There is a limited amount of computational work, using metabolic reconstructions, performed in this field for the better understanding of T2DM. In this study, a new algorithm for generating tissue-specific metabolic models is presented, along with the resulting multi-confidence level (MCL) multi-tissue model. The effect of T2DM on liver, muscle, and fat in MKR mice was first studied by microarray analysis and subsequently the changes in gene expression of frank T2DM MKR mice versus healthy mice were applied to the multi-tissue model to test the effect. Using the first multi-tissue genome-scale model of all metabolic pathways in T2DM, we found out that branched-chain amino acids' degradation and fatty acids oxidation pathway is downregulated in T2DM MKR mice. Microarray data showed low expression of genes in MKR mice versus healthy mice in the degradation of branched-chain amino acids and fatty-acid oxidation pathways. In addition, the flux balance analysis using the MCL multi-tissue model showed that the degradation pathways of branched-chain amino acid and fatty acid oxidation were significantly downregulated in MKR mice versus healthy mice. Validation of the model was performed using data derived from the literature regarding T2DM. Microarray data was used in conjunction with the model to predict fluxes of various other metabolic pathways in the T2DM mouse model and alterations in a number of pathways were detected. The Type 2 Diabetes MCL multi-tissue model may explain the high level of branched-chain amino acids and free fatty acids in plasma of Type 2 Diabetic subjects from a metabolic fluxes perspective.Computational models using metabolic reconstructions for  Type 2 Diabetes Mellitus (T2DM), the most common form of Diabetes in America, is becoming a global pandemic with the greatest increase in cases in many developing countries. The pathophysiology of T2DM primarily involves defects in three organ systems– liver, peripheral target tissues , and pancreatic β-cells In the patients with T2DM, withdrawal of insulin treatment has been shown to be associated with increased levels of branched-chain amino acids (BCAAs) in the plasma It is also known that elevated free fatty acid (FFA) levels in plasma is linked to T2DM in patients in silico genome scale metabolic reconstruction models to study the causes of various metabolic disorders in silico. Accounting for more than 3000 human metabolic reactions, Recon1 provides a firm basis for studying human metabolism and metabolic disorders such as cancer, diabetes, obesity, and inherited gene and enzyme deficiencies In contrast to the wealth of knowledge available for the concentrations of circulating BCAAs and FFAs in T2DM patients, the actual mechanisms leading to these changes at the metabolic and genetic levels are less understood. With the emergence of systems biology tools associated with high-throughput data, it is now feasible to create Following Recon1 coming into existence, several tissue-specific models have also been generated in silico model to T2DM phenotype. The current study introduces a comprehensive multi-tissue-specific model to study interdependence of hepatocytes, mycoytes, and adipocytes in the T2DM condition. Insulin resistance leading to Type 2 Diabetes Mellitus (T2DM) is regulated by more than one tissue system requiring analysis at multi-tissue level. Major tissues involved in T2DM are skeletal muscle, liver, adipose, pancreas, brain, and gastrointestinal tract h) consists of 1110 reactions and 1593 metabolites. The final medium confidence reaction list (Cm) consists of 1099 reactions and 1643 metabolites. The final low confidence reaction list (Cx) consists of 4433 reactions and 3679 metabolites. The algorithm required six iterations before completing to give multi-confidence level (MCL) multi-tissue model with 4704 reactions and 3131 metabolites. Completion is indicated by the fact that the objective function for the whole model is at a maximum for a particular set of flux distributions and no more reactions can be added in subsequent iterations .Before generating the model, an algorithm was applied to generate a list of high confidence, medium confidence, and low confidence reactions, based on the source of a particular reaction. The high confidence list comprised reactions from published literature and was not altered by the algorithm; the medium confidence list comprised of reactions from online databases such as HPRD, etc.; and the low confidence list comprised of all remaining reactions that weren't present in high and medium confidence reaction lists, as shown in in silico. S-Adenosylhomocysteine hydrolase is associated with AHCY gene deficiency in silico model was run to predict the phenotype of the disease associated with removing that particular gene(s). The predicted phenotype was then compared to the actual phenotype from the OMIM database. Exchange reactions tell about the concentration and the exchange flux balances indicate the increase or decrease in concentration of a metabolite in the model in the blood/extracellular compartment. This analysis was performed on the MCL multi-tissue model, Recon1, and the multi-tissue version of Recon1 . The results from simulations of Recon1 and the multi-tissue version of Recon1 served as benchmarks to compare to the simulations of MCL multi-tissue model, as shown in receiver-operator curves (ROC) in From the OMIM database Recon1 and the multi-tissue version of Recon1 have an identical curve which is understandable as a multi-tissue version of Recon1 is just a combination of Recon1 models of the three tissues and the external exchange compartment; however, it is necessary to test the differences between the two because the number of type III cycles can increase in the multi-tissue version of Recon1. A type III cycle is one of three types of extreme pathways that can exist in a reaction network  and could cause the behavior of the multi-tissue version to be different than the single tissue version of Recon1. in silico models. The microarray data of the two sets was compared and genes that had statistically significant  fold changes were tabulated. These differentially expressed genes were then mapped to Recon1 and the MCL multi-tissue model to determine sets of upregulated and downregulated reactions. The bounds of these reactions were changed according to the procedure defined elsewhere . The resulting differences in the exchange reactions flux bounds in both models were compared with amino acid data for the Zucker diabetic fatty rat from the literature Subsequent validation analysis involved the application of microarray data from MKR T2DM mice to the aforementioned The difference between the two pairs (Recon 1 and MCL multi-tissue model) of columns in The first two rows in These ROC curves clearly demonstrate the differences between Recon1 and MCL multi-tissue model by providing the clear differences in the area under the curve (AUC) between the two models. In Recon1 was highly inaccurate for transport reactions at each threshold, which demonstrates the difficulty with predicting increases or decreases of exchange from gene expression fold changes. The fact that the MCL multi-tissue model displays an AUC that is roughly 7.5 times greater than the AUC produced by Recon1 provides further validation for the MCL multi-tissue model in these analyses, at least compared to other systems available.in silico model which was less comprehensive in terms of the number of metabolic reactions used in the one presented in this study. In order to use the MCL multi-tissue model for predicting physiological changes in fully T2DM MKR mice as compared to healthy mice, gene expression data was first generated for liver, skeletal muscle, and fat tissues for healthy and diabetic mice. Statistical tests on gene expression data suggested that several genes were differentially regulated between MKR and healthy mice. The statistical test – Fisher's exact test, providing significance of the association of the experimental gene expression values and the Ingenuity Pathway Analysis canonical pathways, was done using the Ingenuity software (www.ingenuity.com). From gene expression fold change analysis in the three tissues, it was found that for BCAA degradation and FA oxidation pathways, some of the genes are upregulated and some are downregulated in liver, while the same were predominantly downregulated in the T2DM MKR mice's fat and muscle tissues when compared to their healthy euglycemic littermates, as shown in After the two extensive validations outlined in sections 2.1 and 2.2, the model was used to study physiological behaviors during T2DM condition – higher plasma concentration of branched-chain amino acids (BCAAs) and free fatty acids (FFAs) in T2DM subjects. Branched-chain amino acid metabolism has been studied in T2DM condition previously The liver tissues' FA degradation pathway genes did not provide a clear explanation of high concentration of FFAs in the plasma of T2DM subjects. However, the biosynthesis pathway from Ingenuity Pathway Analysis  for fattin silico T2DM condition simulation. Then, flux variability analysis is performed to find out the reactions without fluxes, which are then removed. The remaining reactions then represent an active context-specific metabolic network. This active model was used to find out the differences between biochemical reaction activity between T2DM and healthy states.In order to perform systems level analysis of the gene expression data, to achieve a better understanding of BCAA and FA metabolism, we next used the gene expression data along with the MCL multi-tissue model to generate flux predictions. Gene expression data was used for generating a context-specific MCL multi-tissue network using an algorithm which uses gene expression data to remove the reactions associated with no gene expression, thereby creating a context-specific metabolic network for the Cholesterol metabolism is upregulated in adipose tissue  – D and It is important to note that in most of the research work done on studying behavior of these subsystems deal with studying differences in gene expression in the two physiological conditions; however, in this study we present differences in fluxes in the biochemical reactions in the two physiological conditions . Figures S1–S15 in In the present study, microarray technology was used to elucidate the relation of free fatty acid and branched-chain amino acids levels under T2DM and normal condition and the gene expression profiles in three different tissues – liver, muscle, and adipose of diabetic MKR mice. The findings from microarray analysis show that MKR mice have a downregulated fatty acid oxidation profile in muscle and adipose tissues. In liver, the entire fatty acid oxidation profile is not downregulated. On the contrary, fatty acid biosynthesis in liver tissues is considerably upregulated as shown in Wang et al. Subsequently, an algorithm for building a multi-tissue model is presented in the current paper. The algorithm presented in this paper uses as few linear programming solutions as possible to achieve an optimal solution, so that the solution can be found in a reasonable