Thirteen years of building constraint-based in silico models of Escherichia coli

A neural-mechanistic hybrid approach improving the predictive power of genome-scale metabolic models

Constraint-based metabolic models have been used for decades to predict the phenotype of microorganisms in different environments. However, quantitative predictions are limited unless labor-intensive measurements of media uptake fluxes are performed. We show how hybrid neural-mechanistic models can serve as an architecture for machine learning providing a way to improve phenotype predictions. We illustrate our hybrid models with growth rate predictions of Escherichia coli and Pseudomonas putida grown in different media and with phenotype predictions of gene knocked-out Escherichia coli mutants. Our neural-mechanistic models systematically outperform constraint-based models and require training set sizes orders of magnitude smaller than classical machine learning methods. Our hybrid approach opens a doorway to enhancing constraint-based modeling: instead of constraining mechanistic models with additional experimental measurements, our hybrid models grasp the power of machine learning while fulfilling mechanistic constrains, thus saving time and resources in typical systems biology or biological engineering projects.

The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms

The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.

DCcov: Repositioning of drugs and drug combinations for SARS-CoV-2 infected lung through constraint-based modeling

The 2019 coronavirus disease (COVID-19) became a worldwide pandemic with currently no approved effective antiviral drug. Flux balance analysis (FBA) is an efficient method to analyze metabolic networks. Here, FBA was applied on human lung cells infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to reposition metabolic drugs and drug combinations against the virus replication within the host tissue. Making use of expression datasets of infected lung tissue, genome-scale COVID-19-specific metabolic models were reconstructed. Then, host-specific essential genes and gene pairs were determined through in silico knockouts that permit reducing the viral biomass production without affecting the host biomass. Key pathways that are associated with COVID-19 severity in lung tissue are related to oxidative stress, ferroptosis, and pyrimidine metabolism. By in silico screening of Food and Drug Administration (FDA)-approved drugs on the putative disease-specific essential genes and gene pairs, 85 drugs and 52 drug combinations were predicted as promising candidates for COVID-19 (https://github.com/sysbiolux/DCcov).

Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges

This review is a part of the SI 'Genome-Scale Modeling of Microorganisms in the Real World'. The goal of GEM is the accurate prediction of the phenotype from its respective genotype under specified environmental conditions. This review focuses on the dynamic phenotype; prediction of the real-life behaviors of microorganisms, such as cell proliferation, dormancy, and mortality; balanced and unbalanced growth; steady-state and transient processes; primary and secondary metabolism; stress responses; etc. Constraint-based metabolic reconstructions were successfully started two decades ago as FBA, followed by more advanced models, but this review starts from the earlier nongenomic predecessors to show that some GEMs inherited the outdated biokinetic frameworks compromising their performances. The most essential deficiencies are: (i) an inadequate account of environmental conditions, such as various degrees of nutrients limitation and other factors shaping phenotypes; (ii) a failure to simulate the adaptive changes of MMCC (MacroMolecular Cell Composition) in response to the fluctuating environment; (iii) the misinterpretation of the SGR (Specific Growth Rate) as either a fixed constant parameter of the model or independent factor affecting the conditional expression of macromolecules; (iv) neglecting stress resistance as an important objective function; and (v) inefficient experimental verification of GEM against simple growth (constant MMCC and SGR) data. Finally, we propose several ways to improve GEMs, such as replacing the outdated Monod equation with the SCM (Synthetic Chemostat Model) that establishes the quantitative relationships between primary and secondary metabolism, growth rate and stress resistance, process kinetics, and cell composition.

Intelligent host engineering for metabolic flux optimisation in biotechnology

Optimising the function of a protein of length N amino acids by directed evolution involves navigating a 'search space' of possible sequences of some 20N. Optimising the expression levels of P proteins that materially affect host performance, each of which might also take 20 (logarithmically spaced) values, implies a similar search space of 20P. In this combinatorial sense, then, the problems of directed protein evolution and of host engineering are broadly equivalent. In practice, however, they have different means for avoiding the inevitable difficulties of implementation. The spare capacity exhibited in metabolic networks implies that host engineering may admit substantial increases in flux to targets of interest. Thus, we rehearse the relevant issues for those wishing to understand and exploit those modern genome-wide host engineering tools and thinking that have been designed and developed to optimise fluxes towards desirable products in biotechnological processes, with a focus on microbial systems. The aim throughput is 'making such biology predictable'. Strategies have been aimed at both transcription and translation, especially for regulatory processes that can affect multiple targets. However, because there is a limit on how much protein a cell can produce, increasing kcat in selected targets may be a better strategy than increasing protein expression levels for optimal host engineering.

An integrated in vivo and in silico analysis of the metabolism disrupting effects of CPI-613 on embryo-larval zebrafish (Danio rerio)

CPI-613 is a mitochondrial metabolism disrupter that inhibits tricarboxylic acid (TCA) cycle activity. The consequences of TCA cycle disruption on various metabolic pathways and overall organismal physiology are not fully known. The present study integrates in vivo experimental data with an in silico stoichiometric metabolism model of zebrafish to study the metabolic pathways perturbed under CPI-613 exposure. Embryo-larval life stages of zebrafish (Danio rerio) were exposed to 1 μM CPI-613 for 20 days. Whole-organism respirometry measurements showed an initial suppression of O₂ consumption at Day 5 of exposure, followed by recovery comparable to the solvent control (0.01% DMSO) by Day 20. Comparison of whole-transcriptome RNA-sequencing at Day 5 vs. 20 of exposure showed functional categories related to O₂ binding and transport, antioxidant activity, FAD binding, and hemoglobin complexes, to be commonly represented. Metabolic enzyme gene expression changes and O₂ consumption rate was used to parametrize two in silico stoichiometric metabolic models representative of Day 5 or 20 of exposure. Computational simulations predicted impaired ATP synthesis, α-ketoglutarate dehydrogenase (KGDH) activity, and fatty acid β-oxidation at Day 5 vs. 20 of exposure. These results show that the targeted disruption of KGDH may also impact oxidative phosphorylation (ATP synthesis) and fatty acid metabolism (β-oxidation), in turn influencing cellular bioenergetics and the observed reduction in whole-organism O₂ consumption rate. The results of this study provide an integrated in vivo and in silico framework to study the impacts of metabolic disruption on organismal physiology.

