Production of chemicals from engineered organisms in a batch culture involves an inherent trade-off between productivity, yield, and titer. Existing strategies for strain design typically focus on designing mutations that achieve the highest yield possible while maintaining growth viability. While these methods are computationally tractable, an optimum productivity could be achieved by a dynamic strategy in which the intracellular division of resources is permitted to change with time. New methods for the design and implementation of dynamic microbial processes, both computational and experimental, have therefore been explored to maximize productivity. However, solving for the optimal metabolic behavior under the assumption that all fluxes in the cell are free to vary is a challenging numerical task. Previous studies have therefore typically focused on simpler strategies that are more feasible to implement in practice, such as the time-dependent control of a single flux or control variable.Escherichia coli and Actinobacillus succinogenes, and demonstrate that maximum productivities can be more than doubled under dynamic control regimes.This work presents an efficient method for the calculation of a maximum theoretical productivity of a batch culture system using a dynamic optimization framework. The proposed method follows traditional assumptions of dynamic flux balance analysis: first, that internal metabolite fluxes are governed by a pseudo-steady state, and secondly that external metabolite fluxes are dynamically bounded. The optimization is achieved via collocation on finite elements, and accounts explicitly for an arbitrary number of flux changes. The method can be further extended to calculate the complete Pareto surface of productivity as a function of yield. We apply this method to succinate production in two engineered microbial hosts, The maximum theoretical yield is a measure that is well established in the metabolic engineering literature and whose use helps guide strain and pathway selection. We present a robust, efficient method to calculate the maximum theoretical productivity: a metric that will similarly help guide and evaluate the development of dynamic microbial bioconversions. Our results demonstrate that nearly optimal yields and productivities can be achieved with only two discrete flux stages, indicating that near-theoretical productivities might be achievable in practice. Microbial bioconversion plays a critical role in efforts to enable sustainable production of commodity chemicals from renewable feedstocks. The economic feasibility of the integrated biorefinery concept therefore hinges sharply on the productivity, yield, and titers that can be achieved by a given microbial host . Flux baExperimental studies have investigated the use of multi-stage fermentations to increase productivity and/or yield. These techniques range from simple manipulations, such as changing from aerobic to anaerobic conditions , 11, to The calculation of maximum theoretical yield is well established in the metabolic engineering literature, and its use helps guide strain design and pathway selection for static knockout and/or overexpression efforts. Maximum yields are useful even though they are not physically realizable: they reveal the cofactor balancing and pathway split ratios necessary to achieve optimum carbon conservation. In an analogous fashion, an estimate of the maximum theoretical productivity of a batch culture system would prove equally useful for the growing field of designing dynamic metabolic interventions. However, due to the computational burden associated with optimizing over all feasible flux profiles, no generalized framework for such an estimate currently exists.Escherichia coli and native Actinobacillus succinogenes. Succinic acid is a precursor to commodity chemicals in several industries, and a promising intermediate in the development of sustainable chemical production routes [In this article, we present an efficient method for calculating the maximum theoretical productivity of a batch system based on dynamic optimization . Dynamicn routes . We showj produced (or consumed) by reaction i. Fluxes through each reaction are represented by the vector In flux balance analysis (FBA) models, intracellular metabolic reactions are represented by a stoichiometric matrix −1. The resulting dynamic flux balance analysis (DFBA) model takes the form of an ordinary differential equation with an embedded linear program, for which efficient methods for the solution of the initial value problem have been developed [FBA models can be extended to consider the dynamics of substrate consumption and biomass formation by including specific bounds on exchange fluxes and allowing the accumulation or depletion of external metabolites. The dynamic system for cell growth considered in this paper iseveloped . HoweverThe objective considered in this paper is to maximize productivity of the desired metabolite, mentclass2pt{minimTo select the optimal metabolic pathways, we calculate elementary flux modes (EFMs) for both of the considered metabolic networks. An EFM is a vector ument}ri , 25. EFMcument}r . Becausecument}r . We furtWe find the flux profiles that achieve the maximum productivity via orthogonal collocation on finite elements, a method for solving endpoint problems involving a dynamic system without an embedded ordinary differential equation (ODE) integrator . In the mentclass2pt{minimmentclass2pt{minimt of the fermentation is divided into The time domain Solution of the problem involves the constrained optimization over the variables found in Table ess Eqs. , 9, 10. Metabolic models are specified using cobrapy . EFMs foE. coli and A. succinogenes. In a developing a DFBA model, we integrate knowledge of the core-carbon metabolic pathways present in the organism together with experimental data on biomass production and substrate uptake rates. An overview of the computational method is provided in Fig. We demonstrate the usefulness of the method by calculating the maximum theoretical productivities of succinic acid from glucose for two organisms, A. succinogenes was created based on genomic evidence and a previous metabolic reconstruction [A. succinogenes cell growth was constructed from a number of experimental measurements. First, a biomass yield was calculated from measured values of the specific growth rate and glucose uptake rate, E. coli core-carbon model [A. succinogenes have previously been quantified with a Han–Levenspiel model [−1 glucose−1, the experimentally determined parameters were converted to constraints on glucose uptake:A stoichiometric model of core-carbon metabolism in truction . The modectively . As the on model , and scaon model . Energeton model . A nongroworkers  by findiel model . Using tE. coli central metabolism was taken from Orth et al. [E. coli typically assume Michaelis–Menten kinetics, in which high concentrations of glucose ultimately saturate the import mechanisms at their maximum value [A. succinogenes. Additional bounds on ATP maintenance and oxygen uptake were adapted from those determined by Feist and coworkers [A core-carbon model for h et al. , which cum value –39. Howeoworkers :\documenA. succinogenes, 4763 EFMs were calculated for growth on glucose and normalized by the glucose uptake rate. After reducing EFMs to the considered boundary species, duplicate EFMs were removed. The boundary species considered for A. succinogenes included biomass, ATP, glucose, succinate, formate, acetate, and pyruvate. Since any feasible flux state can be expressed as a nonnegative combination of elementary flux modes, the flux space in the reduced dimensionality can be spanned without loss of generality by only those EFMs at the vertices of a convex hull. Furthermore, as optimal succinate productivity will be achieved using flux modes on the Pareto front of cell growth, ATP production, and succinate secretion, the reduced set of EFMs were further reduced to a final set of 22 Pareto-optimal modes. As EFMs are normalized by glucose consumption, glucose need not be explicitly included in the Pareto surface. For E. coli, the additional aerobic growth modes led to a total of 100,273 EFMs. The boundary species for E. coli were the same as those used for A. succinogenes, with the addition of oxygen and the omission of pyruvate, which was not found to be present in any optimal growth mode. In addition to biomass, ATP, and succinate production, the convex hull of optimal modes in E. coli must also consider oxygen consumption. After reduction, 137 modes were kept for E. coli.Elementary flux modes were calculated to reduce the dimensionality of the optimization and to alleviate the necessity of enforcing stoichiometric equilibrium constraints during the dynamic optimization. For A. succinogenes, the chosen elementary modes can span the entirety of the yield space for the considered boundary species. In E. coli, modes that consume high amounts of oxygen while yielding low amounts of ATP are omitted by the algorithm, as they are unlikely to be utilized in the optimal productivity solution.The selected EFMs for each organism are shown in Fig. A. succinogenes is shown in Fig. Optimum productivities are found via a dynamic optimization framework. To further reduce the dimensionality of the optimization, and to allow the effects of discrete fermentation stages to be explicitly simulated, we divide the fermentation time into a number of discrete stages. Within each stage, fluxes are represented by a total flux profile through all elementary modes along with a fractional breakdown of flux through each elementary mode. An example optimum solution for maximum productivity from a 3-stage fermentation in A. succinogenes and E. coli. The right-hand side of Fig. E. coli). These constraints are normalized to specific uptake or production rates, and therefore ATP and oxygen uptake constraints remain constant over the fermentation, while the glucose uptake varies based on external concentrations. In all cases, the solutions closely track the maximum allowable glucose uptake rate. In A. succinogenes, the transition from one to two stages allows the cell to divide its succinate production strategy into separate growth and product formation stages. The addition of subsequent stages permits slightly higher productivities by the gradual transition from growth to product formation. Additionally, as the flux ratios are fixed within each fermentation stage, the fraction of input carbon diverted to ATP production is also fixed. Thus, as lower extracellular glucose concentrations result in lower glucose uptake rates, the cell must dynamically allocate a higher percentage of energy towards meeting its ATP maintenance requirement. Higher numbers of stages therefore allow the cell to more efficiently meet the maintenance constraint, as demonstrated by lower excess ATP produced with additional stages.In addition to reducing the dimensionality of the problem, splitting the fermentation time into discrete stages with independent EFM expression allows a systematic investigation into the effect of stage count on maximum theoretical productivity. Relative flux ratios within each stage are fixed, and therefore represent consistent enzyme expression. Optimal productivities achieved for a varying number of fermentation stages are shown in Fig. E. coli, maximum succinate production using a single stage is achieved microaerobically. With the addition of a second stage, the optimal fermentation time drops appreciably as succinate production is divided into an aerobic growth phase followed by a microaerobic production phase. The addition of further stages beyond two has little effect on either the succinate productivity or the concentration profiles, serving mainly to keep ATP production closer to the constrained minimum.In While separate estimates of maximum theoretical yield and productivity can provide information on the economic feasibility of a bioprocess, in optimized settings one often cannot be increased without decreasing the other. We therefore show how the given method can be easily extended to calculate a full productivity–yield Pareto surface: the envelope in the multi-objective optimization on which productivity cannot be increased without sacrificing yield. The surface is found by first calculating the maximum productivity . The method can also easily be generalized for conversion of multiple substrates as long as appropriate experimental data exist to fit detailed models to substrate uptake kinetics. It could also be extended to explicitly optimize final titer instead or in addition to yield and productivity. Overall, this work emphasizes the need for better empirical models of substrate and product exchange rates and growth kinetics in designing dynamic metabolic interventions.


