MOTIVATION: Several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution. RESULTS: By approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction. AVAILABILITY AND IMPLEMENTATION: Open source scripts to reproduce the results are here https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox.

MOTIVATION: Genome-scale metabolic reconstructions have been assembled for thousands of organisms using a wide range of tools. However, metabolite annotations, required to compare and link metabolites between reconstructions, remain incomplete. Here, we aim to further extend metabolite annotation coverage using various databases and chemoinformatic approaches. RESULTS: We developed a COBRA toolbox extension, deemed MetaboAnnotator, which facilitates the comprehensive annotation of metabolites with database independent and dependent identifiers, obtains molecular structure files, and calculates metabolite formula and charge at pH 7.2. The resulting metabolite annotations allow for subsequent cross-mapping between reconstructions and mapping of, e.g., metabolomic data. AVAILABILITY AND IMPLEMENTATION: MetaboAnnotator and tutorials are freely available at https://github.com/opencobra. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Abstract Motivation Manual curation of genome-scale reconstructions is laborious, yet existing automated curation tools do not typically take species-specific experimental and curated genomic data into account. Results We developed Data-drivEn METabolic nEtwork Refinement (DEMETER), a Constraint-Based Reconstruction and Analysis (COBRA) Toolbox extension, which enables the efficient, simultaneous refinement of thousands of draft genome-scale reconstructions, while ensuring adherence to the quality standards in the field, agreement with available experimental data and refinement of pathways based on manually refined genome annotations. Availability and implementation DEMETER and tutorials are freely available at https://github.com/opencobra. Supplementary information Supplementary data are available at Bioinformatics online.

The Disease Maps Project builds on a network of scientific and clinical groups that exchange best practices, share information and develop systems biomedicine tools. The project aims for an integrated, highly curated and user-friendly platform for disease-related knowledge. The primary focus of disease maps is on interconnected signaling, metabolic and gene regulatory network pathways represented in standard formats. The involvement of domain experts ensures that the key disease hallmarks are covered and relevant, up-to-date knowledge is adequately represented. Expert-curated and computer readable, disease maps may serve as a compendium of knowledge, allow for data-supported hypothesis generation or serve as a scaffold for the generation of predictive mathematical models. This article summarizes the 2nd Disease Maps Community meeting, highlighting its important topics and outcomes. We outline milestones on the roadmap for the future development of disease maps, including creating and maintaining standardized disease maps; sharing parts of maps that encode common human disease mechanisms; providing technical solutions for complexity management of maps; and Web tools for in-depth exploration of such maps. A dedicated discussion was focused on mathematical modeling approaches, as one of the main goals of disease map development is the generation of mathematically interpretable representations to predict disease comorbidity or drug response and to suggest drug repositioning, altogether supporting clinical decisions.

MOTIVATION: The application of constraint-based modeling to functionally analyze metagenomic data has been limited so far, partially due to the absence of suitable toolboxes. RESULTS: To address this gap, we created a comprehensive toolbox to model (i) microbe-microbe and host-microbe metabolic interactions, and (ii) microbial communities using microbial genome-scale metabolic reconstructions and metagenomic data. The Microbiome Modeling Toolbox extends the functionality of the constraint-based reconstruction and analysis toolbox. AVAILABILITY AND IMPLEMENTATION: The Microbiome Modeling Toolbox and the tutorials at https://git.io/microbiomeModelingToolbox.

