Flux coupling analysis of genome-scale metabolic network reconstructions

Machine learning for the advancement of genome-scale metabolic modeling

Constraint-based modeling (CBM) has evolved as the core systems biology tool to map the interrelations between genotype, phenotype, and external environment. The recent advancement of high-throughput experimental approaches and multi-omics strategies has generated a plethora of new and precise information from wide-ranging biological domains. On the other hand, the continuously growing field of machine learning (ML) and its specialized branch of deep learning (DL) provide essential computational architectures for decoding complex and heterogeneous biological data. In recent years, both multi-omics and ML have assisted in the escalation of CBM. Condition-specific omics data, such as transcriptomics and proteomics, helped contextualize the model prediction while analyzing a particular phenotypic signature. At the same time, the advanced ML tools have eased the model reconstruction and analysis to increase the accuracy and prediction power. However, the development of these multi-disciplinary methodological frameworks mainly occurs independently, which limits the concatenation of biological knowledge from different domains. Hence, we have reviewed the potential of integrating multi-disciplinary tools and strategies from various fields, such as synthetic biology, CBM, omics, and ML, to explore the biochemical phenomenon beyond the conventional biological dogma. How the integrative knowledge of these intersected domains has improved bioengineering and biomedical applications has also been highlighted. We categorically explained the conventional genome-scale metabolic model (GEM) reconstruction tools and their improvement strategies through ML paradigms. Further, the crucial role of ML and DL in omics data restructuring for GEM development has also been briefly discussed. Finally, the case-study-based assessment of the state-of-the-art method for improving biomedical and metabolic engineering strategies has been elaborated. Therefore, this review demonstrates how integrating experimental and in silico strategies can help map the ever-expanding knowledge of biological systems driven by condition-specific cellular information. This multiview approach will elevate the application of ML-based CBM in the biomedical and bioengineering fields for the betterment of society and the environment.

Genome-scale metabolic modeling of the human milk oligosaccharide utilization by Bifidobacterium longum subsp. infantis

Bifidobacterium longum subsp. infantis is a representative and dominant species in the infant gut and is considered a beneficial microbe. This organism displays multiple adaptations to thrive in the infant gut, regarded as a model for human milk oligosaccharides (HMOs) utilization. These carbohydrates are abundant in breast milk and include different molecules based on lactose. They contain fucose, sialic acid, and N-acetylglucosamine. Bifidobacterium metabolism is complex, and a systems view of relevant metabolic pathways and exchange metabolites during HMO consumption is missing. To address this limitation, a refined genome-scale network reconstruction of this bacterium is presented using a previous reconstruction of B. infantis ATCC 15967 as a template. The latter was expanded based on an extensive revision of genome annotations, current literature, and transcriptomic data integration. The metabolic reconstruction (iLR578) accounted for 578 genes, 1,047 reactions, and 924 metabolites. Starting from this reconstruction, we built context-specific genome-scale metabolic models using RNA-seq data from cultures growing in lactose and three HMOs. The models revealed notable differences in HMO metabolism depending on the functional characteristics of the substrates. Particularly, fucosyl-lactose showed a divergent metabolism due to a fucose moiety. High yields of lactate and acetate were predicted under growth rate maximization in all conditions, whereas formate, ethanol, and 1,2-propanediol were substantially lower. Similar results were also obtained under near-optimal growth on each substrate when varying the empirically observed acetate-to-lactate production ratio. Model predictions displayed reasonable agreement between central carbon metabolism fluxes and expression data across all conditions. Flux coupling analysis revealed additional connections between succinate exchange and arginine and sulfate metabolism and a strong coupling between central carbon reactions and adenine metabolism. More importantly, specific networks of coupled reactions under each carbon source were derived and analyzed. Overall, the presented network reconstruction constitutes a valuable platform for probing the metabolism of this prominent infant gut bifidobacteria.IMPORTANCEThis work presents a detailed reconstruction of the metabolism of Bifidobacterium longum subsp. infantis, a prominent member of the infant gut microbiome, providing a systems view of its metabolism of human milk oligosaccharides.

Control Theory and Systems Biology: Potential Applications in Neurodegeneration and Search for Therapeutic Targets

Control theory, a well-established discipline in engineering and mathematics, has found novel applications in systems biology. This interdisciplinary approach leverages the principles of feedback control and regulation to gain insights into the complex dynamics of cellular and molecular networks underlying chronic diseases, including neurodegeneration. By modeling and analyzing these intricate systems, control theory provides a framework to understand the pathophysiology and identify potential therapeutic targets. Therefore, this review examines the most widely used control methods in conjunction with genomic-scale metabolic models in the steady state of the multi-omics type. According to our research, this approach involves integrating experimental data, mathematical modeling, and computational analyses to simulate and control complex biological systems. In this review, we find that the most significant application of this methodology is associated with cancer, leaving a lack of knowledge in neurodegenerative models. However, this methodology, mainly associated with the Minimal Dominant Set (MDS), has provided a starting point for identifying therapeutic targets for drug development and personalized treatment strategies, paving the way for more effective therapies.

On the representativeness and stability of a set of EFMs

MOTIVATION

Elementary flux modes are a well-known tool for analyzing metabolic networks. The whole set of elementary flux modes (EFMs) cannot be computed in most genome-scale networks due to their large cardinality. Therefore, different methods have been proposed to compute a smaller subset of EFMs that can be used for studying the structure of the network. These latter methods pose the problem of studying the representativeness of the calculated subset. In this article, we present a methodology to tackle this problem.

RESULTS

We have introduced the concept of stability for a particular network parameter and its relation to the representativeness of the EFM extraction method studied. We have also defined several metrics to study and compare the EFM biases. We have applied these techniques to compare the relative behavior of previously proposed methods in two case studies. Furthermore, we have presented a new method for the EFM computation (PiEFM), which is more stable (less biased) than previous ones, has suitable representativeness measures, and exhibits better variability in the extracted EFMs.

AVAILABILITY AND IMPLEMENTATION

Software and additional material are freely available at https://github.com/biogacop/PiEFM.