Mir122a (Mir122a–/–) to infer Warburg-like effects. Elevated expression of MiR-122a target genes in Mir122a–/–mice, especially those encoding for metabolic enzymes, was applied to analyze the flux distributions of the genome-scale metabolic model in normal and deficient states. By definition of the similarity ratio, we compared the flux fold change of the genome-scale metabolic model computational results and metabolomic profiling data measured through a liquid-chromatography with mass spectrometer, respectively, for hepatocytes of 2-month-old mice in normal and deficient states. The Ddc gene demonstrated the highest similarity ratio of 95% to the biological hypothesis of the Warburg effect, and similarity of 75% to the experimental observation. We also used 2, 6, and 11 months of mir-122 knockout mice liver cell to examined the expression pattern of DDC in the knockout mice livers to show upregulated profiles of DDC from the data. Furthermore, through a bioinformatics (LINCS program) prediction, BTK inhibitors and withaferin A could downregulate DDC expression, suggesting that such drugs could potentially alter the early events of metabolomics of liver cancer cells.The liver is a vital organ involving in various major metabolic functions in human body. MicroRNA-122 (miR-122) plays an important role in the regulation of liver metabolism, but its intrinsic physiological functions require further clarification. This study integrated the genome-scale metabolic model of hepatocytes and mouse experimental data with germline deletion of  Mir122a (Mir122a–/–) to infer Warburg-like effects. In silico and in vivo observations indicated that DDC overexpression induced Warburg effect in hepatocyte. Furthermore, through a bioinformatics prediction, BTK inhibitors and withaferin A could downregulate DDC expression, suggesting that such drugs could potentially alter the early events of metabolomics of liver cancer cells.For almost a century, researchers have known that cancer cells have an abnormal metabolism and utilize glucose differently than normal cells do. Aerobic glycolysis or the Warburg effect in cancer cells involves elevated glucose uptake with lactic acid production in the presence of oxygen. MicroRNAs have recently been discovered to be key metabolic regulators that mediate the fine tuning of genes that are involved directly or indirectly in cancer metabolism. MicroRNA-122 (miR-122) plays an important role in the regulation of liver metabolism, but its intrinsic physiological functions require further clarification. This study integrated the genome-scale metabolic modeling (GSMM) of hepatocytes and mouse experimental data with germline deletion of  Cancer cell metabolism is an exciting field of biology that provides a novel approach for treating cancer –8. For aKyoto Encyclopedia of Genes and Genomes (KEGG) [A superior understanding of the genome-scale human metabolic network may lead to the identification of disease genes and related pathways, which may be more appropriate targets for drug development. The development of genome-scale human metabolic networks, such as Recon 1 and 2 , 10, thes (KEGG) . This res (KEGG)  and the s (KEGG) , have bes (KEGG) , 20. TheMir122a–/–) (hereafter referred to as Mir122a–/–mice) are viable but developed temporally controlled steatohepatitis, fibrosis, and HCC [Mir122a–/–mice. Several new targets and inhibitors, which could modulate the Warburg effect, are emerged from this integrated metabolomic analysis and warrant further investigation in a future clinical study.MicroRNAs have recently been discovered to be key metabolic regulators that mediate the fine tuning of genes that are involved directly or indirectly in cancer metabolism . Mouse s and HCC . HoweverMir122a–/–mice were extracted using the Folch method, and the aqueous phases were analyzed by LC-TOFMS in the electrospray positive-ion mode  decarboxylase (DDC), exhibited the highest similarity ratio to the Warburg effect hypothesis  scores > 1  in the lAs stated in the hypothesis of the Warburg effect, the production rates of metabolites in glycolysis, the tricarboxylic acid (TCA) cycle, and glutamine metabolism pathways can be altered by overexpression of a gene –8. In thDdc was overexpressed. The computational prediction was consistent with the experimental result as observed from Tsai et al. [In contrast, glutamine transported from the extracellular matrix was increased by 4.54-FC. Higher levels of glutamine were converted to glutamate (1.39-FC) by glutaminase. This reaction occurs in tumor cells  and was i et al. .DDC and liver cancer. We used the database  [DDC in the liver cancer dataset and then performed the survival analysis. From the dataset of GSE10141 [DDC is associated with a poorer prognosis for patients with liver cancer , which contains 1.3 million L1000 microarray dataset of perturbational profiles spanning chemical compounds and gene knockdowns across multiple cell types. More importantly, LINCS provides a query interface to make inferences on the connections between the queries (e.g. DDC shRNA) and the internal  gene expression profiles. We found that the gene expression profiles of several compounds had similar gene expression profiles with DDC shRNA. Of particular interest, withaferin-A and BTK inhibitor (LFM-A13), which share 91% and 92% identity, respectively, with the DDC knockdown gene expression profile  in Huh7 cells to test whether these compounds could modulate DDC expression level. The IC50 values of both drugs were >10 μM in Huh7 cells   to searcGSE10141 , 44, higr cancer . A ratioin drugs , which m profile . LFM-A13 profile . In addih7 cells , whereasas >2 μM . Treatmeas >2 μM .Mir122a knockout mice for the modeling of metabolic reprogramming, addressed the disturbances in glucose utilization and accompanying pyruvate, lactate, and alanine metabolism at the pre-cancer stage  and the starBase v2.0 (http://starbase.sysu.edu.cn/). Second, miRNA expression profiling of wild-type and Mir122a–/–mouse livers (both 2-months old) was performed using Small RNA sequencing [Mir122a–/–and WT: 0.6≦KO/WT≧1.5) were found only in 40/189 pairs (Mir122a–/–are expressed at low (RPM<10) to moderate (RPM 10–100) levels compared to high level of miR-122-5p in normal mouse liver (RPM 21378.2). Since miR-122 is a highly abundant liver-specific miRNAs, an imbalance of the miRNA homeostasis in Mir122a–/–liver is anticipated. In addition, multiplicity of miRNAs targeting one gene is well noted. Whether those low-to-moderate levels of miRNAs impacted on the gene expression is difficult to evaluate. Clearly our results favor the notion that miR-122 plays a major dominant role in regulating these target genes in normal liver.We selected the 20 genes listed in quencing . We were89 pairs . Most ofDdc, PKM, and Urod exhibited the top three similarity ratios in PKM encodes to pyruvate kinase which catalyzes the transfer of a phosphoryl group from phosphoenolpyruvate to ADP, generating ATP and pyruvate. This kinase exhibited the second high similarity ratio (0.857) to Warburg hypothesis  of the LC/MS experiment but exhibited the third highest ratio (0.810) of the Warburg effect. Furthermore, the computational prediction indicated that the secretion flux for cholesterol in the extracellular space to the extracellular matrix was also reduced due to overexpression of UROD and PKM, respectively.ALDOA if it was greater than 54% overexpressed to upregulate the corresponding reactions catalyzed by fructose bisphosphate aldolase. Its similarity ratio was 0.714 and 0.528 for the Warburg hypothesis and the experimental observation, respectively, with 54% overexpression. Pfkp encoded phosphofructokinase which catalyzes a rate-limiting step in glycolysis. It is highly regulated by small molecules for the promotion of glucose utilization for energy production, termination of glycolysis for gluconeogenesis initiation, or shunting hexoses into the pentose phosphate pathway. Phosphofructokinase should be downregulated due to the deficiency of miR-122a; otherwise, we could not obtain a feasible solution if it were assigned as upregulated. Its similarity ratio was 0.810 and 0.583 for the Warburg effect and the experimental observation, respectively, when Pfkp was 100% downregulated. Cpt1a could not up- or downregulate forward or backward reactions because it encodes as carnitine palmitoyltransferase 1A, which is present in the liver, to manipulate 85 fat acid oxidation reactions in the model. The Cpt1A enzyme is essential for fatty acid oxidation, a multistep process that breaks down fats and converts them into energy. Fatty acid oxidation takes place within mitochondria, which are the energy-producing centers in cells. Cpt1a needs to maintain oxidation-reduction at an equilibrium state if the forward reactions are upregulated, and its corresponding backward reactions should be upregulated simultaneously to maintain an equilibrium level. Here, Cpt1a was knocked out with fluxes of zero. Consequently, its similarity ratio was 0.714 and 0.583 for the Warburg effect and the experimental observation, respectively. Pank3 encodes a protein belonging to the pantothenate kinase family, which is highly expressed in liver and catalyzes the first committed step and is the rate-controlling enzyme in CoA biosynthesis in bacteria and mammals. Pantothenate is the essential precursor for CoA, which is a cofactor for a multitude of metabolic reactions including the oxidation of fatty acids, carbohydrates, pyruvate, lactate, ketone bodies, and amino acids. According to our computation, the regulatory action of Pank3 is similar to that of Cpt1a, which regulates the forward and backward reactions simultaneously to maintain CoA synthesis and catabolism in equilibrium.Four target genes in 13C-pyruvate in Myc-driven mouse liver cancer model. Furthermore, Pavlova and Thompson [In this study, 21 metabolites, consisted of TCA cycle and glutamine metabolism pathways, were used to evaluate the Warburg effects . EighteeThompson  describeThompson . In suchThompson . We founDDC knockdown profiles. Since LINCS has been terminated recently, similar result can be found in the new version of LINCS, CLUE (https://clue.io/). This analysis provides an opportunity to employ these available drugs (or drug repurposing) to target DDC expression. In fact, empirical evidence also suggests that withaferin