Cardinality optimization in constraint-based modelling: application to human metabolism.

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.

Hsp90 inhibition sensitizes DLBCL cells to cisplatin.

PURPOSE: Platinum-containing therapy is standard treatment for relapsed Diffuse Large B-Cell Lymphoma (DLBCL). However, the efficacy of treatment is limited by drug resistance leading to relapse. Cisplatin resistance has been linked to impairments of the DNA damage response, and several DNA repair proteins have been identified as clients of the molecular chaperone Hsp90. Here, we investigated the combinatory treatment of cisplatin and the Hsp90 inhibitor, 17AAG, in DLBCL cells to evaluate if inhibition of Hsp90 could sensitize DLBCL cells to cisplatin treatment. METHODS: Cell viability was assessed for cisplatin and 17AAG as monotherapies and for 25 different combinations in 7 DLBCL cell lines, where the Bliss Independence Model and the Combination Index were applied to assess their interaction. Induction of apoptosis and DNA damage response were evaluated by measuring Annexin V and γH2AX levels after 48 h of exposure. RESULTS: 17AAG synergized with cisplatin in DLBCL cells as detected in both interaction assessment models, resulting in a lower viability after 48 h for the combination-treated cells compared to both vehicle and single drug-treated cells. The combination also induced a stronger apoptotic response and an increase in DNA damage in 17AAG, cisplatin- and combination-treated cells compared to vehicle-treated cells, with the effect of the combination generally being higher than compared to both single drugs. CONCLUSION: This study demonstrates that 17AAG sensitizes DLBCL cells to cisplatin treatment. This effect is correlated with increased apoptotic and DNA damage response, potentially mediated by downregulation of Hsp90 clients in DNA repair pathways. Thus, cisplatin resistance could plausibly be overcome by combining the treatment with an Hsp90 inhibiting drug.

Structural conserved moiety splitting of a stoichiometric matrix.

Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N∈Zm×n, where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m-rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0.

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.

The Virtual Metabolic Human database: integrating human and gut microbiome metabolism with nutrition and disease.

A multitude of factors contribute to complex diseases and can be measured with 'omics' methods. Databases facilitate data interpretation for underlying mechanisms. Here, we describe the Virtual Metabolic Human (VMH, www.vmh.life) database encapsulating current knowledge of human metabolism within five interlinked resources 'Human metabolism', 'Gut microbiome', 'Disease', 'Nutrition', and 'ReconMaps'. The VMH captures 5180 unique metabolites, 17 730 unique reactions, 3695 human genes, 255 Mendelian diseases, 818 microbes, 632 685 microbial genes and 8790 food items. The VMH's unique features are (i) the hosting of the metabolic reconstructions of human and gut microbes amenable for metabolic modeling; (ii) seven human metabolic maps for data visualization; (iii) a nutrition designer; (iv) a user-friendly webpage and application-programming interface to access its content; (v) user feedback option for community engagement and (vi) the connection of its entities to 57 other web resources. The VMH represents a novel, interdisciplinary database for data interpretation and hypothesis generation to the biomedical community.

Comparative evaluation of atom mapping algorithms for balanced metabolic reactions: application to Recon 3D.

The mechanism of each chemical reaction in a metabolic network can be represented as a set of atom mappings, each of which relates an atom in a substrate metabolite to an atom of the same element in a product metabolite. Genome-scale metabolic network reconstructions typically represent biochemistry at the level of reaction stoichiometry. However, a more detailed representation at the underlying level of atom mappings opens the possibility for a broader range of biological, biomedical and biotechnological applications than with stoichiometry alone. Complete manual acquisition of atom mapping data for a genome-scale metabolic network is a laborious process. However, many algorithms exist to predict atom mappings. How do their predictions compare to each other and to manually curated atom mappings? For more than four thousand metabolic reactions in the latest human metabolic reconstruction, Recon 3D, we compared the atom mappings predicted by six atom mapping algorithms. We also compared these predictions to those obtained by manual curation of atom mappings for over five hundred reactions distributed among all top level Enzyme Commission number classes. Five of the evaluated algorithms had similarly high prediction accuracy of over 91% when compared to manually curated atom mapped reactions. On average, the accuracy of the prediction was highest for reactions catalysed by oxidoreductases and lowest for reactions catalysed by ligases. In addition to prediction accuracy, the algorithms were evaluated on their accessibility, their advanced features, such as the ability to identify equivalent atoms, and their ability to map hydrogen atoms. In addition to prediction accuracy, we found that software accessibility and advanced features were fundamental to the selection of an atom mapping algorithm in practice.

CHRR: coordinate hit-and-run with rounding for uniform sampling of constraint-based models.

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: ronan.mt.fleming@gmail.com or vempala@cc.gatech.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks.

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.

Modeling the effects of commonly used drugs on human metabolism.

