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Saa PA, Zapararte S, Drovandi CC, Nielsen LK. LooplessFluxSampler: an efficient toolbox for sampling the loopless flux solution space of metabolic models. BMC Bioinformatics 2024; 25:3. [PMID: 38166586 PMCID: PMC10763395 DOI: 10.1186/s12859-023-05616-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 12/13/2023] [Indexed: 01/04/2024] Open
Abstract
BACKGROUND Uniform random sampling of mass-balanced flux solutions offers an unbiased appraisal of the capabilities of metabolic networks. Unfortunately, it is impossible to avoid thermodynamically infeasible loops in flux samples when using convex samplers on large metabolic models. Current strategies for randomly sampling the non-convex loopless flux space display limited efficiency and lack theoretical guarantees. RESULTS Here, we present LooplessFluxSampler, an efficient algorithm for exploring the loopless mass-balanced flux solution space of metabolic models, based on an Adaptive Directions Sampling on a Box (ADSB) algorithm. ADSB is rooted in the general Adaptive Direction Sampling (ADS) framework, specifically the Parallel ADS, for which theoretical convergence and irreducibility results are available for sampling from arbitrary distributions. By sampling directions that adapt to the target distribution, ADSB traverses more efficiently the sample space achieving faster mixing than other methods. Importantly, the presented algorithm is guaranteed to target the uniform distribution over convex regions, and it provably converges on the latter distribution over more general (non-convex) regions provided the sample can have full support. CONCLUSIONS LooplessFluxSampler enables scalable statistical inference of the loopless mass-balanced solution space of large metabolic models. Grounded in a theoretically sound framework, this toolbox provides not only efficient but also reliable results for exploring the properties of the almost surely non-convex loopless flux space. Finally, LooplessFluxSampler includes a Markov Chain diagnostics suite for assessing the quality of the final sample and the performance of the algorithm.
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Affiliation(s)
- Pedro A Saa
- Department of Chemical and Bioprocess Engineering, School of Engineering, Pontifical Catholic University of Chile, Av. Vicuña Mackenna 4860, 7820436, Santiago, Chile
- Institute for Mathematical and Computational Engineering, Pontifical Catholic University of Chile, Av. Vicuña Mackenna 4860, 7820436, Santiago, Chile
| | - Sebastian Zapararte
- Department of Chemical and Bioprocess Engineering, School of Engineering, Pontifical Catholic University of Chile, Av. Vicuña Mackenna 4860, 7820436, Santiago, Chile
| | - Christopher C Drovandi
- School of Mathematical Sciences and Centre for Data Science, Queensland University of Technology, 2 George Street, Brisbane, Australia
| | - Lars K Nielsen
- Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Building 75, Cnr College Rd and Cooper Rd, Brisbane, Australia.
- The Novo Nordisk Foundation Centre for Biosustainability, Technical University of Denmark, Building, Kemitorvet 220, 2800, Kongens Lyngby, Copenhagen, Denmark.
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2
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Yang X, Mao Z, Huang J, Wang R, Dong H, Zhang Y, Ma H. Improving pathway prediction accuracy of constraints-based metabolic network models by treating enzymes as microcompartments. Synth Syst Biotechnol 2023; 8:597-605. [PMID: 37743907 PMCID: PMC10514394 DOI: 10.1016/j.synbio.2023.09.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 08/12/2023] [Accepted: 09/06/2023] [Indexed: 09/26/2023] Open
Abstract
Metabolic network models have become increasingly precise and accurate as the most widespread and practical digital representations of living cells. The prediction functions were significantly expanded by integrating cellular resources and abiotic constraints in recent years. However, if unreasonable modeling methods were adopted due to a lack of consideration of biological knowledge, the conflicts between stoichiometric and other constraints, such as thermodynamic feasibility and enzyme resource availability, would lead to distorted predictions. In this work, we investigated a prediction anomaly of EcoETM, a constraints-based metabolic network model, and introduced the idea of enzyme compartmentalization into the analysis process. Through rational combination of reactions, we avoid the false prediction of pathway feasibility caused by the unrealistic assumption of free intermediate metabolites. This allowed us to correct the pathway structures of l-serine and l-tryptophan. A specific analysis explains the application method of the EcoETM-like model and demonstrates its potential and value in correcting the prediction results in pathway structure by resolving the conflict between different constraints and incorporating the evolved roles of enzymes as reaction compartments. Notably, this work also reveals the trade-off between product yield and thermodynamic feasibility. Our work is of great value for the structural improvement of constraints-based models.