A and BTK inhibitors can downregulate DDC, but not PKM2, expressions (http://consensuspathdb.org/) [Using the online bioinformatics tool, LINCS, the gene expression profiles of withaferin A and BTK inhibitor share-gene expression profiles similar to the ressions . BTK inhdb.org/)  databasevdirect_bilirubin≤ 5.13 mol/L/day and 5.13 ≤ vindirect_bilirubin≤ 27.36 mol/L/day, respectively. We applied 560 gene-encoded enzymes listed in the model to compute the flux distributions in the normal and cancer states. From the computation, 13 gene-encoded enzymes exhibited high similarity ratios to the Warburg effect  to the Warburg effect and the experimental metabolomics profiling data (0.513) in human HCC case  which contains 69 chemical compounds in the ingredients. Twenty compounds, as listed in Mir122a–/–mice.The wild type and This study employed a liver-specific metabolic network model reconstructed from Recon 2, which is the second version of the largest reconstruction of the human genome . It cons2 following the institutional guidelines. All the studies were conducted in accordance with the Guidelines for the Care and Use of Mammals in Neuroscience and Behavioral Research and were approved by Institutional Animal Care and Use Committee (IACUC) of National Yang Ming University.The animal were euthanized by COin silico flux-based optimization model for predicting the metabolic flux distributions in genome-scale metabolic networks. Such an optimization problem usually includes a cellular objective, . The biomass reaction actually contains in Recon 2-hepatocyte model, but it is a block reaction in the model. We therefore considered FBA with the maximization of ATP production as an objective in this study.vf and vb are the irreversible forward and backward fluxes, respectively, for the production of a metabolite such as ATP, N is an m×n stoichiometric matrix where m is the number of metabolites and n is the number of reactions, vjLB and vjUB are the positive lower and upper bounds of the jth flux, respectively, and viReg is the ith up- or downregulated flux due to the ith enzyme dysregulation. The value for the forward or backward flux is computed by the following equations:vibasal is the basal flux, vimax and vimin are the maximum and minimum fluxes, respectively, at a normal state, and δ is the regulation strength parameter between 0 and 1.FBA is an The optimal flux distribution of the flux-balance problem expressed by Eq  is not ued in Eq . The pro+cbTvb≥z*where z*Flux balance equations in (1) and (4) omit the dilution term during cell growth. The dilution rate should be included in the mass balance equations of the intracellular metabolites to cope with cell growth , 57. Therm) of each intracellular compound at deficient and normal states is respectively evaluated asNij is the stoichiometric coefficient for the ith metabolite participating in the jth reaction. An intracellular compound (or metabolite) exists in different compartments of the metabolic network; therefore, the rates for all compartments, Ωc, are summed to provide the production rate of the metabolite. The production rate is then applied to compute the fold change (FC) at deficient and normal states and to evaluate the similarity ratio between the computational results and experimental observations. The logarithmic FC (LFCm) for the mth metabolite and similarity ratio (SR) are respectively expressed asm) for each metabolite is defined as:In the computational viewpoint, the production rate of a metabolite is involved in different compartments, and it can be calculated through a GSMM. However, this work applied an LC/MS experiment to obtain the metabolomic profiling for the normal and dysregulated cell. According to the protocol of LC/MS experiment, the liver tissues were minced in small chunks and were rapidly frozen in liquid nitrogen, and then the tissue was homogenized to prepare a sample to determine the metabolomic profiling. Such a homogenization was indicated that metabolites contained in different compartments was destroyed. As a result, LC/MC was applied to measure the homogenized metabolite concentrations. In order to compare with LC/MS experiments, the metabolite involved in different compartments has to sum up to yield the overall production rate of the metabolite which is an intracellular compound of the cell. The overall production rate  were transferred to new glass tubes and then dried under a stream of nitrogen. The residues were collected and stored at −80°C. The residues were suspended in 100 μL of 95:5 water/acetonitrile and centrifuged at 14,000 × g for 5 min. The clear supernatant was collected for liquid chromatography–mass spectrometry (LC/MS) analysis.A modified Folch’s method was used for hydrophilic and hydrophobic metabolite extraction . ApproxiLiquid chromatographic separation was achieved on a 100-mm×2.1 = mm Acquity 1.7-μm C8 column  using the ACQUITY UPLC system . The column was maintained at 45°C and a flow rate of 0.5 mL/min. Analytes were eluted from LC column using with a linear gradient: 0–1.25 min: 1%-50% B; 1.25–2.5 min: 50%-99% B; 2.5–5.0 min: 99% B; 5.1–6 min: 1% B for re-equilibration. The mobile phase was 0.1% formic acid in water (solvent A) and acetonitrile (solvent B).+ ion at 311.0814 Da in ESI positive mode) were used. The lock spray frequency was set at 10 s.The eluent was introduced into the Synapt G1 high-definition mass spectrometer  operated in the positive ion mode. It is a time of flight mass spectrometer (TOFMS) and this system is less than 5 ppm mass error in specification. The specification was checked in every study to make sure the mass accuracy. The following conditions were used: the desolvation gas was set to 700 l/h at a temperature of 300°C, the cone gas was set to 25 l/h, and the source temperature set at 80°C. The capillary voltage and cone voltage were set to 3,000 V and 35 V, respectively. The MCP detector voltage was set to 1,650 V. The data acquisition rate was set at 0.1 s with a 0.02 s interscan delay. The data were collected in centroid mode from 20 to 990 m/z. For the long-term study, all analyses of the LCTOFMS were acquired using the lock spray to ensure accuracy and reproducibility. For accurate mass acquisition, a lock-mass of sulfadimethoxine at a concentration of 60 ng/mL and a flow rate of 6 μL/min  in LC-MS performance was also prepared. As to the QC sample, 10 μl aliquot of supernatant that had been extracted of each sample was mixed and the LC-MS experiment was performed together with the samples and replicates from the same LC-MS condition. The QC sample was applied before and after injection of every 20 samples. Each sample was analyzed six replicates. We checked six replicates in the QC and each sample. Each sample including QC was shown highly reproducibility in principal component analysis (PCA) and orthogonal partial least square analysis (OPLS-DA) plots .Raw mass spectrometric data were processed using MassLynx V4.1 and MarkerLynx software . The intensity of each mass ion was normalized with respect to the total ion count to generate a data matrix including the retention time, m/z value, and the normalized peak area. The multivariate data matrix was analyzed by SIMCA-P software . Orthogonal projection to latent structure-discriminant analysis (OPLS-DA) was carried out before the Pareto scaling was applied. This software had been used for multivariate data analysis and representation.http://www.hmdb.ca/) or the METLIN (metlin.scripps.edu/index.php) database. For identifying specific metabolites, standards were subject to UPLC-MS/MS analyses under the conditions that were identical to those of the profiling experiment. MS/MS spectra were collected and confirmed by chemical standards or database match from HMDB or METLIN.Precise molecular mass data for metabolites, which showed significant differences between two groups, were then submitted for database searching, either using either an in-house database or online HMDB . The variable importance in the projection (VIP) value of each variable in the model was calculated to indicate its contribution to the classification. A higher VIP value represents a stronger contribution to discrimination between the groups. The VIP values of those variables greater than 1.0 are considered significantly different. Results are expressed as the mean ± SD for continuous variables and as the number (percentage) for categorical variables. Data were compared by two-sample Among those significantly altered features of metabolomics profiling data, 35 were matched to the human metabolites database (HMDB). The mapped species were assigned an HMDB ID for subsequent MSEA analysis implemented in the MetaboAnalyst assessment .2 at 37°C.The Huh7 cell line was obtained from Dr. Zhong-Zhe Lin, National Taiwan University Hospital, Taiwan. Huh7 cells were cultured in DMEM and supplemented with 10% fetal bovine serum , 10 U/ml penicillin, 1% nonessential amino acids and 2 mM L-glutamate in an incubator with 5% CO5 cells) were seeded in 6-cm tissue culture dishes for overnight incubation and were then treated with ibrutinib , LFM-A13 , and withaferin A , respectively, for 24 hours. Mice liver tissues were harvested from C57BL/6 wildtype and mir-122 knockout mice at 2, 6 and 11 months of age. All samples were lysed in lysis buffer  supplemented with protease inhibitor and phosphatase inhibitor. All samples were denatured by heating at 95°C for 5 minutes. The total protein was electrophoresed on 10%, 12% SDS-polyacrylamide gel and transferred onto PVDF membranes (Millipore). The membrane was blocked with 5% non-fat milk at room temperature for 1 hour. The membrane was incubated with the primary antibody at 4°C overnight. They were washed with TBST three times (10 minutes per time). The membrane was incubated with the HRP-conjugated secondary antibody at room temperature for 1 hour. They were washed with TBST three times (10 minutes per time). The proteins were detected using an enhanced ECL.Cells Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(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.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.S6 TableMir122a–/–and WT (0.68≦KO/WT≧1.5).KO/WT, Expression ratio between (XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S1 FileGAMS file used for evaluating similarity ratio.(ZIP)Click here for additional data file.