Metabolism contributes significantly to the pharmacokinetics and pharmacodynamics of a drug. In addition, diet and genetics have a profound effect on cellular metabolism with respect to both health and disease. In the present study, we assembled a comprehensive, literature-based drug metabolic reconstruction of the 18 most highly prescribed drug groups, including statins, anti-hypertensives, immunosuppressants and analgesics. This reconstruction captures in detail our current understanding of their absorption, intracellular distribution, metabolism and elimination. We combined this drug module with the most comprehensive reconstruction of human metabolism, Recon 2, yielding Recon2_DM1796, which accounts for 2803 metabolites and 8161 reactions. By defining 50 specific drug objectives that captured the overall drug metabolism of these compounds, we investigated the effects of dietary composition and inherited metabolic disorders on drug metabolism and drug-drug interactions. Our main findings include: (a) a shift in dietary patterns significantly affects statins and acetaminophen metabolism; (b) disturbed statin metabolism contributes to the clinical phenotype of mitochondrial energy disorders; and (c) the interaction between statins and cyclosporine can be explained by several common metabolic and transport pathways other than the previously established CYP3A4 connection. This work holds the potential for studying adverse drug reactions and designing patient-specific therapies.

Comparative evaluation of open source software for mapping between metabolite identifiers in metabolic network reconstructions: application to Recon 2.

BACKGROUND: An important step in the reconstruction of a metabolic network is annotation of metabolites. Metabolites are generally annotated with various database or structure based identifiers. Metabolite annotations in metabolic reconstructions may be incorrect or incomplete and thus need to be updated prior to their use. Genome-scale metabolic reconstructions generally include hundreds of metabolites. Manually updating annotations is therefore highly laborious. This prompted us to look for open-source software applications that could facilitate automatic updating of annotations by mapping between available metabolite identifiers. We identified three applications developed for the metabolomics and chemical informatics communities as potential solutions. The applications were MetMask, the Chemical Translation System, and UniChem. The first implements a "metabolite masking" strategy for mapping between identifiers whereas the latter two implement different versions of an InChI based strategy. Here we evaluated the suitability of these applications for the task of mapping between metabolite identifiers in genome-scale metabolic reconstructions. We applied the best suited application to updating identifiers in Recon 2, the latest reconstruction of human metabolism. RESULTS: All three applications enabled partially automatic updating of metabolite identifiers, but significant manual effort was still required to fully update identifiers. We were able to reduce this manual effort by searching for new identifiers using multiple types of information about metabolites. When multiple types of information were combined, the Chemical Translation System enabled us to update over 3,500 metabolite identifiers in Recon 2. All but approximately 200 identifiers were updated automatically. CONCLUSIONS: We found that an InChI based application such as the Chemical Translation System was better suited to the task of mapping between metabolite identifiers in genome-scale metabolic reconstructions. We identified several features, however, that could be added to such an application in order to tailor it to this task.

Steady-state metabolite concentrations reflect a balance between maximizing enzyme efficiency and minimizing total metabolite load.

Steady-state metabolite concentrations in a microorganism typically span several orders of magnitude. The underlying principles governing these concentrations remain poorly understood. Here, we hypothesize that observed variation can be explained in terms of a compromise between factors that favor minimizing metabolite pool sizes (e.g. limited solvent capacity) and the need to effectively utilize existing enzymes. The latter requires adequate thermodynamic driving force in metabolic reactions so that forward flux substantially exceeds reverse flux. To test this hypothesis, we developed a method, metabolic tug-of-war (mTOW), which computes steady-state metabolite concentrations in microorganisms on a genome-scale. mTOW is shown to explain up to 55% of the observed variation in measured metabolite concentrations in E. coli and C. acetobutylicum across various growth media. Our approach, based strictly on first thermodynamic principles, is the first method that successfully predicts high-throughput metabolite concentration data in bacteria across conditions.

Consistent estimation of Gibbs energy using component contributions.

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.

A community-driven global reconstruction of human metabolism.

Multiple models of human metabolism have been reconstructed, but each represents only a subset of our knowledge. Here we describe Recon 2, a community-driven, consensus 'metabolic reconstruction', which is the most comprehensive representation of human metabolism that is applicable to computational modeling. Compared with its predecessors, the reconstruction has improved topological and functional features, including ∼2× more reactions and ∼1.7× more unique metabolites. Using Recon 2 we predicted changes in metabolite biomarkers for 49 inborn errors of metabolism with 77% accuracy when compared to experimental data. Mapping metabolomic data and drug information onto Recon 2 demonstrates its potential for integrating and analyzing diverse data types. Using protein expression data, we automatically generated a compendium of 65 cell type-specific models, providing a basis for manual curation or investigation of cell-specific metabolic properties. Recon 2 will facilitate many future biomedical studies and is freely available at http://humanmetabolism.org/.