amount of time. The model provides users with the ability to predict changes in metabolite levels in the medium after deleting specific metabolic genes, as well as the ability to predict changes in metabolite concentrations in the plasma/medium after applying fold changes to specific genes. Other capabilities include using a quadratic programming solver to apply experimentally derived fluxes to specific reactions in the model and determining the remaining fluxes to examine the behavior of the overall model in given by the experiment The positive aspect of this approach is that metabolic fluxes can be predicted; this is important because metabolic fluxes are difficult to measure in mammalian tissues, and metabolic fluxes provide essential information used for characterizing phenotypes of cellular systems. Flux information can help predict metabolic biomarkers in blood/plasma Figures S7–S12 in in vivo methods of metabolic flux measurement, we did find evidences supporting our results. For example, it is reported that gluconeogenesis flux in humans is decreased in Type 2 Diabetes Statistical significance of the differential regulation of the subsystems was calculated by using a two sample t-test  to determine the statistical significance of the subsystem's deviation from random behavior. For example, if the subsystem is 100% downregulated with two reactions, then, intuitively, this is not very statistically relevant because a random selector can make this selection 1/9 of the time . Thus, sorting by the t-score of each subsystem provides a better understanding of the extent of differential regulation of the subsystems. Figures S1–S12 in The most negative t-score in adipose and muscle tissues is for the carnitine shuttle subsystem. The ‘Nucleotides’ subsystem is also strongly downregulated in both muscle and adipose tissue. Interestingly, liver tissue displays more upregulation than the other tissues, with the carnitine shuttle subsystem showing upregulation. Thus, the carnitine shuttle subsystem appears to be the subsystem most affected in T2DM. The carnitine shuttle is responsible for transport of long chain fatty acids into mitochondria for oxidation. So, a downregulated carnitine shuttle in adipose and muscle tissues implies lower metabolism of the FFAs in those two tissues. Even though the FFA metabolism is higher in liver because of upregulated carnitine shuttle, the biosynthesis pathway of fatty acids is also elevated . This exin silico predictions via constraint-based modeling has facilitated better understanding of the reason behind high BCAA and FFA levels in plasma of T2DM subjects. Prior systems biology studies have shown the ability of constraint-based models to predict metabolic biomarkers In summary, the integration of microarray data and Type 2 diabetes is characterized by two major defects: beta-cell dysfunction and insulin resistance in peripheral tissues. The exact alterations in molecular pathways associated with beta-cell dysfunction in insulin-resistant and diabetic states are not clearly understood. Most of the studies involving T2DM and insulin resistance utilize data from insulin-resistant or diabetic animal models, such as Zucker fatty (ZF) and Zucker diabetic fatty rats (ZDF) In a mammalian system, the specific objective of a particular function of a cell, at a given time and under certain conditions, is difficult to identify, whereas in unicellular systems, the objective function can be assumed to be the maximization of cell growth. This is because mammalian systems are much more complex, especially when attempting to define models for different tissues, because each tissue has a different objective. One may consider that there is an over-arching objective function when considering a system that defines the overall human body as a linear combination of partial Recon1's associated with each tissue, but this again is difficult to define, because the objective of maximizing biomass in unicellular organisms only applies during the exponential growth phase. Thus, maximizing biomass in mammalian systems may be applicable, but only during the growth phase of the mammal.All animal study protocols were approved by the Mount Sinai School of Medicine Institutional Animal Care and Use Committee (IACUC). Mice were housed in The Mount Sinai School of Medicine Center for Comparative Medicine and Surgery, an Association for Assessment and Accreditation of Laboratory Animal Care (AAALAC) and Office of Laboratory Animal Welfare (OLAW) accredited facility, where animal care and maintenance were provided.2. Liver, Skeletal muscle, and fat tissues were flash frozen in liquid nitrogen, stored at −80°C, and shipped on dry ice to NIDDK/NIH facility for further processing.Male 10-weeks old FVB/N – MKR mice were used for the microarray studies. Generation and characterization of MKR mice have been described elsewhere Total RNA from the liver, fat, and skeletal muscle tissues was isolated for three biological replicates for both diseased and healthy animal subjects. Qiagen's Microarray Tissue Mini Kit  was used for RNA isolation purpose according to the manufacturer's instructions. Purified total RNA was quantified using a spectrophotometer (Thermo Scientific Ltd). The absorbance values at 260 and 280 nm were used for assessing the quality of the sample. Only the samples with greater than 1.80 260/280 absorbance ratio were used for microarray analysis +2 hours in hybridization oven rotating at 60 rpm at 45°C . Arrays were processed using Affymetrix 450 Fluidic stations using wash and stain kit (Affymetrix Inc.). Chips were scanned using Affymetrix GeneChip scanner 3000 operated by Gene Chip Operating Software, version 1. 4 (GCOS 1.4) and generated.CEL.CHP and RPT files. To access the efficiency of cDNA synthesis Poly A controls  was spiked to the samples and hybridization controls  were added to monitor labeling efficiency according to the manufacturer's instructions.RNA quality was tested using bioanalyzer  and RIN (RNA Integrity Number) values were above 8.0 for all the samples. 100 ng of RNA from each sample was amplified to generate cDNA using NUGEN Applause WT – Amp ST system , according to the manufacturer's instructions. 2.5 µg of cDNA was fragmented and biotinylated using Encore Biotin module . Resultant sample mix with hybridization reagents (Affymetrix Inc. CA) and injected into Affymetrix Mouse Gene 1.0 ST arrays and incubated for 18The microarray raw data was analyzed using software Partek genomics suite, version 6.3 Copyright 2008 Partek Inc., St. Louis, MO, USA. Raw data were subjected to Robust Multichip Average (RMA) quantile normalization to remove biases introduced by technical and experimental effects. All expression data were log base 2 -transformed to get near normal distribution for accurate statistical inference. Quality control by visualizing the data using Principal Component Analysis cluster plot ensured that no outliers were included for the analysis. Next, two-way ANOVA analysis was performed to obtain a set of differentially expressed genes. A filter of P-value <0.05 and Fold-change >1.5 times was applied to get the significantly differentially expressed genes list. The results of the microarray analysis have been deposited to National Center for Biotechnology Information (NCBI) repository and can be accessed with Gene Omnibus Expression accession: GSE51866.www.ingenuity.com) for finding biological inference. Ingenuity Pathway Analysis is an online software used to study relationship between genes, proteins, and biological reactions. More technical details about the Ingenuity Pathway Analysis' capabilities can be accessed from the Ingenuity Systems website. Statistically significant genes from Partek analysis were overlaid on the Ingenuity Pathway Analysis global molecular network, which is based on information from other databases such as KEGG, HumanCyc, etc. in the Ingenuity knowledge base after applying a filter on species type (mouse) and tissue type (e.g. adipose).The significantly differentially expressed genes list was exported to – Ingenuity Pathway Analysis  was downloaded from the BiGG database in SBML format The algorithm for trimming down the general three tissue version of Recon1 is built by minimizing the number of linear programming problems needed to trim the reconstruction The overall goal of this algorithm is: (1) maintain all high confidence reactions and (2) maximize the number of medium confidence reactions minus 0.5 multiplied by the number of low confidence reactions in the final trimmed version of the reconstruction. Statement (2) can be considered the objective function of the algorithm as shown below –The value 0.5 reflects equal probability of obtaining the most parsimonious model as well as including a maximal number of moderate probability reactions in the partial model using above algorithm p is a partial subset of reactions from Recon1 that defines the solution space for the tissue-specific reconstruction, CM and CX are the medium and low confidence set of reactions, respectively. The algorithm makes more efficient use of all of the information gained from a single linear programming (LP) solution. Every reconstruction can be broken down into elementary flux modes; these can be thought of as the simplest possible flux distributions. Therefore, every reconstruction is a linear combination of elementary flux modes, and thus, each linear programming solution is a smaller linear combination of elementary flux modes. Ideally, the algorithm would identify all elementary flux modes in a reconstruction or even LP solution and find the optimal combination from the elementary flux modes, but as of now, this is computationally infeasible due to combinatorial explosion RThe next step of the algorithm consists of providing scores for each flux distribution. The scores are calculated by subtracting half the number of active low confidence reactions from the number of active medium confidence reactions. If a score is positive, it means that adding the reactions associated with this flux distribution will add to the value of the objective function of the algorithm. Scores are calculated for each column in the matrix. This marks the beginning of the third step of the algorithm. This step involves addition of flux distributions associated with the high confidence set of reactions. It starts by ordering the list of scores associated with the flux distributions from high to low values. Then, the flux distribution with the highest score is checked for any active high confidence reactions; if there are no high confidence reactions, then the flux distribution with the second highest score is checked for high confidence reactions. This procedure continues until the highest scoring flux distribution containing at least one high confidence reaction is found. All of the active reactions within this flux distribution are added to a final list of reactions. Also, any high confidence reactions added to the final list of reactions are removed from the list of remaining high confidence reactions. Then, the rows of the fdMatrix which are associated with the set of active reactions that were recently added to the