Motivation:Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem.Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana. We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs.Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models. Arabidopsis thaliana  is a popular model organism in plant biology  maps for A. thaliana were introduced in 2008  as mathematical formalism for network construction, analysis, and simulation. PNs are mainly applied in computer science, for example, to model distributed systems. Many sound, rigorous analysis and simulation methods of PNs have been evolved over decades for various applications  are based on a concept of communication of automation originally introduced by Carl Adam Petri Petri,  in his dThe first biological application of PNs was published in 1993 by Reddy et al. , signal P and T, respectively. The elements in P are the places graphically represented as circles, and the elements in T are the transitions graphically represented as rectangles. Places stand for the passive system's elements, for example, chemical compounds, metabolites, proteins, and protein complexes. Instances of them are represented by tokens, which define discrete entities. Since the movement of tokens realizes the dynamics of a PN, we introduce the concept of tokens in Section 2.1.1. Transitions are the active system's elements, for example, chemical reactions, degradation processes, and complex assembly processes. Places and transitions are connected by directed, labeled edges. Edges between vertices of the same type are not allowed. Usually, the edges are labeled or weighted, respectively, by integer numbers. In the following, we call a directed, bipartite graph net or net graph, see Definition 2.1. To define a Petri net, we extend that definition, compare Definition 2.2.Petri nets are directed, bipartite, labeled graphs. They consist of two disjunctive sets of vertices, Definition 2.1. Net or net graph.N =  withA net or net graph is a triple P ∩ T = ∅ andF ⊆ (P × T) ∪ (T × P)).P and T places and transitions, respectively. They are the vertices or nodes of the net. We call the elements of the flow relation, F, edges or arcs.We call the elements of x: = {y |  ∈ F} and the set of all post-vertices x•: = {y |  ∈ F}. Accordingly, we write for a set of pre-places, •t, for a set of post-places, t•, for a set of pre-transitions, •p, and for a set of post-transitions, p•.Regarding a net vertex, we define two sets of neighbor vertices, the set of all pre-vertices •read arcs or test arcs. Using read arcs, we can model, for example, catalytic reactions, where the catalyst is necessary to activate the transition (reaction), but will not be consumed, when the transition takes place. A PN without read arcs is a pure PN.We call edges that are going in two opposite directions as Definition 2.2. Petri net. A Petri net or Place/Transition net or P/T net is a six-tuple Y = , ifP, T, F) is a net,,W : F → ℕ (edge weights or label of the edges), andM0:P → ℕ0  with ∀p ∈ P : M0(p) ≤ K(p).tokens which are located on the places and will be removed according to the firing rule. If N is a P/T net, a mapping of the M : P → ℕ0 with ∀p ∈ P : M(p) ≤ K(p) is called a marking of N. We graphically represent the number of tokens of a place, M(p), under a marking, M, by M(p) dots (tokens) on the place, p. We write the capacities ≠∞ and edge weights ≠1 at the places and edges, respectively. The token distribution over all places define a certain state of the net. N. In the following, let M be a fixed marking of N. The number of the tokens can be restricted by the capacity of the place. In most biological applications, the capacity is set to infinite. Additionally, we introduce logical vertices to get an improved layout. A logical vertex has copies of the same name in the graphical representation of the model. Using logical vertices, we can draw PNs in a clearly-arranged way. For example, in metabolic networks, ATP participates in many reactions. This leads to many crossing edges if we model only one place for ATP. To avoid these crossing edges, we copy the place for ATP and mark it as logic place.The dynamics of a net is performed by movable objects called Place/Transition PN (P/T net). The firing rules do not include time relations. A transition fires, or for biochemical networks, a reaction takes place, if the transition is activated or has concession, i.e., if the pre-places carry at least as many tokens as indicated by the weights of the corresponding edges and if the capacity of the post-places is large enough as indicated by he corresponding edge weights. At the moment of firing, the tokens of the pre-places will be consumed, and the tokens on the post-places will be produced, both according to the corresponding edge weights. A new system's state is achieved. The numbers of tokens and the edge weights implement quantitative properties although the system is still discrete. If always at least one transition of the PN is activated, the PN contains no deadlock and is called to be deadlock-free.In this paper, we consider the classical Definition 2.3. Activated transition. A transition, t ∈ T, is activated or has concession under M, written as p ∈ •t : M(p) ≥ W,∀p ∈ t•:M(p) ≤ K(p) − W.∀t fires from M to M′ and write t is activated under M, and M′ arises from M by removal of tokens from the pre-places and production of tokens on the post-places according to the corresponding edge weights:input transitions. Accordingly, we call transitions without post-places output transitions. Input and output transitions were used to model the interface to the system's environment. Figure We say that weights:M′(p)={M(place invariants (PI) for the passive part and the transition invariants (TI) for the active part. The definitions of both invariant types are based on the incidence matrix, we also know as stoichiometry matrix for metabolic networks. This m × n matrix, C, for m places and n transitions indicates for each place, pi ∈ P, the change in the number of tokens, △m, when a transition, tj ∈ T, fires.Using linear invariants, we can define specific dynamic properties of the network. These properties are valid in every system state. They can be used for model verification, but also for model decomposition and network reduction. For PNs, we define the Definition 2.4. Incidence matrix. Let N be a P/T net. The corresponding incidence matrix C is defined by: ∀ 1 ≤ i ≤ m, 1 ≤ j ≤ nF−1 and the third condition. Contrary, for all cases, the third case, Ci, j = W, if ∈ F, would be sufficient, if we consider W as complete mapping to (P × T) ∪ (T × P) and set the weights of non-existing edges to 0.MonaLisa especially designed for PN applications to biological systems . Let N be a P/T net and C the corresponding incidence matrix. A place invariant of N is an m-tuple x ∈ ℤm with CTx = 0.Definition 2.6. Transition invariant (TI). Let N be a P/T net and C the corresponding incidence matrix. A transition invariant of N is an n-tuple y ∈ ℤn with Cy = 0.integer, because we are working at discrete level, semi-positive because there is no interpretation of negative solutions, and minimal because such equation systems can have an infinite number of solutions. In the following, we consider minimal, semi-positive, integer PIs and TIs, writing shortly PIs and TIs, respectively. For discussion of the computational problem, see Schrijver . An invariant x is called minimal, if its support does not contain the support of any other invariant z, i.e.,x is one. Whereas PIs reflect a token or substance conservation, the TIs describe basic functional modules of the system's dynamics at steady state  or covered by TIs (CTI), respectively. The CTI property indicates the network's completeness or consistency. A transition which is not member of at least one TI does not contribute to the systems behavior. Thus, it could be removed without influencing the overall systems behavior. A TI or PI, respectively, defines a connected subnet, consisting of its support, the support's pre- and post-places or pre- and post-transitions, respectively, and all edges in between.The support of a vector, trivial: a reversible reaction, which is split into a forward and a backward transition.INOUT: contains at least one input transition and one output transition.IN: contains an input transition, but no output transition.OUT: contains an output transition, but no input transition.CYC: contains neither an input nor an output transitions forming a cycle in the model.TIs can be classified according to the type of the participating transitions. The classes of TIs are motivated by the involved input and output transitions. We consider the following types of TIs:The explanations for some of the different types of invariants are intuitive. In a metabolic PN, containing reversible reactions, it is not possible to avoid trivial TIs. TIs of the type INOUT represent pathways through the network, a succession of consecutive biochemical reactions, transforming given educts (metabolites produced by input transitions) to the corresponding products (metabolites consumed by output transitions). TIs of the types IN or OUT contain only input or output transitions, respectively. These TIs emerge from internal production or consumption, respectively, of secondary metabolites. TIs of type CYC contain neither input nor output transitions at all. Their firings form cycles in the PN.Figure Maximal Common Transition sets  by their occurrence in the minimal TIs: ∀i, j ∈ {1, …, m} the transitions, ti and tj, are grouped into the same MCT-set, if and only if they participate in exactly the same minimal TIs, i.e., all TIs x hold:{0} denotes the characteristic function, binary indicating whether an argument is equal to zero. This grouping leads to maximal sets of transitions, whereat each set of transitions ϑ holds:X denotes the set of all minimal TIs, x.To support the biological interpretation of TIs, we group the transitions into T, the set of transitions, which leads to a partition of T. The equivalence classes ϑ correspond to the MCT-sets. MCT-sets define also subnets as TIs, but they have not to be connected. The subnets defined by MCT-sets are disjunctive. They represent a further decomposition method of large biochemical networks into rather small subnets at steady state, which often correspond to functional units. Each of the MCT-sets may represent a building block with a special biological meaning.This grouping represents an equivalence relation in Network verification is a crucial part in the process of model construction. For biological PNs, beside structural and behavioral properties such as the connectivity  as two transitions, ti and tj, connected by a place called a connecting place, pc, see Figure tj as well as the connecting place, pc. The transition, ti, absorbed the properties of the deleted transition, tj, i.e., all its pre-places, •ti, and post-places, ti•, as well as the corresponding connecting edges.Here, we used topological reduction techniques as well as steady-state reduction techniques. We considered topological reduction techniques that preserve the CTI-property  as two transitions, ti and tj, representing the forward and backward reaction, respectively, of a reversible reaction and connecting two places, pi and pj, see Figures ti, tj), as well as