Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, Saudi Arabia.
PLoS One. 2023 Mar 23;18(3):e0277806. doi: 10.1371/journal.pone.0277806. eCollection 2023.
Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.
化学动力学是化学的一个分支，其基础是理解化学反应速率。化学动力学与宇宙学、地质学甚至在某些情况下的心理学都有很多关联。这些化学反应需要进行数学建模。因此，本研究基于基于化学动力学的建模和酶反应动力学。本研究着眼于两步底物-酶可逆反应。在两步可逆反应中，底物与酶结合，然后分两步进一步转化为产物。该模型通过流程图展示，然后转换为常微分方程。Atangana-Baleanu 时间分数算子和 Mittag-Leffler 核用于将原始的高度非线性耦合整数阶常微分方程组转换为分数阶模型。此外，还表明所研究的分数阶模型的解是唯一的、有界的，可以通过其响应速度来表示。采用基于 MATLAB 软件的牛顿多项式插值技术的数值方案，即 Atangana-Toufik 方法，以找到图形结果。通过各种图形展示了不同反应速率下的反应动力学。可以观察到，正向反应速率会增加反应速度，而反向反应速率会降低反应速度。