final list of reactions are set to rows filled with zeros. This is done because these reactions are now in the final list of reactions and therefore do not contribute to the objective score anymore. Changing the values in the rows changes the scores associated with each column/flux distribution in fdMatrix, thus the scores must be re-calculated to reflect the changes in the rows. These re-calculated scores are sorted again to reveal the columns/flux distributions with the highest scores. Then, the highest scoring column/flux distribution with at least one reaction that is in the list of remaining high confidence reactions is selected, and the whole cycle repeats itself. This cycle is repeated until there are no reactions left in the list of remaining high confidence reactions, which means that all of the high confidence reactions were added to the list of final reactions, which is one of the requirements of the algorithm. Also, it's important to note that the high confidence reactions were added in a way that maximizes the score/objective function of the algorithm.The next step of the algorithm involves adding other flux distributions that increase the value of the objective function. After adding all of the high confidence reactions, the number of medium confidence reactions added to the reconstruction was optimized. The process for adding flux distributions that adds a positive value to the objective function is very similar to the process that added all of the high confidence reactions. Each of the remaining flux distributions is assigned an objective score based on the number of medium confidence reactions and low confidence reactions remaining within that distribution. These scores are sorted to find the distribution with the highest objective value. If the highest objective score is above zero, then the reactions of that distribution are added to the reconstruction. Then, the rows that correspond to the reactions that were just added are filled with zeros to prevent double counting toward the objective function. This process is repeated as long as the highest objective score is greater than zero. This means that reactions are added only if the corresponding distributions increase the objective function, and reactions are no longer added when the objective function cannot be increased by the randomly created distributions, meaning that the objective function is at a maximum for this particular set of flux distributions.Then, this whole process is repeated again; a new set of random flux distributions is created based on the partial model this time , and reactions from the high confidence list are added along with their associated reactions determined by the flux distributions, and medium confidence reactions are optimized. As part of the model building algorithm during the reconstruction process, maximizing the flux to ascertain activity/inactivity of a reaction is needed. A random flux distribution is used only in the reconstruction process which is subjected to our algorithm to find out whether each reaction adds to biological meaning or not. This process repeats itself until the model doesn't change in size from one iteration to the next. The time required to solve a problem associated with a three tissue system varies from 0.05–0.1 seconds. The number of reactions maximized in each iteration is variable; in the first iteration, all reactions are maximized. In the second iteration, all reactions that had zero flux in the solution to the first linear programming iteration are maximized, and so on. This continues until either all reactions are proven to carry a flux (have a non-zero solution to any linear programming problem), or some set of reactions are proven to be unable to carry flux (the set of reactions is maximized/minimized and no flux profiles result). The latter is explicitly proven by performing distinct linear programming problems and maximizing/minimizing each reaction in the set individually as explained in f tissue-specific model building algorithm.Robustness analysis of the algorithm was performed by generating 5 replicate models with starting point as 5 different randomized stoichiometric matrices. All 5 of the replicate models were similar in size . After the lower bounds are changed, flux variability analysis is performed on the model For reaction ‘i’:Disease reaction flux < wild-type reaction flux if,Disease reaction flux > wild-type reaction flux if,Where:i’ are the set of exchange reactions of metabolites that have been identified in the phenotype descriptions of the OMIM database. In this validation, they are amino acids. The variables diseaseMax and diseaseMin are the flux bounds of the amino acids in the disease version of the model with particular genes knocked out. The variables refMin and refMax are the flux bounds of the amino acids in the healthy model that has no genes knocked out. The variable ε represents the threshold value used for the receiver-operator characteristic (ROC) curves.The set of reactions represented by the variable ‘The results of this validation are depicted via ROC curves in the Results section. In this simulation, the threshold value is varied to distinguish between very large changes in flux bounds and very small changes in flux bounds. Thus, for a given threshold value and disease, upregulated and downregulated predictions are made for each amino acid exchange reaction. These predictions are checked against the known phenotype of that specific disease. This generates a list of true positive, false positive, true negative, and false negative predictions for the specific disease at a particular threshold. This analysis is repeated using the same threshold value for each disease in the validation. All of the predictions from each disease are added together, to provide a number of true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN) for that particular threshold value. Then, the false positive rate (FPR) and the true positive rate (TPR) are calculated as below.o is proportion of unchanged metabolites in the data; Where, TPR  =  true positive rate; (number of true positives)/.FPR  =  false positive rate; /.These values for FPR and TPR are calculated for a range of threshold values; typically from 0 to 1000, and plotted with FPR on the x-axis and TPR is on the y-axis. The area under the curve (AUC) of this plot is the indicator of the quality of the reconstruction network. An AUC of 0.5 represents a random classifier; any AUC over 0.5 represents a system that is better than a random guessing.The gene expression of adipose, liver, and muscle tissue for MKR mice model was examined. The MKR mouse model was developed by over-expressing the IGF-I receptor in skeletal muscle max in enzyme kinetics equations. Vmax is equal to kcat multiplied by enzyme concentration; therefore, a lower enzyme concentration decreases the maximum reaction velocity . Reactions that are determined to be affected by gene regulation have upper bounds initially set to 100 and lower bounds initially set to −100 or 0 depending on reversibility. Unaffected reactions have normal reaction bounds (upper bounds are 1000 and lower bounds are −1000 or 0). Initial FVA is then performed. Then, upregulated reactions have bounds doubled downregulated reactions have bounds halved. Then, FVA is performed, and resulting bounds are compared to initial FVA results for comparison and analysis. The reasoning for initially changing affected reaction bounds from 1000 to 100 was to magnify the effect of upgregulating reactions. If reaction bounds of affected reactions are kept at normal 1000 values, then doubling the reaction bounds due to upregulation may not display downstream upregulation or display the far-reaching effects of gene upregulation. The lower bound and upper bound for exchange reactions are 1 and 1000 respectively.Transcription levels of genes do not directly correspond to reaction fluxes, but a few assumptions can be made to demonstrate the effect of the levels. The main assumption is that relative gene transcription levels correlate with relative protein concentrations. With this assumption, the effect of increased or decreased protein concentration manifests itself in the upper and lower bounds of the reactions that are associated with the protein. The reason for this is because enzyme concentration only affects VThe first step is to identify all upregulated and downregulated reactions, and change the associated bounds to one-tenth of the initial value. This is done so that the effect of increases in reaction bounds due to upregulation will have an effect in a steady-state model. Then, FVA is performed on the model to establish a control set of bounds. After that, the bounds of upregulated reactions are doubled and downregulated reactions are halved. Then, FVA is performed again to generate a disease-state set of bounds. Then, the difference between the two sets of bounds is determined by the following:For a given reaction ‘Literature results were obtained for specific concentrations of amino acids in the plasma for T2DM rat versus healthy rat. The effect on each of the transport fluxes of each amino acid were considered to determine an increase or decrease in concentration in the plasma. This was done instead of simply inspecting the exchange reactions for each amino acid because the full effect of the gene expression changes may not be observed on an exchange reaction if an unaffected pathway exists that involves the exchange reaction in question. Taking all transport reactions into account generates a more complete picture of the uptake or secretion of metabolites.File S1Supporting figures. Figure S1. Adipose Chart 1: Percentage of Reactions Retained by Subsystem in Adipose Tissue – 1. Figure S2. Adipose Chart 2: Percentage of Reactions Retained by Subsystem in Adipose Tissue – 2. Figure S3. Liver Chart 1: Percentage of Reactions Retained by Subsystem in Liver Tissue – 1. Figure S4. Liver Chart 2: Percentage of Reactions Retained by Subsystem in Liver Tissue – 2. Figure S5. Skeletal Muscle Chart 1: Percentage of Reactions Retained by Subsystem in Skeletal Muscle Tissue – 1. Figure S6. Skeletal Muscle Chart 2: Percentage of Reactions Retained by Subsystem in Skeletal Muscle Tissue – 2. Figure S7. Adipose Fold Change 1: Fold Change Analysis in Adipose Tissue – 1. Figure S8. Adipose Fold Change 2: Fold Change Analysis in Adipose Tissue – 2. Figure S9. Liver Fold Change 1: Fold Change Analysis in Liver Tissue – 1. Figure S10. Liver Fold Change 2: Fold Change Analysis in Liver Tissue – 2. Figure S11. Skeletal Muscle Fold Change 1: Fold Change Analysis in Skeletal Muscle Tissue – 1. Figure S12. Skeletal Muscle Fold Change 2: Skeletal Fold Change Analysis in Muscle Tissue – 2. Figure S13. OMIM gene data analysis: OMIM data analysis including random selector. Figure S14. OMIM gene data analysis – closeup: OMIM data analysis including random selector zoomed in version. Figure S15. Robustness analysis results: Table in the figure shows number of reactions in each replicate models and the bar plot gives clear visualization of the same.(PPT)Click here for additional data file.File S2(XLS)Click here for additional data file.