the place pj. The place pi absorbed the properties of the deleted place pj, i.e., all its pre-transitions, •pi, and post-transitions, pj•, as well as the corresponding connecting edges and the markings.To reduce reversible reactions, we defined ctp(ti+tj)”. If we identified, for example, the two reactions E151 and E152 connected by metabolite 87 as a potentially reducible CTP, we connected all edges from reaction E152 to reaction E151, removed metabolite 87 and reaction E152, and renamed reaction E151 to ctp(E151 + E152).To indicate a reduction, we changed in each reduction the names of the reactions and the metabolites. If two reactions were merged in a CTP reduction, we provided a new name for the merged transition, e.g., “E24_f and E24_b, which connect the metabolites 76 and 50, by an ITP reduction, we would connect all edges from metabolite 50 to metabolite 76, remove the reactions E24_f and E24_b and the metabolite 50, and rename metabolite 76 to itp(76 + 50).If the reduction was based on an ITP, we renamed the merged metabolites. According to the CTP reduction, we connected the names of the two metabolites in the same way preceeded by an ITP. If we reduce, for example, the reactions itp(76 + 50) could be identified as an ITP with another place in the next step. Each step of the reduction could be followed by the nomenclature and produced a timescale of reductions, compare with the Tables Additionally, we reduced parallel reactions, i.e., if two transitions had the same input place and the same output place, and the same weights on the corresponding edges, we combined both transitions into one without changing the net behavior Murata, . We adopti ∈ T, if the transition pair, , D-fructose (place 63), D-galactose (place 73), coenzyme A , acetyl-CoA (place 92), ammonia (place 29), or citrulline (place 94). In turn, the output reactions create 22 metabolites  is experimentally proven. The complete PN model consists of 134 metabolites and 243 reactions, which are connected via 572 edges. Figure A. thaliana . The biosynthesis of CoA was not modeled, and thus, the precursor of CoA, pantothenate  the sucrose Figure , blue,  by R (for reaction) in the names of such reactions. More precisely, in Figure E46, transforms α-D-glucose 1-phosphate to ADP-glucose, which can be consumed for further production of starch.The metabolism became obvious by inspecting the synthesis and degradation of starch in detail based on Figure Due to the polymer character of the starch molecule, it was difficult to model its synthesis and degradation in detail. There is literature  and glutamine (metabolite 33) (blue), the citric acid cycle (red), and the glyoxylate cycle (green), part of the biosynthesis of uridine 5′-phosphate (violet), and completes the pathway of glycolysis (yellow). Glutamine and glutamate play a central role in the transfer of ammonia (metabolite 29). The citric acid cycle is part of the energy metabolism in aerobic species. The glyoxylate cycle (glyoxylate: metabolite 13) plays a major role in the anabolic synthesis of carbohydrates. The reactions of glycolysis complement the part of the cycle integrated in the sucrose subnet by converting glycerate 3-phosphate (metabolite 40) to pyruvate (metabolite 20) (yellow). The biosynthesis of uridine 5′-phosphate  is only partially present in this subnet and was completed in the UTP subnet (purple).a and 30b) synthesis. The synthesis of lignin is e.g., explicitly included as a part of the biomass function in a genome scale flux balance model of maize (Zea mays)  while syringyl lignin is produced from sinapyl alcohol (metabolite 48)  and CTPs (Common Transition Pairs) using an extended version of a previously published algorithm , glycerate 3-phosphate (metabolite 40), glycerate 1,3-bisphosphate (metabolite 41), glyceraldehyde 3-phosphate (metabolite 42), and dihydroxyacetone phosphate (metabolite 68), which were also part of the Calvin cycle.Figure A. thaliana, the glycolysis and the Calvin cycle shared several enzymes , glyceraldehyde 3-phosphatedehydrogenase , triosephosphate isomerase , seduheptulosebisphosphate aldolase , and fructose bisphosphatase . The sharing of these reactions suggested that the participating compounds were shared as well. In this case, the shared metabolites would be: glycerate 3-phosphate (metabolite 40), glycerate 1,3-bisphosphate (metabolite 41), glyceraldehyde 3-phosphate (metabolite 42), D-fructose 1,6-bisphosphate (metabolite 43), D-fructose 6-phosphate (metabolite 44), and dihydroxyacetone phosphate (metabolite 68) besides D-fructose 1,6-bisphosphate (metabolite 43) and D-fructose 6-phosphate (metabolite 44). The absence of D-fructose 1,6-bisphosphate (metabolite 43) and D-fructose 6-phosphate (metabolite 44) in the reduced place was caused by restrictions in the reduction process. A merging of places by an ITP reduction was only allowed if all involved edges had a weight of 1. This was not the case for the reactions connecting metabolite 43 with 42 and 68 (transition E14). The merging of parts of the citric acid cycle, namely succinate (metabolite 4), fumarate (metabolite 6), malate (metabolite 8), and oxalacetate (metabolite 12), was inspired by the reversible reactions between the compounds, which was the main idea behind an ITP reduction. The combination of this part of the citric acid cycle and the last steps of the glycolysis, producing phosphoenolpyruvate and pyruvate, was induced by the synthesis pathway of oxalacetate from phosphoenolpyruvate  to the corresponding products (metabolites consumed by output transitions). All TIs, containing OUT only, which exist in the sucrose module, could be explained easily.We could show that a mapping of reduced invariants to invariants of the unreduced net will be possible.E129_1 and E129_2) and thereby an implicit IN TI of carbon dioxide. This implicit modeling reduced all OUT TIs to INOUT pathways. Transition E129_1 modeled the carboxylation reaction  of rubisco, and transition E129_2 the oxygenation reaction (photorespiration)  two times. The substrates of this reaction were oxalacetate and glutamate and the products L-aspartate and α-ketoglutarate , ctp(E5 + E4) , and E127 . Please note that a number of reactions in the overall synthesis of 5-phosphoribosyl 1-pyrophosphate was affected by the reduction process, and the precursor of transition E127 combined several compounds. The remaining reactions, E106_f and E109, were required to regenerate two glutamate and two glutamine, thereby using four ammonia. Glutamine is an important part of the nitrogen metabolism of conifers  + ctp(E44 + ctp(E61_119 + E61_80))). In the recursive reduction process, all of the reactions, forming the de novo synthesis of uridine 5–phosphate, fulfilled the conditions necessary for a CTP reduction. As transition E42 was part of the citrate module it could not be part of this MCTS. Nevertheless, the possible CTP reduction of the complete reaction chain, including E42, suggested a strong connection between the reactions of the uridine 5′ phosphate de novo synthesis and could indicate an MCTS in the PN, covering all of them.This MCTS consists of the transitions E103, E104_f, E105, and E113_f. This configuration occurred in the citrate module of the biologically driven decomposition as well as in the reduced network. Compared to the decompositions and the original network, the connections of the transitions have changed during the reduction process. In the subnets, the transitions form the reactions:MCTS 2 consists of the transitions E103 (as metabolite 4), E104_f (as metabolite 20), and E113_f (as metabolite 20) and led to the reduced reaction systemwith 2 = glutamate, 3 = γ-aminobutyric acid (GABA), 4 = succinate, 9 = α-ketoglutarate, 20 = pyruvate, 21 = phosphoenolpyruvate, and 79 = succinate semialdehyde. In the reduced network, the metabolites 4 and 20 were combined by an ITP reduction, forming a new place. The connections of this new place were the combined connections of the merged original places, i.e., the new place connected to X = the merged place (4 + 20). While the pathways for these transitions mentioned in the AraCyc database are glutamate degradation , and alanine degradation (E113f), other literature declare them as the GABA shunt , 9 = α-ketoglutarate, 21 = phosphoenolpyruvate, 79 = succinate semialdehyde, and E40, E133_f, E134, E135, and E136 in the citrate module. The transitions E40, E133_f, E134, and E135 formed the urea cycle , which was further flattened to ctp(ctp(E135 + E40) + E136) by the inclusion of E136. Together with E134 and E133_f, this new reduced transition formed an MCTS in the reduced network. Urea is an important nitrogen source for plants  and mainly believed to be predominantly synthesized by the urea cycle (Reinbothe and Mothes, A. thaliana.This MCTS constitutes of the transitions A. thaliana based on recent literature. Similar to a network of barley (Grafahrend-Belau et al., In this paper, we presented a new semi-quantitative Petri net model of the metabolism of The final size of the complete PN model was 134 metabolites, 243 reactions, and 572 edges. The complexity of this model did not allow to compute all its transition invariants, which form the base for further analysis. To get a manageable set of TIs, we followed two strategies. First, we divided the model into four biology-driven subnetworks, the sucrose, the citrate, the UTP, and the shikimate subnetwork, and defined two modules, each consisting of two subnetworks. The sucrose module covers the sucrose and the UTP subnetwork, while the citrate module compiles the citrate and the shikimate subnetwork. The second strategy followed a graph-theoretic reduction of the model, applying common transition pairs and invariant transition pairs. Through the reduction, the network size decreased by ~50%. For all three subnetworks, we computed the TIs, easily showing that the subnetworks were CTI. To handle the amount of 27,646 TIs for the reduced model, we classified the TIs into trivial, INOUT, IN, OUT, and cyclic TIs. Because we could not discuss all the 27,646 TIs, we considered exemplarily one cyclic TI that describes a part of the starch synthesis and degradation and one TI that expresses a combination of parts of the nitrogen economy, the oxalacetate synthesis, the synthesis of 5-phosphoribosyl 1-pyrophosphate, and the synthesis of pyrimidines.de novo synthesis of uridine-5–monophosphate, the γ-aminobutyric acid shunt, and the urea cycle.We demonstrated that the carbon fixation phase and the regeneration phase of the Calvin cycle strongly depends on each other. Additionally, potential steady-state pathways exist, which provided the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. Moreover, the analysis showed a close cooperation of important metabolic pathways, e.g., the The presented model provides a solid basis for further refinement, for example, by concentrations, gene expression data, and kinetic data for a quantitative analysis.ES and IK initiated and supervised the project. JN has performed the network construction and analysis. All authors wrote the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer GR and handling editor declared their shared affiliation, and the handling editor states that the process nevertheless met the standards of a fair and objective review.


