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Olavarria K, Becker MV, Sousa DZ, van Loosdrecht MC, Wahl SA. Design and thermodynamic analysis of a pathway enabling anaerobic production of poly-3-hydroxybutyrate in Escherichia coli. Synth Syst Biotechnol 2023; 8:629-639. [PMID: 37823039 PMCID: PMC10562921 DOI: 10.1016/j.synbio.2023.09.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2023] [Revised: 09/14/2023] [Accepted: 09/19/2023] [Indexed: 10/13/2023] Open
Abstract
Utilizing anaerobic metabolisms for the production of biotechnologically relevant products presents potential advantages, such as increased yields and reduced energy dissipation. However, lower energy dissipation may indicate that certain reactions are operating closer to their thermodynamic equilibrium. While stoichiometric analyses and genetic modifications are frequently employed in metabolic engineering, the use of thermodynamic tools to evaluate the feasibility of planned interventions is less documented. In this study, we propose a novel metabolic engineering strategy to achieve an efficient anaerobic production of poly-(R)-3-hydroxybutyrate (PHB) in the model organism Escherichia coli. Our approach involves re-routing of two-thirds of the glycolytic flux through non-oxidative glycolysis and coupling PHB synthesis with NADH re-oxidation. We complemented our stoichiometric analysis with various thermodynamic approaches to assess the feasibility and the bottlenecks in the proposed engineered pathway. According to our calculations, the main thermodynamic bottleneck are the reactions catalyzed by the acetoacetyl-CoA β-ketothiolase (EC 2.3.1.9) and the acetoacetyl-CoA reductase (EC 1.1.1.36). Furthermore, we calculated thermodynamically consistent sets of kinetic parameters to determine the enzyme amounts required for sustaining the conversion fluxes. In the case of the engineered conversion route, the protein pool necessary to sustain the desired fluxes could account for 20% of the whole cell dry weight.
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Affiliation(s)
- Karel Olavarria
- Laboratory of Microbiology, Wageningen University and Research, Stippenenweg 4, 6708 WE, Wageningen, The Netherlands
- Centre for Living Technologies, Eindhoven-Wageningen-Utrecht Alliance, Princetonlaan 6, 3584 CB, Utrecht, The Netherlands
| | - Marco V. Becker
- Department of Biotechnology, Applied Sciences Faculty, Delft University of Technology, van der Maasweg 9, 2629 HZ, Delft, The Netherlands
| | - Diana Z. Sousa
- Laboratory of Microbiology, Wageningen University and Research, Stippenenweg 4, 6708 WE, Wageningen, The Netherlands
- Centre for Living Technologies, Eindhoven-Wageningen-Utrecht Alliance, Princetonlaan 6, 3584 CB, Utrecht, The Netherlands
| | - Mark C.M. van Loosdrecht
- Department of Biotechnology, Applied Sciences Faculty, Delft University of Technology, van der Maasweg 9, 2629 HZ, Delft, The Netherlands
| | - S. Aljoscha Wahl
- Lehrstuhl für Bioverfahrenstechnik, Friedrich-Alexander-Universität, Paul-Gordan-Strasse 3, 91052, Erlangen, Germany
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2
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Chen J, Huang Y, Zhong C. Minimizing enzyme mass to decompose flux distribution for identifying biologically relevant elementary flux modes. Biosystems 2023; 231:104981. [PMID: 37442363 DOI: 10.1016/j.biosystems.2023.104981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Revised: 07/06/2023] [Accepted: 07/09/2023] [Indexed: 07/15/2023]
Abstract
The flux distribution in metabolic network can be decomposed as non-negative linear combinations of elementary flux modes (EFMs). Identifying biologically relevant EFM combination by decomposing flux distribution in metabolic network is a useful method to study metabolisms in systems biology. However, the occurrence of biologically irrelevant EFMs hinders the application of such methods. In this paper, we introduce a novel method for identifying EFM combination by minimizing enzyme mass. Our proposed method, called EMMD (Enzyme Mass Minimization Decomposition), takes into consideration both thermodynamic and enzymatic constraints in stoichiometry metabolic models. By implementing EMMD, we can decompose the flux distributions in metabolic network to detect biologically relevant EFM combinations. We demonstrate the effectiveness of our method by applying it to the core Escherichia coli metabolic network and show that the optimal EFM combinations identified by EMMD are unique. Moreover, the optimal EFM combination identified by EMMD not only aligns more closely with experimental values in terms of estimated growth rate, but it also demonstrates more favorable thermodynamics. Finally, we investigated the growth of the core Escherichia coli metabolic network in Luria-Bertani medium containing different carbon sources, revealing the impact of various carbon sources on the growth rate of flux distribution. EMMD thus could be a promising complement to the existing flux decomposition tools.
