . These fE.coli TRN can be attributed to the fact that the transcription of some genes can be stimulated by different transcriptional factors. For example, two redundant ExPas shown in Figure b2243 in the same environment, but they employ the regulatory rules of 'CRP_noRIB AND Fnr AND NOT(GlpR)' and 'CRP_noRIB AND ArcA AND NOT(GlpR)', respectively. From Figure E.coli MN is more flexible than TTN and TRN.Except sTC, the other networks/sub-networks all have ExPa pairs with identical inputs and identical outputs. These ExPas are redundant pathways which fulfill completely identical function through systemically independent routes. ExPa redundancy was demonstrated in genome-scale MNs ,24, as wE.coli TRN and TTN. A horizontal comparison was performed for the five networks/sub-networks: TRN, sACL, sMM, sTC, sTL from five aspects: (1) Total number of ExPas and the P/R ratios; (2) ExPa length distribution and L/R ratios; (3) Reaction participation rates; (4) Correlated reaction sets and adjacent ratios; (5) Inter-connectivity of ExPas.ExPa analysis were applied to two new models, the Reactions in TTN represent actual biochemical reactions like those in MN, and thus, ExPas in TTN characterize the steady-states of the corresponding biological systems. In contrast, columns in TRN represent the transcriptional regulatory rules and coefficents only reflect the qualitative information describing the presence or absence of the corresponding components rather than the quantitative information describing reaction stoichiometries as in TTN and MN. Therefore, an ExPa in TRN characterizes a specific transcriptional regulatory state, namely which transcriptional regulatory rules are activated and which genes are expressed in a specific environmental state.ExPa analysis emphasizes the functional and systemic properties of biologcial process as ExPas are systemically independent functional units. The total number of ExPas and the P/R ratios characterize the flexibility of the networks/sub-networks. ExPa length corresponds to the reaction steps needed to form a steady state, therefore showing a close relation to network complexity. Crosstalk enables the analysis of pathway redundancy and network determinacy. Comparisons from these aspects indicate that MN is more flexible but less deterministic than TRN and TTN. Environmental cues affect transcriptional regulation, which controls the following transcription and translation processes. Then the resulting gene products (enzymes) enter the metabolic system to catalyze the corresponding reactions. It is necessary for a cell to respond accurately to the environment and produce the required enzymes. MN is more robust to environmental changes, which reflects the struggle of a cell to achieve an alternative steady-state to provide substance support for TRN and TTN and maintain life.The distributions of reaction participation in the five networks/sub-networks are similar except that there are more reactions participating in more than 10% ExPas in sACL and sMM. Only a small percent of the reactions participate in a large number of ExPas, which indicates the phenotypic potentials of TRN, TTN and MN are affected greatly by a small number of important reactions. Evaluations on the representatives show that reactions with high participation rates often play an important role in certain biological processes. These reactions are the relatively weak part of the networks because a large number of ExPas will be destroyed when these reactions become invalid, which may cause the loss of various functions. These reactions may be used as drug targets and further direct the design of new drugs.CoSets were identified via the calculation of reaction participation. Besides the expected topological connections, the topologically unconnected reactions in a CoSet may indicate the information of transcriptional coregulation in MN. However, most Cosets of TRN and TTN are trivial, and thus have few chances to be a clue giving novel information like in MN.E.coli TRN model which we studied in the paper has 776 components whose availability  constitute the environmental condition, including environmental stimuli, transcription factors or proteins. It is impossible to enumerate all the possible conditions due to "combination explosion" without mentioning the calculation of the ExPas under each condition. However, using the approach we proposed, it took only about 45 seconds to computing the whole ExPa set on a PC with four 3.2-GHz Intel(R) XEON processors and 16GB RAM . We believe that this approach could be helpful for readers who