In Silico Analysis of Functionalized Hydrocarbon Production Using Ehrlich Pathway and Fatty Acid Derivatives in an Endophytic Fungus

Functionalized hydrocarbons have various ecological and industrial uses, from signaling molecules and antifungal/antibacterial agents to fuels and specialty chemicals. The potential to produce functionalized hydrocarbons using the cellulolytic, endophytic fungus, Ascocoryne sarcoides, was quantified using genome-enabled, stoichiometric modeling. In silico analysis identified available routes to produce these hydrocarbons, including both anabolic- and catabolic-associated strategies, and determined correlations between the type and size of the hydrocarbons and culturing conditions. The analysis quantified the limits of the wild-type metabolic network to produce functionalized hydrocarbons from cellulose-based substrates and identified metabolic engineering targets, including cellobiose phosphorylase (CP) and cytosolic pyruvate dehydrogenase complex (PDHcyt). CP and PDHcyt activity increased the theoretical production limits under anoxic conditions where less energy was extracted from the substrate. The incorporation of both engineering targets resulted in near-complete conservation of substrate electrons in functionalized hydrocarbons. The in silico framework was integrated with in vitro fungal batch growth experiments to support O₂ limitation and functionalized hydrocarbon production predictions. The metabolic reconstruction of this endophytic filamentous fungus describes pathways for both specific and general production strategies of 161 functionalized hydrocarbons applicable to many eukaryotic hosts.

Reaction lumping in metabolic networks for application with thermodynamic metabolic flux analysis

Thermodynamic metabolic flux analysis (TMFA) can narrow down the space of steady-state flux distributions, but requires knowledge of the standard Gibbs free energy for the modelled reactions. The latter are often not available due to unknown Gibbs free energy change of formation [Formula: see text], of metabolites. To optimize the usage of data on thermodynamics in constraining a model, reaction lumping has been proposed to eliminate metabolites with unknown [Formula: see text]. However, the lumping procedure has not been formalized nor implemented for systematic identification of lumped reactions. Here, we propose, implement, and test a combined procedure for reaction lumping, applicable to genome-scale metabolic models. It is based on identification of groups of metabolites with unknown [Formula: see text] whose elimination can be conducted independently of the others via: (1) group implementation, aiming to eliminate an entire such group, and, if this is infeasible, (2) a sequential implementation to ensure that a maximal number of metabolites with unknown [Formula: see text] are eliminated. Our comparative analysis with genome-scale metabolic models of Escherichia coli, Bacillus subtilis, and Homo sapiens shows that the combined procedure provides an efficient means for systematic identification of lumped reactions. We also demonstrate that TMFA applied to models with reactions lumped according to the proposed procedure lead to more precise predictions in comparison to the original models. The provided implementation thus ensures the reproducibility of the findings and their application with standard TMFA.

Rare genetic variants affecting urine metabolite levels link population variation to inborn errors of metabolism

Metabolite levels in urine may provide insights into genetic mechanisms shaping their related pathways. We therefore investigate the cumulative contribution of rare, exonic genetic variants on urine levels of 1487 metabolites and 53,714 metabolite ratios among 4864 GCKD study participants. Here we report the detection of 128 significant associations involving 30 unique genes, 16 of which are known to underlie inborn errors of metabolism. The 30 genes are strongly enriched for shared expression in liver and kidney (odds ratio = 65, p-FDR = 3e-7), with hepatocytes and proximal tubule cells as driving cell types. Use of UK Biobank whole-exome sequencing data links genes to diseases connected to the identified metabolites. In silico constraint-based modeling of gene knockouts in a virtual whole-body, organ-resolved metabolic human correctly predicts the observed direction of metabolite changes, highlighting the potential of linking population genetics to modeling. Our study implicates candidate variants and genes for inborn errors of metabolism.

Simultaneous cross-evaluation of heterogeneous E. coli datasets via mechanistic simulation

The extensive heterogeneity of biological data poses challenges to analysis and interpretation. Construction of a large-scale mechanistic model of Escherichia coli enabled us to integrate and cross-evaluate a massive, heterogeneous dataset based on measurements reported by various groups over decades. We identified inconsistencies with functional consequences across the data, including that the total output of the ribosomes and RNA polymerases described by data are not sufficient for a cell to reproduce measured doubling times, that measured metabolic parameters are neither fully compatible with each other nor with overall growth, and that essential proteins are absent during the cell cycle-and the cell is robust to this absence. Finally, considering these data as a whole leads to successful predictions of new experimental outcomes, in this case protein half-lives.

Current Status and Future Prospects of Genome-Scale Metabolic Modeling to Optimize the Use of Mesenchymal Stem Cells in Regenerative Medicine

Mesenchymal stem cells are a promising source for externally grown tissue replacements and patient-specific immunomodulatory treatments. This promise has not yet been fulfilled in part due to production scaling issues and the need to maintain the correct phenotype after re-implantation. One aspect of extracorporeal growth that may be manipulated to optimize cell growth and differentiation is metabolism. The metabolism of MSCs changes during and in response to differentiation and immunomodulatory changes. MSC metabolism may be linked to functional differences but how this occurs and influences MSC function remains unclear. Understanding how MSC metabolism relates to cell function is however important as metabolite availability and environmental circumstances in the body may affect the success of implantation. Genome-scale constraint based metabolic modeling can be used as a tool to fill gaps in knowledge of MSC metabolism, acting as a framework to integrate and understand various data types (e.g., genomic, transcriptomic and metabolomic). These approaches have long been used to optimize the growth and productivity of bacterial production systems and are being increasingly used to provide insights into human health research. Production of tissue for implantation using MSCs requires both optimized production of cell mass and the understanding of the patient and phenotype specific metabolic situation. This review considers the current knowledge of MSC metabolism and how it may be optimized along with the current and future uses of genome scale constraint based metabolic modeling to further this aim.