Predictive evolution of metabolic phenotypes using model-designed environments

Adaptive evolution under controlled laboratory conditions has been highly effective in selecting organisms with beneficial phenotypes such as stress tolerance. The evolution route is particularly attractive when the organisms are either difficult to engineer or the genetic basis of the phenotype is complex. However, many desired traits, like metabolite secretion, have been inaccessible to adaptive selection due to their trade-off with cell growth. Here, we utilize genome-scale metabolic models to design nutrient environments for selecting lineages with enhanced metabolite secretion. To overcome the growth-secretion trade-off, we identify environments wherein growth becomes correlated with a secondary trait termed tacking trait. The latter is selected to be coupled with the desired trait in the application environment where the trait manifestation is required. Thus, adaptive evolution in the model-designed selection environment and subsequent return to the application environment is predicted to enhance the desired trait. We experimentally validate this strategy by evolving Saccharomyces cerevisiae for increased secretion of aroma compounds, and confirm the predicted flux-rerouting using genomic, transcriptomic, and proteomic analyses. Overall, model-designed selection environments open new opportunities for predictive evolution.

Rapid-SL identifies synthetic lethal sets with an arbitrary cardinality

The multidrug resistance of numerous pathogenic microorganisms is a serious challenge that raises global healthcare concerns. Multi-target medications and combinatorial therapeutics are much more effective than single-target drugs due to their synergistic impact on the systematic activities of microorganisms. Designing efficient combinatorial therapeutics can benefit from identification of synthetic lethals (SLs). An SL is a set of non-essential targets (i.e., reactions or genes) that prevent the proliferation of a microorganism when they are "knocked out" simultaneously. To facilitate the identification of SLs, we introduce Rapid-SL, a new multimodal implementation of the Fast-SL method, using the depth-first search algorithm. The advantages of Rapid-SL over Fast-SL include: (a) the enumeration of all SLs that have an arbitrary cardinality, (b) a shorter runtime due to search space reduction, (c) embarrassingly parallel computations, and (d) the targeted identification of SLs. Targeted identification is important because the enumeration of higher order SLs demands the examination of too many reaction sets. Accordingly, we present specific applications of Rapid-SL for the efficient targeted identification of SLs. In particular, we found up to 67% of all quadruple SLs by investigating about 1% of the search space. Furthermore, 307 sextuples, 476 septuples, and over 9000 octuples are found for Escherichia coli genome-scale model, iAF1260.

The topology of genome-scale metabolic reconstructions unravels independent modules and high network flexibility

The topology of metabolic networks is recognisably modular with modules weakly connected apart from sharing a pool of currency metabolites. Here, we defined modules as sets of reversible reactions isolated from the rest of metabolism by irreversible reactions except for the exchange of currency metabolites. Our approach identifies topologically independent modules under specific conditions associated with different metabolic functions. As case studies, the E.coli iJO1366 and Human Recon 2.2 genome-scale metabolic models were split in 103 and 321 modules respectively, displaying significant correlation patterns in expression data. Finally, we addressed a fundamental question about the metabolic flexibility conferred by reversible reactions: “Of all Directed Topologies (DTs) defined by fixing directions to all reversible reactions, how many are capable of carrying flux through all reactions?”. Enumeration of the DTs for iJO1366 model was performed using an efficient depth-first search algorithm, rejecting infeasible DTs based on mass-imbalanced and loopy flux patterns. We found the direction of 79% of reversible reactions must be defined before all directions in the network can be fixed, granting a high degree of flexibility.

Genome-scale metabolic reconstructions represent all biochemical reactions that an organism can accomplish. These reconstructions are complex and often difficult to study in great detail. A way to overcome this limitation is to focus on specific pathways or subsystems. We present a novel method to identify metabolic modules based on the network topology. The method relies on reaction directions and ignores currency metabolites, which artificially connect distant metabolic reactions. In this way, topologically independent modules are built, where inputs and outputs are controlled by irreversible reactions. The method is automatic and unbiased, and, the result is a set of condition specific modules with defined metabolic functions. As a proof-of-concept we generated biologically relevant modules for the E.coli and Human genome-scale metabolic reconstructions supported by transcriptomic data. Finally, we applied the novel approach to study the network flexibility conferred by reversible reactions. In the case of the E. coli model, we found that the direction of 79% of structurally reversible reactions (those not directionally constrained by surrounding irreversible reactions) must be fixed to determine all the reaction directions in the network. Therefore, reversible reactions operate practically independent of each other.

The hidden simplicity of metabolic networks is revealed by multireaction dependencies

Understanding the complexity of metabolic networks has implications for manipulation of their functions. The complexity of metabolic networks can be characterized by identifying multireaction dependencies that are challenging to determine due to the sheer number of combinations to consider. Here, we propose the concept of concordant complexes that captures multireaction dependencies and can be efficiently determined from the algebraic structure and operational constraints of metabolic networks. The concordant complexes imply the existence of concordance modules based on which the apparent complexity of 12 metabolic networks of organisms from all kingdoms of life can be reduced by at least 78%. A comparative analysis against an ensemble of randomized metabolic networks shows that the metabolic network of Escherichia coli contains fewer concordance modules and is, therefore, more tightly coordinated than expected by chance. Together, our findings demonstrate that metabolic networks are considerably simpler than what can be perceived from their structure alone.

Relative flux trade-offs and optimization of metabolic network functionalities

Trade-offs between traits are present across different levels of biological systems and ultimately reflect constraints imposed by physicochemical laws and the structure of underlying biochemical networks. Yet, mechanistic explanation of how trade-offs between molecular traits arise and how they relate to optimization of fitness-related traits remains elusive. Here, we introduce the concept of relative flux trade-offs and propose a constraint-based approach, termed FluTOr, to identify metabolic reactions whose fluxes are in relative trade-off with respect to an optimized fitness-related cellular task, like growth. We then employed FluTOr to identify relative flux trade-offs in the genome-scale metabolic networks of Escherichia coli, Saccharomyces cerevisiae, and Arabidopsis thaliana. For the metabolic models of E. coli and S. cerevisiae we showed that: (i) the identified relative flux trade-offs depend on the carbon source used and that (ii) reactions that participated in relative trade-offs in both species were implicated in cofactor biosynthesis. In contrast to the two microorganisms, the relative flux trade-offs for the metabolic model of A. thaliana did not depend on the available nitrogen sources, reflecting the differences in the underlying metabolic network as well as the considered environments. Lastly, the established connection between relative flux trade-offs allowed us to identify overexpression targets that can be used to optimize fitness-related traits. Altogether, our computational approach and findings demonstrate how relative flux trade-offs can shape optimization of metabolic tasks, important in biotechnological applications.

