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Mathematical modeling and analysis for Michaelis–Menten kinetics Michaelis-Menten动力学的数学建模与分析
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-07-11 DOI: 10.1007/s10910-025-01739-4
Gülnihal Meral, Derya Altıntan
{"title":"Mathematical modeling and analysis for Michaelis–Menten kinetics","authors":"Gülnihal Meral,&nbsp;Derya Altıntan","doi":"10.1007/s10910-025-01739-4","DOIUrl":"10.1007/s10910-025-01739-4","url":null,"abstract":"<div><p>In this paper, the Michaelis–Menten dynamics are studied by reducing the original system to a new set of two nonlinear ordinary differential equations obtained via conservation relations and variable transformations. A stability analysis of the reduced system reveals the existence of a stable equilibrium point. The properties of boundedness, positivity, existence, and uniqueness of the solutions are established by constructing two sequences, which are subsequently proven to be Cauchy sequences. Finally, numerical simulations are performed to validate the theoretical results and illustrate the expected behavior of the model.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 8","pages":"1753 - 1766"},"PeriodicalIF":2.0,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum expectation values and Shannon entropy in diatomic molecular systems 双原子分子系统中的量子期望值和香农熵
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-06-04 DOI: 10.1007/s10910-025-01738-5
Etido P. Inyang
{"title":"Quantum expectation values and Shannon entropy in diatomic molecular systems","authors":"Etido P. Inyang","doi":"10.1007/s10910-025-01738-5","DOIUrl":"10.1007/s10910-025-01738-5","url":null,"abstract":"<div><p>This study investigates the expectation values and Shannon entropy of selected diatomic molecules—HCl, CO, and LiH—within the framework of the Kratzer plus Generalized Morse Potential. The energy eigenvalues and wave functions are determined using the parametric Nikiforov–Uvarov approach, enabling a detailed analysis of key quantum mechanical properties, including kinetic energy, squared momentum, and inverse square distance expectation values. Furthermore, Shannon entropy is applied to examine wave function localization in both position and momentum spaces, emphasizing the impact of screening parameters on molecular behavior. The findings indicate that an increase in the rotational quantum number results in higher energy spectra and expectation values. The Shannon entropy analysis reinforces the uncertainty principle by demonstrating an inverse relationship between position and momentum entropy. These insights contribute to quantum information measures in molecular systems, with potential applications in spectroscopy, molecular modeling, and quantum chemistry.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 8","pages":"1732 - 1752"},"PeriodicalIF":2.0,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pattern evolution of coupled reaction–diffusion models arises in chemical systems using modified trigonometric cubic B-spline functions 利用修正三角三次b样条函数研究化学系统中耦合反应扩散模型的模式演化
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-28 DOI: 10.1007/s10910-025-01736-7
Jitender Kumar, Vikas Kumar, Sapna Pandit, Sardor Dadabaev Usmanovich, Norqulova Ziyoda Nabi Qizi
{"title":"Pattern evolution of coupled reaction–diffusion models arises in chemical systems using modified trigonometric cubic B-spline functions","authors":"Jitender Kumar,&nbsp;Vikas Kumar,&nbsp;Sapna Pandit,&nbsp;Sardor Dadabaev Usmanovich,&nbsp;Norqulova Ziyoda Nabi Qizi","doi":"10.1007/s10910-025-01736-7","DOIUrl":"10.1007/s10910-025-01736-7","url":null,"abstract":"<div><p>This approach captures the different patterns of coupled nonlinear reaction–diffusion (RD) models which arises in chemical systems of biology and chemistry. To accomplish this task, a new algorithm based on modified trigonometric cubic B-spline functions is developed. Also, the computational complexity of the algorithm is discussed. From numerical experiments point of view, a test problem for accuracy, 1D and 2D Brusselator models and Grey-Scott model are considered. </p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 8","pages":"1715 - 1731"},"PeriodicalIF":2.0,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis and numerical solution of singularly perturbed partial differential equations with large spatial delays and integral boundary conditions: applications in chemical and catalytic systems 具有大空间延迟和积分边界条件的奇摄动偏微分方程的分析和数值解：在化学和催化系统中的应用
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-26 DOI: 10.1007/s10910-025-01737-6
Parvin Kumari, Jesus Vigo-Aguiar, Garima Agarwal