BACKGROUND: The interplay between metabolic processes and signalling pathways remains poorly understood. Global, detailed and comprehensive reconstructions of human metabolism and signalling pathways exist in the form of molecular maps, but they have never been integrated together. We aim at filling in this gap by integrating of both signalling and metabolic pathways allowing a visual exploration of multi-level omics data and study of cross-regulatory circuits between these processes in health and in disease. RESULTS: We combined two comprehensive manually curated network maps. Atlas of Cancer Signalling Network (ACSN), containing mechanisms frequently implicated in cancer; and ReconMap 2.0, a comprehensive reconstruction of human metabolic network. We linked ACSN and ReconMap 2.0 maps via common players and represented the two maps as interconnected layers using the NaviCell platform for maps exploration ( https://navicell.curie.fr/pages/maps_ReconMap%202.html ). In addition, proteins catalysing metabolic reactions in ReconMap 2.0 were not previously visually represented on the map canvas. This precluded visualisation of omics data in the context of ReconMap 2.0. We suggested a solution for displaying protein nodes on the ReconMap 2.0 map in the vicinity of the corresponding reaction or process nodes. This permits multi-omics data visualisation in the context of both map layers. Exploration and shuttling between the two map layers is possible using Google Maps-like features of NaviCell. The integrated networks ACSN-ReconMap 2.0 are accessible online and allows data visualisation through various modes such as markers, heat maps, bar-plots, glyphs and map staining. The integrated networks were applied for comparison of immunoreactive and proliferative ovarian cancer subtypes using transcriptomic, copy number and mutation multi-omics data. A certain number of metabolic and signalling processes specifically deregulated in each of the ovarian cancer sub-types were identified. CONCLUSIONS: As knowledge evolves and new omics data becomes more heterogeneous, gathering together existing domains of biology under common platforms is essential. We believe that an integrated ACSN-ReconMap 2.0 networks will help in understanding various disease mechanisms and discovery of new interactions at the intersection of cell signalling and metabolism. In addition, the successful integration of metabolic and signalling networks allows broader systems biology approach application for data interpretation and retrieval of intervention points to tackle simultaneously the key players coordinating signalling and metabolism in human diseases.

SUMMARY: In constraint-based metabolic modelling, physical and biochemical constraints define a polyhedral convex set of feasible flux vectors. Uniform sampling of this set provides an unbiased characterization of the metabolic capabilities of a biochemical network. However, reliable uniform sampling of genome-scale biochemical networks is challenging due to their high dimensionality and inherent anisotropy. Here, we present an implementation of a new sampling algorithm, coordinate hit-and-run with rounding (CHRR). This algorithm is based on the provably efficient hit-and-run random walk and crucially uses a preprocessing step to round the anisotropic flux set. CHRR provably converges to a uniform stationary sampling distribution. We apply it to metabolic networks of increasing dimensionality. We show that it converges several times faster than a popular artificial centering hit-and-run algorithm, enabling reliable and tractable sampling of genome-scale biochemical networks. AVAILABILITY AND IMPLEMENTATION: https://github.com/opencobra/cobratoolbox . CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: Flux balance analysis and its variants are widely used methods for predicting steady-state reaction rates in biochemical reaction networks. The exploration of high dimensional networks with such methods is currently hampered by software performance limitations. Results: DistributedFBA.jl is a high-level, high-performance, open-source implementation of flux balance analysis in Julia. It is tailored to solve multiple flux balance analyses on a subset or all the reactions of large and huge-scale networks, on any number of threads or nodes. Availability and Implementation: The code is freely available on github.com/opencobra/COBRA.jl. The documentation can be found at opencobra.github.io/COBRA.jl. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Motivation: A genome-scale reconstruction of human metabolism, Recon 2, is available but no interface exists to interactively visualize its content integrated with omics data and simulation results. Results: We manually drew a comprehensive map, ReconMap 2.0, that is consistent with the content of Recon 2. We present it within a web interface that allows content query, visualization of custom datasets and submission of feedback to manual curators. Availability and Implementation: ReconMap can be accessed via http://vmh.uni.lu , with network export in a Systems Biology Graphical Notation compliant format released under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. A Constraint-Based Reconstruction and Analysis (COBRA) Toolbox extension to interact with ReconMap is available via https://github.com/opencobra/cobratoolbox . Contact: [email protected].

The metabolic phenotype of cancer cells is reflected by the metabolites they consume and by the byproducts they release. Here, we use quantitative, extracellular metabolomic data of the NCI-60 panel and a novel computational method to generate 120 condition-specific cancer cell line metabolic models. These condition-specific cancer models used distinct metabolic strategies to generate energy and cofactors. The analysis of the models' capability to deal with environmental perturbations revealed three oxotypes, differing in the range of allowable oxygen uptake rates. Interestingly, models based on metabolomic profiles of melanoma cells were distinguished from other models through their low oxygen uptake rates, which were associated with a glycolytic phenotype. A subset of the melanoma cell models required reductive carboxylation. The analysis of protein and RNA expression levels from the Human Protein Atlas showed that IDH2, which was an essential gene in the melanoma models, but not IDH1 protein, was detected in normal skin cell types and melanoma. Moreover, the von Hippel-Lindau tumor suppressor (VHL) protein, whose loss is associated with non-hypoxic HIF-stabilization, reductive carboxylation, and promotion of glycolysis, was uniformly absent in melanoma. Thus, the experimental data supported the predicted role of IDH2 and the absence of VHL protein supported the glycolytic and low oxygen phenotype predicted for melanoma. Taken together, our approach of integrating extracellular metabolomic data with metabolic modeling and the combination of different network interrogation methods allowed insights into the metabolism of cells.