Methods are also required to enable the interpretation of plant transcriptome data to study how cellular metabolic activity varies under different growth conditions or even within different organs, tissues, and developmental stages. Such methods depend extensively on the accuracy with which genes have been mapped to the biochemical reactions in the plant metabolic pathways. Errors in these mappings lead to metabolic reconstructions with an inflated number of reactions and possible generation of unreliable metabolic phenotype predictions. Here we introduce a new evidence-based genome-scale metabolic reconstruction of maize, with significant improvements in the quality of the gene-reaction associations included within our model. We also present a new approach for applying our model to predict active metabolic genes based on transcriptome data. This method includes a minimal set of reactions associated with low expression genes to enable activity of a maximum number of reactions associated with high expression genes. We apply this method to construct an organ-specific model for the maize leaf, and tissue specific models for maize embryo and endosperm cells. We validate our models using fluxomics data for the endosperm and embryo, demonstrating an improved capacity of our models to fit the available fluxomics data. All models are publicly available via the DOE Systems Biology Knowledgebase and PlantSEED, and our new method is generally applicable for analysis transcript profiles from any plant, paving the way for further  The ability of a plant to grow and survive is linked to its metabolic network  and by the relative ease of sequencing a collection of cDNAs as opposed to predicting gene models in plant chromosomes  and the PlantSEED resource  an expanded and improved biomass composition; (ii) improved gene-protein-reaction associations where low confidence gene-reaction mappings based on poor evidence or purely computational predictions have been removed; and (iii) improved compartmentalization of reactions to subcellular organelles based on a combination of literature evidence, curation, and gapfilling algorithms. The improved gene-reaction associations in our new model were critical to our use of maize transcript profiles  sets the bounds on the flux through reaction i, where vi is the flux and zi is a binary use variable equal to zero when the flux is zero and equal to one otherwise. Equation (3) ensures that the forward and backward components of the same reaction may not both be active at the same time; in our formulation, this constraint is the sole reason for using binary variables. Equation (4) establishes the growth conditions for the gapfilling analysis; metabolites present in the growth media  have a γi of 1 in Equation (4). Otherwise γi is zero.Equation (1) represents the mass balance constraints, where In addition to these standard constraints, we applied a new constraint that introduces a slack flux for all reactions found in the original un-gapfilled model:i  and the slack flux for reaction i (δi) must be greater than or equal to 0.01. As a result of this constraint, a reaction can only have a net flux of zero if the corresponding slack flux is 0.01. Thus, the slack flux is a variable used to identify reactions that carry no flux in the model. We utilize this new slack flux for this purpose in the objective function for our gapfilling.Equation (5) states that the sum of the net flux through reaction activate, i, dictates the cost of leaving a gene-associated reaction inactive, while the gapfilling coefficient, γgapfill, i, dictates the cost of adding a gapfilled reaction to the model. In our gapfilling studies, we set γactivate, i equal to one for all gene-associated reactions, while we computed γgapfill, i as described in our previous work  –(9), the reaction expression score, Reactions with an expression score falling below 0.2 were categorized as being “low expression.” Biologically, a score of 0.2 means that the critical genes associated with the reaction are expressed at 20% of their average expression across all 37 conditions included in our transcriptomics data. This represents a conservative calling of “low expression” genes. We then applied the gapfilling algorithm as described in Equations (1)–(6) with two modifications: (i) the mass-balance constraints encoded by Equation (1) only included the stoichiometry of the reactions in the gapfilled full genome model (stoichiometry was not expanded to include the entire biochemistry database as done in full gapfilling); and (ii) the objective function was altered to maximize the high expression reaction activity while minimizing flux through low-expression reactions (Equation 10).a in our objective function, which scales the cost of leaving some high expression reactions inactive against the cost of activating some low expression reactions. We explored values for a ranging from 0.01 to 0.25, with only minimal effect on the solutions produced. We found an a of 0.1 generated the most well-balanced solutions.Similar to our gapfilling formulation, this objective function minimizes the flux through the low expression reactions while also minimizing the slack fluxes associated with all high expression reactions. This maximizes the number of high expression reactions with a non-zero flux while setting the flux through as many low expression reactions as possible to zero. Again, we use a scaling factor In order to calculate how well the metabolic model can match experimentally measured flux data for a list of specific reactions, we applied a QP where we minimized the distance between the predicted fluxes and the experimentally measured fluxes. The QP utilized the standard FBA constraints:Nmodel is the stoichiometry matrix for all model reactions and v is the vector of fluxes through all model reactions. Unlike our gapfilling formulation, in this study, reversible reactions were not decomposed. Equation (12) represents the bounds on the flux through each reaction, with the lower bound vmin, i being zero if a reaction is irreversible and −1000 is a reaction is reversible. As in our gapfilling formulation, Equation (13) sets the bounds of uptake of nutrients from the environment.Equation (11) represents our mass balance constraints, where iv) from the experimentally measured fluxes :In the quadratic objective function of our QP, we minimize the deviation of our predicted fluxes , and we added reactions to the appropriate compartment whenever they were associated with a localized gene. We find that the gene localization data led to more than 700 reactions being placed in new locations that are not otherwise designated in the databases and published models used as sources; the “None” column in Figure By using the protein localization data collected from various sources, we were able to confirm the presence of ~2000 reactions in eight compartments . We collected gene localization data for 12,398 As stated above, we wish to refine our Full metabolic reconstructions to only contain reactions with reliable evidence for gene-reaction associations. Almost every gene-reaction association found in KEGG, and in any plant BioCyc databases that is not AraCyc, are computationally predicted  and Mevalonate diphosphate decarboxylase (MVD) localize to the peroxisomes  that attempts to generate biomass and simultaneously activate all reactions with associated genes. The pathway gapfilling recommended reactions to add to our models to produce biomass and improve the function of all the pathways included in the model. We tested our gapfilled models by simulating growth on heterotrophic media in the KBase environment before applying the transcript profiles.http://qteller.com/, downloaded on 02/04/2014). The data consists of 37 experiments from nine sources, covering a range of cells, tissues, organs, and conditions. As an initial exploration of how the transcript profiles may affect a transcriptome-based model, we computed, for each of the datasets, and at 10 different thresholds, the number of reactions in the genome-scale Full and Evidenced metabolic models for maize that would be active in the organ or tissue, and conditions from which the transcript profiles were retrieved , which is an important reminder that, when performing in silico experiments using transcript profiles, one must ensure they come from the same source.We built transcriptome-based metabolic reconstructions of maize, derived directly from the gapfilled genome-scale Evidenced metabolic model, such that each transcriptome-based model will be a subset of the Evidenced metabolic model. To generate these transcriptome-based metabolic reconstructions, we used RNA-Seq data collated at qTeller . Finally, further evidence was used to deduce the biomass fraction of inositol Teas, .The cell wall of maize is considered to contain two main types of phenolic derivatives: p-coumaric acid and ferulic acid . We used these three transcript profiles in particular because they came from the same experiments and, therefore, were processed in a similar manner.We used the novel transcriptome-based gapfilling approach  along with three separate transcript profiles to generate metabolic models that are specific to the leaf, endosperm and embryo, which are named “Leaves 20-day old seedling – field,” “Endosperm 25 days after pollination,” and “Embryo 25 days after pollination”  to generate three separate metabolic models that can grow in heterotrophic media. All three metabolic models contained an average of 2302 reactions Table , which iWe have described a process that generates and refines metabolic models in three steps, generating metabolic models at each step. We can now show how these metabolic models not only compare with fluxomics data, but how that comparison improves at each step, resulting in transcriptome-based models with the closest fit to the original fluxomics data.14C labeling in two different tissues, the embryo and endosperm . In succession, we created two Full metabolic reconstructions for Our approach allows us to create relatively large metabolic reconstructions that compare favorably to the prior published metabolic models, albeit with a smaller set of gene-reaction associations. This enables us to apply transcriptome data with a high degree of confidence. The approach is validated by the fact that the embryo and endosperm models retained nearly every reaction of central carbon metabolism. This was done both by the body of evidence available for the gene-reaction associations, and the pathway gapfilling method which included reactions with a low expression score, but were essential to the models. Finally, it was shown that the same models can be active and able to replicate the activity observed in published experimental fluxomics datasets. To date, we believe we are the first to apply such wide-ranging body of evidence to the generation of large-scale metabolic reconstructions.http://kbase.us/), an open software and data platform that aim to enable researchers to predict and ultimately design biological function. The data is publicly available within KBase workspaces named “Maize_Tissue_Models”  and also via the PlantSEED website (http://plantseed.theseed.org). The KBase software environment allows researchers to copy the individual metabolic models and to explore the models using the suite of modeling tools available.All of our work was carried out through the DOE Systems Biology Knowledgebase (KBase; 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.