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Affiliation(s)
- Jingning Chen
- School of Computer and Electronics Information, Guangxi University, Nanning, 530004, China
| | - Yiran Huang
- School of Computer and Electronics Information, Guangxi University, Nanning, 530004, China; Guangxi Key Laboratory of Multimedia Communications Network Technology, Nanning, 530004, China.
| | - Cheng Zhong
- School of Computer and Electronics Information, Guangxi University, Nanning, 530004, China; Guangxi Key Laboratory of Multimedia Communications Network Technology, Nanning, 530004, China
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3
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Gurdo N, Volke DC, McCloskey D, Nikel PI. Automating the design-build-test-learn cycle towards next-generation bacterial cell factories. N Biotechnol 2023; 74:1-15. [PMID: 36736693 DOI: 10.1016/j.nbt.2023.01.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Revised: 01/15/2023] [Accepted: 01/22/2023] [Indexed: 02/04/2023]
Abstract
Automation is playing an increasingly significant role in synthetic biology. Groundbreaking technologies, developed over the past 20 years, have enormously accelerated the construction of efficient microbial cell factories. Integrating state-of-the-art tools (e.g. for genome engineering and analytical techniques) into the design-build-test-learn cycle (DBTLc) will shift the metabolic engineering paradigm from an almost artisanal labor towards a fully automated workflow. Here, we provide a perspective on how a fully automated DBTLc could be harnessed to construct the next-generation bacterial cell factories in a fast, high-throughput fashion. Innovative toolsets and approaches that pushed the boundaries in each segment of the cycle are reviewed to this end. We also present the most recent efforts on automation of the DBTLc, which heralds a fully autonomous pipeline for synthetic biology in the near future.
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Affiliation(s)
- Nicolás Gurdo
- The Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, 2800 Kongens, Lyngby, Denmark
| | - Daniel C Volke
- The Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, 2800 Kongens, Lyngby, Denmark
| | - Douglas McCloskey
- The Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, 2800 Kongens, Lyngby, Denmark
| | - Pablo Iván Nikel
- The Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, 2800 Kongens, Lyngby, Denmark.
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4
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Parameter Identification in Metabolic Reaction Networks by Means of Multiple Steady-State Measurements. Symmetry (Basel) 2023. [DOI: 10.3390/sym15020368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
In this work, we investigate some theoretical aspects related to the estimation approach proposed by Liebermeister and Klipp, 2006, in which general rate laws, derived from standardized enzymatic mechanisms, are exploited to kinetically describe the fluxes of a metabolic reaction network, and multiple metabolic steady-state measurements are exploited to estimate the unknown kinetic parameters. Further mathematical details are deeply investigated, and necessary conditions on the amount of information required to solve the identification problem are given. Moreover, theoretical results for the parameter identifiability are provided, and symmetrical and modular properties of the proposed approach are highlighted when the global identification problem is decoupled into smaller and simpler identification problems related to the single reactions of the network. Among the advantages of the proposed innovative approach are (i) non-restrictive conditions to guarantee the solvability of the parameter estimation problem, (ii) the unburden of the usual computational complexity for such identification problems, and (iii) the ease of obtaining the required number of measurements, which are actually steady-state data, experimentally easier to obtain with respect to the time-dependent ones. A simple example concludes the paper, highlighting the mentioned advantages of the method and the implementation of the related theoretical result.
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5
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Gawthrop PJ, Pan M. Network thermodynamics of biological systems: A bond graph approach. Math Biosci 2022; 352:108899. [PMID: 36057321 DOI: 10.1016/j.mbs.2022.108899] [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: 05/04/2022] [Revised: 08/26/2022] [Accepted: 08/26/2022] [Indexed: 10/14/2022]
Abstract
Edmund Crampin (1973-2021) was at the forefront of Systems Biology research and his work will influence the field for years to come. This paper brings together and summarises the seminal work of his group in applying energy-based bond graph methods to biological systems. In particular, this paper: (a) motivates the need to consider energy in modelling biology; (b) introduces bond graphs as a methodology for achieving this; (c) describes extensions to modelling electrochemical transduction; (d) outlines how bond graph models can be constructed in a modular manner and (e) describes stoichiometric approaches to deriving fundamental properties of reaction networks. These concepts are illustrated using a new bond graph model of photosynthesis in chloroplasts.
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Affiliation(s)
- Peter J Gawthrop
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Victoria 3010, Australia.
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Victoria 3010, Australia; School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
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6
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Shahidi N, Pan M, Tran K, Crampin EJ, Nickerson DP. A semantics, energy-based approach to automate biomodel composition. PLoS One 2022; 17:e0269497. [PMID: 35657966 PMCID: PMC9165793 DOI: 10.1371/journal.pone.0269497] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 05/20/2022] [Indexed: 11/19/2022] Open
Abstract
Hierarchical modelling is essential to achieving complex, large-scale models. However, not all modelling schemes support hierarchical composition, and correctly mapping points of connection between models requires comprehensive knowledge of each model's components and assumptions. To address these challenges in integrating biosimulation models, we propose an approach to automatically and confidently compose biosimulation models. The approach uses bond graphs to combine aspects of physical and thermodynamics-based modelling with biological semantics. We improved on existing approaches by using semantic annotations to automate the recognition of common components. The approach is illustrated by coupling a model of the Ras-MAPK cascade to a model of the upstream activation of EGFR. Through this methodology, we aim to assist researchers and modellers in readily having access to more comprehensive biological systems models.