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Affiliation(s)
- Xue Yang
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
| | - Zhitao Mao
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
| | - Jianfeng Huang
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
| | - Ruoyu Wang
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
| | - Huaming Dong
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
- School of Environmental Ecology and Biological Engineering, Wuhan Institute of Technology, Wuhan, 430205, China
| | - Yanfei Zhang
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
| | - Hongwu Ma
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China
- National Technology Innovation Center of Synthetic Biology, Tianjin, 300308, China
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3
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Wendering P, Nikoloski Z. Model-driven insights into the effects of temperature on metabolism. Biotechnol Adv 2023; 67:108203. [PMID: 37348662 DOI: 10.1016/j.biotechadv.2023.108203] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Revised: 05/22/2023] [Accepted: 06/18/2023] [Indexed: 06/24/2023]
Abstract
Temperature affects cellular processes at different spatiotemporal scales, and identifying the genetic and molecular mechanisms underlying temperature responses paves the way to develop approaches for mitigating the effects of future climate scenarios. A systems view of the effects of temperature on cellular physiology can be obtained by focusing on metabolism since: (i) its functions depend on transcription and translation and (ii) its outcomes support organisms' development, growth, and reproduction. Here we provide a systematic review of modelling efforts directed at investigating temperature effects on properties of single biochemical reactions, system-level traits, metabolic subsystems, and whole-cell metabolism across different prokaryotes and eukaryotes. We compare and contrast computational approaches and theories that facilitate modelling of temperature effects on key properties of enzymes and their consideration in constraint-based as well as kinetic models of metabolism. In addition, we provide a summary of insights from computational approaches, facilitating integration of omics data from temperature-modulated experiments with models of metabolic networks, and review the resulting biotechnological applications. Lastly, we provide a perspective on how different types of metabolic modelling can profit from developments in machine learning and models of different cellular layers to improve model-driven insights into the effects of temperature relevant for biotechnological applications.
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Affiliation(s)
- Philipp Wendering
- Bioinformatics, Institute of Biochemistry and Biology, University of Potsdam, 14476 Potsdam, Germany; Systems Biology and Mathematical Modeling, Max Planck Institute of Molecular Plant Physiology, 14476 Potsdam, Germany
| | - Zoran Nikoloski
- Bioinformatics, Institute of Biochemistry and Biology, University of Potsdam, 14476 Potsdam, Germany; Systems Biology and Mathematical Modeling, Max Planck Institute of Molecular Plant Physiology, 14476 Potsdam, Germany.
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4
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Fleming RMT, Haraldsdottir HS, Minh LH, Vuong PT, Hankemeier T, Thiele I. Cardinality optimization in constraint-based modelling: application to human metabolism. Bioinformatics 2023; 39:btad450. [PMID: 37697651 PMCID: PMC10495685 DOI: 10.1093/bioinformatics/btad450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 05/12/2023] [Indexed: 09/13/2023] Open
Abstract
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.
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Affiliation(s)
- Ronan M T Fleming
- Metabolomics and Analytics Center, Leiden Academic Centre for Drug Research, Leiden University, Wassenaarseweg 76, Leiden 2333 CC, The Netherlands
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 avenue du Swing, Belvaux L-4362, Luxembourg
- School of Medicine, National University of Ireland, University Rd, Galway H91 TK33, Ireland
| | - Hulda S Haraldsdottir
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 avenue du Swing, Belvaux L-4362, Luxembourg
| | - Le Hoai Minh
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 avenue du Swing, Belvaux L-4362, Luxembourg
| | - Phan Tu Vuong
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 avenue du Swing, Belvaux L-4362, Luxembourg
- Mathematical Sciences School, University of Southampton, University Road, Southampton SO17 1BJ, United Kingdom
| | - Thomas Hankemeier