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.

MOTIVATION: Genome-scale metabolic reconstructions summarize current knowledge about a target organism in a structured manner and as such highlight missing information. Such gaps can be filled algorithmically. Scalability limitations of available algorithms for gap filling hinder their application to compartmentalized reconstructions. RESULTS: We present fastGapFill, a computationally efficient tractable extension to the COBRA toolbox that permits the identification of candidate missing knowledge from a universal biochemical reaction database (e.g. Kyoto Encyclopedia of Genes and Genomes) for a given (compartmentalized) metabolic reconstruction. The stoichiometric consistency of the universal reaction database and of the metabolic reconstruction can be tested for permitting the computation of biologically more relevant solutions. We demonstrate the efficiency and scalability of fastGapFill on a range of metabolic reconstructions. AVAILABILITY AND IMPLEMENTATION: fastGapFill is freely available from http://thielelab.eu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like integrated networks that represent metabolism and macromolecular synthesis, are inherently multiscale because reaction rates can vary over many orders of magnitude. They require special methods for accurate analysis because naive use of standard optimization systems can produce inaccurate or erroneously infeasible results. RESULTS: We describe techniques enabling off-the-shelf optimization software to compute accurate solutions to the poorly scaled optimization problems arising from flux balance analysis of multiscale biochemical reaction networks. We implement lifting techniques for flux balance analysis within the openCOBRA toolbox and demonstrate our techniques using the first integrated reconstruction of metabolism and macromolecular synthesis for E. coli. CONCLUSION: Our techniques enable accurate flux balance analysis of multiscale networks using off-the-shelf optimization software. Although we describe lifting techniques in the context of flux balance analysis, our methods can be used to handle a variety of optimization problems arising from analysis of multiscale network reconstructions.

Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.

MOTIVATION: In flux balance analysis of genome scale stoichiometric models of metabolism, the principal constraints are uptake or secretion rates, the steady state mass conservation assumption and reaction directionality. Here, we introduce an algorithmic pipeline for quantitative assignment of reaction directionality in multi-compartmental genome scale models based on an application of the second law of thermodynamics to each reaction. Given experimental or computationally estimated standard metabolite species Gibbs energy and metabolite concentrations, the algorithms bounds reaction Gibbs energy, which is transformed to in vivo pH, temperature, ionic strength and electrical potential. RESULTS: This cross-platform MATLAB extension to the COnstraint-Based Reconstruction and Analysis (COBRA) toolbox is computationally efficient, extensively documented and open source. AVAILABILITY: http://opencobra.sourceforge.net.

Metabolic network reconstructions represent valuable scaffolds for '-omics' data integration and are used to computationally interrogate network properties. However, they do not explicitly account for the synthesis of macromolecules (i.e., proteins and RNA). Here, we present the first genome-scale, fine-grained reconstruction of Escherichia coli's transcriptional and translational machinery, which produces 423 functional gene products in a sequence-specific manner and accounts for all necessary chemical transformations. Legacy data from over 500 publications and three databases were reviewed, and many pathways were considered, including stable RNA maturation and modification, protein complex formation, and iron-sulfur cluster biogenesis. This reconstruction represents the most comprehensive knowledge base for these important cellular functions in E. coli and is unique in its scope. Furthermore, it was converted into a mathematical model and used to: (1) quantitatively integrate gene expression data as reaction constraints and (2) compute functional network states, which were compared to reported experimental data. For example, the model predicted accurately the ribosome production, without any parameterization. Also, in silico rRNA operon deletion suggested that a high RNA polymerase density on the remaining rRNA operons is needed to reproduce the reported experimental ribosome numbers. Moreover, functional protein modules were determined, and many were found to contain gene products from multiple subsystems, highlighting the functional interaction of these proteins. This genome-scale reconstruction of E. coli's transcriptional and translational machinery presents a milestone in systems biology because it will enable quantitative integration of '-omics' datasets and thus the study of the mechanistic principles underlying the genotype-phenotype relationship.