Metabolic diversity in microorganisms can provide the basis for creating novel biochemical products. However, most metabolic engineering projects utilize a handful of established model organisms and thus, a challenge for harnessing the potential of novel microbial functions is the ability to either heterologously express novel genes or directly utilize non-model organisms. Genetic manipulation of non-model microorganisms is still challenging due to organism-specific nuances that hinder universal molecular genetic tools and translatable knowledge of intracellular biochemical pathways and regulatory mechanisms. However, in the past several years, unprecedented progress has been made in synthetic biology, molecular genetics tools development, applications of omics data techniques, and computational tools that can aid in developing non-model hosts in a systematic manner. In this review, we focus on concerns and approaches related to working with non-model microorganisms including developing molecular genetics tools such as shuttle vectors, selectable markers, and expression systems. In addition, we will discuss: (1) current techniques in controlling gene expression , (2) advances in site-specific genome engineering tools [homologous recombination (HR) and clustered regularly interspaced short palindromic repeats (CRISPR)], and (3) advances in genome-scale metabolic models (GSMMs) in guiding design of non-model species. Application of these principles to metabolic engineering strategies for consolidated bioprocessing (CBP) will be discussed along with some brief comments on foreseeable future prospects. Figure 1). First, it is a sustainable green approach that can significantly reduce greenhouse gas emissions. Second, many renewable feedstocks (lignocelluloses) are readily available, inexpensive resources that can lower material costs. Third, CBP is able to eliminate labor and capital cost of biomass processing by employing a single process step. CBP is widely recognized as the ideal configuration for sustainable, low-cost hydrolysis and fermentation of cellulosic biomass  of naturally renewable biomass such as lignocelluloses has been attractive to researchers in recent years . The CBP biomass . In prinClostridium sp. harbors native acetone-butanol-ethanol pathways); (3) They are derived from diverse environmental backgrounds  and possess beneficial attributes . However, development of non-model microorganisms is relatively slow and largely hindered by limited molecular genetic tools and lack of knowledge about their complicated metabolic pathways and regulation.Microorganisms natively possess the ability to metabolize different sugars, but the specific sugars and regulation of sugar catabolism vary. Species that are good CBP candidates typically have several characteristics: (1) They express a cohort of genes that synergistically degrade sugar polymers (most organisms metabolize monomeric sugars); (2) They have biochemical capabilities that connect renewable feedstock input to downstream biochemical production pathways . The lower cost of synthesizing DNA enables the redeployment of standard biological parts  and development of new parts in a plug-and-play fashion .With recent advances in synthetic biology, molecular tool development, applications of omics data techniques, reconstruction of GSMMs, metabolic flux analysis and genome engineering, non-model microorganisms can now be leveraged to help understand, design, and engineer non-model microorganisms in a systematic manner. Synthetic biology has promoted enthusiasm in understanding and developing novel biological components and has provoked a usage of standard parts into different systems  It must contain efficient and robust selectable markers; (3) It needs to have low homology to the host’s chromosome ; (4) It must harbor functional expression elements .Development of an efficient, stable, and robust shuttle vector is an important tool for engineering a non-model microorganism, as it is a decisive step for delivering foreign genes into cells, heterologous expression of foreign genes, and is an approach for delivering donor DNA for genome engineering. An effective shuttle vector should possess the following characteristics: (1) It must be able to replicate in the non-model strain or E. coli). A variety of E. coli replication origins that have different functionalities (copy numbers) have been studied and characterized  It does not pose a requirement of an E. coli replication origin; (2) It reduces the amount of bench work; (3) It develops a potential platform for high-throughput screening of a heterogenic pool of mutants. However, the authors also indicated that the transformation efficiency might largely decrease in the presence of restriction modification (RM) systems.At this point, shuttle vectors containing only one replication origin seem to be superior. E. coli RM systems, Dam (GmATC) and Dcm [CmC(A/T)GG] methylation systems are two well-characterized methods. For instance, Clostridium thermocellum exhibits sequence-specific restriction endonuclease activity (GATC) with little non-specific exonuclease activity. Protection from digestion was observed when plasmids were prepared from a Dam+ (GmATC) E. coli strain, while plasmids prepared from a Dam-E. coli strain were digested by the cell extract cocktail  systems on a molecular level (base-to-base) can help develop and improve transformation efficiency. Among cocktail . Howeveret hosts . Recentl DSM1313 . AlthougTable 1. Dominant markers usually confer a new ability to the host strain such as bacteriocin immunity/resistance (thyA) (lacF) (lacG)   in a new organism, is to conduct an initial screen to test native resistance by increasing antibiotic concentrations. However, this approach sometimes requires intensive manual labor especially for the expression of genes that hinder the host growth. Less viable approaches include identifying or developing new antibiotic resistance genes or discovery of new antibiotics based upon design-screen-test approaches . In somesistance , heat-shsistance , or sugasistance . On the e (thyA) , lactose) (lacF)  or phosp) (lacG) , and alaG)  .Promoters are key tools in controlling gene expression since they initiate gene transcription. Promoter regions can be hard to predict in a non-model organism. Therefore, libraries of well-characterized promoters are often only available in well-established organisms. Thus, transcription of foreign genes or activation of cryptic endogenous clusters is one main obstacle for heterologous gene expression or for understanding cryptic novel endogenous cluster functions, respectively. With the advent of high-throughput sequencing technology (mRNA-seq), gene expression levels can be determined with low cost, reliable results, and high efficiency according to the intracellular transcriptomics data. Accordingly, promoters can be rationally designed based on transcription level and tested by using reporter proteins .Saccharomyces cerevisiae, C. thermocellum, as well as Streptomyces sp.  or CRISPR/dCas9 that inactivates at the translational or transcriptional level, respectively.Clostridium sp.  was constructed by introducing the D10A and H840A mutations into each nuclease domain, which removed the nuclease activity while maintaining its ability to bind to the target site . This moUpregulation of a gene expression from a single copy number level can be beneficial to the host without introducing an exogenous part. Upregulation can be accomplished either by increasing transcriptional rate through addition of an UP element or by accelerating translational initiation rate through reprogramming a stronger RBS sequence.E. coli and Bacillus subtilis . UP elements have been reported to enhance bacterial promoter strength in subtilis , and recsubtilis . A novelromoters . In the de novo design of the RBS sequence at a certain TIR  and prediction of an RBS sequence and calculation of the TIR in a bacterial genome  characterization. The author also showed that the expression was further tuned by 2-fold with redesign of RBS and insertion of UP-elements  in conjugation with an exogenous DNA into non-model hosts . The lambda-Red HR facilitates the ssDNA’s targeting at the lagging strand of the replicating genome to introduce mutations. In the MAGE application paper, the authors demonstrated engineering 20 gene RBSs for optimizing the 1-deoxy-D-xylose-5-phosphate (DXP) pathway to produce lycopene  performed higher editing efficiency (100% versus 25%) than the heterologous Type II CRISPR/Cas9 system (E. coli)   or overeE. coli) . Another editing .With the advent of modern genome sequencing, GSMMs have been developed as a powerful and indispensable tool to study and predict microorganism metabolism, physiology, and phenotype. In general, GSMM is based upon a stoichiometric mathematical model through integrating genome annotation, biochemical knowledge and every reaction information in a target organism. By bridging the gap between genome-based biochemical information and metabolic phenotype in a principled manner, GSMM offers an overall perspective on the metabolism of whole cells. A general four-step protocol for GSMM reconstruction was summarized as draft reconstruction, manual curation, conversion to a computational format, and network evaluation and validation .in silico design for predicting key genetic targets to guide experimental implementation in microbial chemical production has been given with various successes. It can be accomplished by predicting the flux intervention through gene knock-out (Table 3).GSMM based nock-out , upregulnock-out , and hetnock-out ; Table 3The first computational-aided strain design program, Optknock, was developed for simulating gene deletion by employing a bi-level optimization program to seek reaction knock-out targets that would yield overproduction of a desired compound while maintaining optimal growth . Soon thin silico strain design involves predicting and simulating target gene amplification. This approach can be reached by computational identification of the flux changes (following by gene-protein-reaction) in response to the pathway toward the target chemical and can be experimentally achievable by increasing the expression of related genes. For example, the method named FSEOF is aiming to identify gene amplification targets by scanning the changes of all the metabolic fluxes in response to the enhancement of the flux toward the target compound   . Such mo modules . The autThese computational methods can be readily deployed to study non-model organisms if their genome has been sequenced. When developing the initial model, care must be taken to look at potentially novel functions that cannot be adequately described by homology. In addition, non-model organisms may use familiar biochemical pathways in a novel map (novel metabolic cycles and regulation), so experimental testing of a new computational model is always beneficial.Mycobacterium tuberculosis metabolism and the model was able to identify 7 of 8 known inhibitors and predict several candidate inhibitors for potential therapeutics.With the significant decrease of the cost of data generation and analysis, omics data can be implemented for an organism in a very short time. Integration of the omics data to the GSMM can help improve the accuracy of prediction for the metabolic fluxes. One approach to deploy the omics data to the GSMM is called “the switch approach,” which controls on/off reaction fluxes based on threshold expression levels (lower bound and upper bound) . The keyL-lysine production in Corynebacterium glutamicum (from zero to hero), where the final engineered strain produce a titer of 120 g/L L-lysine with a high yield of 0.55 g/g glucose  efficiently degrading and hydrolyzing natural biomass into available sugar; and (2) reinforcing metabolic fluxes toward a desired compound. However, due to the recalcitrant nature of cellulosic biomass, degradation and hydrolysis on untreated biomass is a slow and difficult process.bgl2), increasing the activator (overexpression clrB) and relieving the repression (deletion creA) simultaneously in Penicillium oxalicum. The optimized strain enabled an increase of cellulase activities from 10- to 50-fold  after photosynthesis while the acetyl-CoA dependent pathway barely detected 1-butanol (6.5 mg/L)  .