Examining organic acid production potential and growth-coupled strategies in Issatchenkia orientalis using constraint-based modeling

Growth-coupling product formation can facilitate strain stability by aligning industrial objectives with biological fitness. Organic acids make up many building block chemicals that can be produced from sugars obtainable from renewable biomass. Issatchenkia orientalis is a yeast strain tolerant to acidic conditions and is thus a promising host for industrial production of organic acids. Here, we use constraint-based methods to assess the potential of computationally designing growth-coupled production strains for I. orientalis that produce 22 different organic acids under aerobic or microaerobic conditions. We explore native and engineered pathways using glucose or xylose as the carbon substrates as proxy constituents of hydrolyzed biomass. We identified growth-coupled production strategies for 37 of the substrate-product pairs, with 15 pairs achieving production for any growth rate. We systematically assess the strain design solutions and categorize the underlying principles involved.

Genome-Scale Metabolic Modeling Enables In-Depth Understanding of Big Data

Genome-scale metabolic models (GEMs) enable the mathematical simulation of the metabolism of archaea, bacteria, and eukaryotic organisms. GEMs quantitatively define a relationship between genotype and phenotype by contextualizing different types of Big Data (e.g., genomics, metabolomics, and transcriptomics). In this review, we analyze the available Big Data useful for metabolic modeling and compile the available GEM reconstruction tools that integrate Big Data. We also discuss recent applications in industry and research that include predicting phenotypes, elucidating metabolic pathways, producing industry-relevant chemicals, identifying drug targets, and generating knowledge to better understand host-associated diseases. In addition to the up-to-date review of GEMs currently available, we assessed a plethora of tools for developing new GEMs that include macromolecular expression and dynamic resolution. Finally, we provide a perspective in emerging areas, such as annotation, data managing, and machine learning, in which GEMs will play a key role in the further utilization of Big Data.

Metabolism perturbation Causedby the overexpression of carbon monoxide dehydrogenase/Acetyl-CoA synthase gene complex accelerated gas to acetate conversion rate ofEubacterium limosumKIST612

Microbial conversion of carbon monoxide (CO) to acetate is a promising upcycling strategy for carbon sequestration. Herein, we demonstrate that CO conversion and acetate production rates of Eubacterium limosum KIST612 strain can be improved by in silico prediction and in vivo assessment. The mimicked CO metabolic model of KIST612 predicted that overexpressing the CO dehydrogenase (CODH) increases CO conversion and acetate production rates. To validate the prediction, we constructed mutant strains overexpressing CODH gene cluster and measured their CO conversion and acetate production rates. A mutant strain (ELM031) co-overexpressing CODH, coenzyme CooC2 and ACS showed a 3.1 × increased specific CO oxidation rate as well as 1.4 × increased specific acetate production rate, compared to the wild type strain. The transcriptional and translational data with redox balance analysis showed that ELM031 has enhanced reducing potential from up-regulation of ferredoxin and related metabolism directly linked to energy conservation.

A structural property for reduction of biochemical networks

Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

Systematizing the different notions of growth-coupled product synthesis and a single framework for computing corresponding strain designs

A widely used design principle for metabolic engineering of microorganisms aims to introduce interventions that enforce growth-coupled product synthesis such that the product of interest becomes a (mandatory) by-product of growth. However, different variants and partially contradicting notions of growth-coupled production (GCP) exist. Herein, we propose an ontology for the different degrees of GCP and clarify their relationships. Ordered by coupling degree, we distinguish four major classes: potentially, weakly, and directionally growth-coupled production (pGCP, wGCP, dGCP) as well as substrate-uptake coupled production (SUCP). We then extend the framework of Minimal Cut Sets (MCS), previously used to compute dGCP and SUCP strain designs, to allow inclusion of implicit optimality constraints, a feature required to compute pGCP and wGCP designs. This extension closes the gap between MCS-based and bilevel-based strain design approaches and enables computation (and comparison) of designs for all GCP classes within a single framework. By computing GCP strain designs for a range of products, we illustrate the hierarchical relationships between the different coupling degrees. We find that feasibility of coupling is not affected by the chosen GCP degree and that strongest coupling (SUCP) requires often only one or two more interventions than wGCP and dGCP. Finally, we show that the principle of coupling can be generalized to couple product synthesis with other cellular functions than growth, for example, with net ATP formation. This work provides important theoretical results and algorithmic developments and a unified terminology for computational strain design based on GCP.

Characterization of effects of genetic variants via genome-scale metabolic modelling

Genome-scale metabolic networks for model plants and crops in combination with approaches from the constraint-based modelling framework have been used to predict metabolic traits and design metabolic engineering strategies for their manipulation. With the advances in technologies to generate large-scale genotyping data from natural diversity panels and other populations, genome-wide association and genomic selection have emerged as statistical approaches to determine genetic variants associated with and predictive of traits. Here, we review recent advances in constraint-based approaches that integrate genetic variants in genome-scale metabolic models to characterize their effects on reaction fluxes. Since some of these approaches have been applied in organisms other than plants, we provide a critical assessment of their applicability particularly in crops. In addition, we further dissect the inferred effects of genetic variants with respect to reaction rate constants, abundances of enzymes, and concentrations of metabolites, as main determinants of reaction fluxes and relate them with their combined effects on complex traits, like growth. Through this systematic review, we also provide a roadmap for future research to increase the predictive power of statistical approaches by coupling them with mechanistic models of metabolism.

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.

