Modelling hyaluronan degradation by streptococcus pneumoniae hyaluronate lyase

Mai, Vinh; Vo, Tuoi T. N.; Meere, Martin

doi:10.1016/j.mbs.2018.07.002

Cited by 12 publications

(11 citation statements)

References 30 publications

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“…We now briefly describe the sensitivity indices. The discussion given here largely mirrors that given in Mai et al [58] and is reproduced here for the convenience of the reader. For the parameter q i , the associated first-order sensitivity index S i is given by:…”

Section: Global Sensitivity Analysismentioning

confidence: 77%

Modelling the Phosphorylation of Glucose by Human hexokinase I

Mai

Meere

2021

Mathematics

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In this paper, we develop a comprehensive mathematical model to describe the phosphorylation of glucose by the enzyme hexokinase I. Glucose phosphorylation is the first step of the glycolytic pathway, and as such, it is carefully regulated in cells. Hexokinase I phosphorylates glucose to produce glucose-6-phosphate, and the cell regulates the phosphorylation rate by inhibiting the action of this enzyme. The cell uses three inhibitory processes to regulate the enzyme: an allosteric product inhibitory process, a competitive product inhibitory process, and a competitive inhibitory process. Surprisingly, the cellular regulation of hexokinase I is not yet fully resolved, and so, in this study, we developed a detailed mathematical model to help unpack the behaviour. Numerical simulations of the model produced results that were consistent with the experimentally determined behaviour of hexokinase I. In addition, the simulations provided biological insights into the abstruse enzymatic behaviour, such as the dependence of the phosphorylation rate on the concentration of inorganic phosphate or the concentration of the product glucose-6-phosphate. A global sensitivity analysis of the model was implemented to help identify the key mechanisms of hexokinase I regulation. The sensitivity analysis also enabled the development of a simpler model that produced an output that was very close to that of the full model. Finally, the potential utility of the model in assisting experimental studies is briefly indicated.

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Section: Global Sensitivity Analysismentioning

confidence: 77%

Modelling the Phosphorylation of Glucose by Human hexokinase I

Mai

Meere

2021

Mathematics

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“…This implies that diusive eects in the degradation process can be neglected, and that the concentrations of the various species in the mixture can be described by functions of time only. This further implies that the evolution of the system can be modelled by a coupled system of nonlinear ordinary dierential equations, and that a partial dierential equations model is not required [11].…”

Section: Modelling Assumptionsmentioning

confidence: 99%

“…(ii) We assume mass action kinetics throughout; this implies that the rate of a reaction is taken to be proportional to the product of the concentrations of the reactants. We emphasize here that more complex formulas, such as the MichaelisâMenten formula for the rate of product production in an enzyme-catalysed reaction, are derivable from more fundamental mass action considerations under simplifying assumptions [5,11]. k −2 − desorption rate of product molecules from enzyme-product complexes (s −1 )…”

Section: Modelling Assumptionsmentioning

confidence: 99%

Numerical analysis of coupled systems of ODEs and applications to enzymatic competitive inhibition by product

Mai

Nhan²

2021

Advances in the Theory of Nonlinear Analysis and Its Application

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Enzymatic inhibition is one of the key regulatory mechanisms in cellular metabolism, especially the enzymatic competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we derive a mathematical model describing the enzymatic competitive inhibition by product. The model consists of a coupled system of nonlinear ordinary dierential equations for the species of interest. Using nondimensionalization analysis, a formula for product formation rate for this mechanism is obtained in a transparent manner. Further analysis for this formula yields qualitative insights into the maximal reaction velocity and apparent Michaelis-Menten constant. Integrating the model numerically, the eects of the model parameters on the model output are also investigated. Finally, a potential application of the model to realistic enzymes is briey discussed.

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“…This implies that diffusive effects in the reaction process can be neglected, and that the concentrations of the various species in the mixture can be described by functions of time only. This further implies that the evolution of the system can be modeled by a coupled system of nonlinear ordinary differential equations, and that a partial differential equations model is not required [21][22][23].…”

Section: Modeling Assumptionsmentioning

confidence: 99%

“…(b) We assume mass action kinetics throughout; this implies that the rate of a reaction is taken to be proportional to the product of the concentrations of the reactants. We emphasize here that more complex formulas, such as the MichaelisMenten formula for the rate of product formation in an enzyme-catalyzed reaction, are derivable from more fundamental mass action considerations under simplifying assumptions [4,[22][23][24].…”

Section: Modeling Assumptionsmentioning

confidence: 99%

A mathematical model of enzymatic non-competitive inhibition by product and its applications

Mai¹,

Nhan²,

Hammouch³

2021

Phys. Scr.

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Enzymes are biological catalysts naturally present in living organisms, and they are capable of accelerating biochemical reactions in the metabolism process. Cells use many regulatory mechanisms to regulate the concentrations of cellular metabolites at physiological levels. Enzymatic inhibition is one of the key regulatory mechanisms naturally occurring in cellular metabolism, especially the enzymatic non-competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we develop a novel mathematical model describing the enzymatic non-competitive inhibition by product. The model consists of a coupled system of nonlinear ordinary differential equations for the species of interest. Using nondimensionalization analysis, a formula for product formation rate for this mechanism is obtained in a transparent manner. Further analysis for this formula yields qualitative insights into the maximal reaction velocity and apparent Michaelis-Menten constant. Asymptotic solutions of the model are carefully given by using the homotopy perturbation analysis. A good agreement between the asymptotic solutions and numerical solutions are found. In addition, a Sobol global sensitivity analysis is implemented to help identify the key mechanisms of the enzyme activities. The results of this analysis show that the rate of product formation is relatively sensitive to the following factors: the catalytic rate of the enzyme, the rates of binding/unbinding of the product to/from the enzyme/enzyme complex. The numerical simulations provide insights into how variations in the model parameters affect the model output. Finally, an application of the model to the phosphorylation of glucose by mutant-hexokinase I enzyme is briefly discussed.

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Modelling hyaluronan degradation by streptococcus pneumoniae hyaluronate lyase

Cited by 12 publications

References 30 publications

Modelling the Phosphorylation of Glucose by Human hexokinase I

Modelling the Phosphorylation of Glucose by Human hexokinase I

Numerical analysis of coupled systems of ODEs and applications to enzymatic competitive inhibition by product

A mathematical model of enzymatic non-competitive inhibition by product and its applications

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