Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix

K. Saranya; V. Mohan; L. Rajendran

doi:doi:10.11648/j.acm.20170602.16

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Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix

K. Saranya, V. Mohan, L. Rajendran

Published in Applied and Computational Mathematics (Volume 6, Issue 2)

Received: 15 March 2017 Accepted: 28 March 2017 Published: 27 April 2017

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Abstract

In this paper the theoretical model of glucose–oxidaise loaded in chitosan-aliginate microsphere and hydrogen peroxide production is discussed. The glucose and oxygen in the medium diffuse into the microsphere and react, as a catalyst by glucose oxidase, to produce gluconic acid and hydrogen peroxide. The model involves the system of nonlinear nonsteady-state reaction-diffusion equations. Analytical expressions for the concentrations of glucose, oxygen, gluconic acid and hydrogen peroxide are derived from these equations using homotopy perturbation and the reduction of order method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed. The effect of various parameters (glucose concentration in the external solution, particle size, enzyme loading and Michaelis constant etc.) on the concentration of gluconic acid and hydrogen peroxide release is discussed. Sensitivity analysis of parameters is also discussed.

Published in	Applied and Computational Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.acm.20170602.16
Page(s)	111-128
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Mathematical Modeling, Enzyme–Encapsulated Polymer, Microspheres, Hydrogen Peroxide Generation, Release Kinetics

References

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[5]	Joy RA, Rajendran L (2012) Mathematical modeling and transient analytical solution of a glucose sensitive composite membrane for closed-loop insulin delivery using He’s Variational iteration method. Int.Rev.Chem.Eng4: 516-523
[6]	Yu, J, Zhang, Y, Ye, DiSanto, R,Sun, W,Ranson ,D,Ligler, FS, Buse, JB, Gu, Z(2015). Micro needle-array patches loaded with hypoxia-sensitive vesicles provide fast glucose-responsive insulin delivery. Proceeding s of the National Academy of Sciences 112: 8260-8265.
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K. Saranya, V. Mohan, L. Rajendran. (2017). Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix. Applied and Computational Mathematics, 6(2), 111-128. https://doi.org/10.11648/j.acm.20170602.16

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ACS Style

K. Saranya; V. Mohan; L. Rajendran. Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix. Appl. Comput. Math. 2017, 6(2), 111-128. doi: 10.11648/j.acm.20170602.16

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AMA Style

K. Saranya, V. Mohan, L. Rajendran. Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix. Appl Comput Math. 2017;6(2):111-128. doi: 10.11648/j.acm.20170602.16

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@article{10.11648/j.acm.20170602.16,
  author = {K. Saranya and V. Mohan and L. Rajendran},
  title = {Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {2},
  pages = {111-128},
  doi = {10.11648/j.acm.20170602.16},
  url = {https://doi.org/10.11648/j.acm.20170602.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170602.16},
  abstract = {In this paper the theoretical model of glucose–oxidaise loaded in chitosan-aliginate microsphere and hydrogen peroxide production is discussed. The glucose and oxygen in the medium diffuse into the microsphere and react, as a catalyst by glucose oxidase, to produce gluconic acid and hydrogen peroxide. The model involves the system of nonlinear nonsteady-state reaction-diffusion equations. Analytical expressions for the concentrations of glucose, oxygen, gluconic acid and hydrogen peroxide are derived from these equations using homotopy perturbation and the reduction of order method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed. The effect of various parameters (glucose concentration in the external solution, particle size, enzyme loading and Michaelis constant etc.) on the concentration of gluconic acid and hydrogen peroxide release is discussed. Sensitivity analysis of parameters is also discussed.},
 year = {2017}
}

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TY - JOUR
T1 - Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix
AU - K. Saranya
AU - V. Mohan
AU - L. Rajendran
Y1 - 2017/04/27
PY - 2017
N1 - https://doi.org/10.11648/j.acm.20170602.16
DO - 10.11648/j.acm.20170602.16
T2 - Applied and Computational Mathematics
JF - Applied and Computational Mathematics
JO - Applied and Computational Mathematics
SP - 111
EP - 128
PB - Science Publishing Group
SN - 2328-5613
UR - https://doi.org/10.11648/j.acm.20170602.16
AB - In this paper the theoretical model of glucose–oxidaise loaded in chitosan-aliginate microsphere and hydrogen peroxide production is discussed. The glucose and oxygen in the medium diffuse into the microsphere and react, as a catalyst by glucose oxidase, to produce gluconic acid and hydrogen peroxide. The model involves the system of nonlinear nonsteady-state reaction-diffusion equations. Analytical expressions for the concentrations of glucose, oxygen, gluconic acid and hydrogen peroxide are derived from these equations using homotopy perturbation and the reduction of order method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed. The effect of various parameters (glucose concentration in the external solution, particle size, enzyme loading and Michaelis constant etc.) on the concentration of gluconic acid and hydrogen peroxide release is discussed. Sensitivity analysis of parameters is also discussed.
VL - 6
IS - 2
ER -

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Author Information

K. Saranya

Thiagarajar College of Engineering, Madurai, India
V. Mohan

Thiagarajar College of Engineering, Madurai, India
L. Rajendran

Department of Mathematics, Sethu Institute of Technology, Kariapatti, India

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APA Style

K. Saranya, V. Mohan, L. Rajendran. (2017). Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix. Applied and Computational Mathematics, 6(2), 111-128. https://doi.org/10.11648/j.acm.20170602.16

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ACS Style

K. Saranya; V. Mohan; L. Rajendran. Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix. Appl. Comput. Math. 2017, 6(2), 111-128. doi: 10.11648/j.acm.20170602.16

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AMA Style

K. Saranya, V. Mohan, L. Rajendran. Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix. Appl Comput Math. 2017;6(2):111-128. doi: 10.11648/j.acm.20170602.16

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@article{10.11648/j.acm.20170602.16,
  author = {K. Saranya and V. Mohan and L. Rajendran},
  title = {Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {2},
  pages = {111-128},
  doi = {10.11648/j.acm.20170602.16},
  url = {https://doi.org/10.11648/j.acm.20170602.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170602.16},
  abstract = {In this paper the theoretical model of glucose–oxidaise loaded in chitosan-aliginate microsphere and hydrogen peroxide production is discussed. The glucose and oxygen in the medium diffuse into the microsphere and react, as a catalyst by glucose oxidase, to produce gluconic acid and hydrogen peroxide. The model involves the system of nonlinear nonsteady-state reaction-diffusion equations. Analytical expressions for the concentrations of glucose, oxygen, gluconic acid and hydrogen peroxide are derived from these equations using homotopy perturbation and the reduction of order method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed. The effect of various parameters (glucose concentration in the external solution, particle size, enzyme loading and Michaelis constant etc.) on the concentration of gluconic acid and hydrogen peroxide release is discussed. Sensitivity analysis of parameters is also discussed.},
 year = {2017}
}

Copy | Download