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Affiliation(s)
- Niloofar Shahidi
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia
- ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Melbourne, Victoria, Australia
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Victoria, Australia
| | - Kenneth Tran
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Edmund J. Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, Victoria, Australia
- ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Melbourne, Victoria, Australia
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Victoria, Australia
- School of Medicine, University of Melbourne, Melbourne, Victoria, Australia
| | - David P. Nickerson
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
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7
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Zhao G, Straub RH, Meyer-Hermann M. The transition between acute and chronic infections in light of energy control: a mathematical model of energy flow in response to infection. J R Soc Interface 2022; 19:20220206. [PMID: 35730176 PMCID: PMC9214282 DOI: 10.1098/rsif.2022.0206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Background: Different parts of an organism like the gut, endocrine, nervous and immune systems constantly exchange information. Understanding the pathogenesis of various systemic chronic diseases increasingly relies on understanding how these subsystems orchestrate their activities. Methods: We started from the working hypothesis that energy is a fundamental quantity that governs activity levels of all subsystems and that interactions between subsystems control the distribution of energy according to acute needs. Based on physiological knowledge, we constructed a mathematical model for the energy flow between subsystems and analysed the resulting organismal responses to in silico infections. Results: The model reproduces common behaviour in acute infections and suggests several host parameters that modulate infection duration and therapeutic responsiveness. Moreover, the model allows the formulation of conditions for the induction of chronic infections and predicts that alterations in energy released from fat can lead to the transition from clearance of acute infections to a chronic inflammatory state. Impact: These results suggest a fundamental role for brain and fat in controlling immune response through systemic energy control. In particular, it suggests that lipolysis resistance, which is known to be involved in obesity and ageing, might be a survival programme for coping with chronic infections.
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Affiliation(s)
- Gang Zhao
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Rebenring 56, 38106 Braunschweig, Germany
| | - Rainer H Straub
- Laboratory of Experimental Rheumatology and Neuroendocrine Immunology, Department of Internal Medicine, University Hospital Regensburg, 93042 Regensburg, Germany
| | - Michael Meyer-Hermann
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Rebenring 56, 38106 Braunschweig, Germany.,Institute for Biochemistry, Biotechnology and Bioinformatics, Technische Universität Braunschweig, Braunschweig, Germany
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8
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Liebermeister W. Structural Thermokinetic Modelling. Metabolites 2022; 12:metabo12050434. [PMID: 35629936 PMCID: PMC9144996 DOI: 10.3390/metabo12050434] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Revised: 04/12/2022] [Accepted: 04/14/2022] [Indexed: 11/16/2022] Open
Abstract
To translate metabolic networks into dynamic models, the Structural Kinetic Modelling framework (SKM) assumes a given reference state and replaces the reaction elasticities in this state by random numbers. A new variant, called Structural Thermokinetic Modelling (STM), accounts for reversible reactions and thermodynamics. STM relies on a dependence schema in which some basic variables are sampled, fitted to data, or optimised, while all other variables can be easily computed. Correlated elasticities follow from enzyme saturation values and thermodynamic forces, which are physically independent. Probability distributions in the dependence schema define a model ensemble, which allows for probabilistic predictions even if data are scarce. STM highlights the importance of variabilities, dependencies, and covariances of biological variables. By varying network structure, fluxes, thermodynamic forces, regulation, or types of rate laws, the effects of these model features can be assessed. By choosing the basic variables, metabolic networks can be converted into kinetic models with consistent reversible rate laws. Metabolic control coefficients obtained from these models can tell us about metabolic dynamics, including responses and optimal adaptations to perturbations, enzyme synergies and metabolite correlations, as well as metabolic fluctuations arising from chemical noise. To showcase STM, I study metabolic control, metabolic fluctuations, and enzyme synergies, and how they are shaped by thermodynamic forces. Considering thermodynamics can improve predictions of flux control, enzyme synergies, correlated flux and metabolite variations, and the emergence and propagation of metabolic noise.
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9
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Thornburg ZR, Bianchi DM, Brier TA, Gilbert BR, Earnest TM, Melo MC, Safronova N, Sáenz JP, Cook AT, Wise KS, Hutchison CA, Smith HO, Glass JI, Luthey-Schulten Z. Fundamental behaviors emerge from simulations of a living minimal cell. Cell 2022; 185:345-360.e28. [PMID: 35063075 PMCID: PMC9985924 DOI: 10.1016/j.cell.2021.12.025] [Citation(s) in RCA: 60] [Impact Index Per Article: 30.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 11/01/2021] [Accepted: 12/17/2021] [Indexed: 01/18/2023]
Abstract
We present a whole-cell fully dynamical kinetic model (WCM) of JCVI-syn3A, a minimal cell with a reduced genome of 493 genes that has retained few regulatory proteins or small RNAs. Cryo-electron tomograms provide the cell geometry and ribosome distributions. Time-dependent behaviors of concentrations and reaction fluxes from stochastic-deterministic simulations over a cell cycle reveal how the cell balances demands of its metabolism, genetic information processes, and growth, and offer insight into the principles of life for this minimal cell. The energy economy of each process including active transport of amino acids, nucleosides, and ions is analyzed. WCM reveals how emergent imbalances lead to slowdowns in the rates of transcription and translation. Integration of experimental data is critical in building a kinetic model from which emerges a genome-wide distribution of mRNA half-lives, multiple DNA replication events that can be compared to qPCR results, and the experimentally observed doubling behavior.