Addressing uncertainty in genome-scale metabolic model reconstruction and analysis

The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Essential gene prediction using limited gene essentiality information-An integrative semi-supervised machine learning strategy

Essential gene prediction helps to find minimal genes indispensable for the survival of any organism. Machine learning (ML) algorithms have been useful for the prediction of gene essentiality. However, currently available ML pipelines perform poorly for organisms with limited experimental data. The objective is the development of a new ML pipeline to help in the annotation of essential genes of less explored disease-causing organisms for which minimal experimental data is available. The proposed strategy combines unsupervised feature selection technique, dimension reduction using the Kamada-Kawai algorithm, and semi-supervised ML algorithm employing Laplacian Support Vector Machine (LapSVM) for prediction of essential and non-essential genes from genome-scale metabolic networks using very limited labeled dataset. A novel scoring technique, Semi-Supervised Model Selection Score, equivalent to area under the ROC curve (auROC), has been proposed for the selection of the best model when supervised performance metrics calculation is difficult due to lack of data. The unsupervised feature selection followed by dimension reduction helped to observe a distinct circular pattern in the clustering of essential and non-essential genes. LapSVM then created a curve that dissected this circle for the classification and prediction of essential genes with high accuracy (auROC > 0.85) even with 1% labeled data for model training. After successful validation of this ML pipeline on both Eukaryotes and Prokaryotes that show high accuracy even when the labeled dataset is very limited, this strategy is used for the prediction of essential genes of organisms with inadequate experimentally known data, such as Leishmania sp. Using a graph-based semi-supervised machine learning scheme, a novel integrative approach has been proposed for essential gene prediction that shows universality in application to both Prokaryotes and Eukaryotes with limited labeled data. The essential genes predicted using the pipeline provide an important lead for the prediction of gene essentiality and identification of novel therapeutic targets for antibiotic and vaccine development against disease-causing parasites.

Flux Coupling and the Objective Functions' Length in EFMs

Structural analysis of constraint-based metabolic network models attempts to find the network's properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems.

Genome-scale metabolic reconstruction of the non-model yeast Issatchenkia orientalis SD108 and its application to organic acids production

Many platform chemicals can be produced from renewable biomass by microorganisms, with organic acids making up a large fraction. Intolerance to the resulting low pH growth conditions, however, remains a challenge for the industrial production of organic acids by microorganisms. Issatchenkia orientalis SD108 is a promising host for industrial production because it is tolerant to acidic conditions as low as pH 2.0. With the goal to systematically assess the metabolic capabilities of this non-model yeast, we developed a genome-scale metabolic model for I. orientalis SD108 spanning 850 genes, 1826 reactions, and 1702 metabolites. In order to improve the model’s quantitative predictions, organism-specific macromolecular composition and ATP maintenance requirements were determined experimentally and implemented. We examined its network topology, including essential genes and flux coupling analysis and drew comparisons with the Yeast 8.3 model for Saccharomyces cerevisiae. We explored the carbon substrate utilization and examined the organism’s production potential for the industrially-relevant succinic acid, making use of the OptKnock framework to identify gene knockouts which couple production of the targeted chemical to biomass production. The genome-scale metabolic model iIsor850 is a data-supported curated model which can inform genetic interventions for overproduction.

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Genome-scale metabolic model iIsor850 describes metabolism of I. orientalis SD108.

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Customized biomass reaction highlights differences with S. cerevisiae.

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Chemostat data elucidate growth-associated ATP maintenance.

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Substrate utilization and CRISPR/Cas9 gene knockout phenotypes validate model.

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Model pinpoints candidate gene deletions coupling succinic acid production to growth.

VFFVA: dynamic load balancing enables large-scale flux variability analysis

BACKGROUND

Genome-scale metabolic models are increasingly employed to predict the phenotype of various biological systems pertaining to healthcare and bioengineering. To characterize the full metabolic spectrum of such systems, Fast Flux Variability Analysis (FFVA) is commonly used in parallel with static load balancing. This approach assigns to each core an equal number of biochemical reactions without consideration of their solution complexity.

RESULTS

Here, we present Very Fast Flux Variability Analysis (VFFVA) as a parallel implementation that dynamically balances the computation load between the cores in runtime which guarantees equal convergence time between them. VFFVA allowed to gain a threefold speedup factor with coupled models and up to 100 with ill-conditioned models along with a 14-fold decrease in memory usage.

CONCLUSIONS

VFFVA exploits the parallel capabilities of modern machines to enable biological insights through optimizing systems biology modeling. VFFVA is available in C, MATLAB, and Python at https://github.com/marouenbg/VFFVA .

Model-driven analysis of mutant fitness experiments improves genome-scale metabolic models of Zymomonas mobilis ZM4

Genome-scale metabolic models have been utilized extensively in the study and engineering of the organisms they describe. Here we present the analysis of a published dataset from pooled transposon mutant fitness experiments as an approach for improving the accuracy and gene-reaction associations of a metabolic model for Zymomonas mobilis ZM4, an industrially relevant ethanologenic organism with extremely high glycolytic flux and low biomass yield. Gene essentiality predictions made by the draft model were compared to data from individual pooled mutant experiments to identify areas of the model requiring deeper validation. Subsequent experiments showed that some of the discrepancies between the model and dataset were caused by polar effects, mis-mapped barcodes, or mutants carrying both wild-type and transposon disrupted gene copies-highlighting potential limitations inherent to data from individual mutants in these high-throughput datasets. Therefore, we analyzed correlations in fitness scores across all 492 experiments in the dataset in the context of functionally related metabolic reaction modules identified within the model via flux coupling analysis. These correlations were used to identify candidate genes for a reaction in histidine biosynthesis lacking an annotated gene and highlight metabolic modules with poorly correlated gene fitness scores. Additional genes for reactions involved in biotin, ubiquinone, and pyridoxine biosynthesis in Z. mobilis were identified and confirmed using mutant complementation experiments. These discovered genes, were incorporated into the final model, iZM4_478, which contains 747 metabolic and transport reactions (of which 612 have gene-protein-reaction associations), 478 genes, and 616 unique metabolites, making it one of the most complete models of Z. mobilis ZM4 to date. The methods of analysis that we applied here with the Z. mobilis transposon mutant dataset, could easily be utilized to improve future genome-scale metabolic reconstructions for organisms where these, or similar, high-throughput datasets are available.

Computation-Driven Analysis of Model Polyextremo-tolerant Fungus Exophiala dermatitidis: Defensive Pigment Metabolic Costs and Human Applications

The polyextremotolerant black yeast Exophiala dermatitidis is a tractable model system for investigation of adaptations that support growth under extreme conditions. Foremost among these adaptations are melanogenesis and carotenogenesis. A particularly important question is their metabolic production cost. However, investigation of this issue has been hindered by a relatively poor systems-level understanding of E. dermatitidis metabolism. To address this challenge, a genome-scale model (iEde2091) was developed. Using iEde2091, carotenoids were found to be more expensive to produce than melanins. Given their overlapping protective functions, this suggests that carotenoids have an underexplored yet important role in photo-protection. Furthermore, multiple defensive pigments with overlapping functions might allow E. dermatitidis to minimize cost. Because iEde2091 revealed that E. dermatitidis synthesizes the same melanins as humans and the active sites of the key tyrosinase enzyme are highly conserved this model may enable a broader understanding of melanin production across kingdoms.

