Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States

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 mod...

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Autores principales:	Wolfram Liebermeister, Elad Noor
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	metabolic model enzyme kinetic constant parameter estimation convex optimality problem parameter balancing enzyme cost minimisation Microbiology QR1-502
Acceso en línea:	https://doaj.org/article/9430ea81edfd400eb5fb37d31353089d
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spelling	oai:doaj.org-article:9430ea81edfd400eb5fb37d31353089d2021-11-25T18:20:38ZModel Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States10.3390/metabo111107492218-1989https://doaj.org/article/9430ea81edfd400eb5fb37d31353089d2021-10-01T00:00:00Zhttps://www.mdpi.com/2218-1989/11/11/749https://doaj.org/toc/2218-1989Enzyme 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 <i>E. coli</i> central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in <i>E. coli</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mi>cat</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mi mathvariant="normal">M</mi></msub></semantics></math></inline-formula> 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.Wolfram LiebermeisterElad NoorMDPI AGarticlemetabolic modelenzyme kinetic constantparameter estimationconvex optimality problemparameter balancingenzyme cost minimisationMicrobiologyQR1-502ENMetabolites, Vol 11, Iss 749, p 749 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	metabolic model enzyme kinetic constant parameter estimation convex optimality problem parameter balancing enzyme cost minimisation Microbiology QR1-502
spellingShingle	metabolic model enzyme kinetic constant parameter estimation convex optimality problem parameter balancing enzyme cost minimisation Microbiology QR1-502 Wolfram Liebermeister Elad Noor Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States
description	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 <i>E. coli</i> central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in <i>E. coli</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mi>cat</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mi mathvariant="normal">M</mi></msub></semantics></math></inline-formula> 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.
format	article
author	Wolfram Liebermeister Elad Noor
author_facet	Wolfram Liebermeister Elad Noor
author_sort	Wolfram Liebermeister
title	Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States
title_short	Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States
title_full	Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States
title_fullStr	Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States
title_full_unstemmed	Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States
title_sort	model balancing: a search for in-vivo kinetic constants and consistent metabolic states
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/9430ea81edfd400eb5fb37d31353089d
work_keys_str_mv	AT wolframliebermeister modelbalancingasearchforinvivokineticconstantsandconsistentmetabolicstates AT eladnoor modelbalancingasearchforinvivokineticconstantsandconsistentmetabolicstates
_version_	1718411332437409792

Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States

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