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Affiliation(s)
- Zane R. Thornburg
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - David M. Bianchi
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Troy A. Brier
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Benjamin R. Gilbert
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Tyler M. Earnest
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Marcelo C.R. Melo
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Nataliya Safronova
- Technische Universität Dresden, B CUBE Center for Molecular Bioengineering, 01307 Dresden, Germany
| | - James P. Sáenz
- Technische Universität Dresden, B CUBE Center for Molecular Bioengineering, 01307 Dresden, Germany
| | | | - Kim S. Wise
- J. Craig Venter Institute, La Jolla, CA 92037, USA
| | | | | | | | - Zaida Luthey-Schulten
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA; NSF Center for the Physics of Living Cells, Urbana, IL 61801, USA; NIH Center for Macromolecular Modeling and Bioinformatics, Urbana, IL 61801, USA.
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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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11
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Pan M, Gawthrop PJ, Cursons J, Crampin EJ. Modular assembly of dynamic models in systems biology. PLoS Comput Biol 2021; 17:e1009513. [PMID: 34644304 PMCID: PMC8544865 DOI: 10.1371/journal.pcbi.1009513] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Revised: 10/25/2021] [Accepted: 09/30/2021] [Indexed: 11/18/2022] Open
Abstract
It is widely acknowledged that the construction of large-scale dynamic models in systems biology requires complex modelling problems to be broken up into more manageable pieces. To this end, both modelling and software frameworks are required to enable modular modelling. While there has been consistent progress in the development of software tools to enhance model reusability, there has been a relative lack of consideration for how underlying biophysical principles can be applied to this space. Bond graphs combine the aspects of both modularity and physics-based modelling. In this paper, we argue that bond graphs are compatible with recent developments in modularity and abstraction in systems biology, and are thus a desirable framework for constructing large-scale models. We use two examples to illustrate the utility of bond graphs in this context: a model of a mitogen-activated protein kinase (MAPK) cascade to illustrate the reusability of modules and a model of glycolysis to illustrate the ability to modify the model granularity.
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Affiliation(s)
- Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria, Australia
- ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Parkville, Victoria, Australia
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Parkville, Victoria, Australia
| | - Peter J. Gawthrop
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria, Australia
| | - Joseph Cursons
- Department of Biochemistry and Molecular Biology, Monash Biomedicine Discovery Institute, Monash University, Melbourne, Victoria, Australia
| | - Edmund J. Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria, Australia
- ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Parkville, Victoria, Australia
- School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Parkville, Victoria, Australia
- School of Medicine, University of Melbourne, Parkville, Victoria, Australia
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12
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Löwe H, Kremling A. In-Depth Computational Analysis of Natural and Artificial Carbon Fixation Pathways. BIODESIGN RESEARCH 2021; 2021:9898316. [PMID: 37849946 PMCID: PMC10521678 DOI: 10.34133/2021/9898316] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 08/02/2021] [Indexed: 10/19/2023] Open
Abstract
In the recent years, engineering new-to-nature CO2- and C1-fixing metabolic pathways made a leap forward. New, artificial pathways promise higher yields and activity than natural ones like the Calvin-Benson-Bassham (CBB) cycle. The question remains how to best predict their in vivo performance and what actually makes one pathway "better" than another. In this context, we explore aerobic carbon fixation pathways by a computational approach and compare them based on their specific activity and yield on methanol, formate, and CO2/H2 considering the kinetics and thermodynamics of the reactions. Besides pathways found in nature or implemented in the laboratory, this included two completely new cycles with favorable features: the reductive citramalyl-CoA cycle and the 2-hydroxyglutarate-reverse tricarboxylic acid cycle. A comprehensive kinetic data set was collected for all enzymes of all pathways, and missing kinetic data were sampled with the Parameter Balancing algorithm. Kinetic and thermodynamic data were fed to the Enzyme Cost Minimization algorithm to check for respective inconsistencies and calculate pathway-specific activities. The specific activities of the reductive glycine pathway, the CETCH cycle, and the new reductive citramalyl-CoA cycle were predicted to match the best natural cycles with superior product-substrate yield. However, the CBB cycle performed better in terms of activity compared to the alternative pathways than previously thought. We make an argument that stoichiometric yield is likely not the most important design criterion of the CBB cycle. Still, alternative carbon fixation pathways were paretooptimal for specific activity and product-substrate yield in simulations with C1 substrates and CO2/H2 and therefore hold great potential for future applications in Industrial Biotechnology and Synthetic Biology.