Genome-Scale Metabolic Network Models of Bacillus Species Suggest that Model Improvement is Necessary for Biotechnological Applications

Background

A genome-scale metabolic network model (GEM) is a mathematical representation of an organism’s metabolism. Today, GEMs are popular tools for computationally simulating the biotechnological processes and for predicting biochemical properties of (engineered) strains.

Objectives

In the present study, we have evaluated the predictive power of two GEMs, namely iBsu1103 (for Bacillus subtilis 168) and iMZ1055 (for Bacillus megaterium WSH002).

Materials and Methods

For comparing the predictive power of Bacillus subtilis and Bacillus megaterium GEMs, experimental data were obtained from previous wet-lab studies included in PubMed. By using these data, we set the environmental, stoichiometric and thermodynamic constraints on the models, and FBA is performed to predict the biomass production rate, and the values of other fluxes. For simulating experimental conditions in this study, COBRA toolbox was used.

Results

By using the wealth of data in the literature, we evaluated the accuracy of in silico simulations of these GEMs. Our results suggest that there are some errors in these two models which make them unreliable for predicting the biochemical capabilities of these species. The inconsistencies between experimental and computational data are even greater where B. subtilis and B. megaterium do not have similar phenotypes.

Conclusions

Our analysis suggests that literature-based improvement of genome-scale metabolic network models of the two Bacillus species is essential if these models are to be successfully applied in biotechnology and metabolic engineering.

Identification of critical connectors in the directed reaction-centric graphs of microbial metabolic networks

BACKGROUND

Detection of central nodes in asymmetrically directed biological networks depends on centrality metrics quantifying individual nodes' importance in a network. In topological analyses on metabolic networks, various centrality metrics have been mostly applied to metabolite-centric graphs. However, centrality metrics including those not depending on high connections are largely unexplored for directed reaction-centric graphs.

RESULTS

We applied directed versions of centrality metrics to directed reaction-centric graphs of microbial metabolic networks. To investigate the local role of a node, we developed a novel metric, cascade number, considering how many nodes are closed off from information flow when a particular node is removed. High modularity and scale-freeness were found in the directed reaction-centric graphs and betweenness centrality tended to belong to densely connected modules. Cascade number and bridging centrality identified cascade subnetworks controlling local information flow and irreplaceable bridging nodes between functional modules, respectively. Reactions highly ranked with bridging centrality and cascade number tended to be essential, compared to reactions that other central metrics detected.

CONCLUSIONS

We demonstrate that cascade number and bridging centrality are useful to identify key reactions controlling local information flow in directed reaction-centric graphs of microbial metabolic networks. Knowledge about the local flow connectivity and connections between local modules will contribute to understand how metabolic pathways are assembled.

Laboratory evolution reveals a two-dimensional rate-yield tradeoff in microbial metabolism

Growth rate and yield are fundamental features of microbial growth. However, we lack a mechanistic and quantitative understanding of the rate-yield relationship. Studies pairing computational predictions with experiments have shown the importance of maintenance energy and proteome allocation in explaining rate-yield tradeoffs and overflow metabolism. Recently, adaptive evolution experiments of Escherichia coli reveal a phenotypic diversity beyond what has been explained using simple models of growth rate versus yield. Here, we identify a two-dimensional rate-yield tradeoff in adapted E. coli strains where the dimensions are (A) a tradeoff between growth rate and yield and (B) a tradeoff between substrate (glucose) uptake rate and growth yield. We employ a multi-scale modeling approach, combining a previously reported coarse-grained small-scale proteome allocation model with a fine-grained genome-scale model of metabolism and gene expression (ME-model), to develop a quantitative description of the full rate-yield relationship for E. coli K-12 MG1655. The multi-scale analysis resolves the complexity of ME-model which hindered its practical use in proteome complexity analysis, and provides a mechanistic explanation of the two-dimensional tradeoff. Further, the analysis identifies modifications to the P/O ratio and the flux allocation between glycolysis and pentose phosphate pathway (PPP) as potential mechanisms that enable the tradeoff between glucose uptake rate and growth yield. Thus, the rate-yield tradeoffs that govern microbial adaptation to new environments are more complex than previously reported, and they can be understood in mechanistic detail using a multi-scale modeling approach.

This study reconciles multiple existing microbial rate-yield tradeoff theories with experimental data. There is great interest in developing quantitative descriptions of the relationship between growth rate and growth yield [1]. However, some reported experiments [2–4] in the literature do not agree with existing theories [5–7]. Specifically, overflow metabolism in E. coli can either be coupled [5, 8] or decoupled [2–4] from growth rate. We found that adaptive laboratory evolution (ALE) experiments of E. coli reveal a two-dimensional rate-yield tradeoff in adapted strains where the dimensions are (i) a tradeoff between growth rate and growth yield, previously reported by [5], and (ii) a tradeoff between substrate uptake rate and growth yield. The appearance of this two-dimensional tradeoff during adaptation suggests that microorganisms adapting to new environments are subject to a more complex set of rate-yield tradeoffs than previously reported [5, 6]. In this study, the two-dimensional rate-yield tradeoff is quantitatively explained through our multi-scale modeling approach, combining a previously reported small-scale proteome allocation model [5] with a genome-scale model of metabolism and gene-expression (ME-model) [9]. The modeling approach is also instrumental to future studies.

Flux prediction using artificial neural network (ANN) for the upper part of glycolysis

The selection of optimal enzyme concentration in multienzyme cascade reactions for the highest product yield in practice is very expensive and time-consuming process. The modelling of biological pathways is a difficult process because of the complexity of the system. The mathematical modelling of the system using an analytical approach depends on the many parameters of enzymes which rely on tedious and expensive experiments. The artificial neural network (ANN) method has been successively applied in different fields of science to perform complex functions. In this study, ANN models were trained to predict the flux for the upper part of glycolysis as inferred by NADH consumption, using four enzyme concentrations i.e., phosphoglucoisomerase, phosphofructokinase, fructose-bisphosphate-aldolase, triose-phosphate-isomerase. Out of three ANN algorithms, the neuralnet package with two activation functions, “logistic” and “tanh” were implemented. The prediction of the flux was very efficient: RMSE and R² were 0.847, 0.93 and 0.804, 0.94 respectively for logistic and tanh functions using a cross validation procedure. This study showed that a systemic approach such as ANN could be used for accurate prediction of the flux through the metabolic pathway. This could help to save a lot of time and costs, particularly from an industrial perspective. The R-code is available at: https://github.com/DSIMB/ANN-Glycolysis-Flux-Prediction.