Flux-based hierarchical organization of Escherichia coli's metabolic network

Biological networks across scales exhibit hierarchical organization that may constrain network function. Yet, understanding how these hierarchies arise due to the operational constraint of the networks and whether they impose limits to molecular phenotypes remains elusive. Here we show that metabolic networks include a hierarchy of reactions based on a natural flux ordering that holds for every steady state. We find that the hierarchy of reactions is reflected in experimental measurements of transcript, protein and flux levels of Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes. Our findings point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the constraints imposed by the network structure at steady state. Since reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering.

Network reduction methods for genome-scale metabolic models

Genome-scale metabolic models (GSMs) provide a comprehensive representation of cellular metabolism. GSMs provide a mechanistic link between cellular genotypes and metabolic phenotypes, and are thus widely used to analyze metabolism at the systems level. GSMs consist of hundreds or thousands of reactions. They have thus largely been analyzed with computationally efficient constraint-based methods such as flux-balance analysis, limiting their scope and phenotype prediction accuracy. Computationally more demanding but potentially more informative methods, such as kinetic and dynamic modeling, are currently limited to small or medium-sized models. Thus, it is desirable to achieve unbiased stoichiometric reductions of large-scale metabolic models to small, coarse-grained model representations that capture significant metabolic modules. Here, we review published automated and semiautomated methods used for large-scale metabolic model reduction. The top-down methods discussed provide minimal networks that retain a set of user-protected phenotypes, but may reduce the model's metabolic and phenotypic versatility. In contrast, the two bottom-up approaches reviewed retain a more unbiased set of phenotypes; at the same time, these methods require the partitioning of the GSM into metabolic subsystems by the user, and make strong assumptions on the subsystems' connections and their states, respectively.

Distributed flux balance analysis simulations of serial biomass fermentation by two organisms

Intelligent biorefinery design that addresses both the composition of the biomass feedstock as well as fermentation microorganisms could benefit from dedicated tools for computational simulation and computer-assisted optimization. Here we present the BioLego Vn2.0 framework, based on Microsoft Azure Cloud, which supports large-scale simulations of biomass serial fermentation processes by two different organisms. BioLego enables the simultaneous analysis of multiple fermentation scenarios and the comparison of fermentation potential of multiple feedstock compositions. Thanks to the effective use of cloud computing it further allows resource intensive analysis and exploration of media and organism modifications. We use BioLego to obtain biological and validation results, including (1) exploratory search for the optimal utilization of corn biomasses-corn cobs, corn fiber and corn stover-in fermentation biorefineries; (2) analysis of the possible effects of changes in the composition of K. alvarezi biomass on the ethanol production yield in an anaerobic two-step process (S. cerevisiae followed by E. coli); (3) analysis of the impact, on the estimated ethanol production yield, of knocking out single organism reactions either in one or in both organisms in an anaerobic two-step fermentation process of Ulva sp. into ethanol (S. cerevisiae followed by E. coli); and (4) comparison of several experimentally measured ethanol fermentation rates with the predictions of BioLego.

Towards scaling elementary flux mode computation

While elementary flux mode (EFM) analysis is now recognized as a cornerstone computational technique for cellular pathway analysis and engineering, EFM application to genome-scale models remains computationally prohibitive. This article provides a review of aspects of EFM computation that elucidates bottlenecks in scaling EFM computation. First, algorithms for computing EFMs are reviewed. Next, the impact of redundant constraints, sensitivity to constraint ordering and network compression are evaluated. Then, the advantages and limitations of recent parallelization and GPU-based efforts are highlighted. The article then reviews alternative pathway analysis approaches that aim to reduce the EFM solution space. Despite advances in EFM computation, our review concludes that continued scaling of EFM computation is necessary to apply EFM to genome-scale models. Further, our review concludes that pathway analysis methods that target specific pathway properties can provide powerful alternatives to EFM analysis.

Metabolic Modeling of Streptococcus mutans Reveals Complex Nutrient Requirements of an Oral Pathogen

Streptococcus mutans is a Gram-positive bacterium that thrives under acidic conditions and is a primary cause of tooth decay (dental caries). To better understand the metabolism of S. mutans on a systematic level, we manually constructed a genome-scale metabolic model of the S. mutans type strain UA159. The model, called iSMU, contains 675 reactions involving 429 metabolites and the products of 493 genes. We validated iSMU by comparing simulations with growth experiments in defined medium. The model simulations matched experimental results for 17 of 18 carbon source utilization assays and 47 of 49 nutrient depletion assays. We also simulated the effects of single gene deletions. The model's predictions agreed with 78.1% and 84.4% of the gene essentiality predictions from two experimental data sets. Our manually curated model is more accurate than S. mutans models generated from automated reconstruction pipelines and more complete than other manually curated models. We used iSMU to generate hypotheses about the S. mutans metabolic network. Subsequent genetic experiments confirmed that (i) S. mutans catabolizes sorbitol via a sorbitol-6-phosphate 2-dehydrogenase (SMU_308) and (ii) the Leloir pathway is required for growth on complex carbohydrates such as raffinose. We believe the iSMU model is an important resource for understanding the metabolism of S. mutans and guiding future experiments.IMPORTANCE Tooth decay is the most prevalent chronic disease in the United States. Decay is caused by the bacterium Streptococcus mutans, an oral pathogen that ferments sugars into tooth-destroying lactic acid. We constructed a complete metabolic model of S. mutans to systematically investigate how the bacterium grows. The model provides a valuable resource for understanding and targeting S. mutans' ability to outcompete other species in the oral microbiome.