are also interested in the ExPas of TRNs.Last but not least, an improved approach was introduced to calculate the ExPas on TRN models. Compared to the existing method, the biggest advantage of ours is the high efficiency in calculating all the extreme pathways of a TRN, especially for the one which may work under huge amount of environmental conditions. For example, the This study presents the first horizontal comparison among the E.coli TRN, MN and TTN through ExPa analysis. The results show that ExPa also has biological meanings in TRN and TTN. Different properties of ExPas reflect the biological nature of each biological process. Along with the the increase of reconstructed models on TRNs and TTNs as well as the development of new methods, ExPa analysis may reveal more biological properties and get larger space of application in the medical and biochemical fields.The COBRA framework stoichiometrically represents a biochemical network as a matrix where e system .Given the reversibility of reactions, an internal reversible reaction can be divided into a forward and a backward sub-reactions, each taking a non-negative flux. The model's solution space is now a convex polyhedral cone in high-dimensional space ,40, whic,41. All For a given network, the ExPa set has the following properties: (1) It is unique; (2) Each ExPa uses fewest reactions to form a function unit; (3) It is systemically independent which means an ExPa cannot be represented by a nonnegative linear combination of other ExPas ,43.expa' [E.coli MN and TTN models were divided into small sub-networks using the method proposed in [ExPas were calculated using an open source tool 'expa' . The E.cposed in .A TRN is composed of a set of transcriptional regulatory rules which describe cells' transcriptional responses to environmental signals. A regulatory network matrix of a TRN . It was  protein ,45. DiffFor example, given a toy TRN with three regulatory rules:where A, B, C and D are four metabolites enacting as signalling stimuli.The corresponding converses are:The matrix In order to calculate all the ExPas of the TRN, all the environmental states, namely all possible tal cues . Therefon environmental inputs expa' [The gist of the method is to improve Gianchandani's method by employing two columns instead of one to delineate the presence and absence of a unique envionment cue respectively, by which a new environment matrix l 'expa' .Notably, some infeasible steady states employing contradictory inputs may be involved in the right null space of Figures Algorithm 1.Given Data: // // // // Result: For to do End forFor to doIf do            Else if do    If do                    Else if                     End if        End if    End forAlgorithm 1: Procedure of normalizing In a normalized ExPa Here we prove that Statement 1: each ExPa in Proof: given Algorithm 2):Data: // // // // Result: // For to do End forFor to doIf do            Else if             End if    End forAlgorithm 2: Procedure of transforming For roven in ,  and G′Statement 2: each feasible ExPa in Proof: Since any environmental cue is impossible to be both present and absent in a specific environment, Algorithm 2, a legal From statements (1) and (2), we conclude that ExPas fall into three classes, in which class III stands for internal reaction cycles with no exchange flux . Class ICOBRA: Constraint-based Reconstruction and Analysis; MN: Metabolic Network: ExPa: Extreme Pathway; TRN: Transcriptinal Regulatory Network; TTN: Transcriptional and Translational Network; sACL: The subnetwork of Amino acid, arbohydrate and Lipid metabolism; sMM: The subnetowrk of Membrane and Murein metabolism; sTC: The subnetwork of Transcription in the TTN; sTL: The subnetwork of Translation in the TTN; ORF: Open Reading Frame; P/R: the Number-based Ratios of ExPa to Reaction; L/R: the Ratio of Average ExPa Length to Reaction Number; RPR: the Reaction Participation Rate; TCF: Transcription Factor; CRP: C-reactive Protein; PDH: Pyruvate Dehydrogenase; ACP: Acyl-carrier Protein; IF: Initiation Factor; 70SIC: 70S Initiation Complex; rib_30_IF1_IF3: 30S Ribosomal Subunit/IF1/IF3 Complex; rib_50_inact: 50S Ribosomal Subunit; CoSet: Correlated Reaction Set.The authors declare that they have no competing interests.YX conceived and designed the study, participated in drafting and revising the manuscript. YZ carried out the analysis and drafted the manuscript. LW interpreted the results biologically. FW supervised the study, participated in its design and to revise the manuscript. All authors read and approved the final manuscript.


Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention.Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution.We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems.The online version of this article (doi:10.1186/s12918-016-0259-2) contains supplementary material, which is available to authorized users. Mathematical models of cellular metabolism are a complementary tool to experimentation for analyzing and engineering metabolic function. Over the past several decades, flux balance analysis (FBA) based on stoichiometric descriptions of cellular metabolism has emerged as the dominant approach for microbial metabolic modeling. FBA involves the formulation of stoichiometric equations describing the metabolic network followed by linear program solution of the underdetermined linear equation system subject to an assumed cellular objective such as growth rate maximization . The advClassical FBA methods assume time invariant and spatially homogeneous extracellular conditions and generate steady-state predictions consistent with well-mixed, continuous cultures . Most mi2 concentrations decrease as the gas flows up the column due to cellular consumption [In contrast to the dynamic case, the development of metabolic models that account for spatially varying environments has received little attention. Such problems are very common in natural and engineered microbial systems. For example, naturally occurring microbial biofilms typically exhibit strong spatial gradients due to differential nutrient availability at the biofilm boundaries . Spatialsumption . The incsumption –13, lattsumption , 15 and sumption . These mz for simplicity. Additional modeling assumptions include that constant gas and liquid phase volume fractions and velocities, constant gas–liquid mass transfer coefficients, constant cell and metabolite diffusion coefficients, and cell incompressibility. The last assumption allows a simple convection term to be used in the species mass balance equations. While cell compressibility could be included in the model if necessary, we expect that this effect would negligible under the low velocity liquid flows encountered in the examples consider here as well as in most practical applications.The class of spatiotemporal metabolic models considered below is sufficiently general to encompass a wide variety of potential applications including microbial communities with interacting species and multiphase systems in which the liquid and gas phases move relative to each other. The framework is based on the standard dynamic flux balance modeling assumption that the intracellular metabolism is much faster than the extracellular dynamics, which we do not believe is any more restrictive when the environment exhibits spatial variations. Furthermore, we assume that spatial variations occur only in a single direction Under these assumptions, a general set of model equations can be written as,i-th microbial species where Xi is the biomass concentration, μi is the growth rate obtained from the genome-scale metabolic model, μdi is the death rate, uL is the liquid phase velocity, DiX is the cellular diffusion coefficient that accounts for cell motility. The second equation represents a mass balance on the j-th liquid phase metabolite where vij is the net flux of metabolite j into the liquid phase from species i, DjL is the liquid-phase metabolite diffusion coefficient, kj is the gas–liquid mass transfer coefficient, and Mj* is saturation concentration in the liquid phase calculated from the associated gas-phase concentration using Henry’s law. The net flux vij is calculated as the difference between the synthesis rate obtained from the genome-scale metabolic model and the uptake rate calculated from Michaelis-Menten type kinetic expressions [j-th gas phase component where uG is the gas phase velocity, DjG is the gas-phase diffusion coefficient.The first equation represents a mass balances on the ressions , 18. TheBoundary conditions for these equations are problem specific and can account for the supply/removal of liquid and/or gas phase components at the domain boundaries. Although not discussed here, the general model formulation can be extended to include a moving boundary as would be required for biofilm expansion. In the Appendix, two examples of formulated spatiotemporal metabolic models are presented: 1) a bubble column reactor for bacterial conversion of synthesis gas to ethanol; and (2) a bacterial biofilm associated with chronic wound infections. For the most part, these two models adhere to the general set of equations presented above. However, the species mass balance equation for the biofilm model  with embedded linear programs. The efficient and stable solution of such models is a challenging problem at the forefront of microbial metabolic modeling. Our solution approach is based on spatial discretization such that the PDEs are converted into a large set of ordinary differential equations (ODEs) in time with embedded LPs. The spatial domain is discretized with Our approach for solving such large discretized models involves the use of DFBAlab , a MATLADFBAlab is