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生物数学学报 1996年第4期11卷 6-11页

作者： Ding Yong（Department of Biomathematics，Nanjing Medical University，Nanjing 210029）

For drugs obeying parallel first-order and michaelis-menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:where Xo is the intravenous loading dose,Cb the plasma concentration level desired in clinical therapy,V the apparent distribution volume,k0 the rate constant of intravenouns infusion,K the first－order elimination rate constant,Vm the theoretical maximum rate of the michaelis－menten elimination process,Km the michaelis *** this dosage regimen,plasma level maintains a constant Cb during the administration *** K=0 the dosage regimen above is also suitable for drugs obeying michaelis-menten elimination kinetics.

关键词： Intravenous infusion Optimum dosage regimen michaelis-menten elimination kinetics Mathematical analysis

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基于michaelis-menten型呼吸速率模型的实验研究

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上海交通大学学报 2004年第7期38卷 1170-1173页

作者：刘颖李云飞王如竹田平海杨宏顺上海交通大学制冷与低温工程研究所上海交通大学食品科学与工程系上海201101

冷藏结合气调包装是果蔬采后保持品质的有效手段 ,呼吸速率是系统设计的必要依据 .以黄桃为例 ,确定了 0、5、1 0、1 5和 2 5°C下呼吸速率随 O2 、CO2 浓度的变化规律 ,建立了基于酶动力学原理的 michaelis- menten型黄桃呼吸速率模型 ... 详细信息

冷藏结合气调包装是果蔬采后保持品质的有效手段 ,呼吸速率是系统设计的必要依据 .以黄桃为例 ,确定了 0、5、1 0、1 5和 2 5°C下呼吸速率随 O2 、CO2 浓度的变化规律 ,建立了基于酶动力学原理的 michaelis- menten型黄桃呼吸速率模型 .结果显示 ,呼吸速率随 CO2 浓度的增加而减小 ,最大呼吸速率随温度的增加而增加 ,并满足 Arrhenius关系 .该方法适用于包括非平衡状态在内的任何阶段 .

关键词： michaelis-menten 呼吸速率酶动力学气调包装冷藏

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Analysis of non-linear reaction-diffusion processes with michaelis-menten kinetics by a new Homotopy perturbation method

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Natural Science 2013年第9期5卷 1034-1046页

作者： Devaraj Shanthi Vembu Ananthaswamy Lakshmanan Rajendran Department of Mathematics The Madura College Madurai India Government Higher Secondary School Madurai India

This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to michaelis-menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.

关键词： Oxygen Diffusion michaelis-menten Non-Linear Differential Equations New Homotopy Perturbation Method Numerical Simulation

michaelis-menten型消除动力学稳态特性的数学研究

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科技通报 1985年第4期 20-22页

作者：周怀梧浙江医科大学

michaelis-menten型消除动力学(简称米氏型消除)是非线性药物动力学中较常见而重要的一类。乙醇、苯妥英、茶碱、水杨酸盐等的体内过程都具有这类动力学特性。在一次给药下,描述血药浓度C随时间t变化的动力学方程都是非线性微分方程。... 详细信息

michaelis-menten型消除动力学(简称米氏型消除)是非线性药物动力学中较常见而重要的一类。乙醇、苯妥英、茶碱、水杨酸盐等的体内过程都具有这类动力学特性。在一次给药下,描述血药浓度C随时间t变化的动力学方程都是非线性微分方程。因而在多次给药下(临床药物治疗通常都需多次给药),相应的C-t方程难以导出。为拟订最佳剂量方案,必须了解在多次给药下,血药浓度达到稳定状态所需要的时间,以及稳态血药浓度的高低。作者导出了平均稳态浓度方程,以及达到稳态所需时间的计算公式。此外,提出了临床

关键词：稳态特性静态特性计算公式 michaelis-menten 最佳剂量数学研究方程平均参数值动力学

关于酶催化反应动力学——michaelis-menten常数严格确定法

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科学通报 1986年第14期31卷 1084-1086页

作者：常棉大连轻工业学院

从酶促反应实验结果的规律性出发,通过线性模拟分析,提出了严格确定michaelis-Metnen常数法,从而在数值上校正了定态近似来确定动力学方程所带来的偏差,消除了传统作图法确定M-M常数所造成的主观误差,方法简捷而具有普适性。由于酶催化... 详细信息

从酶促反应实验结果的规律性出发,通过线性模拟分析,提出了严格确定michaelis-Metnen常数法,从而在数值上校正了定态近似来确定动力学方程所带来的偏差,消除了传统作图法确定M-M常数所造成的主观误差,方法简捷而具有普适性。由于酶催化反应条件适宜(常温常压下)和惊人的催化效率以及高度选择专一性,使得酶

关键词：方程酶催化反应酶促反应底物 michaelis-menten 常数数学

Analytical expressions of the concentrations of substrate and product in enzyme inhibition process

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Natural Science 2013年第9期5卷 1047-1055页

作者： Sankaranarayanan Muthukumar Lakshmanan Rajendran Department of Mathematics The Madura College Madurai India

The initial and boundary value problem in enzyme reactions mechanism for inhabitation process is discussed. Approximate analytical expressions for the concentrations of substrate and product are presented. Approximate analytical solutions of non-linear reaction equations containing non-linear terms related to enzymatic reaction mechanism are solved using Homotopy perturbation method. The relevant analytical expression for the substrate and product concentration profiles is discussed in terms of dimensionless reaction diffusion parameters α, β, γE, and γS. Numerical solution is also obtained using Matlab program. Our analytical expression compared with numerical estimation and good agreement is noted.

