An old paper revisited: “A mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load” by V.V. Dynnik, R. Heinrich and E.E. Sel’kov

Nazaret, Christine; Mazat, Jean‐Pierre

doi:10.1016/j.jtbi.2008.01.003

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…In this study, the motto of modelling was to keep the model as simple as possible while making it as complex as required. Several models for glucose catabolism or glycolysis, using ODE's similar to the model developed in this study, can be found, for example, in the BioModels repository, which vary in their complexities and sophistication [ 80 , 81 , 82 , 83 ]. These models could not, however, be easily adapted to simulate the experimental ECA responses, as they were not developed specifically to simulate the end‐point kinetics and do not demonstrate similar interaction of cytoplasmic and mitochondrial counterparts necessary to simulate the two metabolic phases.…”

Section: Discussionmentioning

confidence: 99%

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays

Patil,

Mirveis,

Byrne

2024

FEBS Open Bio

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This study aims to demonstrate the benefits of augmenting commercially available, real‐time, in vitro glycolysis assays with phenomenological rate equation‐based kinetic models, describing the contributions of the underpinning metabolic pathways. To this end, a commercially available glycolysis assay, sensitive to changes in extracellular acidification (extracellular pH), was used to derive the glycolysis pathway kinetics. The pathway was numerically modelled using a series of ordinary differential rate equations, to simulate the obtained experimental results. The sensitivity of the model to the key equation parameters was also explored. The cellular glycolysis pathway kinetics were determined for three different cell‐lines, under nonmodulated and modulated conditions. Over the timescale studied, the assay demonstrated a two‐phase metabolic response, representing the differential kinetics of glycolysis pathway rate as a function of time, and this behaviour was faithfully reproduced by the model simulations. The model enabled quantitative comparison of the pathway kinetics of three cell lines, and also the modulating effect of two known drugs. Moreover, the modelling tool allows the subtle differences between different cell lines to be better elucidated and also allows augmentation of the assay sensitivity. A simplistic numerical model can faithfully reproduce the differential pathway kinetics for three different cell lines, with and without pathway‐modulating drugs, and furthermore provides insights into the cellular metabolism by elucidating the underlying mechanisms leading to the pathway end‐product. This study demonstrates that augmenting a relatively simple, real‐time, in vitro assay with a model of the underpinning metabolic pathway provides considerable insights into the observed differences in cellular systems.

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Section: Discussionmentioning

confidence: 99%

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays

Patil,

Mirveis,

Byrne

2024

FEBS Open Bio

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“…Nevertheless, we can still achieve good results compared to the real differential Jacobian matrix with the structure information of these off diagonal perturbations. The evaluation models are: a, carbohydrate energy metabolism model [50]; b, AMPK-mTOR pathway model [51]; c, hepatic glucose metabolism model [52] and d, blood cell metabolism model [53]. For each subplot a-d, the left is the real differential Jacobian matrix; the middle is the inverse differential Jacobian results with D structure information; and the right is the results without D structure information.…”

Section: Improved Differential Jacobian Reconstruction When Consideri...mentioning

confidence: 99%

Enzyme fluctuations data improve inference of metabolic interaction networks with an inverse differential Jacobian approach

Li,

Weckwerth,

Waldherr

2023

Preprint

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The development of next-generation sequencing and single-cell technology has generated vast genome-scale multi-omics datasets. Dedicated mathematical algorithms are required to dissect intricate molecular causality within metabolic networks using these datasets. Based on the network analysis, recent research has introduced the inverse differential Jacobian algorithm, which combines metabolic interaction network construction and covariance matrix analysis of genome-scale metabolomics data to elucidate system regulatory factors near steady-state dynamics. Traditionally, these studies assumed metabolomics variations solely resulted from metabolic system fluctuations, acting independently on each metabolite. However, emerging evidence highlights the role of internal network fluctuations, particularly from the gene expression fluctuations, leading to correlated perturbations on metabolites.In this article, we propose a novel approach that exploits these correlations to reconstruct relevant metabolic interactions. Thereby, enzymes exhibiting significant variances in activity values serve as indicators of large fluctuations in their catalyzed reactions. By integrating this information in an inverse Jacobian algorithm, we are able to exploit the underlying reaction network structure to improve the construction of the fluctuation matrix required in the inverse Jacobian algorithm. After a comprehensive assessment of three critical factors affecting the algorithm’s accuracy, we conclude that using the enzyme fluctuation data significantly enhances the inverse Jacobian algorithm’s performance. We applied this approach to a breast cancer dataset with two different cell lines, which highlighted metabolic interactions where fluctuations in enzyme gene expression yield a relevant difference between the cell lines.

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“…Metabolic modeling has proved to be a very powerful tool to get a better insight into the metabolism of an organism, while assessing the main fluxes throughout its metabolic network. 1,2 This approach has gained accuracy in the last decades and turned out to be particularly efficient to improve the production of target molecules, by understanding the biological processes that influence the metabolites. For example, metabolic modeling has clarified the production of triacylglycerols from microalgae and carbohydrates from cyanobacteria.…”

Section: Introductionmentioning

confidence: 99%

Dynamical reduction of linearized metabolic networks through quasi steady state approximation

2018

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Metabolic modeling has gained accuracy in the last decades, but the resulting models are of high dimension and difficult to use for control purpose. Here we propose a mathematical approach to reduce high dimensional linearized metabolic models, which relies on time scale separation and the quasi steady state assumption. Contrary to the flux balance analysis assumption that the whole system reaches an equilibrium, our reduced model depends on a small system of differential equations which represents the slow variables dynamics. Moreover, we prove that the concentration of metabolites in quasi steady state is one order of magnitude lower than the concentration of metabolites with slow dynamics (under some flux conditions). Also, we propose a minimization strategy to estimate the reduced system parameters. The reduction of a toy network with the method presented here is compared with other approaches. Finally, our reduction technique is applied to an autotrophic microalgae metabolic network.Reactions from metabolites in QSS are faster than those from metabolites with slow dynamics. The input is I(t) = k[cos(t Á ω) + 1]. [Color figure can be viewed at wileyonlinelibrary.com]Notice that the all the metabolite concentrations have the same order of magnitude, as a consequence of defining Y i = X i /ε for the metabolites in the fast part. The parameters considered are specified in Table 1.

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An old paper revisited: “A mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load” by V.V. Dynnik, R. Heinrich and E.E. Sel’kov

Cited by 7 publications

References 9 publications

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays

Enzyme fluctuations data improve inference of metabolic interaction networks with an inverse differential Jacobian approach

Dynamical reduction of linearized metabolic networks through quasi steady state approximation

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