- Metabolomics and Analytics Center, Leiden Academic Centre for Drug Research, Leiden University, Wassenaarseweg 76, Leiden 2333 CC, The Netherlands
| | - Ines Thiele
- School of Medicine, National University of Ireland, University Rd, Galway H91 TK33, Ireland
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5
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Jadebeck JF, Wiechert W, Nöh K. Practical sampling of constraint-based models: Optimized thinning boosts CHRR performance. PLoS Comput Biol 2023; 19:e1011378. [PMID: 37566638 PMCID: PMC10446239 DOI: 10.1371/journal.pcbi.1011378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Revised: 08/23/2023] [Accepted: 07/21/2023] [Indexed: 08/13/2023] Open
Abstract
Thinning is a sub-sampling technique to reduce the memory footprint of Markov chain Monte Carlo. Despite being commonly used, thinning is rarely considered efficient. For sampling constraint-based models, a highly relevant use-case in systems biology, we here demonstrate that thinning boosts computational and, thereby, sampling efficiencies of the widely used Coordinate Hit-and-Run with Rounding (CHRR) algorithm. By benchmarking CHRR with thinning with simplices and genome-scale metabolic networks of up to thousands of dimensions, we find a substantial increase in computational efficiency compared to unthinned CHRR, in our examples by orders of magnitude, as measured by the effective sample size per time (ESS/t), with performance gains growing with polytope (effective network) dimension. Using a set of benchmark models we derive a ready-to-apply guideline for tuning thinning to efficient and effective use of compute resources without requiring additional coding effort. Our guideline is validated using three (out-of-sample) large-scale networks and we show that it allows sampling convex polytopes uniformly to convergence in a fraction of time, thereby unlocking the rigorous investigation of hitherto intractable models. The derivation of our guideline is explained in detail, allowing future researchers to update it as needed as new model classes and more training data becomes available. CHRR with deliberate utilization of thinning thereby paves the way to keep pace with progressing model sizes derived with the constraint-based reconstruction and analysis (COBRA) tool set. Sampling and evaluation pipelines are available at https://jugit.fz-juelich.de/IBG-1/ModSim/fluxomics/chrrt.
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Affiliation(s)
- Johann F. Jadebeck
- Institute of Bio- and Geosciences, IBG-1: Biotechnology, Forschungszentrum Jülich, Jülich, Germany
- Computational Systems Biotechnology (AVT.CSB), RWTH Aachen University, Aachen, Germany
| | - Wolfgang Wiechert
- Institute of Bio- and Geosciences, IBG-1: Biotechnology, Forschungszentrum Jülich, Jülich, Germany
- Computational Systems Biotechnology (AVT.CSB), RWTH Aachen University, Aachen, Germany
| | - Katharina Nöh
- Institute of Bio- and Geosciences, IBG-1: Biotechnology, Forschungszentrum Jülich, Jülich, Germany
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6
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Fröhlich F, Gerosa L, Muhlich J, Sorger PK. Mechanistic model of MAPK signaling reveals how allostery and rewiring contribute to drug resistance. Mol Syst Biol 2023; 19:e10988. [PMID: 36700386 PMCID: PMC9912026 DOI: 10.15252/msb.202210988] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 11/29/2022] [Accepted: 12/15/2022] [Indexed: 01/27/2023] Open
Abstract
BRAF is prototypical of oncogenes that can be targeted therapeutically and the treatment of BRAFV600E melanomas with RAF and MEK inhibitors results in rapid tumor regression. However, drug-induced rewiring generates a drug adapted state thought to be involved in acquired resistance and disease recurrence. In this article, we study mechanisms of adaptive rewiring in BRAFV600E melanoma cells using an energy-based implementation of ordinary differential equation (ODE) modeling in combination with proteomic, transcriptomic and imaging data. We develop a method for causal tracing of ODE models and identify two parallel MAPK reaction channels that are differentially sensitive to RAF and MEK inhibitors due to differences in protein oligomerization and drug binding. We describe how these channels, and timescale separation between immediate-early signaling and transcriptional feedback, create a state in which the RAS-regulated MAPK channel can be activated by growth factors under conditions in which the BRAFV600E -driven channel is fully inhibited. Further development of the approaches in this article is expected to yield a unified model of adaptive drug resistance in melanoma.
