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Luthey-Schulten Z, Thornburg ZR, Gilbert BR. Integrating cellular and molecular structures and dynamics into whole-cell models. Curr Opin Struct Biol 2022; 75:102392. [PMID: 35623188 DOI: 10.1016/j.sbi.2022.102392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Revised: 04/19/2022] [Accepted: 04/21/2022] [Indexed: 11/03/2022]
Abstract
A complete description of the state of the cell requires knowledge of its size, shape, components, intracellular reactions, and interactions with its environment-all of these as a function of time and cell growth. Adding to this list is the need for theoretical models and simulations that integrate and help to interpret this daunting amount of experimental data. It seems like an overwhelming list of requirements, but progress is being made on many fronts. In this review, we discuss the current challenges and problems in obtaining sufficient information about each aspect of a dynamical whole-cell model (DWCM) for simple and well-studied bacterial systems.
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Affiliation(s)
- Zaida Luthey-Schulten
- Department of Chemistry, University of Illinois at Urbana-Champaign, USA; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, USA; Center for the Physics of the Living Cell, University of Illinois at Urbana-Champaign, USA.
| | - Zane R Thornburg
- Department of Chemistry, University of Illinois at Urbana-Champaign, USA
| | - Benjamin R Gilbert
- Department of Chemistry, University of Illinois at Urbana-Champaign, USA
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2
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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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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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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: 48] [Impact Index Per Article: 16.0] [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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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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Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches. Processes (Basel) 2021. [DOI: 10.3390/pr9020322] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.
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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: 12] [Impact Index Per Article: 4.0] [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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Tanıl E, Nikerel E. Black-box kinetic modeling of growth and citric acid production and estimation of ATP maintenance parameters for Candida oleophila ATCC20177. Biotechnol Appl Biochem 2020; 68:148-156. [PMID: 32125024 DOI: 10.1002/bab.1905] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2019] [Accepted: 02/21/2020] [Indexed: 11/09/2022]
Abstract
Mathematical modeling represents and predicts biological systems, explains underlying mechanisms, constituting one of the key focus points for fundamental and applied research to improve our understanding and to decrease costs. Organic acids are used in several industries such as monomers for bioplastics, food preservatives and additives, pharmaceuticals, and agriculture. Nonpetrochemical, sustainable production of organic acids is therefore of great interest. An important step in production of organic acids is the determination of growth and acid production dynamics, as the product itself may have direct and indirect inhibitory effects on the host's metabolism. The aim of this study it twofold: (i) to determine the parameters related to energetics of growth and production as growth ( K x ) and nongrowth associated (mATP ) maintenance constants and (ii) to set up and analyze an unstructured, black-box kinetic model to describe the dynamics of the growth and production of citric acid by Candida oleophila ATCC20177 using published batch fermentation data. K x and mATP were found to be 2.3 ± 1.7 and 5.25 ± 2.75, respectively, for the published P/O ratio of 1.45. The parameter sensitivities and correlations are determined using the Monte Carlo approach, and the final model is tested using chemostat data.
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Affiliation(s)
- Ezgi Tanıl
- Department of Genetics and Bioengineering, Faculty of Engineering, Yeditepe University, Istanbul, Turkey
| | - Emrah Nikerel
- Department of Genetics and Bioengineering, Faculty of Engineering, Yeditepe University, Istanbul, Turkey
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