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Affiliation(s)
- Hannes Löwe
- Systems Biotechnology, Technical University of Munich, Germany
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13
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van Rosmalen RP, Smith RW, Martins Dos Santos VAP, Fleck C, Suarez-Diez M. Model reduction of genome-scale metabolic models as a basis for targeted kinetic models. Metab Eng 2021; 64:74-84. [PMID: 33486094 DOI: 10.1016/j.ymben.2021.01.008] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Revised: 01/05/2021] [Accepted: 01/15/2021] [Indexed: 11/26/2022]
Abstract
Constraint-based, genome-scale metabolic models are an essential tool to guide metabolic engineering. However, they lack the detail and time dimension that kinetic models with enzyme dynamics offer. Model reduction can be used to bridge the gap between the two methods and allow for the integration of kinetic models into the Design-Built-Test-Learn cycle. Here we show that these reduced size models can be representative of the dynamics of the original model and demonstrate the automated generation and parameterisation of such models. Using these minimal models of metabolism could allow for further exploration of dynamic responses in metabolic networks.
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Affiliation(s)
- R P van Rosmalen
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands
| | - R W Smith
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands
| | - V A P Martins Dos Santos
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands; Lifeglimmer GmbH, Berlin, Germany
| | - C Fleck
- Freiburg Center for Data Analysis and Modelling University of Freiburg Freiburg Germany; Control Theory and Systems Biology Laboratory, Department of Biosystems Science and En- gineering, ETH Zürich, Basel, Switzerland
| | - M Suarez-Diez
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands.
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14
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Lubitz T, Liebermeister W. Parameter balancing: consistent parameter sets for kinetic metabolic models. Bioinformatics 2020; 35:3857-3858. [PMID: 30793200 PMCID: PMC6761981 DOI: 10.1093/bioinformatics/btz129] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2018] [Revised: 01/07/2019] [Accepted: 02/19/2019] [Indexed: 11/25/2022] Open
Abstract
Summary Measured kinetic constants are key input data for metabolic models, but they are often uncertain, inconsistent and incomplete. Parameter balancing translates such data into complete and consistent parameter sets while accounting for predefined ranges and physical constraints. Based on Bayesian regression, it determines a most plausible parameter set as well as uncertainty ranges for all model parameters. Our tools for parameter balancing support standard model and data formats and enable an easy customization of prior distributions and constraints for biochemical constants. Modellers can balance kinetic constants, thermodynamic data and metabolomic data to obtain thermodynamically consistent metabolic states that comply with user-defined flux directions. Availability and implementation An online tool for parameter balancing, a stand-alone Python command line tool, a Python package and a Matlab toolbox (which uses the CPLEX solver) are freely available at www.parameterbalancing.net.
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Affiliation(s)
- Timo Lubitz
- Theoretische Biophysik, Institut für Biologie, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Wolfram Liebermeister
- INRA, UR1404, MaIAGE, Université Paris-Saclay, Jouy-en-Josas, France
- Institut für Biochemie, Charité, Universitätsmedizin Berlin, Berlin, Germany
- To whom correspondence should be addressed. E-mail:
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15
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Abstract
The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.
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Affiliation(s)
- Hugo Dourado
- Institute for Computer Science & Department of Biology, Heinrich Heine University, 40221, Düsseldorf, Germany
| | - Martin J Lercher
- Institute for Computer Science & Department of Biology, Heinrich Heine University, 40221, Düsseldorf, Germany.
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16
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Smith RW, van Rosmalen RP, Martins Dos Santos VAP, Fleck C. DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems. BMC SYSTEMS BIOLOGY 2018; 12:72. [PMID: 29914475 PMCID: PMC6006996 DOI: 10.1186/s12918-018-0584-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Accepted: 05/14/2018] [Indexed: 12/21/2022]
Abstract
Background Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. Results In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. Conclusion The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future. Electronic supplementary material The online version of this article (10.1186/s12918-018-0584-8) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Robert W Smith
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands.,LifeGlimmer GmbH, Markelstrasse 38, Berlin, 12163, Germany
| | - Rik P van Rosmalen
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands
| | - Vitor A P Martins Dos Santos
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands.,LifeGlimmer GmbH, Markelstrasse 38, Berlin, 12163, Germany
| | - Christian Fleck
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands.