Genome-Scale Metabolic Model of a Microbial Cell Factory (Brevibacillus thermoruber 423) with Multi-Industry Potentials for Exopolysaccharide Production

Brevibacillus thermoruber 423 is a thermophilic bacterium capable of producing high levels of exopolysaccharide (EPS) that has broad applications in nutrition, feed, cosmetics, pharmaceutical, and chemical industries, not to mention in health and bionanotechnology sectors. EPS is a natural, nontoxic, and biodegradable polymer of sugar residues and plays pivotal roles in cell-to-cell interactions, adhesion, biofilm formation, and protection of cell against environmental extremes. This bacterium is a thermophilic EPS producer while exceeding other thermophilic producers by virtue of high level of polymer synthesis. Recently, B. thermoruber 423 was noted for relevance to multiple industry sectors because of its capacity to use xylose, and produce EPS, isoprenoids, ethanol/butanol, lipases, proteases, cellulase, and glucoamylase enzymes as well as its resistance to arsenic. A key step in understanding EPS production with a systems-based approach is the knowledge of microbial genome sequence. To speed biotechnology and industrial applications, this study reports on a genome-scale metabolic model (GSMM) of B. thermoruber 423, constructed using the recently available high-quality genome sequence that we have subsequently validated using physiological data on batch growth and EPS production on seven different carbon sources. The model developed contains 1454 reactions (of which 1127 are assigned an enzyme commission number) and 1410 metabolites from 925 genes. This GSMM offers the promise to enable and accelerate further systems biology and industrial scale studies, not to mention the ability to calculate metabolic flux distribution in large networks and multiomic data integration.

Metabolic network reconstruction and phenome analysis of the industrial microbe, Escherichia coli BL21(DE3)

Escherichia coli BL21(DE3) is an industrial model microbe for the mass-production of bioproducts such as biofuels, biorefineries, and recombinant proteins. However, despite its important role in scientific research and biotechnological applications, a high-quality metabolic network model for metabolic engineering is yet to be developed. Here, we present the comprehensive metabolic network model of E. coli BL21(DE3), named iHK1487, based on the latest genome reannotation and phenome analysis. The metabolic model consists of 1,164 unique metabolites, 2,701 metabolic reactions, and 1,487 genes. The model was validated and improved by comparing the simulation results with phenome data from phenotype microarray tests. Previous transcriptome profile data was incorporated during model reconstruction, and flux prediction was simulated using the model. iHK1487 was simulated to explore the metabolic features of BL21(DE3) such as broad spectrum amino acid utilization and enhanced flux through the upper glycolytic pathway and TCA cycle. iHK1487 will contribute to systematic understanding of cellular physiology and metabolism of E. coli BL21(DE3) and highlight its biotechnological applications.

Gut microbiota dysbiosis is associated with malnutrition and reduced plasma amino acid levels: Lessons from genome-scale metabolic modeling

Malnutrition is a severe non-communicable disease, which is prevalent in children from low-income countries. Recently, a number of metagenomics studies have illustrated associations between the altered gut microbiota and child malnutrition. However, these studies did not examine metabolic functions and interactions between individual species in the gut microbiota during health and malnutrition. Here, we applied genome-scale metabolic modeling to model the gut microbial species, which were selected from healthy and malnourished children from three countries. Our analysis showed reduced metabolite production capabilities in children from two low-income countries compared with a high-income country. Additionally, the models were also used to predict the community-level metabolic potentials of gut microbes and the patterns of pairwise interactions among species. Hereby we found that due to bacterial interactions there may be reduced production of certain amino acids in malnourished children compared with healthy children from the same communities. To gain insight into alterations in the metabolism of malnourished (stunted) children, we also performed targeted plasma metabolic profiling in the first 2 years of life of 25 healthy and 25 stunted children. Plasma metabolic profiling further revealed that stunted children had reduced plasma levels of essential amino acids compared to healthy controls. Our analyses provide a framework for future efforts towards further characterization of gut microbial metabolic capabilities and their contribution to malnutrition.

Predicting the accumulation of storage compounds by Rhodococcus jostii RHA1 in the feast-famine growth cycles using genome-scale flux balance analysis

Feast-famine cycles in biological wastewater resource recovery systems select for bacterial species that accumulate intracellular storage compounds such as poly-β-hydroxybutyrate (PHB), glycogen, and triacylglycerols (TAG). These species survive better the famine phase and resume rapid substrate uptake at the beginning of the feast phase faster than microorganisms unable to accumulate storage. However, ecophysiological conditions favouring the accumulation of either storage compounds remain to be clarified, and predictive capabilities need to be developed to eventually rationally design reactors producing these compounds. Using a genome-scale metabolic modelling approach, the storage metabolism of Rhodococcus jostii RHA1 was investigated for steady-state feast-famine cycles on glucose and acetate as the sole carbon sources. R. jostii RHA1 is capable of accumulating the three storage compounds (PHB, TAG, and glycogen) simultaneously. According to the experimental observations, when glucose was the substrate, feast phase chemical oxygen demand (COD) accumulation was similar for the three storage compounds; when acetate was the substrate, however, PHB accumulation was 3 times higher than TAG accumulation and essentially no glycogen was accumulated. These results were simulated using the genome-scale metabolic model of R. jostii RHA1 (iMT1174) by means of flux balance analysis (FBA) to determine the objective functions capable of predicting these behaviours. Maximization of the growth rate was set as the main objective function, while minimization of total reaction fluxes and minimization of metabolic adjustment (environmental MOMA) were considered as the sub-objective functions. The environmental MOMA sub-objective performed better than the minimization of total reaction fluxes sub-objective function at predicting the mixture of storage compounds accumulated. Additional experiments with ¹³C-labelled bicarbonate (HCO₃⁻) found that the fluxes through the central metabolism reactions during the feast phases were similar to the ones during the famine phases on acetate due to similarity in the carbon sources in the feast and famine phases (i.e., acetate and poly-β-hydroxybutyrate, respectively); this suggests that the environmental MOMA sub-objective function could be used to analyze successive environmental conditions such as the feast and famine cycles while the metabolically similar carbon sources are taken up by microorganisms.