关键词： Initial and Boundary Value Problems Enzyme Kinetics Non-Linear Reaction Equations Homotopy Perturbation Method michaelis-menten Kinetics

Stability Analysis for the Cellular Signaling Systems Composed of Two Phosphorylation-Dephosphorylation Cyclic Reactions

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Computational Molecular Bioscience 2017年第3期7卷 33-45页

作者： Chinasa Sueyoshi Takashi Naka Graduate School of Information Science Kyushu Sangyo University Fukuoka Japan Department of Information Science Kyushu Sangyo University Fukuoka Japan

The regulatory mechanisms in cellular signaling systems have been studied intensively from the viewpoint that the malfunction of the regulation is thought to be one of the substantial causes of cancer formation. On the other hand, it is rather difficult to develop the theoretical framework for investigation of the regulatory mechanisms due to their complexity and nonlinearity. In this study, more general approach is proposed for elucidation of characteristics of the stability in cellular signaling systems by construction of mathematical models for a class of cellular signaling systems and stability analysis of the models over variation of the network architectures and the parameter values. The model system is formulated as regulatory network in which every node represents a phosphorylation-dephosphorylation cyclic reaction for respective constituent enzyme. The analysis is performed for all variations of the regulatory networks comprised of two nodes with multiple feedback regulation loops. It is revealed from the analysis that the regulatory networks become mono-stable, bi-stable, tri-stable, or oscillatory and that the negative mutual feedback or positive mutual feedback is favorable for multi-stability, which is augmented by a negatively regulated node with a positive auto-regulation. Furthermore, the multi-stability or the oscillation is more likely to emerge in the case of low value of the michaelis constant than in the case of high value, implying that the condition of higher saturation levels induces stronger nonlinearity in the networks. The analysis for the parameter regions yielding the multi-stability and the oscillation clarified that the stronger regulation shifts the systems toward multi-stability.

关键词： Cellular Signaling Systems Regulatory Networks Cyclic Reaction michaelis-menten Mechanism Multi-Stability Oscillation

Parameter Estimation in Different Enzyme Reactions

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Advances in Enzyme Research 2014年第1期2卷 14-26页

作者： Sudarshan R. Nelatury Charles F. Nelatury Mary C. Vagula Biology Department Gannon University Erie USA Department of ECE College of Engineering Drexel University Philadelphia USA Department of ECE School of Engineering Penn State Erie Erie USA

Enzyme kinetic parameters have been estimated using MATLAB software via the Wilkinson non-linear regression technique. The MATLAB script file written to implement this technique is short and very straightforward. Several software tools are commercially available for this purpose, with many graphical user interface (GUI) features. A routine use of these packages might offer immediate satisfaction of interactive hands-on experience;but in some cases the researcher might wish to write his/her own code and compare the results for further confirmation. Today MATLAB is in use in almost all the schools and laboratories as a standard software tool. So this paper is aimed at helping enzyme researchers to make use of this powerful software for estimation of parameters. It enables the incorporation of the analytical steps behind parameter estimation in an easy-to-follow manner and furnishes better visualization.

关键词： michaelis-menten Equation Dixon Plot Hill Equation Wilkinson Nonlinear Regression MATLAB

Analytical Expression for the Concentration of Substrate and Product in Immobilized Enzyme System in Biofuel/Biosensor

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Applied Mathematics 2015年第7期6卷 1148-1160页

作者： R. Malini Devi O. M. Kirthiga L. Rajendran Department of Mathematics The Standard Fireworks Rajaratnam College for Women Sivakasi India Department of Mathematics The Madura College Madurai India

In this paper, an approximate analytical method to solve the non-linear differential equations in an immobilized enzyme film is presented. Analytical expressions for concentrations of substrate and product have been derived for all values of dimensionless parameter. Dimensionless numbers that can be used to study the effects of enzyme loading, enzymatic gel thickness, and oxidation/ reduction kinetics at the electrode in biosensor/biofuel cell performance were identified. Using the dimensionless numbers identified in this paper, and the plots representing the effects of these dimensionless numbers on concentrations and current in biosensor/biofuel cell are discussed. Analytical results are compared with simulation results and satisfactory agreement is noted.

关键词： michaelis-menten Kinetics Biofuel and Biosensor Homotopy Perturbation Method Immobilized Enzyme Systems

Iterative approximate solutions of kinetic equations for reversible enzyme reactions

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Natural Science 2013年第6期5卷 740-755页

作者： Sarbaz H. A. Khoshnaw Department of Mathematics University of Leicester Leicester UK

We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.

关键词： Enzyme Kinetics Homotopy Perturbation Method Iteration Method michaelis-menten Kinetics Quasi-Steady State Approximation