Metabolic Model of the Phytophthora infestans-Tomato Interaction Reveals Metabolic Switches during Host Colonization

The oomycete pathogen Phytophthora infestans causes potato and tomato late blight, a disease that is a serious threat to agriculture. P. infestans is a hemibiotrophic pathogen, and during infection, it scavenges nutrients from living host cells for its own proliferation. To date, the nutrient flux from host to pathogen during infection has hardly been studied, and the interlinked metabolisms of the pathogen and host remain poorly understood. Here, we reconstructed an integrated metabolic model of P. infestans and tomato (Solanum lycopersicum) by integrating two previously published models for both species. We used this integrated model to simulate metabolic fluxes from host to pathogen and explored the topology of the model to study the dependencies of the metabolism of P. infestans on that of tomato. This showed, for example, that P. infestans, a thiamine auxotroph, depends on certain metabolic reactions of the tomato thiamine biosynthesis. We also exploited dual-transcriptome data of a time course of a full late blight infection cycle on tomato leaves and integrated the expression of metabolic enzymes in the model. This revealed profound changes in pathogen-host metabolism during infection. As infection progresses, P. infestans performs less de novo synthesis of metabolites and scavenges more metabolites from tomato. This integrated metabolic model for the P. infestans-tomato interaction provides a framework to integrate data and generate hypotheses about in planta nutrition of P. infestans throughout its infection cycle.IMPORTANCE Late blight disease caused by the oomycete pathogen Phytophthora infestans leads to extensive yield losses in tomato and potato cultivation worldwide. To effectively control this pathogen, a thorough understanding of the mechanisms shaping the interaction with its hosts is paramount. While considerable work has focused on exploring host defense mechanisms and identifying P. infestans proteins contributing to virulence and pathogenicity, the nutritional strategies of the pathogen are mostly unresolved. Genome-scale metabolic models (GEMs) can be used to simulate metabolic fluxes and help in unravelling the complex nature of metabolism. We integrated a GEM of tomato with a GEM of P. infestans to simulate the metabolic fluxes that occur during infection. This yields insights into the nutrients that P. infestans obtains during different phases of the infection cycle and helps in generating hypotheses about nutrition in planta.

Machine and deep learning meet genome-scale metabolic modeling

Omic data analysis is steadily growing as a driver of basic and applied molecular biology research. Core to the interpretation of complex and heterogeneous biological phenotypes are computational approaches in the fields of statistics and machine learning. In parallel, constraint-based metabolic modeling has established itself as the main tool to investigate large-scale relationships between genotype, phenotype, and environment. The development and application of these methodological frameworks have occurred independently for the most part, whereas the potential of their integration for biological, biomedical, and biotechnological research is less known. Here, we describe how machine learning and constraint-based modeling can be combined, reviewing recent works at the intersection of both domains and discussing the mathematical and practical aspects involved. We overlap systematic classifications from both frameworks, making them accessible to nonexperts. Finally, we delineate potential future scenarios, propose new joint theoretical frameworks, and suggest concrete points of investigation for this joint subfield. A multiview approach merging experimental and knowledge-driven omic data through machine learning methods can incorporate key mechanistic information in an otherwise biologically-agnostic learning process.

Probabilistic controllability approach to metabolic fluxes in normal and cancer tissues

Recent research has shown that many types of cancers take control of specific metabolic processes. We compiled metabolic networks corresponding to four healthy and cancer tissues, and analysed the healthy–cancer transition from the metabolic flux change perspective. We used a Probabilistic Minimum Dominating Set (PMDS) model, which identifies a minimum set of nodes that act as driver nodes and control the entire network. The combination of control theory with flux correlation analysis shows that flux correlations substantially increase in cancer states of breast, kidney and urothelial tissues, but not in lung. No change in the network topology between healthy and cancer networks was observed, but PMDS analysis shows that cancer states require fewer controllers than their corresponding healthy states. These results indicate that cancer metabolism is characterised by more streamlined flux distributions, which may be focused towards a reduced set of objectives and controlled by fewer regulatory elements.

Metabolic rewiring is a feature of many cancers. Here, the authors combine control theory and flux correlation analysis to study the transition of healthy metabolic networks to cancer states, and find that cancer metabolism is characterized by more streamlined flux distributions.

Improving the accuracy of flux balance analysis through the implementation of carbon availability constraints for intracellular reactions

Constraint-based modeling methods, such as Flux Balance Analysis (FBA), have been extensively used to decipher complex, information rich -omics datasets to elicit system-wide behavioral patterns of cellular metabolism. FBA has been successfully used to gain insight in a wide range of applications, such as range of substrate utilization, product yields and to design metabolic engineering strategies to improve bioprocess performance. A well-known challenge associated with large genome-scale metabolic networks is that they result in underdetermined problem formulations. Consequently, rather than unique solutions, FBA and related methods examine ranges of reaction flux values that are consistent with the studied physiological conditions. The wider the reported flux ranges, the higher the uncertainty in the determination of basic reaction properties, limiting interpretability of and confidence in the results. Herein, we propose a new, computationally efficient approach that refines flux range predictions by constraining reaction fluxes on the basis of the elemental balance of carbon. We compared carbon constraint FBA (ccFBA) against experimentally-measured intracellular fluxes using the latest CHO GEM (iCHO1766) and were able to substantially improve the accuracy of predicted flux values compared with FBA. ccFBA can be used as a stand-alone method but is also compatible with and complimentary to other constraint-based approaches.

Evolutionary design principles in metabolism

Microorganisms are ubiquitous and adapt to various dynamic environments to sustain growth. These adaptations accumulate, generating new traits forming the basis of evolution. Organisms adapt at various levels, such as gene regulation, signalling, protein-protein interactions and metabolism. Of these, metabolism forms the integral core of an organism for maintaining the growth and function of a cell. Therefore, studying adaptations in metabolic networks is crucial to understand the emergence of novel metabolic capabilities. Metabolic networks, composed of enzyme-catalysed reactions, exhibit certain repeating paradigms or design principles that arise out of different selection pressures. In this review, we discuss the design principles that are known to exist in metabolic networks, such as functional redundancy, modularity, flux coupling and exaptations. We elaborate on the studies that have helped gain insights highlighting the interplay of these design principles and adaptation. Further, we discuss how evolution plays a role in exploiting such paradigms to enhance the robustness of organisms. Looking forward, we predict that with the availability of ever-increasing numbers of bacterial, archaeal and eukaryotic genomic sequences, novel design principles will be identified, expanding our understanding of these paradigms shaped by varied evolutionary processes.