a modified MATLAB implementation of our previously developed simulator . DFBAlabMinimize infeasibilities: If the first objective is equal to zero, the LP is feasible and all other objectives are consistent with the solution of the original FBA LP; otherwise, the objective is positive. If the original FBA LP is infeasible, the reformulated Phase I lexicographic LP still returns values for growth rate and exchange fluxes allowing the integration process to continue. This objective can be integrated to obtain a penalty function. This penalty function can provide useful insights on why and under what conditions the FBA model becomes infeasible.Maximize growth rate: this is the traditional FBA objective.n fluxes appearing in the right hand side of the ODEs, the vector-valued objective will require at most n + 2 elements to obtain a unique right-hand side.Maximize/minimize all of the exchange fluxes appearing in the right-hand side of the ODEs. Each one of these objectives involves a linear combination of fluxes that can be minimized or maximized as appropriate. If there are More specifically, DFBAlab reformulates the FBA LP as a Phase I lexicographic LP to obtain all information required by the right-hand side of the ODEs as a unique vector-valued solution with the following order of objectives:i-th species in a bubble column reactor:DFBAlab is designed to solve ODE systems; however, it provides a flexible framework that enables the solution of PDE models if the equations can be transformed into ODEs. Consider the following equation that describes the biomass concentration of the j in the spatial domain and each species i:This PDE can be easily converted into an ODE by discretizing the spatial domain. If a simple backward difference formula is used to approximate the convection term, then the following set of ODEs is obtained for each point L is the length of the spatial domain, ΔL = L/n and n is the number of discretization points. In addition, Xi,0 = Xfeed = 0 and the outlet biomass concentration of the bubble column reactor is Xi,n. A more detailed explanation for the single species case can be found in Fig. i and the secretion exchange fluxes vij were set equal to zero whenever DFBAlab detected that the LP for the i-th species was infeasible. This situation occurred when local nutrient uptake rates were insufficient to meet the non-growth ATP maintenance requirements. While this approach had the potential to make the right-hand side of the ODEs discontinuous, we found that DFBAlab had little problem integrating through such points because the growth rates and byproduct secretion rates tended to be very small immediately prior to an infeasibility occurring.where From a biological perspective, the additional objectives involving the exchange fluxes represent lower level cellular strategies than the main objective of growth rate maximization. The choice of these objectives is problem dependent and requires assumptions about the cellular metabolism. We typically assume that the cell regulation machinery is configured to maximize substrate uptake fluxes and minimize byproduct secretion fluxes, which is consistent with the main objective by maximizing the input of carbon containing and electron accepting metabolites and minimizing the output of carbon wasting byproducts. While DFBAlab requires specification of these lower level objectives, they impact the lexicographic optimization only when alternative optima occur. Our experiences with the two examples discussed in the following sections and other problems solved with DFBAlab is that the ordering of these objectives has a negligible impact on spatiotemporal model solutions because alternative optima typically occur only for short periods of simulation time. In other words, DFBAlab allows the integrator to reliably transition across short periods where alternative optima exist.https://yoric.mit.edu/dfbalab. Any entity desiring permission to incorporate this software or a work based on the software into commercial products or otherwise use it for commercial purposes should contact Dr. Paul Barton (pib@mit.edu). Simulation codes for the synthesis gas bubble column reactor and bacterial biofilm models can be obtained from www.ecs.umass.edu/che/henson_group/downloads.html.All simulations were performed with MATLAB 8.5 (R2015a) using DFAlab for dynamic flux balance model solution and Gurobi 6.0 for linear program solution. DFBAlab is freely available for both education and non-profit research purposes from 2/CO/CO2) by specialized CO fermenting microbes. Because syngas can be produced relatively cheaply from a wide variety of biomass feedstocks [2 concentrations decrease as the gas flows up the column due to cellular consumption, the column can have strong spatial gradients that affect cellular growth and product synthesis. The development of model-based techniques for simulating and optimizing these complex multiphase reactors is important to advance syngas fermentation technology.An emerging route for the large-scale production of renewable fuels and chemicals is direct fermentation of waste gas streams and synthesis gas  