Constraint-Based Modeling Highlights Cell Energy, Redox Status and α-Ketoglutarate Availability as Metabolic Drivers for Anthocyanin Accumulation in Grape Cells Under Nitrogen Limitation

Anthocyanin biosynthesis is regulated by environmental factors (such as light, temperature, and water availability) and nutrient status (such as carbon, nitrogen, and phosphate nutrition). Previous reports show that low nitrogen availability strongly enhances anthocyanin accumulation in non carbon-limited plant organs or cell suspensions. It has been hypothesized that high carbon-to-nitrogen ratio would lead to an energy excess in plant cells, and that an increase in flavonoid pathway metabolic fluxes would act as an "energy escape valve," helping plant cells to cope with energy and carbon excess. However, this hypothesis has never been tested directly. To this end, we used the grapevine Vitis vinifera L. cultivar Gamay Teinturier (syn. Gamay Freaux or Freaux Tintorier, VIVC #4382) cell suspension line as a model system to study the regulation of anthocyanin accumulation in response to nitrogen supply. The cells were sub-cultured in the presence of either control (25 mM) or low (5 mM) nitrate concentration. Targeted metabolomics and enzyme activity determinations were used to parametrize a constraint-based model describing both the central carbon and nitrogen metabolisms and the flavonoid (phenylpropanoid) pathway connected by the energy (ATP) and reducing power equivalents (NADPH and NADH) cofactors. The flux analysis (2 flux maps generated, for control and low nitrogen in culture medium) clearly showed that in low nitrogen-fed cells all the metabolic fluxes of central metabolism were decreased, whereas fluxes that consume energy and reducing power, were either increased (upper part of glycolysis, shikimate, and flavonoid pathway) or maintained (pentose phosphate pathway). Also, fluxes of flavanone 3β-hydroxylase, flavonol synthase, and anthocyanidin synthase were strongly increased, advocating for a regulation of the flavonoid pathway by alpha-ketoglutarate levels. These results strongly support the hypothesis of anthocyanin biosynthesis acting as an energy escape valve in plant cells, and they open new possibilities to manipulate flavonoid production in plant cells. They do not, however, support a role of anthocyanins as an effective mechanism for coping with carbon excess in high carbon to nitrogen ratio situations in grape cells. Instead, constraint-based modeling output and biomass analysis indicate that carbon excess is dealt with by vacuolar storage of soluble sugars.

A curated genome-scale metabolic model of Bordetella pertussis metabolism

The Gram-negative bacterium Bordetella pertussis is the causative agent of whooping cough, a serious respiratory infection causing hundreds of thousands of deaths annually worldwide. There are effective vaccines, but their production requires growing large quantities of B. pertussis. Unfortunately, B. pertussis has relatively slow growth in culture, with low biomass yields and variable growth characteristics. B. pertussis also requires a relatively expensive growth medium. We present a new, curated flux balance analysis-based model of B. pertussis metabolism. We enhance the model with an experimentally-determined biomass objective function, and we perform extensive manual curation. We test the model’s predictions with a genome-wide screen for essential genes using a transposon-directed insertional sequencing (TraDIS) approach. We test its predictions of growth for different carbon sources in the medium. The model predicts essentiality with an accuracy of 83% and correctly predicts improvements in growth under increased glutamate:fumarate ratios. We provide the model in SBML format, along with gene essentiality predictions.

Metabolic flux models have been used to understand how organisms adapt their metabolism under different growth conditions, and are finding increasing application in synthetic biology and biotechnology. One barrier to progress in this field is the construction and curation of metabolic flux models for new organisms. Here we present a curated genome-scale metabolic flux model for Bordetella pertussis, the causative agent of whooping cough. Producing vaccines against whooping cough requires growing B. pertussis in large volumes. However, its growth is relatively slow, final yields of biomass are relatively low and growth characteristics can be variable. Understanding B. pertussis metabolism has applications to improving vaccine production, as well as in understanding the basic biology of this organism.

Combining Targeted Metabolomic Data with a Model of Glucose Metabolism: Toward Progress in Chondrocyte Mechanotransduction

Osteoarthritis is a debilitating disease likely involving altered metabolism of the chondrocytes in articular cartilage. Chondrocytes can respond metabolically to mechanical loads via cellular mechanotransduction, and metabolic changes are significant because they produce the precursors to the tissue matrix necessary for cartilage health. However, a comprehensive understanding of how energy metabolism changes with loading remains elusive. To improve our understanding of chondrocyte mechanotransduction, we developed a computational model to calculate the rate of reactions (i.e. flux) across multiple components of central energy metabolism based on experimental data. We calculated average reaction flux profiles of central metabolism for SW1353 human chondrocytes subjected to dynamic compression for 30 minutes. The profiles were obtained solving a bounded variable linear least squares problem, representing the stoichiometry of human central energy metabolism. Compression synchronized chondrocyte energy metabolism. These data are consistent with dynamic compression inducing early time changes in central energy metabolism geared towards more active protein synthesis. Furthermore, this analysis demonstrates the utility of combining targeted metabolomic data with a computational model to enable rapid analysis of cellular energy utilization.