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17
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Winter F, Bludszuweit-Philipp C, Wolkenhauer O. Mathematical analysis of the influence of brain metabolism on the BOLD signal in Alzheimer's disease. J Cereb Blood Flow Metab 2018; 38:304-316. [PMID: 28271954 PMCID: PMC5951012 DOI: 10.1177/0271678x17693024] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Blood oxygen level-dependent functional magnetic resonance imaging (BOLD-fMRI) is a standard clinical tool for the detection of brain activation. In Alzheimer's disease (AD), task-related and resting state fMRI have been used to detect brain dysfunction. It has been shown that the shape of the BOLD response is affected in early AD. To correctly interpret these changes, the mechanisms responsible for the observed behaviour need to be known. The parameters of the canonical hemodynamic response function (HRF) commonly used in the analysis of fMRI data have no direct biological interpretation and cannot be used to answer this question. We here present a model that allows relating AD-specific changes in the BOLD shape to changes in the underlying energy metabolism. According to our findings, the classic view that differences in the BOLD shape are only attributed to changes in strength and duration of the stimulus does not hold. Instead, peak height, peak timing and full width at half maximum are sensitive to changes in the reaction rate of several metabolic reactions. Our systems-theoretic approach allows the use of patient-specific clinical data to predict dementia-driven changes in the HRF, which can be used to improve the results of fMRI analyses in AD patients.
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Affiliation(s)
- Felix Winter
- 1 ASD Advanced Simulation and Design GmbH, Rostock, Germany.,2 Department of Systems Biology and Bioinformatics, Rostock University, Rostock, Germany
| | | | - Olaf Wolkenhauer
- 2 Department of Systems Biology and Bioinformatics, Rostock University, Rostock, Germany.,3 Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Stellenbosch, South Africa
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18
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Wortel MT, Noor E, Ferris M, Bruggeman FJ, Liebermeister W. Metabolic enzyme cost explains variable trade-offs between microbial growth rate and yield. PLoS Comput Biol 2018; 14:e1006010. [PMID: 29451895 PMCID: PMC5847312 DOI: 10.1371/journal.pcbi.1006010] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Revised: 03/12/2018] [Accepted: 01/30/2018] [Indexed: 11/25/2022] Open
Abstract
Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.
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Affiliation(s)
- Meike T. Wortel
- Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, Oslo, Norway
- Systems Bioinformatics Section, Amsterdam Institute for Molecules, Medicines and Systems (AIMMS), Vrije Universiteit, Amsterdam, The Netherlands
| | - Elad Noor
- Institute of Molecular Systems Biology, Eidgenössische Technische Hochschule, Zürich, Switzerland
| | - Michael Ferris
- Computer Sciences Department and Wisconsin Institute for Discovery, University of Wisconsin, Madison, Wisconsin, United States of America
| | - Frank J. Bruggeman
- Systems Bioinformatics Section, Amsterdam Institute for Molecules, Medicines and Systems (AIMMS), Vrije Universiteit, Amsterdam, The Netherlands
| | - Wolfram Liebermeister
- INRA, UR1404, MaIAGE, Université Paris-Saclay, Jouy-en-Josas, France
- Institute of Biochemistry, Charité – Universitätsmedizin Berlin, Berlin, Germany
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19
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Lessons on enzyme kinetics from quantitative proteomics. Curr Opin Biotechnol 2017; 46:81-89. [DOI: 10.1016/j.copbio.2017.02.007] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2016] [Accepted: 02/15/2017] [Indexed: 11/24/2022]
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20
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Noor E, Flamholz A, Bar-Even A, Davidi D, Milo R, Liebermeister W. The Protein Cost of Metabolic Fluxes: Prediction from Enzymatic Rate Laws and Cost Minimization. PLoS Comput Biol 2016; 12:e1005167. [PMID: 27812109 PMCID: PMC5094713 DOI: 10.1371/journal.pcbi.1005167] [Citation(s) in RCA: 102] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2016] [Accepted: 09/27/2016] [Indexed: 02/03/2023] Open
Abstract
Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell’s capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified. “Enzyme cost”, the amount of protein needed for a given metabolic flux, is crucial for the metabolic choices cells have to make. However, due to the technical limitations of linear optimization methods, this cost has traditionally been ignored by constraint-based metabolic models such as Flux Balance Analysis. On the other hand, more detailed kinetic models which use ordinary differential equations to simulate fluxes for different choices of enzyme allocation, are computationally demanding and not scalable enough. In this work, we developed a method which utilizes the full kinetic model to predict steady-state enzyme costs, using a scalable and robust algorithm based on convex optimization. We show that the minimization of enzyme cost is a meaningful optimality principle by comparing our predictions to measured enzyme and metabolite levels in exponentially growing E. coli. This method could be used to quantify the enzyme cost of many other pathways and explain why evolution has selected some low-yield metabolic strategies, including aerobic fermentation in yeast and cancer cells. Furthermore, future metabolic engineering projects could benefit from our method by choosing pathways that reduce the total amount of enzyme required for the synthesis of a value-added product.
