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Unprecedented homotopy perturbation method for solving nonlinear equations in the enzymatic reaction of glucose in a spherical matrix

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Abstract

The theory of glucose-responsive composite membranes for the planar diffusion and reaction process is extended to a microsphere membrane. The theoretical model of glucose oxidation and hydrogen peroxide production in the chitosan-aliginate microsphere has been discussed in this manuscript for the first time. We have successfully reported an analytical derived methodology utilizing homotopy perturbation to perform the numerical simulation. The influence and sensitive analysis of various parameters on the concentrations of gluconic acid and hydrogen peroxide are also discussed. The theoretical results enable to predict and optimize the performance of enzyme kinetics.

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Abbreviations

\(C{}_{g}\) :

Concentration of glucose (mol/cm3)

\({C_{{\text{OX}}}}\) :

Concentration of oxygen (mol/cm3)

\({C_a}\) :

Concentration of gluconic acid:mol/cm3

\({C_h}\) :

Concentration of hydrogen peroxide (mol/cm3)

\({D_g}\) :

Diffusion coefficient of glucose (cm2/s)

\({D_{{\text{OX}}}}\) :

Diffusion coefficient of oxygen (cm2/s)

\({D_a}\) :

Diffusion coefficient of gluconic acid (cm2/s)

\({D_h}\) :

Diffusion coefficient of hydrogen peroxide (cm2/s)

\({K_g}\) :

Michaelis–Menten constant for glucose:mol/cm3

\({K_{{\text{OX}}}}\) :

Michaelis–Menten constant for oxygen (mol/cm3)

\({V_{\hbox{max} }}\) :

Maximal reaction velocity (cm/s)

\(\begin{gathered} {v_g},{v_{OX}}, \hfill \\ {v_a}\,{\text{and}}\,{v_h} \hfill \\ \end{gathered} \) :

Stoichiometric coefficients (None)

\(t\) :

Time (S)

\(C_{g}^{*}\) :

Concentration of glucose in the external solution (mol/cm3)

\(C_{{{\text{OX}}}}^{*}\) :

Concentration of glucose in the oxygen solution (mol/cm3)

S:

Radius of the microsphere (\(\mu {\text{m}}\) )

u:

Dimensionless concentration of glucose (None)

v:

Dimensionless concentration of oxygen (None)

w:

Dimensionless concentration of gluconic acid (None)

H:

Dimensionless concentration of hydrogen peroxide (None)

\(\Re \) :

Overall reaction rate (None)

T:

Dimensionless time (None)

\(\begin{gathered} {\gamma _g},\,{\gamma _{{\text{OX}}}}, \hfill \\ {\gamma _a},{\gamma _h},\alpha \hfill \\ \beta \,\& \,k \hfill \\ \end{gathered} \) :

Dimensionless reaction diffusion parameters (None)

R:

Dimensionless radius (None)

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Authors and Affiliations

  1. Department of Mathematics, Thiagarajar College of Engineering Madurai, Madurai, 625 015, India

    K. Saranya & V. Mohan

  2. Central Laboratories, Faculty of Pharmacy, University of Veterinary and Pharmaceutical Sciences Brno, Palackeho 1946/1, 612 42, Brno, Czech Republic

    R. Kizek

  3. Department of Biomedical and Environmental Analyses, Wroclaw Medical University, Borowska 211, 50-556, Wroclaw, Poland

    R. Kizek

  4. School of Pharmacy and Life Sciences, Robert Gordon University, Aberdeen, AB107GJ,, UK

    C. Fernandez

  5. Department of Mathematics, Sethu Institute of Technology, Kariapatti, 626115, India

    L. Rajendran

Authors
  1. K. Saranya
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  2. V. Mohan
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  3. R. Kizek
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  4. C. Fernandez
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  5. L. Rajendran
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Correspondence to L. Rajendran.

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Saranya, K., Mohan, V., Kizek, R. et al. Unprecedented homotopy perturbation method for solving nonlinear equations in the enzymatic reaction of glucose in a spherical matrix. Bioprocess Biosyst Eng 41, 281–294 (2018). https://doi.org/10.1007/s00449-017-1865-0

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  • DOI: https://doi.org/10.1007/s00449-017-1865-0

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