Stoichiometric modelling of assimilatory and dissimilatory biomass utilisation in a microbial community

Assimilatory and dissimilatory utilisation of autotroph biomass by heterotrophs is a fundamental mechanism for the transfer of nutrients and energy across trophic levels. Metagenome data from a tractable, thermoacidophilic microbial community in Yellowstone National Park was used to build an in silico model to study heterotrophic utilisation of autotroph biomass using elementary flux mode analysis and flux balance analysis. Assimilatory and dissimilatory biomass utilisation was investigated using 29 forms of biomass-derived dissolved organic carbon (DOC) including individual monomer pools, individual macromolecular pools and aggregate biomass. The simulations identified ecologically competitive strategies for utilizing DOC under conditions of varying electron donor, electron acceptor or enzyme limitation. The simulated growth environment affected which form of DOC was the most competitive use of nutrients; for instance, oxygen limitation favoured utilisation of less reduced and fermentable DOC while carbon-limited environments favoured more reduced DOC. Additionally, metabolism was studied considering two encompassing metabolic strategies: simultaneous versus sequential use of DOC. Results of this study bound the transfer of nutrients and energy through microbial food webs, providing a quantitative foundation relevant to most microbial ecosystems.

The Need for Integrated Approaches in Metabolic Engineering

This review highlights state-of-the-art procedures for heterologous small-molecule biosynthesis, the associated bottlenecks, and new strategies that have the potential to accelerate future accomplishments in metabolic engineering. We emphasize that a combination of different approaches over multiple time and size scales must be considered for successful pathway engineering in a heterologous host. We have classified these optimization procedures based on the "system" that is being manipulated: transcriptome, translatome, proteome, or reactome. By bridging multiple disciplines, including molecular biology, biochemistry, biophysics, and computational sciences, we can create an integral framework for the discovery and implementation of novel biosynthetic production routes.

Cell scale host-pathogen modeling: another branch in the evolution of constraint-based methods

Constraint-based models have become popular methods for systems biology as they enable the integration of complex, disparate datasets in a biologically cohesive framework that also supports the description of biological processes in terms of basic physicochemical constraints and relationships. The scope, scale, and application of genome scale models have grown from single cell bacteria to multi-cellular interaction modeling; host-pathogen modeling represents one of these examples at the current horizon of constraint-based methods. There are now a small number of examples of host-pathogen constraint-based models in the literature, however there has not yet been a definitive description of the methodology required for the functional integration of genome scale models in order to generate simulation capable host-pathogen models. Herein we outline a systematic procedure to produce functional host-pathogen models, highlighting steps which require debugging and iterative revisions in order to successfully build a functional model. The construction of such models will enable the exploration of host-pathogen interactions by leveraging the growing wealth of omic data in order to better understand mechanism of infection and identify novel therapeutic strategies.

The Warburg effect: a balance of flux analysis

Cancer metabolism is characterized by increased macromolecular syntheses through coordinated increases in energy and substrate metabolism. The observation that cancer cells produce lactate in an environment of oxygen sufficiency (aerobic glycolysis) is a central theme of cancer metabolism known as the Warburg effect. Aerobic glycolysis in cancer metabolism is accompanied by increased pentose cycle and anaplerotic activities producing energy and substrates for macromolecular synthesis. How these processes are coordinated is poorly understood. Recent advances have focused on molecular regulation of cancer metabolism by oncogenes and tumor suppressor genes which regulate numerous enzymatic steps of central glucose metabolism. In the past decade, new insights in cancer metabolism have emerged through the application of stable isotopes particularly from 13C carbon tracing. Such studies have provided new evidence for system-wide changes in cancer metabolism in response to chemotherapy. Interestingly, experiments using metabolic inhibitors on individual biochemical pathways all demonstrate similar system-wide effects on cancer metabolism as in targeted therapies. Since biochemical reactions in the Warburg effect place competing demands on available precursors, high energy phosphates and reducing equivalents, the cancer metabolic system must fulfill the condition of balance of flux (homeostasis). In this review, the functions of the pentose cycle and of the tricarboxylic acid (TCA) cycle in cancer metabolism are analyzed from the balance of flux point of view. Anticancer treatments that target molecular signaling pathways or inhibit metabolism alter the invasive or proliferative behavior of the cancer cells by their effects on the balance of flux (homeostasis) of the cancer metabolic phenotype.

Using Genome-scale Models to Predict Biological Capabilities

Constraint-based reconstruction and analysis (COBRA) methods at the genome scale have been under development since the first whole-genome sequences appeared in the mid-1990s. A few years ago, this approach began to demonstrate the ability to predict a range of cellular functions, including cellular growth capabilities on various substrates and the effect of gene knockouts at the genome scale. Thus, much interest has developed in understanding and applying these methods to areas such as metabolic engineering, antibiotic design, and organismal and enzyme evolution. This Primer will get you started.

Sequence-based Network Completion Reveals the Integrality of Missing Reactions in Metabolic Networks

Genome-scale metabolic models are central in connecting genotypes to metabolic phenotypes. However, even for well studied organisms, such as Escherichia coli, draft networks do not contain a complete biochemical network. Missing reactions are referred to as gaps. These gaps need to be filled to enable functional analysis, and gap-filling choices influence model predictions. To investigate whether functional networks existed where all gap-filling reactions were supported by sequence similarity to annotated enzymes, four draft networks were supplemented with all reactions from the Model SEED database for which minimal sequence similarity was found in their genomes. Quadratic programming revealed that the number of reactions that could partake in a gap-filling solution was vast: 3,270 in the case of E. coli, where 72% of the metabolites in the draft network could connect a gap-filling solution. Nonetheless, no network could be completed without the inclusion of orphaned enzymes, suggesting that parts of the biochemistry integral to biomass precursor formation are uncharacterized. However, many gap-filling reactions were well determined, and the resulting networks showed improved prediction of gene essentiality compared with networks generated through canonical gap filling. In addition, gene essentiality predictions that were sensitive to poorly determined gap-filling reactions were of poor quality, suggesting that damage to the network structure resulting from the inclusion of erroneous gap-filling reactions may be predictable.

Computing the functional proteome: recent progress and future prospects for genome-scale models

Constraint-based models enable the computation of feasible, optimal, and realized biological phenotypes from reaction network reconstructions and constraints on their operation. To date, stoichiometric reconstructions have largely focused on metabolism, resulting in genome-scale metabolic models (M-Models). Recent expansions in network content to encompass proteome synthesis have resulted in models of metabolism and protein expression (ME-Models). ME-Models advance the predictions possible with constraint-based models from network flux states to the spatially resolved molecular composition of a cell. Specifically, ME-Models enable the prediction of transcriptome and proteome allocation and limitations, and basal expression states and regulatory needs. Continued expansion in reconstruction content and constraints will result in an increasingly refined representation of cellular composition and behavior.