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Affiliation(s)
- Elad Noor
- Institute of Molecular Systems Biology, Eidgenössische Technische Hochschule, Zürich, Switzerland
| | - Avi Flamholz
- Department of Molecular and Cellular Biology, University of California, Berkeley, Berkeley, California, United States of America
| | - Arren Bar-Even
- Max Planck Institute for Molecular Plant Physiology, Golm, Germany
| | - Dan Davidi
- Department of Plant Sciences, The Weizmann Institute of Science, Rehovot, Israel
| | - Ron Milo
- Department of Plant Sciences, The Weizmann Institute of Science, Rehovot, Israel
| | - Wolfram Liebermeister
- Institute of Biochemistry, Charité Universitätsmedizin Berlin, Berlin, Germany
- * E-mail:
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21
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Lubitz T, Hahn J, Bergmann FT, Noor E, Klipp E, Liebermeister W. SBtab: a flexible table format for data exchange in systems biology. Bioinformatics 2016; 32:2559-61. [PMID: 27153616 PMCID: PMC4978929 DOI: 10.1093/bioinformatics/btw179] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Accepted: 03/31/2016] [Indexed: 02/06/2023] Open
Abstract
Summary: SBtab is a table-based data format for Systems Biology, designed to support automated data integration and model building. It uses the structure of spreadsheets and defines conventions for table structure, controlled vocabularies and semantic annotations. The format comes with predefined table types for experimental data and SBML-compliant model structures and can easily be customized to cover new types of data. Availability and Implementation: SBtab documents can be created and edited with any text editor or spreadsheet tool. The website www.sbtab.net provides online tools for syntax validation and conversion to SBML and HTML, as well as software for using SBtab in MS Excel, MATLAB and R. The stand-alone Python code contains functions for file parsing, validation, conversion to SBML and HTML and an interface to SQLite databases, to be integrated into Systems Biology workflows. A detailed specification of SBtab, including examples and descriptions of table types and available tools, can be found at www.sbtab.net. Contact: wolfram.liebermeister@gmail.com
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Affiliation(s)
- Timo Lubitz
- Theoretical Biophysics, Institute of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Jens Hahn
- Theoretical Biophysics, Institute of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Frank T Bergmann
- COS/Bioquant, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | - Elad Noor
- Institute of Molecular Systems Biology, Eidgenössische Technische Hochschule Zürich, Zurich, Switzerland
| | - Edda Klipp
- Theoretical Biophysics, Institute of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
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22
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Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro kcat measurements. Proc Natl Acad Sci U S A 2016; 113:3401-6. [PMID: 26951675 DOI: 10.1073/pnas.1514240113] [Citation(s) in RCA: 148] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Turnover numbers, also known as kcat values, are fundamental properties of enzymes. However, kcat data are scarce and measured in vitro, thus may not faithfully represent the in vivo situation. A basic question that awaits elucidation is: how representative are kcat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate kmax(vivo), the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation ofr(2)= 0.62 in log scale (p < 10(-10)), with a root mean square difference of 0.54 (3.5-fold in linear scale), indicating that in vivo and in vitro maximal rates generally concur. By accounting for the degree of saturation of enzymes and the backward flux dictated by thermodynamics, we further refine the correspondence between kmax(vivo) and kcat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a high-throughput method for extracting enzyme kinetic constants from omics data.
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23
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Cvijovic M, Almquist J, Hagmar J, Hohmann S, Kaltenbach HM, Klipp E, Krantz M, Mendes P, Nelander S, Nielsen J, Pagnani A, Przulj N, Raue A, Stelling J, Stoma S, Tobin F, Wodke JAH, Zecchina R, Jirstrand M. Bridging the gaps in systems biology. Mol Genet Genomics 2014; 289:727-34. [DOI: 10.1007/s00438-014-0843-3] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Accepted: 03/21/2014] [Indexed: 12/17/2022]
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24
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Kowald A, Klipp E. Mathematical models of mitochondrial aging and dynamics. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2014; 127:63-92. [PMID: 25149214 DOI: 10.1016/b978-0-12-394625-6.00003-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Research on the role of mitochondria in aging and disease is rapidly growing. Furthermore, in recent years, it also became clear that mitochondria are dynamic structures undergoing constant and rapid cycles of fusion and fission. The involvement of mitochondria in multiple complex processes makes them a prime target for mathematical and computational modeling. This review consists of two parts. In the first (Section 2), we provide a detailed introduction to the underlying concepts of mathematical modeling to help the reader who is not so familiar with these techniques to judge the requirements and results that can be obtained through modeling. In the second part (Section 3), we review existing mathematical and computational models that investigate mitochondrial dynamics and the role of mitochondria for the aging process.
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Affiliation(s)
- Axel Kowald
- Theoretical Biophysics, Institute for Biology, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Edda Klipp
- Theoretical Biophysics, Institute for Biology, Humboldt-Universität zu Berlin, Berlin, Germany
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25
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Stanford NJ, Lubitz T, Smallbone K, Klipp E, Mendes P, Liebermeister W. Systematic construction of kinetic models from genome-scale metabolic networks. PLoS One 2013; 8:e79195. [PMID: 24324546 PMCID: PMC3852239 DOI: 10.1371/journal.pone.0079195] [Citation(s) in RCA: 91] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2012] [Accepted: 09/19/2013] [Indexed: 12/24/2022] Open
Abstract
The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.