{"title":"Analysis and numerical solution of singularly perturbed partial differential equations with large spatial delays and integral boundary conditions: applications in chemical and catalytic systems","authors":"Parvin Kumari,&nbsp;Jesus Vigo-Aguiar,&nbsp;Garima Agarwal","doi":"10.1007/s10910-025-01737-6","DOIUrl":"10.1007/s10910-025-01737-6","url":null,"abstract":"<div><p>This work proposes a hybrid numerical strategy to effectively solve the singularly perturbed partial differential equations (SPPDEs) with integral boundary conditions and substantial spatial delays. For the time discretization, the Crank-Nicolson scheme was chosen because of its stability and second-order precision. In order to maximize accuracy in the vicinity of layers coming from the tiny perturbation parameter and delay parameter, the computational implementation will be carried out using a non-uniform Shishkin-type mesh for spatial discretization using cubic spline interpolation. The approach is tested numerically to verify its robustness and efficiency with respect to integral boundary conditions and delayed feedback. Applications to reaction-diffusion systems, catalytic reactions in porous media, and transport-reaction dynamics in tubular reactors are presented to illustrate the effectiveness of the proposed approach.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 8","pages":"1689 - 1714"},"PeriodicalIF":2.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Floating spherical Gaussian orbital model: a brief overview 浮动球面高斯轨道模型：简要概述
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-17 DOI: 10.1007/s10910-025-01735-8
Hiteshi Tandon, Tanmoy Chakraborty
{"title":"Floating spherical Gaussian orbital model: a brief overview","authors":"Hiteshi Tandon,&nbsp;Tanmoy Chakraborty","doi":"10.1007/s10910-025-01735-8","DOIUrl":"10.1007/s10910-025-01735-8","url":null,"abstract":"<div><p>The Floating spherical Gaussian orbital model has existed for nearly half a century, yet it remains one of the lesser researched areas. Considering the potential of the model to address significant quantum-based or molecular problems, this article aims to bring renewed attention to this long neglected concept. This review presents, a brief overview of the background, literature and current status of the method, and concludes with suggestions for future research.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1555 - 1565"},"PeriodicalIF":2.0,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The numerical solution of the adsorption integral equation with Langmuir-kernel Part 1: approximations langmuir核吸附积分方程的数值解。第1部分：近似
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-16 DOI: 10.1007/s10910-025-01724-x
Steffen Arnrich, Grit Kalies
{"title":"The numerical solution of the adsorption integral equation with Langmuir-kernel Part 1: approximations","authors":"Steffen Arnrich,&nbsp;Grit Kalies","doi":"10.1007/s10910-025-01724-x","DOIUrl":"10.1007/s10910-025-01724-x","url":null,"abstract":"<div><p>The qualitative relationship between the adsorption energy distribution of a microporous adsorbent and its total isotherms is modeled by the adsorption integral equation with Langmuir kernel. Due to the instability of the adsorption integral equation, a regularization is required. Recently, we have developed a general regularization using a transformation that will now be specialized for numerical application. In this paper, we perform the first step to this end, namely the construction of an approximation of the transformed total isotherm from finitely many measurement points. The method presented here is based on discrete convolution and is also suitable for the approximation of more general functions and their spectral functions. A full error analysis is given. In particular, the influences of the measurement error, the discretization error and the truncation error on the quality of the approximation of the transformed total isotherm are investigated.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1650 - 1678"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01724-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Magnetic and thermal properties of phosphorene quantum rings 磷系量子环的磁性和热性质
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-16 DOI: 10.1007/s10910-025-01732-x
Xilong Bai, Zhensheng Lu, Liu Long
{"title":"Magnetic and thermal properties of phosphorene quantum rings","authors":"Xilong Bai,&nbsp;Zhensheng Lu,&nbsp;Liu Long","doi":"10.1007/s10910-025-01732-x","DOIUrl":"10.1007/s10910-025-01732-x","url":null,"abstract":"<div><p>We consider an electron confined in a quantum ring (QR) defined electrostatically within the phosphorene monolayer. A confinement potential with an elliptical shape is employed to account for the anisotropy of the effective masses. The Schrödinger equation is solved, leading to the determination of the energy levels. Subsequently, the Shannon formalism is applied to compute the probability distribution and partition function of the system. Finally, the magnetic and thermodynamic properties of the phosphorene QR are analyzed. The results reveal that the magnetic susceptibility exhibits a negative value, indicative of diamagnetic behavior. A maximum value of magnetic susceptibility is observed at low temperatures and high magnetic fields. At elevated magnetic temperatures, the specific heat remains constant, even in the absence of an external magnetic field.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1636 - 1649"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Beyond the SNR-resolution uncertainty principle: Optimized derivative fast Fourier transform for NMR diagnostics in medicine 超越信噪比分辨率不确定原理：用于医学核磁共振诊断的优化导数快速傅立叶变换
