Nashrieh Shimi va Mohandesi Shimi Iran

Nashrieh Shimi va Mohandesi Shimi Iran

Modeling of Enzymes Reaction-Diffusion in Immobilized Biocatalysts Using Homotopy Perturbation, Third Approximation and Numerical Methods

Document Type : Research Article

Authors
Armin Fazlinezhad 1
Moslem Fattahi 2
Farshad Jokar 3
1 Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, I.R. IRAN
2 Department of Chemical Engineering, Abadan School of Petroleum Engineering, Abadan University of Petroleum Industry, Abadan, I.R. IRAN
3 Department of Chemical Engineering, Faculty of Chemical Engineering, Shiraz University, Shiraz, I.R. IRAN
Abstract
In this research, the concentration of the enzyme in a spherical immobilized biocatalyst through
the reaction-diffusion equation has been investigated. The Michaelis-Menten type was utilized for the kinetic mechanism of enzyme reaction. The obtained equation is a second-order nonlinear ordinary differential equation (ODE) with variable coefficients. So, the Homotopy Perturbation Method (HPM) and Third Approximation Method were utilized as semi-analytical methods to solve the reaction-diffusion equation. Besides, the obtained ordinary differential equation is also solved by numerical method. The profiles of dimensionless substrate concentration and effectiveness factor versus dimensionless distance of biocatalyst for different values of Michaelis-Menten constant and Thiele Modulus were obtained. Then, the amount of deviation from numerical solution for each approximation method has been analyzed. The results show that the Third Approximation Method only in high values of Michaelis-Menten constant and low values of Thiele modulus has good agreement with the numerical method, while the HPM has a great match with the numerical method in all values of Michaelis-Menten constant and Thiele Modulus. Moreover, the effectiveness factor has been analyzed by HPM and it has been found that appropriate conditions for a high-value effectiveness factor are and. The HPM and Third Approximation Method results on two types of real and laboratory catalysts have also been compared with real data, the results show that HPM has more accurate and better results than the Third Approximation Method. Finally, the HPM has been used for analyzing dimensionless substrate concentration of different geometries of biocatalysts including spherical, cylindrical, and slab catalysts.
Keywords
Enzyme
Modeling
Michaelis-Menten
Reaction-diffusion
Homotopy perturbation method

Subjects

[1] Li X., Chen X.D., Chen N., A Third-Order Approximate Solution of the Reaction-Diffusion Process in an Immobilized Biocatalyst Particle, Biochemical Engineering Journal, 17(1): 65-69 (2004).
[2] Aris R., “The Mathematical Theory of Diffusion and Reaction In Permeable Catalysts”, Oxford University Press (1975).
[3] Cheviollotte P., Relation between the Reaction Cytochrome Oxidase-Oxygen and Oxygen Uptake in Cells in Vivo: The Role of Diffusion, Journal of Theoretical Biology, 39(2): 277-295 (1973)
[4] Moo-Young M., Kobayashi T., Effectiveness Factors for Immobilized-Enzyme Reactions, Canadian Journal of Chemical Engineering, 50(2): 162-167 (1972).
[5] Kataoka M., Kita K., Wada M., Yasohara Y., Hasegawa J., Shimizu S., Novel Bioreduction System for the Production of Chiral Alcohols, Applied Microbiology and Biotechnology, 62(5-6): 437-445 (2003).
[6] Ran N., Zhao L., Chen Z., Tao J., Recent Applications of Biocatalysis In Developing Green Chemistry for Chemical Synthesis at the Industrial Scale, Green Chemistry, 10: 361-372 (2008).
[7] Ananthaswamy V., Padmavathi P., Rajendran L., Simple Analytical Expressions of the Steady State Concentration and Flux in Immobilized Glucose Isomerase of Packed-Bed Reactors, Review of Bioinformatics and Biometrics (RBB), 3: 29-37 (2014).
[8] Meena V., Ganesan SP., Rajendran L., Analytical Versus Numerical Solution of the Non-Linear Reaction-Diffusion Process in an Immobilized Biocatalyst Particle, International Journal of Applied Engineering Research, 10(55):4184-4189 (2015).
[9] Ramos J.I., Linearization Methods for Reaction-Diffusion Equations: Multidimensional Problems, Applied Mathematics and Computation Journal, 88(2-3): 225-254 (1997).
[10] Villadsen J., Michelsen M.L., “Solution of Differential Equation Models by Polynomial Approximation”, Prentice-Hall, Englewood Cliffs, 273 (1978).
[11] Loghambal S., Rajendran L., Mathematical Modeling of Diffusion and Kinetics in Amperometric Immobilized Enzyme Electrodes, Electrochimica Acta, 55(18): 5230-5238 (2010).
[12] Thiagarajan S., Meena A., Rajendran L., Approximate Solution of Non-Steady Concentration and Current at a Hemispherical Microelectrode-Homotopy Perturbation Approach, Physical Chemistry: An Indian Journal, 6(2): 96-104 (2011).
[13] Sivasankari M.K., Rajendran L., Analytical expression of the Concentration of Species and Effectiveness Factors in Porous Catalysts Using the Adomian Decomposition Method, Kinetics and Catalysis, 54(1): 95-105 (2013)
[14] Muthukaruppan S., Eswari A., Rajendran L., Mathematical Modelling of o Biofilm: The Adomian Decomposition Method, Natural Science, 5(4): 456-462 (2013).
[15] Narayanan K.L., Meena V., Rajendran L., Gao J., Subbiah S.P., Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis-Menten Mechanism, Applied and Computational Mathematics, 6(3): 143-160 (2017).
[16] Zeibi Shirejini S., Fattahi M., Mathematical Modeling and Analytical Solution of Two-Phase Flow Transport in an Immobilized-Cell Photo Bioreactor Using the Homotopy Perturbation Method (HPM), International Journal of Hydrogen Energy, 41(41):18405-18417 (2016).