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电位型生物传感器的数学建模分析

Analysis of mathematical modelling on potentiometric biosensors.

作者信息

Mehala N, Rajendran L

机构信息

Department of Mathematics, K.L.N. College of Engineering, Sivagangai, Tamil Nadu, India.

Department of Mathematics, The Madura College, Madurai, Tamil Nadu 625 011, India.

出版信息

ISRN Biochem. 2014 May 7;2014:582675. doi: 10.1155/2014/582675. eCollection 2014.

DOI:10.1155/2014/582675
PMID:25969765
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4393009/
Abstract

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

摘要

已建立了用于非稳态电位酶电极的数学模型。该模型基于描述酶层内底物和产物浓度的米氏形式的两个耦合非线性时变反应扩散方程组。使用新的同伦摄动法，针对所有参数值推导了底物和产物浓度以及相应通量响应的解析表达式。此外，本文采用复反演公式来解决边值问题。所获得的解析解仅允许对两个动力学参数（不饱和/饱和参数和反应/扩散参数）的响应曲线进行完整描述。给出了两种极限情况（零级和一级动力学）的理论描述，并提出了一般情况的相对简单方法。所有解析结果均与使用Scilab/Matlab程序的模拟结果进行了比较。数值结果与相应理论相符。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/a7cf710bfac3/ISRN.BIOCHEMISTRY2014-582675.008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/b16fc02deb72/ISRN.BIOCHEMISTRY2014-582675.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/d5434b6f362e/ISRN.BIOCHEMISTRY2014-582675.002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/385f3b0be316/ISRN.BIOCHEMISTRY2014-582675.003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/ffc4c00307d4/ISRN.BIOCHEMISTRY2014-582675.004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/a7b2ed9da157/ISRN.BIOCHEMISTRY2014-582675.005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/82eb5894f3c3/ISRN.BIOCHEMISTRY2014-582675.006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/1cfed77ad0e0/ISRN.BIOCHEMISTRY2014-582675.007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/a7cf710bfac3/ISRN.BIOCHEMISTRY2014-582675.008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/b16fc02deb72/ISRN.BIOCHEMISTRY2014-582675.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/d5434b6f362e/ISRN.BIOCHEMISTRY2014-582675.002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/385f3b0be316/ISRN.BIOCHEMISTRY2014-582675.003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/ffc4c00307d4/ISRN.BIOCHEMISTRY2014-582675.004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/a7b2ed9da157/ISRN.BIOCHEMISTRY2014-582675.005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/82eb5894f3c3/ISRN.BIOCHEMISTRY2014-582675.006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/1cfed77ad0e0/ISRN.BIOCHEMISTRY2014-582675.007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1ddc/4393009/a7cf710bfac3/ISRN.BIOCHEMISTRY2014-582675.008.jpg

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