Chlamydomonas reinhardtii under varied CO2 inputs. The metabolic network model of Chlamydomonas was updated based on the genome annotation data and sensitivity analysis revealed CO2 sensitive reactions. Biological experiments were performed with cells cultivated at 0.04% (air), 2.5, 5, 8, and 10% CO2 concentration under controlled conditions and cell growth profiles and biomass content were measured. Pigments, lipids, proteins, and starch were further quantified for the reference low (0.04%) and high (10%) CO2 conditions. The expression level of candidate genes of sensitive reactions was measured and validated by quantitative real time PCR. The sensitive analysis revealed mitochondrial compartment as the major affected by changes on the CO2 concentrations and glycolysis/gluconeogenesis, glyoxylate, and dicarboxylate metabolism among the affected metabolic pathways. Genes coding for glycerate kinase (GLYK), glycine cleavage system, H-protein (GCSH), NAD-dependent malate dehydrogenase (MDH3), low-CO2 inducible protein A (LCIA), carbonic anhydrase 5 (CAH5), E1 component, alpha subunit (PDC3), dual function alcohol dehydrogenase/acetaldehyde dehydrogenase (ADH1), and phosphoglucomutase (GPM2), were defined, among other genes, as sensitive nodes in the metabolic network simulations. These genes were experimentally responsive to the changes in the carbon fluxes in the system. We performed metabolomics analysis using mass spectrometry validating the modulation of carbon dioxide responsive pathways and metabolites. The changes on CO2 levels mostly affected the metabolism of amino acids found in the photorespiration pathway. Our updated metabolic network was compared to previous model and it showed more consistent results once considering the experimental data. Possible roles of the sensitive pathways in the biomass metabolism are discussed.The development of microalgae sustainable applications needs better understanding of microalgae biology. Moreover, how cells coordinate their metabolism toward biomass accumulation is not fully understood. In this present study, flux balance analysis (FBA) was performed to identify sensitive metabolic pathways of  BiomassChlamydomonas reinhardtii has been extensively considered as a model organism to the study of different cellular mechanisms under distinct environmental conditions . This approach takes in consideration a linear programming strategy to solve and describe the fluxes in a systems at steady state   enzyme by increasing the cellular inorganic carbon (Ci) pools favoring the carboxylase activity of RubisCO; thus, carbon fixation through photosynthesis. Moreover, some Ci transporters located in the plasma membranes and chloroplast have been suggested as main proteins on the carbon uptake process  were retrieved from NCBI database  and the CO2 fluxes modified to evaluate the effects of different conditions of CO2 supply at the steady state of the cell metabolism and other parameters were established as previously described  is the objective function (biomass).Where 2 level response was performed through the identification of reactions affected under different CO2 fluxes through FBA simulations. FBA was resolved at five different CO2 conditions  and the resulting magnitudes defined the CO2-sensitive reactions by the flux variation coefficient ρ  in a R'ALF Plus solo 6.7 L bioreactor  in constant and continuous illumination with cool-white LED (average 400 μE·m−2·s−1). The cultures remained in a batch mode with starting culture volume of 4 L, in open system with automatic controlled CO2 gas flow in air, no pH control and continuous stir at 60 rpm. Cell inoculation was carried out with a 10 mL pre-inoculum taken from a sample at steady state. Cells were harvested by centrifugation at the late exponential phase of cell growth (O.D.750nm ≈ 0.9) for biomass characterization.The Cell growth monitoring was performed daily with measurements of O.D. at 750 nm and cell counting using Neubauer chamber. Growth rates were calculated as previously described  or two biological replicates , each one with three technical replicates, were considered for statistical analysis.Cell pellets from 50-mL cell culture aliquots at the late exponential phase were washed three times with 2 mL of de-mineralized water to remove inorganic salts and the final cell suspension was transferred to previously weigh empty Petri dishes. Plates containing the biomass were kept overnight at 90°C, and the dry weight was measured. Three (0.04 and 10% CO2 (10%) were harvested in 50-mL aliquots  and centrifuged at 3000 × g in a swing rotor bench centrifuge for 5 min at 4°C. Cell pellets were kept at −80°C until further processing. Frozen cell pellets were macerated until conversion into a light green powder. Protein extraction was performed using a buffer containing 100 mM Tris pH 7.5, 4 mM EDTA, 5 mM 2-mercaptoethanol, 10% glycerol, and 0.05% Triton X-100. Protein content was determined by Bradford assay  and high CO2 changes [low CO2  and high CO2 (10% CO2)] were selected to further gene expression analysis through the relative quantification by qRT-PCR. These candidate genes were previously annotated to the following routes and mechanisms: CCM, Calvin cycle, Glycolysis/Gluconeogenesis metabolism, and Glyoxylate/dicarboxylated.Based on our results on the sensitivity analysis using FBA approach on the model described by Chang et al.  and litewww.quantprime.de) following the criteria as follows: Tm = 60 ± 1°C, length 18–25 bases, preferentially on exon-exon junctions. When possible, primers were designed to have a GC content of 45–55%, generating a single PCR product sizing between 60 and 150 bp. Primers were synthesized by Macrogen .Cells for RNA extraction were harvested in 2-mL aliquots by centrifugation for 2 min, 3000 × g, at 4°C, and the cell pellets were immediately frozen and kept at −80°C until further use. Total RNA extraction was performed using the RNeasy Plant Mini Kit  as previously described  as primer for the synthesis of the first complementary DNA strand. Two genes [Actin (ACT) and Ubiquitin protein ligase (UBQ)] were selected as reference genes. All the cDNA samples were amplified in 96-well plates in an Applied BioSystems ABI7500 FAST system. The qPCR reaction was carried out in 10 μL containing 1 μM primers and SYBR Green qPCR Master Mix (Roche). The primer sequences used in this study are presented in Supplemental Table 2) were performed.Three micrograms of total RNA were used for cDNA synthesis employing the SuperScript III First Strand System  according to the manufacturer's instructions, using oligo-(dT750 ≈ 0.9) at low (0.04%) and high CO2 concentration (10%). Metabolites were extracted with methanol-chloroform-water HPLC grade (2.5:1:1.4) mixture and three biological replicates for low CO2 (0.04%) and two biological replicates for high CO2 (10%) were considered. Samples were immediately frozen in liquid nitrogen and lyophilized for storage. Extraction and derivatization of metabolites were performed as outlined previously , coupled to an Agilent 7890 A gas chromatograph—Leco Pegasus HT time-of-flight mass spectrometer . Identical chromatogram acquisition parameters were used as those previously described  or PMN (http://pmn.plantcyc.org/CHLAMY/) that report proteins and curated metabolic data, showed that only a small group of enzymes of Chlamydomonas has been discovered and functionally characterized. Considering this, our homology analysis was performed comparing all annotated proteins in KEGG database to identify the EC numbers and the associated reactions. In order to simplify the reconstruction, only the reactions with reported reactants in Chang et al.  were associated. After removing the reactions that already exist in the work of Chang et al. , 1803 neChlamydomonas. These results indicated that manual curation is still necessary and mandatory to guarantee feasible models.We found that some reactions and metabolites have generic names in KEGG database, especially those associated to lipid and starch metabolism. This inconsistent information provides new reactions and metabolites that cannot be interconnected affecting viable results from the FBA analysis. Gaps within the different pathways were observed when looking at the rows of the stoichiometric matrix and manual interconnection had to be assumed to consume products based on metabolic maps. Furthermore, unlikely reactions were found associated to homology parameters, reactions belonging to penicillin, and cephalosporin biosynthesis were rejected because no information was confronted with 2 input fluxes. However, in our complemented reconstruction, more, and novel sensitive reactions appeared related to the amino acid metabolism of alanine, threonine, tryptophan, and propionate metabolism  , and transport of compounds such as ethanol, ammonia, and O2. The mitochondria is important to the maintenance of intracellular redox gradients, impacting the rates of photorespiration, and efficiency of photosynthesis , reaching the highest content when evaluated at 10% ; this information corroborate previous results  and high (10%) CO2 conditions, showed a positive increase at high CO2 concentration. However, no significant changes were found for starch . Moreover, we observed that cell culture at 5% CO2 produced similar amounts of total biomass than cells cultured at 10% CO2, suggesting the existence of a saturation trend in the biomass production once cells are cultivated in CO2 concentration higher than 5%.Cell growth was measured daily Figure  and a si% Figure . Therefo2 conditions  showed similar profiles but cellular density was higher and statistically different from those cell cultures under low CO2 (0.04%). Thus, the exposure to high CO2 lead to an increased number of cells per culture volume and enhanced cellular capability to accumulate biomass, likely affecting mitosis-related cell cycle and energy metabolism.Furthermore, the cell growth curves observed on high CO2 sensitive metabolic reactions included gene expression analysis of selected genes and a metabolomics approach focused in the identification and relative quantification of the main metabolites of primary metabolism.The experimental validation of our results on the identification of CO2 related mechanisms may be determinant to biomass accumulation and CAHs play an important role on cellular carbon uptake . Similar results were shown by previous studies on the Carbon Concentrating Mechanism , glycine cleavage system, H-protein (GCSH), NAD-dependent malate dehydrogenase (MDH3), low-CO2 inducible protein A (LCIA), low-CO2-inducible protein 23 (LCI23), mitochondrial pyruvate dehydrogenase complex, E1 component, alpha subunit (PDC3), fructose-1,6-bisphosphate aldolase (FBA2), glyceraldehyde-3-phosphate dehydrogenase (GAP1), dual function alcohol dehydrogenase/acetaldehyde dehydrogenase (ADH1), and phosphoglucomutase (GPM2), were defined as sensitive nodes in the metabolic network simulations and found to be responsive to the changes in the carbon fluxes in the system.In Figure As discussed previously, the sensitivity analysis may generate different outputs depending on the completeness of the metabolic network used as input for simulation. Genes coding for GLN1, CIS1, ATP2, PRK1, and FBP1, which were found to be sensitive in Chang et al. , showed 2 concentrations. The metabolomics analysis performed using GC-TOF-MS permitted the quantification of 67 metabolites in the two compared CO2 concentrations  and high (10%) CO2 sensitive reactions of 13 out of the 67 metabolites identified. Our model was able to predict the behavior of these 13 metabolites at high and low CO2 concentrations regarding the amount and presence within the cells, being consistent with experimental results at the two growth conditions, except