+ oxidoreductase is the main supply for NADH regeneration. The results showed that overexpression of rnf genes resulted in an increase in ethanol production of about 30%  can contribute to increasing alcohol production by increasing electron supply . Papanekbout 30% .C. cellulovorans and C. beijerinckii. Under an optimized condition, the co-culture produced 11.9 g/L of solvents from 68.6 g/L alkali pretreated corn cobs  Microbial biofuel production titer is unsatisfactory to meet an industrial scale ; (2) Few publications have been reported using direct untreated raw materials; (3) Progress with hosts for the native CBP microorganism is slower because tools are less developed.We believe that research related to CBP should be focused on several aspects. First, strain improvements will focus on industry-scale conditions . A recent interesting study was conducted to fit the industry-level at 100 g/L cellulose . It was Second, cost should be taken into account on an industry-level basis . A rough PubMed literature search utilizing the keyword of “consolidated bioprocessing” revealed a total of 254 publications, while less than 40 publications used untreated or chemically/mechanically pre-treated cellulose/hemicellulose biomass, less than 10 publications used untreated cellulose/hemicelluloses biomass. Fermentation data of using untreated raw biomass should be valuable for guiding strain improvements during chemical production. Strain development coupled with fermentation strategies should also be investigated based on a ‘real-world’ condition.Clostridium sp. during biofuel fermentation. Such complexity and nature of the systematic process is still unclear, hindering understanding and optimization of solvent production. GSMMs can provide an insightful prediction on a system level. C. acetobutylicum response to butyric acid and butanol stress on a genetic regulation basis using GSMM and CoreReg algorithm. The model predicted a core regulation at arginine and amino acid metabolism at butanol stress while a core regulation at arginine and pyrimidine metabolism at butyric acid stress  . AnnuallMetabolic engineering of non-model microorganisms have recently received an enormous amount of research interest due to their high diversity of properties and capabilities of these organisms. However, progress on developing non-model strains is slow, mainly due to the lack of developed genetic engineering tools and their less well-defined systems. In this review, we discussed methods and considerations for developing molecular genetic tools. Methods for controlling gene expression are evaluated both for downregulation and upregulation. Current genome engineering methodologies and design concerns were provided. GSMM computational frameworks were summarized as a tool for strain design. A stare-of-art CBP application was updated with metabolic engineering strategies. Future prospects were proposed: (1) more research should focus on industry-level condition ; (2) a combination of GSMM-based strain design and experimental implementation is expected; (3) an extension of CBP application to other raw biomass should be developed.All authors listed, have made a substantial, direct and intellectual contribution to the work. QY wrote and revised this manuscript; SF revised this manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Escherichia coli. The model obtained suggests that actually activated reaction steps and feedback are inhibitions within the pathway.Measuring the concentrations of metabolites and estimating the reaction rates of each reaction step consisting of metabolic pathways are significant for an improvement in microorganisms used in maximizing the production of materials. Although the reaction pathway must be identified for such an improvement, doing so is not easy. Numerous reaction steps have been reported; however, the actual reaction steps activated vary or change according to the conditions. Furthermore, to build mathematical models for a dynamical analysis, the reaction mechanisms and parameter values must be known; however, to date, sufficient information has yet to be published for many cases. In addition, experimental observations are expensive. A new mathematical approach that is applicable to small sample data, and that requires no detailed reaction information, is strongly needed. S-system is one such model that can use smaller samples than other ordinary differential equation models. We propose a simplified S-system to apply minimal quantities of samples for a dynamic analysis of the metabolic pathways. We applied the model to the phenyl lactate production pathway of  The artificial and industrial uses of microorganisms for material production have a long history of more than a thousand years. Recently, genetic operations have been widely applied to improve production. Two generally considered approaches introduce enzymes that have higher activities from other organisms or species and introduce enzymes to realize metabolic pathways that do not naturally occur in the microorganisms. The former method is popular because its operation is simpler and improvements are more predictable than with the latter method. Conventional gene modifications using ultraviolet or other radiation types are easy to achieve and have been widely applied in many industries. Nevertheless, the efficiency of such improvements is quite low because gene modifications occur accidentally and uncontrollably, and progress is made serendipitously. Therefore, gene introduction is currently used along with conventional methods.Target genes for modification are chosen based on information including the reaction rates of the respective reaction steps within the metabolic pathway and include the production materials and substrates of microorganisms, as well as changes in the reaction rates through changes in the concentrations of the metabolites that consist of the pathway. Bottleneck reaction steps and feedback loop inhibitions are suggested based on this information. The genes of enzymes used in such reactions are candidates for modification.2 Several formulae are established for the types of enzymic reactions, such as inhibition schemes. The most popular is the Michaelis-Menten law4 for a simple one-to-one enzymic reaction without any inhibition or catalysis using an enzyme. The reaction rate is modeled based on the following reaction scheme:The rates of enzymic reactions are generally defined as the limit of changes in the compounds over time.in which 6Therein, a pair of square brackets denotes the concentration of the compound, 7 the values of the kinetic parameters have not been sufficiently published or accumulated. An enzyme generally has different parameter values for the various conditions and species of organisms. Moreover, the parameter values generally differ between in vitro and in vivo (in living cells) conditions.9 For most industrial applications, a dynamical analysis of the pathways must be conducted without reaction scheme information or kinetic parameter values.Generally, finding the parameter values is difficult and expensive because it requires enzyme isolation and measurements of the reaction rates in test tubes (in vitro measurements). Although the amount of enzyme information in the literature and public databases is growing,6 is one such canonical ODE model. For a reaction scheme with 2 reactions, the following is used:The ODE systems in canonical forms are applicable because they are independent of the molecular mechanism of the reaction scheme. The S-systemwhere where 6 which can be presented as follows:The S-system above is a simplified form of the general mass action law,Therein, the 10 because several sets of different parameter values are generally found for the given observed time series data. Restrictions and limitations are effective for difficulties such as fixing some The parameter values of Numerical optimizations require a sufficient number of observed samples. Smaller needs are better because observations entail a certain amount of costs. A mathematical model with fewer parameters requires fewer samples. We propose a canonical ODE model for small samples through the simplification of the second term of By the mass action law, the decomposition rate of a compound depends solely on its concentration in many biological processes, such as Michaelis-Menten–type reactions shown in our model includes a nonlinear decomposition term because we suspect that a linear term might be too simple for the metabolite in a complex biological network system containing many unknown reactions. Our assumption is reasonable when regulation of the degradation processes by these unknown reactions is not significant.The resulting time series of the model based on a numerical integration varies greatly through a change in the initial value. Finding the best initial value is difficult because the observed initial value frequently has errors, particularly for small sample data sets. Therefore, we compare the model and data in differential spaces. The differential of the observed data can be calculated through a numerical differentiation, and the parameter values can be evaluated by comparing the differential values with the values of Escherichia coli. For a pathway that includes branches and feedback loops, we estimated the actually activated reaction steps and activities of the feedback inhibitions suggesting strategies for an improvement in production.We evaluated the proposed method according to its application to the phenyl lactate (PL) production pathway from glucose using First, we build a pathway map based on information from the literature and different databases. We then choose some metabolites in the map as observation targets. A pathway map is reconstructed using only the target metabolites. The observations are measurements of the target metabolite concentration at sampling time points with equal intervals. A simplified S-system model is defined based on the reconstructed pathway map by fixing some 10 or differential evolution11 to minimize the difference between differentials of the observed data through a numerical differentiation and those from 1215  pathways. Phenyl lactate is produced from phenyl pyruvate (PP), PP is from phenylalanine (PA), and PA is from prephenic acid. In addition, prephenic acid is from chorismic acid in the SA pathway. Choosing phosphoenolpyruvate (PEP), erythrose 4-phosphate (E4P), SA, PA, PP, and PL as the observation targets, we then reconstruct the pathway for these 6 metabolites . The patChanges in concentration of metabolites in the reconstructed pathway are modeled mathematically using the following ODE models:Actually, production of PEP and E4P is not controlled by any other metabolites, and these compounds are independent variables in the ODE system above. Their respective dynamics are not modeled. Parameter 11 to find the parameter values that minimize the differences between the differential of the concentration values calculated using the ODE system, as shown below:Time differential values of the metabolite concentration are calculable using the ODE system by determining all parameter values. We introduce the differential evolution algorithmt of the observed data. Here, Therein, The ODE system with the determined parameter values is shown below :The ODE system suggests that the reaction chain to SA from PEP is more active than that from E4P. In addition, PP production is inhibited by feedback loops from both PA and PL.13 These negative parameters may suggest unknown regulatory pathways whose effects look substrate inhibitions.There are 3 negative value parameters. Reaction steps that are represented by these parameters consist of only productive enzymic reactions in the literature.The changes in metabolite concentration over time can be modeled using the Michaelis-Menten law, as shown below:For each metabolite, there are 8 parameters for SA, 10 for PP, 6 for PA, and 4 for PL because a model of the reaction step (single enzymic reaction) has 2 parameters. Changes of concentrations in time of SA and PP cannot be modeled using the 6 sampling data in this study. There are a total of 16 parameters for the reconstructed pathway because some parameters are common (1 of the outgoing reactions of SA is an incoming reaction of PP). Some numerical optimization methods can search for the 16 parameters simultaneously. However, such a simultaneous nonlinear numerical optimization is not easy, and the difficulty increases significantly with an increase in the number of parameters .The form of the S-system model is reduction or simplification of general mass action (GMA) law model shown as follows:For each metabolite, there are 7 S-system parameters for SA, 8 for PP, 5 for PA, and 4 for PL, or 18 in total because some of the parameters are the same. The number of parametes are reduced for SA, PP, and PA compared with Michaelis-Menten models; however, concentrations of SA and PP cannot be modeled even when using the GMA. In our proposed model, the corresponding numbers are 5, 6, 5, and 4, or 20 in all, which is not a small number; however, it is not a problem that the total number of parameters is larger than in the S-system because no parameters are common to any 2 metabolites, and the parameters of each metabolite are optimized independently of the other metabolites. Our model has fewer parameters for each metabolite, which indicates that our model is more robust against errors than the S-system and Michaelis-Menten models.The less number of model parameters means that the model needs a less number of data. Michaelis-Menten model consists of 2 parameters for each reaction, thus Although the model and data do not match perfectly because the data generally include errors in the probabilistic distributions, the optimization precision of the parameters (model fitness to the data) shown in The parameter values of the Two negative feedback loops exist: PP production is inhibited by PL, and PA production is inhibited by PP. Although it can be readily imagined that the inhibition of the feedback reactions increases the production of PL, the main inhibitory effect on PP production is from the SA. Disrupting one or more genes of the reactions to PP from SA might improve the PL production.Phenylalanine decreases gradually , but shoIn conclusion, the results show that the reliability of the estimated parameter values might not be the best or even very high because the reconstructed pathway and the ODE system are simplified. These values suggest that the target genes can be modified for an industrial improvement in production using microorganisms. This case study presents several suggestions that may be useful when constrained to only a few samples or low observation costs.


Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.The online version of this article (doi:10.1186/s12859-016-1240-1) contains supplementary material, which is available to authorized users. Constraint-based reconstruction and analysis (COBRA) methods enable systems level computation of cellular functions using genome-scale biochemical reaction networks, including metabolism . Metabolv is the vector of fluxes, vL and vU are lower and upper flux bounds, S is the stoichiometric matrix, and c is the vector of objective coefficients . We refer to , bisection converges to specified accuracy ε in log2((b−a)/ε) iterations. We implemented bisection as Algorithm bisectME using the simplex method in quad precision  as in . Dattorrn) as in  proves tad MINOS ).μk, k=0,1,2,… }. (The objective function for each subproblem is an augmented Lagrangian.) If MINOS converges, it will be to a global optimum μ∗. Furthermore, the subproblems converge quadratically when μk is close enough to μ∗ .μ0 and the MINOS scaling option on the computation time and final solution. Empirical tests showed that μ0=0.0 should be avoided, as should μ0>μ∗   for imprtart Eq.  reliablyμ-dependent)  Fig. . For morCompared to the combined solveME, bisectME (with golden section search) took an average of 75 and 103 s for 3 and 6 decimal points respectively, while binary search (not GSS) required an average of 93 and 124 s for 3- and 6-digit precision in growth rate. All runs were performed in quad-precision using Quad MINOS.In summary, the combined solveME was up to 10 and 34 % faster than golden section search, or 27 and 45 % faster than binary search, for 3- and 6-digit accuracy in growth rate. Another advantage of the combined solveME over bisection methods was that the growth rate was always returned to about 15 digits because of the tolerances set for Quad MINOS; therefore solution time was not a function of final solution precision. To reach the same precision, bisection would require about 50 iterations, or over 400 s. Furthermore, double-precision solvers would have difficulty achieving even 6 or 7 digits.−9 but are not certain to achieve them. Using quad-precision, we achieved feasibility and optimality tolerances below 10−15, and often less than 10−20.In particular, commercial double-precision solvers such as CPLEX and Gurobi handle feasibility and optimality tolerances as small as 10In addition to growth rate maximization, we developed quad-precision flux variability analysis (FVA)  for ME mEmpirical tests demonstrated the importance of quad-precision when FVA is applied to ME models. Specifically, without quad-precision, errors such as maximum flux being less than the minimum flux were observed Table . AnotherWhen varyME was performed at growth rates below the maximum, non-zero flux variability was observed Fig. . Again, E. coli and T. maritima ME models, respectively  using tly Table . This reME models have imminent utility for systems metabolic engineering. In particular, biochemical overproduction strain design often involves gene knockouts and modulating the expression of production pathways. These genetic manipulations impact host fitness in part by forcing reallocation of the host proteome away from growth and stress response functions. ME models now allow genome-wide accounting of proteome reallocation for engineered strains.sdhCDAB) knockout, together with overexpression of fumarate reductase (frdABCD), isocitrate lyase (aceA), or both.To demonstrate, we analyzed the overproduction of succinate using growth-coupled designs that had been found using a metabolic reconstruction , 19. In sdhCDAB, we set zero upper bounds for the translation reactions of the four sdhCDAB subunit genes. Overexpression of frdABCD and aceA was performed in three steps. First, we determined the maximum growth rate with sdhCDAB deleted. We then used varyME to determine the feasible flux ranges for the complex formation fluxes of the overexpressed enzymes with growth rate fixed to a small fraction  of the maximum. We then set the lower bound of complex formation fluxes to linearly spaced fractions of the maximum expression flux, from 0.05 to 0.95. Since we were investigating two production pathways, we sampled a grid of 11 by 11 samples for a total of 121 combinations of pathway expression levels. For each expression combination, we solved Eq.  increased with product yield, as expected. Interestingly, the remaining (Other) proteome increased in mass fraction up to four-fold, from 1.6 to 6.7 %, as product yield increased. Therefore, production pathway overexpression entailed a significant proteomic cost.The ME model revealed trends in proteome re-allocation with increasing product yield. Specifically, we traced the relative mass fraction of five proteome sectors, by summing the product of translation rate (mmol/gDW/h) with the protein molecular weight (g/mol) over all proteins in each sector. The core proteome and glucose-niche proteome sector definitions were based on . The cor4frdABCD vs. aceA translation rates varied strongly, such that only one pathway was expressed at varying expression levels. However, higher succinate yields were achieved when both pathways were expressed simultaneously at a relatively constant ratio  , and Pearson correlation of 0.87 (p=0.025)   ratio  led to t87 p=0.02 Fig. 5)p=0.017),p<10−15) and Spearman rank correlation of 0.68 (p<10−15). When considering only the core proteome [p<10−15) and Spearman rank correlation of 0.63 (p<10−15)  , 6 have With advances in ME solution methods enabling rapid prototyping, we anticipate the acceleration of ME model development for additional organisms, such as phototrophs . DevelopE. coli. Unlike metabolic reconstructions that predict maximal product yield when the most metabolically efficient production pathway is used, the ME model predicted that simultaneous expression of multiple pathways led to the highest yields when proteome reallocation requirements were considered. These predictions were consistent with literature, where simultaneous expression of two succinate-producing pathways led to increased yield [To demonstrate possible application of our solution methodology in an engineering context, we analyzed growth-coupled succinate overproduction by ed yield . As showed yield –30 to MEWe developed an efficient methodology for solving nonlinear, multiscale models of metabolism and macromolecule expression (ME models). In particular, we showed that the growth rate maximization problem for ME models is a quasiconcave maximization problem in general and quasilinear for special cases as demonstrated here. In both cases, the global optimum is found efficiently using the projected Lagrangian method. Using the quad-precision LP/NLP solver Quad MINOS, we obtained up to 45 % speedup over conventional bisection. Currently, a phylogeny of in silico methods has emerged around metabolic reconstructions . Our newSerial computations were performed on 2.70 GHz Intel(R) Core(TM) i7-4800MQ processors with 8 GB of RAM and the Arch Linux operating system. Parallel computations were performed using resources of the National Energy Research Scientific Computing Center (NERSC).μAv+Bv=Bv−μCv=0 (where C=−A). Here, we show that these constraints are quasilinear. First, recall that a quasilinear function is both quasiconvex and quasiconcave [μ-sublevel sets are all convex while a quasiconcave function has convex μ-superlevel sets. Accordingly, a quasilinear function has all convex μ-level sets. The μ-level set of constraint i∈DIL is For our reduced ME model, the dilution and growth rate-dependent protein-per-RNA constraints are gathered into the general form, iconcave . A quasiμ is fixed in the level set). Therefore, every μ-level set is convex; hence the dilution constraints are quasilinear.which is a 0-level set of the sum of linear functions, i.e., a convex function  problem whose global optimum is again found readily .−15. To determine orders of magnitude of ME fluxes  and for oxygen uptake. Unlike metabolic models that require physiologically determined uptake rate bounds, ME models predict a limit to maximum uptake. This maximum uptake occurs at the max growth rate where additional RNA and protein machinery cannot be produced to meet growth demands .−20) encoding an essential gene. On glucose minimal medium, this flux was 9.35×10−14 mmol/gDW/h. Note that the smallest translation flux was 9.13×10−13 mmol/gDW/h. The maximum flux was 45.4 mmol/gDW/h, for H2O exchange. Thus, on glucose minimal medium, fluxes spanned nearly 15 (14.7) orders of magnitude.To estimate the orders of magnitude spanned by ME fluxes, we first found the smallest transcription flux for genes determined to be essential experimentally and by the ME simulation. Because multiple transcription units (TUs) can encode a gene, and multiple genes can be encoded by a TU, we found the smallest transcription flux greater than the solver feasibility tolerance , the reduced ME model of E. coli has a similar number of reactions but considerably fewer constraints. The reduced ME model has a number of simplifications compared to the full ME models of E. coli: iOL1650 [The reduced ME model of parately  and was