Designing Metabolic Division of Labor in Microbial Communities

Microbes face a trade-off between being metabolically independent and relying on neighboring organisms for the supply of some essential metabolites. This balance of conflicting strategies affects microbial community structure and dynamics, with important implications for microbiome research and synthetic ecology. A "gedanken" (thought) experiment to investigate this trade-off would involve monitoring the rise of mutual dependence as the number of metabolic reactions allowed in an organism is increasingly constrained. The expectation is that below a certain number of reactions, no individual organism would be able to grow in isolation and cross-feeding partnerships and division of labor would emerge. We implemented this idealized experiment using in silico genome-scale models. In particular, we used mixed-integer linear programming to identify trade-off solutions in communities of Escherichia coli strains. The strategies that we found revealed a large space of opportunities in nuanced and nonintuitive metabolic division of labor, including, for example, splitting the tricarboxylic acid (TCA) cycle into two separate halves. The systematic computation of possible solutions in division of labor for 1-, 2-, and 3-strain consortia resulted in a rich and complex landscape. This landscape displayed a nonlinear boundary, indicating that the loss of an intracellular reaction was not necessarily compensated for by a single imported metabolite. Different regions in this landscape were associated with specific solutions and patterns of exchanged metabolites. Our approach also predicts the existence of regions in this landscape where independent bacteria are viable but are outcompeted by cross-feeding pairs, providing a possible incentive for the rise of division of labor. IMPORTANCE Understanding how microbes assemble into communities is a fundamental open issue in biology, relevant to human health, metabolic engineering, and environmental sustainability. A possible mechanism for interactions of microbes is through cross-feeding, i.e., the exchange of small molecules. These metabolic exchanges may allow different microbes to specialize in distinct tasks and evolve division of labor. To systematically explore the space of possible strategies for division of labor, we applied advanced optimization algorithms to computational models of cellular metabolism. Specifically, we searched for communities able to survive under constraints (such as a limited number of reactions) that would not be sustainable by individual species. We found that predicted consortia partition metabolic pathways in ways that would be difficult to identify manually, possibly providing a competitive advantage over individual organisms. In addition to helping understand diversity in natural microbial communities, our approach could assist in the design of synthetic consortia.

Cellular determinants of metabolite concentration ranges

Cellular functions are shaped by reaction networks whose dynamics are determined by the concentrations of underlying components. However, cellular mechanisms ensuring that a component’s concentration resides in a given range remain elusive. We present network properties which suffice to identify components whose concentration ranges can be efficiently computed in mass-action metabolic networks. We show that the derived ranges are in excellent agreement with simulations from a detailed kinetic metabolic model of Escherichia coli. We demonstrate that the approach can be used with genome-scale metabolic models to arrive at predictions concordant with measurements from Escherichia coli under different growth scenarios. By application to 14 genome-scale metabolic models from diverse species, our approach specifies the cellular determinants of concentration ranges that can be effectively employed to make predictions for a variety of biotechnological and medical applications.

We present a computational approach for inferring concentration ranges from genome-scale metabolic models. The approach specifies a determinant and molecular mechanism underling facile control of concentration ranges for components in large-scale cellular networks. Most importantly, the predictions about concentration ranges do not require knowledge of kinetic parameters (which are difficult to specify at a genome scale), provided measurements of concentrations in a reference state. The approach assumes that reaction rates follow the mass action law used in the derivations of other types of kinetics. We apply the approach with large-scale kinetic and stoichiometric metabolic models of organisms from different kingdoms of life to show that we can identify a proportion of metabolites to which our approach is applicable. By challenging the predictions of concentration ranges in the genome-scale metabolic network of E. coli with real-world data sets, we further demonstrate the prediction power and limitations of the approach.

Yeast Genome-Scale Metabolic Models for Simulating Genotype-Phenotype Relations

Understanding genotype-phenotype dependency is a universal aim for all life sciences. While the complete genotype-phenotype relations remain challenging to resolve, metabolic phenotypes are moving within the reach through genome-scale metabolic model simulations. Genome-scale metabolic models are available for commonly investigated yeasts, such as model eukaryote and domesticated fermentation species Saccharomyces cerevisiae, and automatic reconstruction methods facilitate obtaining models for any sequenced species. The models allow for investigating genotype-phenotype relations through simulations simultaneously considering the effects of nutrient availability, and redox and energy homeostasis in cells. Genome-scale models also offer frameworks for omics data integration to help to uncover how the translation of genotypes to the apparent phenotypes is regulated at different levels. In this chapter, we provide an overview of the yeast genome-scale metabolic models and the simulation approaches for using these models to interrogate genotype-phenotype relations. We review the methodological approaches according to the underlying biological reasoning in order to inspire formulating novel questions and applications that the genome-scale metabolic models could contribute to. Finally, we discuss current challenges and opportunities in the genome-scale metabolic model simulations.

An upper limit on Gibbs energy dissipation governs cellular metabolism

The principles governing cellular metabolic operation are poorly understood. Because diverse organisms show similar metabolic flux patterns, we hypothesized that a fundamental thermodynamic constraint might shape cellular metabolism. Here, we develop a constraint-based model for Saccharomyces cerevisiae with a comprehensive description of biochemical thermodynamics including a Gibbs energy balance. Non-linear regression analyses of quantitative metabolome and physiology data reveal the existence of an upper rate limit for cellular Gibbs energy dissipation. By applying this limit in flux balance analyses with growth maximization as the objective function, our model correctly predicts the physiology and intracellular metabolic fluxes for different glucose uptake rates as well as the maximal growth rate. We find that cells arrange their intracellular metabolic fluxes in such a way that, with increasing glucose uptake rates, they can accomplish optimal growth rates but stay below the critical rate limit on Gibbs energy dissipation. Once all possibilities for intracellular flux redistribution are exhausted, cells reach their maximal growth rate. This principle also holds for Escherichia coli and different carbon sources. Our work proposes that metabolic reaction stoichiometry, a limit on the cellular Gibbs energy dissipation rate, and the objective of growth maximization shape metabolism across organisms and conditions.

Quantitative flux coupling analysis

Flux coupling analysis (FCA) aims to describe the functional dependencies among reactions in a metabolic network. Currently studied coupling relations are qualitative in the sense that they identify pairs of reactions for which the activity of one reaction necessitates the activity of the other one, but without giving any numerical bounds relating the possible activity rates. The potential applications of FCA are heavily investigated, however apart from some trivial cases there is no clue of what bottleneck in the metabolic network causes each dependency. In this article, we introduce a quantitative approach to the same flux coupling problem named quantitative flux coupling analysis (QFCA). It generalizes the current concepts as we show that all the qualitative information provided by FCA is readily available in the quantitative flux coupling equations of QFCA, without the need for any additional analysis. Moreover, we design a simple algorithm to efficiently identify these flux coupling equations which scales up to the genome-scale metabolic networks with thousands of reactions and metabolites in an effective way. Furthermore, this framework enables us to quantify the "strength" of the flux coupling relations. We also provide different biologically meaningful interpretations, including one which gives an intuitive certificate of precisely which metabolites in the network enforce each flux coupling relation. Eventually, we conclude by suggesting the probable application of QFCA to the metabolic gap-filling problem, which we only begin to address here and is left for future research to further investigate.