and 600 LPs (6 per point). Despite the substantial computational complexity of this discretized model, we found that a typical 1000 h dynamic simulation for determining a steady-state solution required only about 8 min running DFBAlab and MATLAB version 7.11 on a Dell XPS laptop with Intel Core i7-2760QM processor and 8 GB RAM. Time and spatially resolved predictions obtained for reactor startup with a simulation time of 250 h are shown in Fig. 2 concentrations decreased along the length of the reactor due to gas consumption, while the biomass, acetate and ethanol concentrations increased along the reactor due to liquid flow. The synthesis of CO2 was negligible under these nominal operating conditions. Because the feed gas was relatively rich in CO, the H2 conversion was 62 % while the CO conversion was only 29 %. As a result of H2 being depleted in the first half of the reactor, considerable acetate was produced in the second half of the reactor and the liquid product stream exiting the top of the column contained more acetate than ethanol (ethanol fraction ~40 %). While we are not aware of any published experimental studies that describe the startup dynamics of syngas bubble columns, our model could be a powerful tool for predicting and optimization reactor startup.Our first goal was to investigate the efficiency of DFBAlab for simulating startup of the bubble column reactor with N = 100 node points were sufficient to obtain nearly converged solutions, we performed dynamic simulations for reactor startup with different N values and compared the resulting steady-state solutions obtained at t = 1000 h  and computational time (~8 min per simulation). All remaining simulations were performed with N = 100.To demonstrate that 0 h Fig. . While c2 mixture to a 50/50 CO/H2 mixture. The column exhibited similar dynamics for this H2 rich feed, as the biomass concentration still required approximately 200 h to reach steady state  conversions compared to the nominal case. Our predictions were in qualitative agreement with published experimental studies [Next we performed a dynamic simulation with the CO gas–liquid mass transfer coefficient changed from the nominal value  packing . Consist studies , 29, 30 Pseudomonas growing as biofilms on a complex mixture of wound exudate [Chronic, non-healing wounds are a growing medical challenge associated with diabetes and obesity . These w exudate , 33. Bac exudate . Carbon  exudate , 36. TheP. aeruginosa [P. aeruginosa, we constrained the D-alanine secretion flux to zero such that the only byproducts were acetate and succinate. While other byproducts could be secreted in different biofilm microenvironments, we did not attempt to determine or model other byproducts due to our focus on cellular growth. The spatiotemporal metabolic model was comprised of 5 PDEs for the liquid-phase concentrations of P. aeruginosa biomass, glucose, oxygen, acetate and succinate  and 250 LPs (5 per point). A 1000 h dynamic simulation for determining a steady-state solution required about 15 min on our Dell XPS laptop. This computation time was substantially greater than the 8 min required to simulate the bubble column reactor model over the same time period despite the larger size of the discretized column model . While we hypothesize that the increased computation times obtained with the biofilm model were attributable to the diffusion dominated behavior, these results demonstrate the need to better understand the computational complexity of these large-scale ODE/LP systems.We performed a dynamic simulation for a biofilm thickness of 50 μm with Figure To explore the impact of biofilm thickness on physiology and to further evaluate our modeling framework, we performed a dynamic simulation for a 100 μm thick biofilm Fig. . This th2 was from air at the top of the biofilm, blood plasma has low O2 levels [z = 0 for the O2 mass balance , the main differences from the nominal case were that more biomass was produced near the interface and lower succinate levels were generated throughout the biofilm. When succinate consumption also was introduced (“Succinate Consume”), then biomass was preferentially accumulated at the top of the biofilm due to succinate oxidation, resulting in a less dense region located in the middle. This prediction was consistent with the known physiology of nutrient limited biofilms [Finally we performed a dynamic simulation to investigate the effects of putative succinate reassimilation on biofilm physiology. The thickness was specified as 100 μm and Obiofilms . SuccinaMany natural and engineered microbial systems exist in non-homogeneous environments that require metabolic models that account for both temporal and spatial variations. Our spatiotemporal metabolic modeling framework involves combining genome-scale metabolic reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in the extracellular environment. The PDE model is spatially discretized and the resulting system of ODEs with embedded LPs is integrated using DFBAlab , a MATLAThe datasets supporting the results of this article are included within the article and its additional file.


Genome-scale metabolic models (GEMs) are increasingly applied to investigate the physiology not only of simple prokaryotes, but also eukaryotes, such as plants, characterized with compartmentalized cells of multiple types. While genome-scale models aim at including the entirety of known metabolic reactions, mounting evidence has indicated that only a subset of these reactions is active in a given context, including: developmental stage, cell type, or environment. As a result, several methods have been proposed to reconstruct context-specific models from existing genome-scale models by integrating various types of high-throughput data. Here we present a mathematical framework that puts all existing methods under one umbrella and provides the means to better understand their functioning, highlight similarities and differences, and to help users in selecting a most suitable method for an application. Arabidopsis thaliana  have become a useful tool to investigate metabolism. They present numerous applications, from basic research on metabolic functioning and cell physiology  improve flux predictions through further constraining of the solution space  as well as modern developments . However, gene expression is also at the top of the hierarchical chain of events that govern metabolic fluxes, which may explain the relatively low correlation values between these two quantities, as reported in previous works . More specifically, the inconsistency score is given by the dot product of the flux distribution and the reaction penalty, defined as the vector difference of the associated expression values from the threshold. The reaction associated expression level is obtained following the standard GPR rules , which is more computationally challenging than the LP formulation of GIMME.GIMWhen a given RMF operates in different contexts, the operability constraint may lead to more accurate context-specific model reconstructions and flux distributions. This issue has been evaluated in a recent review : First, it forces each reaction to be active and evaluates the similarity, and then repeats the process in a similar way by forcing each reaction to be inactive. The final outcome is computed by comparing the two obtained similarities. A reaction is termed active if its inclusion results in higher similarity to data, and it is termed as inactive, if its inclusion decreases this similarity. In the case that both similarities are equal, iMAT categorizes the reaction as undetermined.INIT was optimized to integrate evidences from the Human Protein Atlas, although expression data are integrated when proteomic evidences are missing. In this case, INIT does not group reactions in categories in contrast to iMAT. Instead, it adopts experimental data to weight the binary variable of the corresponding reaction, whereby the weight is a function of experimental data  or a set of arbitrary numbers that quantify the color code of the entries of the Human Protein Atlas. In addition, INIT imposes a positive net production of metabolites for which there is experimental support for that context or tissue. Hence, when a metabolite is experimentally determined to be present, its net production is forced to comply with a given lower bound. As a result, INIT allows the integration of metabolomics data in a qualitative way. This method has been applied to generate a human metabolic reaction database  of being active in a certain context. Once these sets are defined, the MBA-like methods prune the GEM by eliminating non-core reactions that are unnecessary to ensure consistency in the core set, i.e., no blocked reaction is allowed in the final model. Thereby, all reactions must carry non-zero flux in at least one feasible solution. As a result, checking model consistency is a crucial part of these methods and also the main difference in comparison to the other methods. FVA have been used to pinpoint blocked reactions, but it is computationally expensive since it requires solving two optimization problems per reaction , if evidence comes from well-curated biochemical knowledge in that particular context, and a set with moderate likelihood (MC) if evidence comes from context-specific high-throughput data. The algorithm performs the pruning iteratively and randomly by selecting a non-core (CN) reaction to be eliminated, and checking consistency at each step: if HC and a user-defined fraction of MC remain unblocked, MBA removes the reaction out of the model along with MC and CN corresponding blocked reactions. This routine is repeated until no reaction is left in CN. The topology of the final model clearly depends on the order in which non-core reactions are eliminated. Therefore, to remove artifacts due to the order, the algorithm is repeated a number of times  and repeats the LP over the remaining set of reactions. If no reaction is found to be active, FVA is applied to each reaction to determine whether it is blocked. The process is repeated until all reactions have been classified either as blocked or unblocked.MBA divides the core set in two subcores: a set with high likelihood to be present in the context-specific model  production of key metabolites is not impaired and (2) the relation between the number of blocked core and non-core reactions matches a predefined ratio. To check model consistency, mCADRE maintains the procedure proposed in MBA, although adapted to use FastFVA , as missing information on one data set can be complemented by another. Moreover, imposing the whole core set inclusion can be highly advantageous, as reactions with overwhelming evidence would always be included in the context-specific model. Moreover, like the iMAT-like family, MBA-like methods are independent of a RMF and, hence, appropriate to be employed if no RMF is known to operate in a given context. Nevertheless, we would like to emphasize that MBA-like