for the measurements of glycine, isocitrate, and sucrose, which were not good represented by the FBA.We further explored the CO2) and 50% of these did not show any alteration through FBA. From this perspective, it is shown that the model assumptions in general terms seem to be consistent with real behavior of maximizing biomass. However, others mechanisms may be activated resulting in saturation trends for CO2 processing and constraints.Other 50 metabolites quantified did not show significant differences between the two growth conditions  in order to satisfy the model constraints. The magnitude of the fluxes are >0 and are contributing to maximize the biomass function. Special attention to those magnitudes were taken into account for glycine transport from chloroplast to mitochondria, serine transport from mitochondria to chloroplast, hydroxypyruvate production, glycerate, and 3-phospoglycerate production in the chloroplast. All these processes may be related to photorespiration and showed positive fluxes in both Chang et al. and our complemented metabolic network models. Although genomic-scale restriction was not considered in the FBA, it is shown that these routes contribute to maximize biomass production.FBA analysis indicated that at low and high CO2 concentrations in the biomass composition of C. reinhardtii cells. Moreover, we identified candidate genes sensitive to the variations on the CO2 concentrations through the use of FBA in an extended metabolic network model presented here. Further experimental validation through gene expression analysis and metabolomics was performed. Our experimental results suggested that cells at high CO2 have increased capability toward biomass production. However, it also indicated that cells cultivated at CO2 concentrations higher than 5% achieved a saturation trend on total biomass accumulation. Although our FBA model was unable to describe this saturation trend, the magnitudes of the growth rate values were consistent between the different CO2 concentrations compared. This may be explained by the fact that the model was resolved using linear optimization and a change in input values, such as any external metabolite, represents a proportional increase in the objective function.In the present work, we compared the effects of varying CO2 concentrations. For the new sensitive routes and genes identified by our FBA, it was noted that many reactions were associated with energy metabolism. These sensitive routes have a number of genes which expression may be affected. Therefore, these genes may be interesting candidates on further biotechnological applications focused in the enhancement of biomass production. Reactions associated to the transport of amino acids, pyruvate, and carboxylate species into the mitochondria and chloroplast were shown to be the most sensitive ones. Moreover, mitochondria resulted as the most sensitive compartment as most reactions detected in our sensitive analysis may occur inside this organelle. Mitochondria presents a fundamental role in growth and biomass production, through its role on energy metabolism.Our results on the FBA sensitivity analysis of the two metabolic reconstructions showed a significant increase of flux in metabolic routes occurring in the chloroplast and mitochondria transport systems, including TCA cycle, glycolysis/gluconeogenesis, and amino acids biosynthesis in cells under high COSensitivity analysis also revealed a high dependence on the metabolic network quality and completeness on the identification of key routes. These routes can vary in differing models making it difficult to achieve consistent results; however, consensus in some main nodes were found and validated by qRT-PCR. Thus, our results revealed novel biochemical routes and candidate genes that may be relate to biomass production, through the modulation of the rate of biosynthetic processes.2 (10%) concentrations suggest that high CO2 concentration in microalgae cell culture may trigger mechanisms that are able to control the carbon fixation by the alternative synthesis of compounds that may have an inhibitory effect on the photosynthesis, or may enhance energy losses through photorespiration. These processes may have a role in the control of the cell biomass content and microalgae cell population, even under non-limiting availability of CO2. Further experiments are now necessary to provide more evidences of these effects.The changes observed in the metabolite profiles of cells at low (0.04%) and high CO2 concentrations. It was observed that many CCM-related genes are overexpressed at low CO2, indicating, as expected, that cells change their metabolism to produce enzymes involved in enhanced carbon uptake and carbonic acid conversion, instead of redirecting energy to build biomass precursors. A previous transcriptomics analysis compared Chlamydomonas cells at high (5%), low (0.05%), and very low (0.02%) CO2 concentrations  was found highly expressed at low CO2 concentration  itself does not depend on the CO2 conditions, we further compared which metabolites were modulated in the two CO2 concentrations (0.04 and 10%). Our metabolomics analysis indicated that the concentration of metabolites possibly related to photorespiration or other alternative route is modulated in response to high CO2 concentration.Besides the identification and validation of the expression of the main CA's under low and high CO2 concentration, indicating possible enhanced needs for light absorption and carbon fixation. However, starch content showed no significant changes which imply that the continuous light conditions may lead cells to control their carbohydrate stocks, probably due to the absence of a dark period and reduced need for starch accumulation or through the activation of alternative processes of carbon usage.Our results on the experimental biomass characterization showed that the pigment content per cell is the most sensitive component and its amount is almost duplicated at high CO2. The control of biomass accumulation may be closely connected to the regulation of biochemical pathways occurring in the mitochondria and the use of energy sources toward the accumulation of proteins and pigments.Altogether, these findings suggest that biomass accumulation does not enhances indefinitely with the enhanced availability of COFW, AG: conceived and designed the work; FW, DP, MM: performed experiments; FW and DP: drafted the manuscript; CC: performed metabolomics analysis; FW, DR, DP, AG: performed data analysis. All authors have read and approved the final version of the manuscript.This project was funded by Universidad de los Andes and FAPESP.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.


Constraint-based analysis of genome-scale metabolic models has become a key methodology to gain insights into functions, capabilities, and properties of cellular metabolism. Since their inception, the size and complexity of genome-scale metabolic reconstructions has significantly increased, with a concomitant increase in computational effort required for their analysis. Many stoichiometric methods cannot be applied to large networks comprising several thousand reactions. Furthermore, basic principles of an organism’s metabolism can sometimes be easier studied in smaller models focusing on central metabolism. Therefore, an automated and unbiased reduction procedure delivering meaningful core networks from well-curated genome-scale reconstructions is highly desirable.NetworkReducer, a new algorithm for an automated reduction of metabolic reconstructions to obtain smaller models capturing the central metabolism or other metabolic modules of interest. The algorithm takes as input a network model and a list of protected elements and functions (phenotypes) and applies a pruning step followed by an optional compression step. Network pruning removes elements of the network that are dispensable for the protected functions and delivers a subnetwork of the full system. Loss-free network compression further reduces the network size but not the complexity (dimension) of the solution space. As a proof of concept, we applied NetworkReducer to the iAF1260 genome-scale model of Escherichia coli  to obtain a reduced model that (i) allows the same maximal growth rates under aerobic and anaerobic conditions as in the full model, and (ii) preserves a protected set of reactions representing the central carbon metabolism. The reduced representation comprises 85 metabolites and 105 reactions which we compare to a manually derived E. coli core model. As one particular strength of our approach, NetworkReducer derives a condensed biomass synthesis reaction that is consistent with the full genome-scale model. In a second case study, we reduced a genome-scale model of the cyanobacterium Synechocystis sp. PCC 6803 to obtain a small metabolic module comprising photosynthetic core reactions and the Calvin-Benson cycle allowing synthesis of both biomass and a biofuel (ethanol).Here we present NetworkReducer algorithm provides a valuable tool for the application of computationally expensive analyses, for educational purposes, as well to identify core models for kinetic modeling and isotopic tracer experiments.Although only genome-scale models provide a complete description of an organism’s metabolic capabilities, an unbiased stoichiometric reduction of large-scale metabolic models is highly useful. We are confident that the The online version of this article (doi:10.1186/s12918-015-0191-x) contains supplementary material, which is available to authorized users. Escherichia coli (E. coli). The first E. coli genome-scale model (iJE660) was published in 2000  and added then also a reaction to “export” this biomass compound. This configuration makes it easier to configure biomass synthesis as a protected function and to keep track of the stoichiometric coefficient of the biomass compound during network compression. The final stoichiometric matrix of the genome-scale model (in the following denoted by ColiGS) was thus slightly extended to 2384 x 1669. Flux constraints in the ColiGS model were specified such that glucose serves as the only carbon substrate.We considered the network spanned by the reactions contained in the ColiCore model contains uptake reactions for glucose but also for some other substrates (including some amino acids). Since we aimed to focus on glucose as the sole carbon substrate, we removed all reactions and metabolites from the ColiCore model that are involved in uptake of these substrates. Analogously to the ColiGS model, we also included a biomass metabolite in the biomass synthesis reaction and a corresponding “biomass export” reaction. With these changes, the final dimension of the ColiCore model was 88 reactions and 69 internal metabolites. Key properties of ColiGS and ColiCore are summarized in Table The ColiGS network could be started. Phenotypes and elements of the genome-scale model to be maintained in the reduced model were specified as follows. All 88 reactions of the ColiCore model were marked as protected reactions (PR ) in the ColiGS model and we also demanded that all these reactions should be feasible (unblocked) in the reduced network. Since all metabolites involved in these reactions are implicitly protected as well we did not explicitly specify protected metabolites (PM = ∅). Concerning protected phenotypes, we demanded that (i) at least 99.9 % of the maximal growth rate  at least 99.9 % of the maximal growth rate in the ColiGS model under anaerobic conditions (0.2309 h−1) should be reachable in the reduced network ))ColiGS nColiPruned) which already decreased the dimension of the genome-scale network from 2384 reactions / 1669 internal metabolites to 455 reactions / 438 internal metabolites. As demanded, the maximal growth