Perturbation Experiments: Approaches for Metabolic Pathway Analysis in Bioreactors

In the last decades, targeted metabolic engineering of microbial cells has become one of the major tools in bioprocess design and optimization. For successful application, a detailed knowledge is necessary about the relevant metabolic pathways and their regulation inside the cells. Since in vitro experiments cannot display process conditions and behavior properly, process data about the cells' metabolic state have to be collected in vivo. For this purpose, special techniques and methods are necessary. Therefore, most techniques enabling in vivo characterization of metabolic pathways rely on perturbation experiments, which can be divided into dynamic and steady-state approaches. To avoid any process disturbance, approaches which enable perturbation of cell metabolism in parallel to the continuing production process are reasonable. Furthermore, the fast dynamics of microbial production processes amplifies the need of parallelized data generation. These points motivate the development of a parallelized approach for multiple metabolic perturbation experiments outside the operating production reactor. An appropriate approach for in vivo characterization of metabolic pathways is presented and applied exemplarily to a microbial L-phenylalanine production process on a 15 L-scale.

Modelling central metabolic fluxes by constraint-based optimization reveals metabolic reprogramming of developing Solanum lycopersicum (tomato) fruit

Modelling of metabolic networks is a powerful tool to analyse the behaviour of developing plant organs, including fruits. Guided by our current understanding of heterotrophic metabolism of plant cells, a medium-scale stoichiometric model, including the balance of co-factors and energy, was constructed in order to describe metabolic shifts that occur through the nine sequential stages of Solanum lycopersicum (tomato) fruit development. The measured concentrations of the main biomass components and the accumulated metabolites in the pericarp, determined at each stage, were fitted in order to calculate, by derivation, the corresponding external fluxes. They were used as constraints to solve the model by minimizing the internal fluxes. The distribution of the calculated fluxes of central metabolism were then analysed and compared with known metabolic behaviours. For instance, the partition of the main metabolic pathways (glycolysis, pentose phosphate pathway, etc.) was relevant throughout fruit development. We also predicted a valid import of carbon and nitrogen by the fruit, as well as a consistent CO2 release. Interestingly, the energetic balance indicates that excess ATP is dissipated just before the onset of ripening, supporting the concept of the climacteric crisis. Finally, the apparent contradiction between calculated fluxes with low values compared with measured enzyme capacities suggest a complex reprogramming of the metabolic machinery during fruit development. With a powerful set of experimental data and an accurate definition of the metabolic system, this work provides important insight into the metabolic and physiological requirements of the developing tomato fruits.

A systematic simulation of the effect of salicylic acid on sphingolipid metabolism

The phytohormone salicylic acid (SA) affects plant development and defense responses. Recent studies revealed that SA also participates in the regulation of sphingolipid metabolism, but the details of this regulation remain to beexplored. Here, we use in silico Flux Balance Analysis (FBA) with published microarray data to construct a whole-cell simulation model, including 23 pathways, 259 reactions, and 172 metabolites, to predict the alterations in flux of major sphingolipid species after treatment with exogenous SA. This model predicts significant changes in fluxes of certain sphingolipid species after SA treatment, changes that likely trigger downstream physiological and phenotypic effects. To validate the simulation, we used (15)N-labeled metabolic turnover analysis to measure sphingolipid contents and turnover rate in Arabidopsis thaliana seedlings treated with SA or the SA analog benzothiadiazole (BTH). The results show that both SA and BTH affect sphingolipid metabolism, altering the concentrations of certain species and also changing the optimal flux distribution and turnover rate of sphingolipids. Our strategy allows us to estimate sphingolipid fluxes on a short time scale and gives us a systemic view of the effect of SA on sphingolipid homeostasis.

A genome-scale metabolic model of Methanococcus maripaludis S2 for CO2 capture and conversion to methane

Methane is a major energy source for heating and electricity. Its production by methanogenic bacteria is widely known in nature. M. maripaludis S2 is a fully sequenced hydrogenotrophic methanogen and an excellent laboratory strain with robust genetic tools. However, a quantitative systems biology model to complement these tools is absent in the literature. To understand and enhance its methanogenesis from CO2, this work presents the first constraint-based genome-scale metabolic model (iMM518). It comprises 570 reactions, 556 distinct metabolites, and 518 genes along with gene-protein-reaction (GPR) associations, and covers 30% of open reading frames (ORFs). The model was validated using biomass growth data and experimental phenotypic studies from the literature. Its comparison with the in silico models of Methanosarcina barkeri, Methanosarcina acetivorans, and Sulfolobus solfataricus P2 shows M. maripaludis S2 to be a better organism for producing methane. Using the model, genes essential for growth were identified, and the efficacies of alternative carbon, hydrogen and nitrogen sources were studied. The model can predict the effects of reengineering M. maripaludis S2 to guide or expedite experimental efforts.

Prediction of metabolic flux distribution from gene expression data based on the flux minimization principle

Prediction of possible flux distributions in a metabolic network provides detailed phenotypic information that links metabolism to cellular physiology. To estimate metabolic steady-state fluxes, the most common approach is to solve a set of macroscopic mass balance equations subjected to stoichiometric constraints while attempting to optimize an assumed optimal objective function. This assumption is justifiable in specific cases but may be invalid when tested across different conditions, cell populations, or other organisms. With an aim to providing a more consistent and reliable prediction of flux distributions over a wide range of conditions, in this article we propose a framework that uses the flux minimization principle to predict active metabolic pathways from mRNA expression data. The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context. We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network. In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values. In contrast to other approaches, our method was able to provide quantitative predictions for both model organisms under a variety of conditions. Our approach requires no prior knowledge or assumption of a context-specific metabolic functionality and does not require trial-and-error parameter adjustments. Thus, our framework is of general applicability for modeling the transcription-dependent metabolism of bacteria and yeasts.