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Affiliation(s)
- Fabian Fröhlich
- Laboratory of Systems Pharmacology, Department of Systems BiologyHarvard Medical SchoolBostonMAUSA
| | - Luca Gerosa
- Laboratory of Systems Pharmacology, Department of Systems BiologyHarvard Medical SchoolBostonMAUSA,Present address:
Genentech, Inc.South San FranciscoCAUSA
| | - Jeremy Muhlich
- Laboratory of Systems Pharmacology, Department of Systems BiologyHarvard Medical SchoolBostonMAUSA
| | - Peter K Sorger
- Laboratory of Systems Pharmacology, Department of Systems BiologyHarvard Medical SchoolBostonMAUSA
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7
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Janasch M, Crang N, Asplund-Samuelsson J, Sporre E, Bruch M, Gynnå A, Jahn M, Hudson EP. Thermodynamic limitations of PHB production from formate and fructose in Cupriavidus necator. Metab Eng 2022; 73:256-269. [PMID: 35987434 DOI: 10.1016/j.ymben.2022.08.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 06/10/2022] [Accepted: 08/06/2022] [Indexed: 11/30/2022]
Abstract
The chemolithotroph Cupriavidus necator H16 is known as a natural producer of the bioplastic-polymer PHB, as well as for its metabolic versatility to utilize different substrates, including formate as the sole carbon and energy source. Depending on the entry point of the substrate, this versatility requires adjustment of the thermodynamic landscape to maintain sufficiently high driving forces for biological processes. Here we employed a model of the core metabolism of C. necator H16 to analyze the thermodynamic driving forces and PHB yields from formate for different metabolic engineering strategies. For this, we enumerated elementary flux modes (EFMs) of the network and evaluated their PHB yields as well as thermodynamics via Max-min driving force (MDF) analysis and random sampling of driving forces. A heterologous ATP:citrate lyase reaction was predicted to increase driving force for producing acetyl-CoA. A heterologous phosphoketolase reaction was predicted to increase maximal PHB yields as well as driving forces. These enzymes were then verified experimentally to enhance PHB titers between 60 and 300% in select conditions. The EFM analysis also revealed that PHB production from formate may be limited by low driving forces through citrate lyase and aconitase, as well as cofactor balancing, and identified additional reactions associated with low and high PHB yield. Proteomics analysis of the engineered strains confirmed an increased abundance of aconitase and cofactor balancing. The findings of this study aid in understanding metabolic adaptation. Furthermore, the outlined approach will be useful in designing metabolic engineering strategies in other non-model bacteria.
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Affiliation(s)
- Markus Janasch
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden.
| | - Nick Crang
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden.
| | - Johannes Asplund-Samuelsson
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden
| | - Emil Sporre
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden
| | - Manuel Bruch
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden
| | - Arvid Gynnå
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden
| | - Michael Jahn
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden
| | - Elton P Hudson
- Science for Life Laboratory, School of Engineering Science in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, P-Box 1031, 171 21, Solna, Sweden.
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8
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Ng RH, Lee JW, Baloni P, Diener C, Heath JR, Su Y. Constraint-Based Reconstruction and Analyses of Metabolic Models: Open-Source Python Tools and Applications to Cancer. Front Oncol 2022; 12:914594. [PMID: 35875150 PMCID: PMC9303011 DOI: 10.3389/fonc.2022.914594] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 05/30/2022] [Indexed: 11/13/2022] Open
Abstract
The influence of metabolism on signaling, epigenetic markers, and transcription is highly complex yet important for understanding cancer physiology. Despite the development of high-resolution multi-omics technologies, it is difficult to infer metabolic activity from these indirect measurements. Fortunately, genome-scale metabolic models and constraint-based modeling provide a systems biology framework to investigate the metabolic states and define the genotype-phenotype associations by integrations of multi-omics data. Constraint-Based Reconstruction and Analysis (COBRA) methods are used to build and simulate metabolic networks using mathematical representations of biochemical reactions, gene-protein reaction associations, and physiological and biochemical constraints. These methods have led to advancements in metabolic reconstruction, network analysis, perturbation studies as well as prediction of metabolic state. Most computational tools for performing these analyses are written for MATLAB, a proprietary software. In order to increase accessibility and handle more complex datasets and models, community efforts have started to develop similar open-source tools in Python. To date there is a comprehensive set of tools in Python to perform various flux analyses and visualizations; however, there are still missing algorithms in some key areas. This review summarizes the availability of Python software for several components of COBRA methods and their applications in cancer metabolism. These tools are evolving rapidly and should offer a readily accessible, versatile way to model the intricacies of cancer metabolism for identifying cancer-specific metabolic features that constitute potential drug targets.