rates under aerobic and anaerobic growth in ColiPruned are identical (anaerobic) or very close (aerobic) to the respective maximal rates in the genome-scale model. The dof of ColiPruned (26) is significantly smaller than in ColiGS (753) and already close to the dof of ColiCore (24) indicating a similar complexity of the solution spaces of ColiPruned and ColiCore. Even though ColiPruned still contains more than 400 reactions, the  elementary modes of this network can be fully enumerated.Network reduction without applying network compression in postprocessing (only pruning) yielded a reduced network model  is much smaller compared to ColiPruned (455 reactions) while neither the dof nor the number of elementary modes and the possible phenotypes changed. The dimension of ColiPrunedComp is now very similar to ColiCore  of these additional elements arises due to a different description of exchange reactions. The ColiCore considers two compartments where metabolites are balanced (cytoplasm and extracellular space) plus (implicitly) an environment. Thus, 3 reactions and 3 balanced species are needed to describe the import of a metabolite M (Menvironment ➔ Mextracellular space ➔ Mcytoplasm) in the ColiCore model . In contrast, ColiGS contains additionally a periplasm compartment, hence, uptake of an exchange metabolite M involves 4 exchange reactions and 4 species (Menvironment ➔ Mextracellular space ➔ Mperiplasm ➔ Mcytoplasm). Since 15 metabolites can be exported/imported to/from the environment in ColiCore, 15 additional species and reactions (for the periplasmic space) must be maintained in the ColiPrunedComp model; they can also not be compressed because they are surrounded by protected reactions.ColiCore model for which we identified two reasons. First, different stoichiometries for biomass synthesis may lead to different biomass yields (discussed below). Second, we found that the remaining two additional (non-exchange) reactions in the ColiGS model not contained in the ColiCore model allow for higher maximal growth rates; these reactions were kept by the pruning algorithm to maintain the protected phenotype of maximal growth in the ColiPrunedComp model . The first of these two reactions is related to hydrogen production which turns out to be necessary to attain the maximal anaerobic growth rate. The second reaction is related to respiratory pathways. The ColiGS model contains two cytochrome oxidases (cytochrome bd and cytochrome bo3 oxidase). Both oxidize ubiquinol but with different stoichiometry for the translocated (pumped) protons:Another observation is that the genome-scale network and its derived reduced models allow higher maximal growth rates than the ColiCore model contains only reaction (ColiCore) was protected when reducing ColiGS, however, to allow maximal growth, the second reaction had also to be kept in ColiPrunedComp. In fact, integration of reaction .Clearly, the second reaction  will leareaction  translocreaction  in the CColiCore and ColiPrunedComp. For the case of ColiCore, the stoichiometric coefficients of the precursor metabolites  in the BSR had to be calculated manually from the known requirements of monomers  in the genome-scale BSR. Accordingly, Orth et al. wrote [Since most of the subunits of the cellular macromolecules, such as nucleic acids and amino acids, are not present in the core model, they could not be directly accounted for the biomass reaction. The metabolites in the core model that those macromolecular subunits are synthesized from are included instead. These are precursor metabolites. For example, the amino acid L-alanine is synthesized from pyruvate and L-glutamate, so both of these metabolites are consumed in the biomass reaction.”These remaining discrepancies can be attributed to different stoichiometric coefficients in the biomass synthesis reaction (BSR) of l. wrote : “Since ColiCore and ColiPrunedComp to identify and understand possible sources of different stoichiometries.Hence, molecules such as amino acids contained in the genome-scale BSR must be translated into a stoichiometric demand for compounds present in the reduced model. Making this translation manually in a genome-scale model is an error-prone and tedious task and an automated approach as ours supports this step and provides a rigorous approach to obtain a BSR in the compressed network that is consistent with the BSR of the full model. We directly compared the BSRs of ColiCore and of the ColiPrunedComp model , it is one advantage of our algorithm that these condensed material balances are automatically calculated and still visible in the reduced model. Note that the (cumulative) amount of periplasmatic protons (H_p) consumed in the condensed BSR of ColiPrunedComp is related to antiport uptake of trace elements.One major difference is that the BSR of ColiCore uses glyceraldehyde-3-phosphate (G3P) as a precursor (− 0.129) whereas ColiPrunedComp uses instead dihydroxyacetone-phosphate with a similar amount (−0.141). Since both metabolites can be converted into each other by a triose-isomerase reaction, both metabolites can in fact be used as precursors. A similar relationship exists for Ribose-5-phosphate (R5P) and Ribulose-5-phosphate (Ru5P). Ru5P occurs only in the BSR of ColiPrunedComp but, due to a simple isomerase reaction between both metabolites, could also be integrated in the value of R5P which is consumed in both BSRs.Further differences in the BSRs may arise by non-unique ways of representing precursor stoichiometries due to different reference points. For example, ColiCore seems to slightly underestimate the demand for most precursors and, to a larger extent, for energy (ATP). On the other hand, the core model consumes a significantly larger amount of NADPH and NADH which, in the final balance and biomass yield, could partially compensate the lower demand for some precursors. As mentioned above, would we add the high efficiency oxidase reaction  would be slightly higher than in the ColiPrunedComp model (0.9288 h−1). We emphasize that we do not claim that the BSR of ColiPrunedComp is necessarily “better” or more realistic than the BSR of the ColiCore model in [ColiCore model which may have led to discrepancies with the condensed BSR calculated herein. Nonetheless, the condensed BSR obtained with the NetworkReducer algorithm is consistent with the full model and allows for quantitative comparisons. Our algorithm thus facilitates the unbiased and reproducible calculation of condensed BSR stoichiometries in reduced network models from their genome-scale representation.Despite those explainable differences, the BSR of reaction  in the Cmodel in . It is pColiPrunedComp we exemplarily perfomed flux variability analyses for three different growth scenarios and compared the results with the original genome-scale model . Such a strongly reduced model may be useful to study basic principles and stoichiometries of, for example, coupled synthesis of biomass and biofuels . The gesee e.g.  (in the see e.g. ) served μmax is the maximal growth rate for a photon uptake of 100 mmol/gDW/h), andrmaxEthanol is the maximal ethanol production rate for a photon uptake of 100 mmol/gDW/h).Since the goal was to extract a network module that represents the Calvin cycle and enables maximal phototrophic growth as well as maximal production of ethanol we protected all reactions of the Calvin Cycle, the pathway to ethanol, biomass and ethanol excretion, and light uptake  is much lower than in the NetworkReducer, a new algorithm for automated reduction of large-scale metabolic network models to obtain meaningful small- or medium-scale models, typically representing the central metabolism or certain modules of interest. The algorithm consists of (i) a pruning step followed by (ii) network compression. Network pruning removes elements of the network that are dispensible for a user-defined set of protected properties and parts. Our algorithm accepts various criteria for specifying protected features. In particular, inequalities as in eqs.  if these are not protected. Network compression works loss-free, that is none of the feasible phenotypes and functions is lost, however, the resulting network is generally not a proper subnetwork of the full system and a mapping of flux distributions (and reactions) between the compressed and the full network can be cumbersome. It will depend on the application whether network compression is applied to the pruned network or not. If, for example, elementary modes are to be calculated in a network, loss-free compression algorithms are commonly used in a preprocessing step , 17. In Whereas network compression delivers always a unique result, the outcome of the network pruning step can be unique or non-unique, depending on network structure, input parameters, and protected functions and parts. Although reactions are removed in the order of their flux range , reactions with identical flux ranges may exist  from which then one is chosen randomly.E. coli case study demonstrated the applicability and potential of our approach. We reduced the genome-scale reconstruction iAF1260 of Feist et al. [E. coli core model. The reactions and metabolites to be maintained were taken from the core model proposed by Orth et al. [iAF1260 serving as a basis. With the protected phenotype that the maximal growth rates of iAF1260 under aerobic and anaerobic conditions must be achievable also in the condensed model, we used our algorithm to reduce the iAF1260 model to its core and compared it with the model of Orth et al. We found a generally good agreement between the manually and the automatically derived model but also some discrepancies. Essentially, two reactions of the iAF1260 not contained in the Orth model were retained by NetworkReducer to ensure that the maximal growth rates can be achieved. Furthermore, the stoichiometries in the condensed biomass synthesis reactions (BSRs) showed some differences. With our algorithm we can ensure that the condensed BSR fully reflects the stoichiometries of the BSR of the original network thus leading also to the same maximal growth rates and biomass yields. The E. coli case study demonstrated the value of our approach for obtaining a fast , unbiased, and exact network reduction.The t et al.  to an E.E. coli study as a typical application scenario for our method, namely to reduce a genome-scale network to its core  thereby protecting important properties such as  biomass or/and product yields. In the general case, a prerequisit is the careful delineation of the central metabolism (to be protected) in the genome-scale network which, however, should be possible for many organisms from prior biological knowledge. Many other reduction problems can be defined as well by using appropriate criteria for protected functions and parts. For example, instead of (or in addition to) the central metabolism, certain modules of a large-scale model  might be maintained in a high resolution while the rest is condensed. The presented case study of extracting a subnetwork of the cyanobacterial metabolism that comprises the Calvin cycle and allows for biomass and biofuel (ethanol) synthesis demonstrated that such an application is also supported by our algorithm. Such extracted subnetworks are also useful for the construction of kinetic models of specific parts of metabolism, while preserving consistency with a genome-scale reconstruction.We consider the NetworkReducer would be to compress the full network of an organism to just one single overall reaction consuming external metabolites  and synthesizing biomass with maximal yield. To simulate this maximal reduction, we again specified maximal aerobic biomass synthesis in E. coli as desired phenotype (ATP maintenance demand was not considered) and protected (only) the biomass export reaction. As a result, a “network” with only one overall reaction was maintained which exclusively converts external substrates and nutrients to external products The stoichiometry of this fully condensed BSR with one degree of freedom (ColiPrunedComp_DOF1) can be found in the An extreme application of NetworkReducer represents a valuable tool for stoichiometric and constraint-based modeling of metabolic networks.Although only genome-scale models can provide a complete view on the full functionality of a metabolic network there are several reasons why reduction of large-scale models can be useful or even necessary. First, computationally extensive analyses, such as full enumeration of elementary modes for metabolic pathway analysis, may only be tractable in smaller models. Methods of metabolic flux analysis seeking to calculate internal metabolic fluxes based on measurements of extracellular fluxes or/and on data from isotopic tracer experiments are able to resolve metabolic fluxes for smaller (core) networks only. Smaller models are also useful for didactic or educational purposes  and, in