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-14 DOI: 10.1007/s10910-025-01733-w
Dževad Belkić, Karen Belkić
{"title":"Beyond the SNR-resolution uncertainty principle: Optimized derivative fast Fourier transform for NMR diagnostics in medicine","authors":"Dževad Belkić,&nbsp;Karen Belkić","doi":"10.1007/s10910-025-01733-w","DOIUrl":"10.1007/s10910-025-01733-w","url":null,"abstract":"<div><p>The present study is on proton magnetic resonance spectroscopy (MRS), as it applies to tumor diagnostics in cancer precision medicine. The goal with the employed patients’ data, subjected to shape estimations alone with no fitting, is to reconstruct self-contained quantitative information of diagnostic relevance. This can be accomplished by proper evaluation of physical metabolites, especially cancer biomarkers (lactates, cholines, citrates,...). Such information is completely opaque in the encoded time signals, but can be transparent in the frequency domain. The optimized derivative fast Fourier transform (dFFT) can meet the challenge. The thorniest stumbling blocks in MRS are abundant overlapping resonances of low resolution and poor signal-to-noise ratio (SNR). Attempts to increase resolution are marred by decreased SNR. The long-sought strategy of MRS, simultaneous improvement of resolution and SNR, is achievable by the optimized dFFT. With the implied aid to decision-making, this is illustrated for ovarian MRS data encoded from benign and malignant human biofluid samples.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1598 - 1635"},"PeriodicalIF":2.0,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01733-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Condensed-to-bond dual descriptor for the analysis of electron density rearrangement in π-conjugated compounds 用于分析π共轭化合物中电子密度重排的缩合-键双描述子
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-10 DOI: 10.1007/s10910-025-01730-z
Ricardo Pino–Rios
{"title":"Condensed-to-bond dual descriptor for the analysis of electron density rearrangement in π-conjugated compounds","authors":"Ricardo Pino–Rios","doi":"10.1007/s10910-025-01730-z","DOIUrl":"10.1007/s10910-025-01730-z","url":null,"abstract":"<div><p>This study proposes the application of the bond dual descriptor, computed using finite difference approximation, to investigate the electron density reorganization in π-conjugated compounds upon nucleophilic/electrophilic attack. Compared to the traditional bond Fukui function analysis, this descriptor offers a simpler approach, reducing the complexity of potential rearrangement scenarios in half and simplifying the interpretation. A series of ethylene derivatives have been tested allowing to explain the activation of the double bond in ethylene derivatives, the rearrangement of the electron density and its reduction in activation energies. In addition, it is shown that it is possible to explain the reactivity on Michael acceptors, the rearrangement of cis-1,3,5-hexatriene to form 1,3-cyclohexadiene and the preference of C<sub>60</sub> to react through its [6,6] over [5,6] bonds. The bond dual descriptor complements the atomic dual descriptor, enabling a comprehensive analysis of the chemical reactivity of π-conjugated compounds.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1588 - 1597"},"PeriodicalIF":2.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
To a mechanical model of synthetic catch-bonds 合成捕获键的机械模型
IF 2 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-08 DOI: 10.1007/s10910-025-01731-y
Wolfgang Quapp, Josep Maria Bofill, Kerim C. Dansuk, Sinan Keten
{"title":"To a mechanical model of synthetic catch-bonds","authors":"Wolfgang Quapp,&nbsp;Josep Maria Bofill,&nbsp;Kerim C. Dansuk,&nbsp;Sinan Keten","doi":"10.1007/s10910-025-01731-y","DOIUrl":"10.1007/s10910-025-01731-y","url":null,"abstract":"<p>We support a preliminary determination of the catch-bond character of a mechanical–chemical toy model using a tweezers construction with some modifications. We discuss a theoretical analysis of the problem using Newton trajectories. We propose a two-dimensional potential energy surfaces for this model. We discuss the slip, ideal and catch-bonds for this model using the previous potential parts of Dansuk and Keten (Matter 1:911, 2019). Chemical examples of the ansatz are allosteric reactions, especially FimH proteins. We note again that Newton trajectories provide the theoretical background of mechanochemistry. Construction of a potential energy surface and use of Newton trajectories by Wolfram Mathematica. Calculation of real catch bond behavior. We get for a tweezers model the catch bond behavior.</p><p> Two barriers under external force, F. The catch-bond barrier increases.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1566 - 1587"},"PeriodicalIF":2.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01731-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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