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Affiliation(s)
- Rachel H. Ng
- Institute for Systems Biology, Seattle, WA, United States
- Department of Bioengineering, University of Washington, Seattle, WA, United States
| | - Jihoon W. Lee
- Medical Scientist Training Program, University of Washington, Seattle, WA, United States
- Program in Immunology, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, WA, United States
| | | | | | - James R. Heath
- Institute for Systems Biology, Seattle, WA, United States
- Department of Bioengineering, University of Washington, Seattle, WA, United States
- *Correspondence: James R. Heath, ; Yapeng Su,
| | - Yapeng Su
- Program in Immunology, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, WA, United States
- Herbold Computational Biology Program, Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA, United States
- *Correspondence: James R. Heath, ; Yapeng Su,
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9
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Beber ME, Gollub MG, Mozaffari D, Shebek KM, Flamholz AI, Milo R, Noor E. eQuilibrator 3.0: a database solution for thermodynamic constant estimation. Nucleic Acids Res 2021; 50:D603-D609. [PMID: 34850162 PMCID: PMC8728285 DOI: 10.1093/nar/gkab1106] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Revised: 10/16/2021] [Accepted: 10/21/2021] [Indexed: 11/29/2022] Open
Abstract
eQuilibrator (equilibrator.weizmann.ac.il) is a database of biochemical equilibrium constants and Gibbs free energies, originally designed as a web-based interface. While the website now counts around 1,000 distinct monthly users, its design could not accommodate larger compound databases and it lacked a scalable Application Programming Interface (API) for integration into other tools developed by the systems biology community. Here, we report on the recent updates to the database as well as the addition of a new Python-based interface to eQuilibrator that adds many new features such as a 100-fold larger compound database, the ability to add novel compounds, improvements in speed and memory use, and correction for Mg2+ ion concentrations. Moreover, the new interface can compute the covariance matrix of the uncertainty between estimates, for which we show the advantages and describe the application in metabolic modelling. We foresee that these improvements will make thermodynamic modelling more accessible and facilitate the integration of eQuilibrator into other software platforms.
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Affiliation(s)
- Moritz E Beber
- Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, Kemitorvet, 2800 Kongens Lyngby, Denmark.,Unseen Biometrics ApS, Fruebjergvej 3, 2100 København Ø, Denmark
| | - Mattia G Gollub
- Department of Biosystems Science and Engineering and SIB Swiss Institute of Bioinformatics, ETH Zürich, Basel 4058, Switzerland
| | - Dana Mozaffari
- Department of Biosystems Science and Engineering and SIB Swiss Institute of Bioinformatics, ETH Zürich, Basel 4058, Switzerland.,Institute of Chemical Sciences and Engineering, EPFL, Lausanne 1015, Switzerland
| | - Kevin M Shebek
- Department of Chemical and Biological Engineering, Chemistry of Life Processes Institute, and Center for Synthetic Biology, Northwestern University, Evanston, IL 60208, USA
| | - Avi I Flamholz
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - Ron Milo
- Department of Plant and Environmental Sciences, Weizmann Institute of Science, Herzl 234, Rehovot 7610001, Israel
| | - Elad Noor
- Department of Plant and Environmental Sciences, Weizmann Institute of Science, Herzl 234, Rehovot 7610001, Israel
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10
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Liebermeister W, Noor E. Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States. Metabolites 2021; 11:749. [PMID: 34822407 PMCID: PMC8621975 DOI: 10.3390/metabo11110749] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2021] [Revised: 10/08/2021] [Accepted: 10/09/2021] [Indexed: 11/16/2022] Open
Abstract
Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. Given measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, these constants may be inferred by model fitting, but the estimation problems are hard to solve if models are large. Here we show how consistent kinetic constants, metabolite concentrations, and enzyme concentrations can be determined from data if metabolic fluxes are known. The estimation method, called model balancing, can handle models with a wide range of rate laws and accounts for thermodynamic constraints between fluxes, kinetic constants, and metabolite concentrations. It can be used to estimate in-vivo kinetic constants, to complete and adjust available data, and to construct plausible metabolic states with predefined flux distributions. By omitting one term from the log posterior-a term for penalising low enzyme concentrations-we obtain a convex optimality problem with a unique local optimum. As a demonstrative case, we balance a model of E. coli central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in E. coli central metabolism. The example shows what information about kinetic constants can be obtained from omics data and reveals practical limits to estimating in-vivo kinetic constants. While noise-free omics data allow for a reasonable reconstruction of in-vivo kcat and KM values, prediction from noisy omics data are worse. Hence, adjusting kinetic constants and omics data to obtain consistent metabolic models is the main application of model balancing.
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Affiliation(s)
| | - Elad Noor
- Department of Plant and Environmental Sciences, Weizmann Institute of Science, Rehovot 7610001, Israel;
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