Lactococcus lactis, subject to perturbations and brief periods of starvation. Supplementing existing methodologies, we show that it is possible to acquire a detailed understanding of the control properties of a corresponding metabolic pathway model that is directly based on experimental observations. In particular, we delineate the role of enzymatic regulation to maintain metabolic stability and metabolic recovery after periods of starvation. It is shown that the feedforward activation of the pyruvate kinase by fructose-1,6-bisphosphate qualitatively alters the bifurcation structure of the corresponding pathway model, indicating a crucial role of enzymatic regulation to prevent metabolic collapse for low external concentrations of glucose. We argue that similar probabilistic methodologies will help our understanding of dynamic properties of small-, medium- and large-scale metabolic networks models.Metabolic pathways are complex dynamic systems whose response to perturbations and environmental challenges are governed by multiple interdependencies between enzyme properties, reactions rates, and substrate levels. Understanding the dynamics arising from such a network can be greatly enhanced by the construction of a computational model that embodies the properties of the respective system. Such models aim to incorporate mechanistic details of cellular interactions to mimic the temporal behavior of the biochemical reaction system and usually require substantial knowledge of kinetic parameters to allow meaningful conclusions. Several approaches have been suggested to overcome the severe data requirements of kinetic modeling, including the use of approximative kinetics and Monte-Carlo sampling of reaction parameters. In this work, we employ a probabilistic approach to study the response of a complex metabolic system, the central metabolism of the lactic acid bacterium  Lactococcus lactisin-silico representation of the pathway is obtained. Despite considerable efforts, however, the construction of such models is still hampered by the extensive data requirements necessary to parametrize each enzymatic step. Several approaches have been suggested to alleviate this problem, including the use of approximative kinetics Lactic acid bacteria (LAB) are industrially important microorganisms used in the fermentation of milk, meat, and certain vegetables Lactococcus lactis. In particular, we seek to understand how allosteric regulation, together with its associated feedback and feedforward loops, influence the control exerted by the various enzymatic steps. Making only minimal assumptions about rate equations and kinetic parameters, and data from direct experimentation, we show that it is possible to study and elucidate the control properties of a metabolic pathway. In a second step, we investigate the dynamics of a corresponding kinetic pathway model in periods of starvation and show that allosteric control and regulatory interactions are crucial to maintaining metabolic viability in times of nutrient scarcity. Our probabilistic approach directly builds upon measured properties, such as the concentrations of metabolic intermediates and flux distributions, rather than enzyme-kinetic parameters, to constrain the possible dynamics of a metabolic pathway. We demonstrate that (i) the control coefficients of biochemical network models show intelligible patterns and trends that are accessible without detailed knowledge of enzyme-kinetic parameters; (ii) the regulatory structure of a biochemical network models has profound effects on the possible dynamics that are largely independent of specific kinetic parameters; and (iii) more specifically, that the topology of the regulation network is instrumental to ensure the stability of an observed state and to enable the patwhay to survive periods of starvation. We expect that our methodology will be of high utility to elucidate and understand the dynamic and regulatory properties that enable large-scale metabolic networks to function reliably in uncertain environments.Building upon these methods, we aim to elucidate and understand the regulatory properties of the central metabolism of the lactic acid bacterium Lactococcus lactis, defined here as the carbon and energy metabolism of this organism that generates most of its free-energy and C3 carbon precursors during fermentative growth. Drawing upon earlier kinetic models L. lactis was selected. A graphical overview is shown in The starting point of our analysis is a stoichiometric representation of the central metabolism of L. lactis central metabolism. Fructose 1,6-bisphosphate (FBP) activates the formation of pyruvate (PYR) by the pyruvate kinase (PYK), activates the conversion from PYR to LAC by the lactate dehydrogenase (LDH), and inhibits the phosphotransferase system (PTS). A potentially important regulator is the concentration of free phosphate. In our model, the total pool of phosphate is constant, therefore the concentration of free inorganic phosphate (Pi) is an (inverse) measure of the amount of the glycolytic intermediates plus ATP. Further reactions that are under regulatory control include the pyruvate dehydrogenase (PDH), as well as the alcohol dehydrogenases (ADH). A complete list of all regulatory interactions is summarized in Beyond the reaction stoichiometries, our model incorporates the currently known regulatory features found in flux control coefficientsTo quantify the extent to which a system property, such as a specific flux or metabolite concentration, is influenced by a specific enzymatic step, we make use of the concepts of Metabolic Control Analysis (MCA). The control coefficient The resulting distribution of flux control coefficients allows us to assess, qualitative and fairly independent of the precise values of the enzyme kinetic parameters, the potential effects of perturbations in enzyme levels on the system flux at the metabolic state. Most importantly, the distributions of the control coefficients were not arbitrarily. Rather, the results shown in L. lactisWe emphasize that the probabilistic distributions shown in las operon, were shown to have no significant control on the glycolytic flux in exponentially growing cells E. coliL. lactis do seem to be consistent with the bulk of the respective distribution.Using a series of mutants with altered GAPDH activity, Solem et al. (2003) As a rather counter-intuitive finding, the distribution of control coefficients indicates that for most sets of parameters the PTS would exert a negative control on flux through the pathway. This finding is in contrast to our expectation that an increase in PTS activity results in higher glucose uptake, hence an increased flux through glycolysis. These results emphasize that the control coefficients are indeed systemic properties of the pathway and may exhibit non-intuitive patterns, depending on the specific metabolic phenotype and details of the pathway stoichiometry and regulation. To verify that the non-intuitive distribution of the influence of the glucose transport upon the glycolytic flux is indeed a true feature of the pathway model, we varied the maximal velocity  the inhibition of PYK by inorganic phosphate, (ii) the activation of PYK by FBP and (iii) the inhibition of PTS by FBP. We showed that in cases of non-recovery the zero-flux metabolic state is an attractor for the system. In the presence of regulation the ability of the system to escape metabolic death is, in the overwhelming number of cases, mirrored by the absence of such attractor.In this sense, we argue that our approach has led to increased understanding of principles of metabolic regulation in typical, given no further knowledge about specific constraints the system is subject to – a tremendously useful information when interpreting experimentally observed data. In this respect, some of the probabilistic distributions are in line with what we expect given the topology of the network, while other properties are counter-intuitive and therefore point the direction for further investigation. Our approach is particularly suited to investigate the qualitative effects that result from changes in pathway topology, in particular from the presence or absence of regulatory interactions. Our computational approach is straightforward to implement and numerically efficient even for large systems. We therefore expect it to be of high utility also in other studies of metabolic, gene-expression and signal transduction systems.In summary, sampling unknown kinetic parameters for a kinetic model of a metabolic pathway, such that all sampled parameters give rise to the same metabolic state, can lead to fundamental insights into the control properties of the underlying system. In particular, the emergent control profile exhibits a structure that helps us to draw conclusions about the possible behavior of the system. The probabilistic control profile represents what dynamics we should expect as Our approach consists of a series of well-defined steps and is based upon related strategies that utilize Monte-Carlo sampling in the study of metabolic networks The probabilistic approach used within this work has been described previously The control coefficients are only evaluated for stable metabolic states, characterized by an invertible Jacobian with all real parts of the eigenvalues below zero. The information required to evaluate the control coefficients therefore consists of: (i) The stoichiometry of the system, as encoded by Our probabilistic evaluation of the system is then based on the fact that the metabolic state is often directly experimentally accessible, whereas information about kinetic parameters, and hence the elasticities, is generally lacking. We therefore evaluate the possible values of the unscaled elasticities by drawing random instances of parameters and evaluating the equations for the control coefficients. In particular, we proceed along the following steps: First, each reaction is associated with a kinetic reaction equation. We adopt general Michaelis-Menten kinetics of the form The number of unknown reaction parameters typically equals the number of associated substrates, products and modifiers  was added and samples were taken at regular time intervals. 400 Bacterial dry weight was measured as described previously Fluxes for lactate, acetate, formate, pyruvate and ethanol were calculated using their fermentation broth concentration, dilution rate Click here for additional data file.Text S2A pdf document providing additional information about computational methods and results.(PDF)Click here for additional data file.File S1A zip file providing all code used in the analysis.(ZIP)Click here for additional data file.