methods provide only a context-specific model reconstruction, in contrast to the iMAT-like methods which generate both a context-specific reconstruction and a flux distribution.MBA-like methods follow two ways to define the core set of reactions: MBA takes into account well-curated biochemical knowledge and a variety of experimental data . While this approach to define the core set of reactions may be more accurate, it is also time-consuming due its manual nature. On the other hand, the definition of the core set in mCADRE allows for full automation, since it relies only on determining a threshold to expression-based evidence.L1-norm to prune non-core reactions renders the pruning step more efficient due to the possibility to remove a once more than one reaction. These modifications make FastCORE the fastest algorithm in this family of methods, as it is able to extract a context-specific model in a computational time two to three orders of magnitude smaller than that expended by mCADRE and MBA . The good time-related performance of FastCORE is due to two main innovations: First, the maximization of the cardinality represents a softer objective than the maximization of the total sum of flux values (used in MBA), since fluxes are only required to be above a small positive value. Consequently, solving this optimization problem usually results in more active reactions per iteration than the MBA counterpart. Second, the computation of the Here we presented a classification of the existing approaches for extracting context-specific metabolic models. We classified the methods into three families according to their mathematical formulation. Furthermore, we also proposed a mathematical generalization for each family, which summarizes the fundamental principles shared by its members.Altogether, the classification and generalization constitutes a mathematical framework that aims to fulfill three main purposes: First, it provides a better understanding of the rationale behind methods, allowing an easy inspection of its main characteristics as well as highlighting the advantages and shortcomings. Second, such structured knowledge may facilitate the envisioning of novel approaches to extract context-specific models. Third, it may help users in choosing a best suited method for their particular problem, since the classification outlines the differences in the data and knowledge requirements as input to the particular methods.3E may depend on the interest to integrate metabolomics data along with transcripts profiles, the computational platform of the current implementations, or the difference in computing time. For instance, the choice is between the COBRA toolbox in Matlab, for GIMME, or its version in Python, for GIM3E (“The OpenCOBRA Project,” 3E.The flow-chart on Figure Without the information about the operability of a particular RMF in a given context, the iMAT-like family may provide the method of choice. To select between iMAT and INIT one could take into account the flexibility on integrating different types of experimental data, since iMAT was developed to integrate transcript profiles, whereas INIT can integrate semi-quantitative proteomic data, transcript profiles and metabolic evidences. In addition, one could consider the possibility of the method to discriminate between multiple optima with same similarity score, together with the computational cost for performing this task.In contrast, if only a context-specific model extraction is required, one may opt for any of the presented method. However, the methods in the MBA-like family have some advantageous properties, namely, the integration of a variety of experimental data sources and the inclusion of reactions for which there is strong experimental evidence in the context-specific reconstruction. One may then choose based on the core set definition of each method as well as on the total computational time required. The MBA-like family proposes two ways to define the core: the MBA semi-automated procedure, whereby reactions are included in the core set if there is sufficient positive evidence across different databases, and the mCADRE automated procedure, whereby reactions are included if the expression value of the respective transcript is larger than a given threshold. Thus, if an appropriate number of databases contain experiments about the context of interest and the computation time is not a primary limitation, the MBA core definition may be a suitable alternative. As previously commented, this procedure can cross-validate the confidence on a reaction to belong to a certain context, due to the simultaneous usage of several databases. Subsequently, one can readily employ MBA to extract the context-specific model, or can opt for FastCORE, which can perform the extraction, using the previously defined core, in a more efficient way. On the other hand, mCADRE could be preferentially applied when an automated core definition is preferred. Moreover, the mCADRE relaxation of whole core inclusion can improve accuracy when a core reaction diminishes the overall coherence with respect to the data, through the inclusion of non-core reactions with negative evidences to ensure consistency. Finally, one can also apply FastCORE to a core set defined in an automated way to benefit of its rapid computation. However, neglecting the characteristic core relaxation and ranking of non-core reactions of mCADRE.Development of new approaches for extraction of context-specific metabolic models can further expand on the advantages of the existing methods, while facilitating efficient computation accounting for the shortcomings. This will allow rapid devising of context-specific models and their interconnection in larger multilevel models, typical for complex eukaryotes, to allow for more realistic simulation scenarios.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.