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Affiliation(s)
- Natalie J. Stanford
- School of Computer Science, Manchester Centre for Integrative Systems Biology, University of Manchester, Manchester, United Kingdom
- * E-mail:
| | - Timo Lubitz
- Institut für Biologie, Theoretische Biophysik, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Kieran Smallbone
- School of Computer Science, Manchester Centre for Integrative Systems Biology, University of Manchester, Manchester, United Kingdom
| | - Edda Klipp
- Institut für Biologie, Theoretische Biophysik, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Pedro Mendes
- School of Computer Science, Manchester Centre for Integrative Systems Biology, University of Manchester, Manchester, United Kingdom
- Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, Virginia, United States of America
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26
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Tummler K, Lubitz T, Schelker M, Klipp E. New types of experimental data shape the use of enzyme kinetics for dynamic network modeling. FEBS J 2013; 281:549-71. [PMID: 24034816 DOI: 10.1111/febs.12525] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 08/27/2013] [Accepted: 09/10/2013] [Indexed: 01/21/2023]
Abstract
Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms.
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Affiliation(s)
- Katja Tummler
- Theoretical Biophysics, Humboldt-Universität zu Berlin, Germany
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27
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Smallbone K, Mendes P. Large-Scale Metabolic Models: From Reconstruction to Differential Equations. Ind Biotechnol (New Rochelle N Y) 2013. [DOI: 10.1089/ind.2013.0003] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Affiliation(s)
- Kieran Smallbone
- Manchester Centre for Integrative Systems Biology and School of Computer Science, University of Manchester, Manchester Institute of Biotechnology, Manchester, UK
| | - Pedro Mendes
- Manchester Centre for Integrative Systems Biology and School of Computer Science, University of Manchester, Manchester Institute of Biotechnology, Manchester, UK
- Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA
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28
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Smallbone K, Messiha HL, Carroll KM, Winder CL, Malys N, Dunn WB, Murabito E, Swainston N, Dada JO, Khan F, Pir P, Simeonidis E, Spasić I, Wishart J, Weichart D, Hayes NW, Jameson D, Broomhead DS, Oliver SG, Gaskell SJ, McCarthy JEG, Paton NW, Westerhoff HV, Kell DB, Mendes P. A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes. FEBS Lett 2013; 587:2832-41. [PMID: 23831062 PMCID: PMC3764422 DOI: 10.1016/j.febslet.2013.06.043] [Citation(s) in RCA: 91] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2013] [Revised: 06/24/2013] [Accepted: 06/25/2013] [Indexed: 11/17/2022]
Abstract
We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a “cycle of knowledge” strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought.
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Affiliation(s)
- Kieran Smallbone
- Manchester Centre for Integrative Systems Biology, Manchester Institute of Biotechnology, The University of Manchester, UK
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29
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Construction of a genome-scale kinetic model of mycobacterium tuberculosis using generic rate equations. Metabolites 2012; 2:382-97. [PMID: 24957639 PMCID: PMC3901218 DOI: 10.3390/metabo2030382] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2012] [Revised: 06/07/2012] [Accepted: 06/25/2012] [Indexed: 12/17/2022] Open
Abstract
The study of biological systems at the genome scale helps us understand fundamental biological processes that govern the activity of living organisms and regulate their interactions with the environment. Genome-scale metabolic models are usually analysed using constraint-based methods, since detailed rate equations and kinetic parameters are often missing. However, constraint-based analysis is limited in capturing the dynamics of cellular processes. In this paper, we present an approach to build a genome-scale kinetic model of Mycobacterium tuberculosis metabolism using generic rate equations. M. tuberculosis causes tuberculosis which remains one of the largest killer infectious diseases. Using a genetic algorithm, we estimated kinetic parameters for a genome-scale metabolic model of M. tuberculosis based on flux distributions derived from Flux Balance Analysis. Our results show that an excellent agreement with flux values is obtained under several growth conditions, although kinetic parameters may vary in different conditions. Parameter variability analysis indicates that a high degree of redundancy remains present in model parameters, which suggests that the integration of other types of high-throughput datasets will enable the development of better constrained models accounting for a variety of in vivo phenotypes.
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30
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Van Hemert JL, Dickerson JA. Discriminating response groups in metabolic and regulatory pathway networks. Bioinformatics 2012; 28:947-54. [DOI: 10.1093/bioinformatics/bts039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Jenkinson G, Goutsias J. Thermodynamically consistent model calibration in chemical kinetics. BMC SYSTEMS BIOLOGY 2011; 5:64. [PMID: 21548948 PMCID: PMC3117730 DOI: 10.1186/1752-0509-5-64] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/07/2011] [Accepted: 05/06/2011] [Indexed: 11/10/2022]
Abstract
Background The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function. Results We introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database. Conclusions TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting.
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Affiliation(s)
- Garrett Jenkinson
- Whitaker Biomedical Engineering Institute, The Johns Hopkins University, Baltimore, MD 21218, USA.
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