Improving the EFMs quality by augmenting their representativeness in LP methods

Background

Although cellular metabolism has been widely studied, its fully comprehension is still a challenge. A main tool for this study is the analysis of meaningful pieces of knowledge called modes and, in particular, specially interesting classes of modes such as pathways and Elementary Flux Modes (EFMs). Its study often has to deal with issues such as the appearance of infeasibilities or the difficulty of finding representative enough sets of modes that are free of repetitions. Mode extraction methods usually incorporate strategies devoted to mitigate this phenomena but they still get a high ratio of repetitions in the set of solutions.

Results

This paper presents a proposal to improve the representativeness of the full set of metabolic reactions in the set of computed modes by penalizing the eventual high frequency of occurrence of some reactions during the extraction. This strategy can be applied to any linear programming based extraction existent method.

Conclusions

Our strategy enhances the quality of a set of extracted EFMs favouring the presence of every reaction in it and improving the efficiency by mitigating the occurrence of repeated solutions. The new proposed strategy can complement other EFMs extraction methods based on linear programming. The obtained solutions are more likely to be diverse using less computing effort and improving the efficiency of the extraction.

Machine Learning Predicts the Yeast Metabolome from the Quantitative Proteome of Kinase Knockouts

A challenge in solving the genotype-to-phenotype relationship is to predict a cell’s metabolome, believed to correlate poorly with gene expression. Using comparative quantitative proteomics, we found that differential protein expression in 97 Saccharomyces cerevisiae kinase deletion strains is non-redundant and dominated by abundance changes in metabolic enzymes. Associating differential enzyme expression landscapes to corresponding metabolomes using network models provided reasoning for poor proteome-metabolome correlations; differential protein expression redistributes flux control between many enzymes acting in concert, a mechanism not captured by one-to-one correlation statistics. Mapping these regulatory patterns using machine learning enabled the prediction of metabolite concentrations, as well as identification of candidate genes important for the regulation of metabolism. Overall, our study reveals that a large part of metabolism regulation is explained through coordinated enzyme expression changes. Our quantitative data indicate that this mechanism explains more than half of metabolism regulation and underlies the interdependency between enzyme levels and metabolism, which renders the metabolome a predictable phenotype.

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The proteome of kinase knockouts is dominated by enzyme abundance changes

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The enzyme expression profiles of kinase knockouts are non-redundant

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Metabolism is regulated by many expression changes acting in concert

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Machine learning accurately predicts the metabolome from enzyme abundance

An appeal to magic? The discovery of a non-enzymatic metabolism and its role in the origins of life

Until recently, prebiotic precursors to metabolic pathways were not known. In parallel, chemistry achieved the synthesis of amino acids and nucleotides only in reaction sequences that do not resemble metabolic pathways, and by using condition step changes, incompatible with enzyme evolution. As a consequence, it was frequently assumed that the topological organisation of the metabolic pathway has formed in a Darwinian process. The situation changed with the discovery of a non-enzymatic glycolysis and pentose phosphate pathway. The suite of metabolism-like reactions is promoted by a metal cation, (Fe(II)), abundant in Archean sediment, and requires no condition step changes. Knowledge about metabolism-like reaction topologies has accumulated since, and supports non-enzymatic origins of gluconeogenesis, the S-adenosylmethionine pathway, the Krebs cycle, as well as CO2 fixation. It now feels that it is only a question of time until essential parts of metabolism can be replicated non-enzymatically. Here, I review the 'accidents' that led to the discovery of the non-enzymatic glycolysis, and on the example of a chemical network based on hydrogen cyanide, I provide reasoning why metabolism-like non-enzymatic reaction topologies may have been missed for a long time. Finally, I discuss that, on the basis of non-enzymatic metabolism-like networks, one can elaborate stepwise scenarios for the origin of metabolic pathways, a situation that increasingly renders the origins of metabolism a tangible problem.

An enormous potential for niche construction through bacterial cross-feeding in a homogeneous environment

Microorganisms modify their environment by excreting by-products of metabolism, which can create new ecological niches that can help microbial populations diversify. A striking example comes from experimental evolution of genetically identical Escherichia coli populations that are grown in a homogeneous environment with the single carbon source glucose. In such experiments, stable communities of genetically diverse cross-feeding E. coli cells readily emerge. Some cells that consume the primary carbon source glucose excrete a secondary carbon source, such as acetate, that sustains other community members. Few such cross-feeding polymorphisms are known experimentally, because they are difficult to screen for. We studied the potential of bacterial metabolism to create new ecological niches based on cross-feeding. To do so, we used genome scale models of the metabolism of E. coli and metabolisms of similar complexity, to identify unique pairs of primary and secondary carbon sources in these metabolisms. We then combined dynamic flux balance analysis with analytical calculations to identify which pair of carbon sources can sustain a polymorphic cross-feeding community. We identified almost 10,000 such pairs of carbon sources, each of them corresponding to a unique ecological niche. Bacterial metabolism shows an immense potential for the construction of new ecological niches through cross feeding.

Biodiversity can emerge in a completely homogeneous environment from populations with initially genetically identical individuals. This striking observation comes from experimental evolution of bacteria, which create new ecological niches when they excrete nutrient-rich waste products that can sustain the life of other bacteria. It is difficult to estimate the potential of any one organism for such metabolic niche construction experimentally, because it is challenging to screen for novel metabolic abilities on a large scale. We therefore used experimentally validated models of bacterial metabolism to predict how many novel niches organisms like Escherichia coli can construct, if a novel niche must be able to sustain a stable community of microbes that differ in the nutrients they consume. We identify thousands of such niches. They differ in their primary carbon source and a secondary carbon source that is excreted by some microbes and used by others. Because we restricted ourselves to chemically simple environments, we may even have underestimated the enormous potential of microbes for niche construction.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering

BACKGROUND

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing.

RESULTS

We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli.

CONCLUSIONS

We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements.