Mathematical modeling for enzyme inhibitors with slow and fast subsystems

Akgül, Ali; Khoshnaw, Sarbaz H. A.; Abdalrahman, Awder S.

doi:10.1080/25765299.2020.1844369

Cited by 7 publications

(3 citation statements)

References 42 publications

(37 reference statements)

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“…According to the mass action law, the forward (R f ) and backward (R b ) reaction rates are as follows [14]:…”

Section: Reaction Kineticsmentioning

confidence: 99%

Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

Hamad,

Khoshnaw,

Shahzad

2024

Phys. Scr.

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The dehydrogenation of butane is a catalytic process that involves the separation of hydrogen atoms from an organic molecule, and it relies on the presence of a catalyst Z, such as Ni, Pt, Pd, Fe, ZnO, Cr 2 O 3, or Fe 2 O 3. In this paper, we introduce two highly effective mathematical techniques known as Lumping Compartments (LC) and Intrinsic Low Dimensional Manifold (ILDM) to simplify the complexity of the dehydrogenation of butane. Initially, the model consists of seven nonlinear differential equations with eight parameters. To streamline the model, we applied LC to ten different cases, considering various initial states and parameters. As a result, the number of compartments significantly decreased from seven to three. The obtained computational results and total differences reveal a remarkable agreement between the complete model and the simplified version, demonstrating a high degree of predictive accuracy. Additionally, ILDM is employed to enhance the initial estimation of the slow invariant manifold. This enables us to easily distinguish between the fast and slow variations at each point, with the variations acting as chemical kinetics attractors. Fast chemical reactions are drawn towards these attractors, while slow chemical reactions occur within the manifolds.

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“…According to the mass action law, the forward (R f ) and backward (R b ) reaction rates are as follows [14]:…”

Section: Reaction Kineticsmentioning

confidence: 99%

Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

Hamad,

Khoshnaw,

Shahzad

2024

Phys. Scr.

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“…In a groundbreaking move, [14] introduced a model for enzymatic non-competitive inhibition driven by a product, a dimension often underemphasized in traditional enzyme kinetics. Extending this modelling approach, [15] harnessed model reductions to encompass competitive and uncompetitive inhibition mechanisms, thus underscoring the versatile utility of mathematical modelling. In a comprehensive endeavour, [16] developed a mathematical model that integrates inhibitory, deactivating, and diffusional phenomena to elucidate glucose oxidase kinetics.…”

Section: Introductionmentioning

confidence: 99%

Exploring the Dynamics of Simple Inhibition Systems in Continuous Stirred-Tank Reactor: Mathematical Modelling and Bifurcation Analysis

Md Desa,

Mohd,

Uzir

2023

Mal. J. Fund. Appl. Sci.

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The simple enzyme inhibition systems consist of competitive inhibition, noncompetitive inhibition and uncompetitive inhibition. In this work, we incorporated these simple inhibition systems in the continuous stirred-tank reactor (CSTR) and analysed the models using some techniques from dynamical systems and bifurcation analysis. Our aim is to investigate the behaviours of such systems and compare their overall dynamics. The phase portrait is constructed to simulate possible behaviours such as stable steady states, stable limit cycle, bistability between the steady state and the stable limit cycle and bistability between two steady states. The systems undergo bifurcational changes in dynamics as enzyme concentration, dilution rate and proportional control constant are varied. Moreover, we conducted a codimension two bifurcation analysis to examine the joint effects of dilution rate and proportional control constant on the systems behaviours. Our results revealed distinct dynamics for each inhibition system. Increasing the dilution rate led to a transition from low to high substrate concentrations, with competitive inhibition showing the highest tipping (or bifurcation) point where dynamical regimes change due to intense substrate-inhibitor competition. Elevating enzyme concentration reduced substrate concentration, particularly in non-competitive inhibition systems due to higher conversion rates. Furthermore, the proportional control constant had varying effects depending on the specific inhibition system. These findings emphasize the on the combined influences of distinct chemical procoesses in controlling reactor heat and optimizing bioprocess efficiency, considering the unique characteristics of each inhibition system. Overall, the dynamical study on these simple inhibition systems enables us to improve our understanding on the chemical processes involving enzymes with multiple types of inhibitors and may give some insights in its controlling process.

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“…On the basis of these models effective control strategies have been provided for compiling useful guidelines for the health officials and taking various steps towards disease control and eradication. Various researchers have used different epidemic models to forecast the long-term behaviors of COVID-19 as well as suggest control strategies [3][4][5][6][7]. COVID-19 and its vaccination remain a challenging issues and therefore require significant attention.…”

Section: Introductionmentioning

confidence: 99%

Modeling the dynamics of the SARS-CoV-2 virus in a population with asymptomatic and symptomatic infected individuals and vaccination

et al. 2021

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The SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics. The pandemic has spread worldwide through human interactions. Since the nature of the disease differs everywhere and it has a stochastic effect, we therefore develop a stochastic mathematical model to investigate its temporal dynamics. Asymptomatic individuals have a major effect on the spreading dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups. Multiple vaccinations have commenced across the globe. In this study, we assume that the vaccine confers permanent immunity. Moreover, due to the unpredictable characteristics of the disease random fluctuations are assumed in every population group. Using this model we show the existence and uniqueness of positive solutions to the proposed problem. We also discuss the disease extinction and persistence in the model to depict how contagious diseases can be eliminated from the community. We use the real data of SARS-CoV-2 virus, reported in Oman from the 1st January 2021 to 23rd May 2021 to parameterize the model. We then perform large-scale computational analysis to show the numerical simulation and verify the analytical findings.

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Mathematical modeling for enzyme inhibitors with slow and fast subsystems

Cited by 7 publications

References 42 publications

Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

Exploring the Dynamics of Simple Inhibition Systems in Continuous Stirred-Tank Reactor: Mathematical Modelling and Bifurcation Analysis

Modeling the dynamics of the SARS-CoV-2 virus in a population with asymptomatic and symptomatic infected individuals and vaccination

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