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi-steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle.

Mapping the inner workings of the microbiome: genomic- and metagenomic-based study of metabolism and metabolic interactions in the human microbiome

The human gut microbiome is a major contributor to human metabolism and health, yet the metabolic processes that are carried out by various community members, the way these members interact with each other and with the host, and the impact of such interactions on the overall metabolic machinery of the microbiome have not yet been mapped. Here, we discuss recent efforts to study the metabolic inner workings of this complex ecosystem. We will specifically highlight two interrelated lines of work, the first aiming to deconvolve the microbiome and to characterize the metabolic capacity of various microbiome species and the second aiming to utilize computational modeling to infer and study metabolic interactions between these species.

Likelihood-based gene annotations for gap filling and quality assessment in genome-scale metabolic models

Genome-scale metabolic models provide a powerful means to harness information from genomes to deepen biological insights. With exponentially increasing sequencing capacity, there is an enormous need for automated reconstruction techniques that can provide more accurate models in a short time frame. Current methods for automated metabolic network reconstruction rely on gene and reaction annotations to build draft metabolic networks and algorithms to fill gaps in these networks. However, automated reconstruction is hampered by database inconsistencies, incorrect annotations, and gap filling largely without considering genomic information. Here we develop an approach for applying genomic information to predict alternative functions for genes and estimate their likelihoods from sequence homology. We show that computed likelihood values were significantly higher for annotations found in manually curated metabolic networks than those that were not. We then apply these alternative functional predictions to estimate reaction likelihoods, which are used in a new gap filling approach called likelihood-based gap filling to predict more genomically consistent solutions. To validate the likelihood-based gap filling approach, we applied it to models where essential pathways were removed, finding that likelihood-based gap filling identified more biologically relevant solutions than parsimony-based gap filling approaches. We also demonstrate that models gap filled using likelihood-based gap filling provide greater coverage and genomic consistency with metabolic gene functions compared to parsimony-based approaches. Interestingly, despite these findings, we found that likelihoods did not significantly affect consistency of gap filled models with Biolog and knockout lethality data. This indicates that the phenotype data alone cannot necessarily be used to discriminate between alternative solutions for gap filling and therefore, that the use of other information is necessary to obtain a more accurate network. All described workflows are implemented as part of the DOE Systems Biology Knowledgebase (KBase) and are publicly available via API or command-line web interface.

Emergent biosynthetic capacity in simple microbial communities

Microbes have an astonishing capacity to transform their environments. Yet, the metabolic capacity of a single species is limited and the vast majority of microorganisms form complex communities and join forces to exhibit capabilities far exceeding those achieved by any single species. Such enhanced metabolic capacities represent a promising route to many medical, environmental, and industrial applications and call for the development of a predictive, systems-level understanding of synergistic microbial capacity. Here we present a comprehensive computational framework, integrating high-quality metabolic models of multiple species, temporal dynamics, and flux variability analysis, to study the metabolic capacity and dynamics of simple two-species microbial ecosystems. We specifically focus on detecting emergent biosynthetic capacity--instances in which a community growing on some medium produces and secretes metabolites that are not secreted by any member species when growing in isolation on that same medium. Using this framework to model a large collection of two-species communities on multiple media, we demonstrate that emergent biosynthetic capacity is highly prevalent. We identify commonly observed emergent metabolites and metabolic reprogramming patterns, characterizing typical mechanisms of emergent capacity. We further find that emergent secretion tends to occur in two waves, the first as soon as the two organisms are introduced, and the second when the medium is depleted and nutrients become limited. Finally, aiming to identify global community determinants of emergent capacity, we find a marked association between the level of emergent biosynthetic capacity and the functional/phylogenetic distance between community members. Specifically, we demonstrate a "Goldilocks" principle, where high levels of emergent capacity are observed when the species comprising the community are functionally neither too close, nor too distant. Taken together, our results demonstrate the potential to design and engineer synthetic communities capable of novel metabolic activities and point to promising future directions in environmental and clinical bioengineering.

Why measure enzyme activities in the era of systems biology?

Information about the abundance and biological activities of proteins is essential to reveal how genes affect phenotypes. Over the past decade, mass spectrometry (MS)-based proteomics has revolutionized the identification and quantification of proteins, and the detection of post-translational modifications. Interpretation of proteomics data depends on information about the biological activities of proteins, which has created a bottleneck in research. This review focuses on enzymes in central metabolism. We examine the methods used for measuring enzyme activities, and discuss how these methods provide information about the kinetic and regulatory properties of enzymes, their turnover, and how this information can be integrated into metabolic models. We also discuss how robotized assays could enable the genetic networks that control enzyme abundance to be analyzed.

Comparison on extreme pathways reveals nature of different biological processes

Background

Constraint-based reconstruction and analysis (COBRA) is used for modeling genome-scale metabolic networks (MNs). In a COBRA model, extreme pathways (ExPas) are the edges of its conical solution space, which is formed by all viable steady-state flux distributions. ExPa analysis has been successfully applied to MNs to reveal their phenotypic capabilities and properties. Recently, the COBRA framework has been extended to transcriptional regulatory networks (TRNs) and transcriptional and translational networks (TTNs), so efforts are needed to determine whether ExPa analysis is also effective on these two types of networks.

Results

In this paper, the ExPas resulting from the COBRA models of E.coli's MN, TRN and TTN were horizontally compared from 5 aspects: (1) Total number and the ratio of their amount to reaction amount; (2) Length distribution; (3) Reaction participation; (4) Correlated reaction sets (CoSets); (5) interconnectivity degree. Significant discrepancies in above properties were observed during the comparison, which reveals the biological natures of different biological processes. Besides, by demonstrating the application of ExPa analysis on E.coli, we provide a practical guidance of an improved approach to compute ExPas on COBRA models of TRNs.

Conclusions

ExPas of E.coli's MN, TRN and TTN have different properties, which are strongly connected with various biological natures of biochemical networks, such as topological structure, specificity and redundancy. Our study shows that ExPas are biologically meaningful on the newborn models and suggests the effectiveness of ExPa analysis on them.