A Kinetic Non-Steady-State Analysis of Immobilized Enzyme Systems Without External Mass Transfer Resistance

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-31
Published: Feb 13, 2024
Cite as:
M. Sivakumar, M. Mallikarjuna, R. Senthamarai, A Kinetic Non-Steady-State Analysis of Immobilized Enzyme Systems Without External Mass Transfer Resistance, Int. J. Anal. Appl., 22 (2024), 31.

Main Article Content

M. Sivakumar, M. Mallikarjuna, R. Senthamarai

Abstract

In this paper, a non-steady-state non-linear reaction diffusion in immobilized enzyme on the nonporous medium is considered for its mathematical analysis. The non-linear terms in this model are related to the Michaelis-Menten kinetics. For the considered model, the approximate analytical expressions of the substrate concentration and the effectiveness factor for the various geometric profiles of immobilized enzyme pellets are obtained using homotopy perturbation method (HPM). The obtained approximate analytical expressions proved to be fit for all values of parameters. Numerical solutions are also provided using the MATLAB software. When comparing the analytical and the numerical solutions, satisfactory results are noted. The effects of Thiele modulus and Michaelis-Menten kinetic constants on the effectiveness factor are also analyzed.

Article Details

References

  1. L. Goldstein, Kinetic Behavior of Immobilized Enzyme Systems, Methods Enzymol. (1976), 397–443. https://doi.org/10.1016/s0076-6879(76)44031-4.
  2. T. Kobayashi, K.J. Laidler, Kinetic Analysis for Solid-Supported Enzymes, Biochim. Biophys. Acta (BBA) - Enzymol. 302 (1973), 1–12. https://doi.org/10.1016/0005-2744(73)90002-8.
  3. A. Kheirolomoom, S. Katoh, E. Sada, K. Yoshida, Reaction Characteristics and Stability of a Membrane-bound Enzyme Reconstituted in Bilayers of Liposomes, Biotech. Bioeng. 37 (1991), 809–813. https://doi.org/10.1002/bit.260370904.
  4. S. Gondo, S. Isayama, K. Kusunoki, Effects of Internal Diffusion on the Lineweaver-Burk Plots for Immobilized Enzymes, Biotech. Bioeng. 17 (1975), 423–431. https://doi.org/10.1002/bit.260170310.
  5. D.J. Fink, T. Na, J.S. Schultz, Effectiveness Factor Calculations for Immobilized Enzyme Catalysts, Biotech. Bioeng. 15 (1973), 879–888. https://doi.org/10.1002/bit.260150505.
  6. M.D. Benaiges, C. Solà, C. De Mas, Intrinsic Kinetic Constants of an Immobilised Glucose-isomerase, J. Chem. Tech. Biotech. 36 (1986), 480–486. https://doi.org/10.1002/jctb.280361008.
  7. O.M. Kirthiga, M. Sivasankari, R. Vellaiammal, L. Rajendran, Theoretical Analysis of Concentration of Lactose Hydrolysis in a Packed Bed Reactor Using Immobilized β-Galactosidase, Ain Shams Eng. J. 9 (2018), 1507-1512. https://doi.org/10.1016/j.asej.2016.10.007.
  8. T. Praveen, P. Valencia, L. Rajendran, Theoretical Analysis of Intrinsic Reaction Kinetics and the Behavior of Immobilized Enzymes System for Steady-State Conditions, Biochem. Eng. J. 91 (2014), 129–139. https://doi.org/10.1016/j.bej.2014.08.001.
  9. P. Jeyabarathi, L. Rajendran, M. Abukhaled, M. Kannan, Semi-Analytical Expressions for the Concentrations and Effectiveness Factor for the Three General Catalyst Shapes, React. Kinet. Mech. Catal. 135 (2022), 1739–1754. https://doi.org/10.1007/s11144-022-02205-x.
  10. M. Sivakumar, R. Senthamarai, L. Rajendran, M.E.G. Lyons, Reaction and Kinetic studies of Immobilized Enzyme Systems: Part-I Without External Mass Transfer Resistance, Int. J. Electrochem. Sci. 17 (2022), 221159. https://doi.org/10.20964/2022.09.69.
  11. M. Sivakumar, R. Senthamarai, L. Rajendran, M.E.G. Lyons, Reaction and Kinetic studies of Immobilized Enzyme Systems: Part-II With External Mass Transfer Resistance, Int. J. Electrochem. Sci. 17 (2022) 221031. https://doi.org/10.20964/2022.10.43.
  12. S.A. Mireshghi, A. Kheirolomoom, F. Khorasheh, Application of an Optimization Algorithm for Estimation of Substrate Mass Transfer Parameters for Immobilized Enzyme Reactions, Sci. Iran. 3 (2001), 189–196.
  13. J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng. 178 (1999), 257–262. https://doi.org/10.1016/s0045-7825(99)00018-3.
  14. J.H. He, M.L. Jiao, K.A. Gepreel, Y. Khan, Homotopy Perturbation Method for Strongly Nonlinear Oscillators, Math. Comput. Simul. 204 (2023), 243–258. https://doi.org/10.1016/j.matcom.2022.08.005.
  15. R. Senthamarai, R. Jana Ranjani, Solution of Non-Steady-State Substrate Concentration in the Action of Biosensor Response at Mixed Enzyme Kinetics, J. Phys.: Conf. Ser. 1000 (2018), 012138. https://doi.org/10.1088/1742-6596/1000/1/012138.
  16. M. Sivakumar, R. Senthamarai, Mathematical Model of Epidemics: Analytical Approach to Sirw Model Using Homotopy Perturbation Method, AIP Conf. Proc. 2277 (2020), 130009. https://doi.org/10.1063/5.0025502.
  17. M.R. Akbari, D.D. Ganji, A. Majidian, A.R. Ahmadi, Solving Nonlinear Differential Equations of Vanderpol, Rayleigh and Duffing by AGM, Front. Mech. Eng. 9 (2014), 177–190. https://doi.org/10.1007/s11465-014-0288-8.
  18. P. Jeyabarathi, L. Rajendran, M.E.G. Lyons, M. Abukhaled, Theoretical Analysis of Mass Transfer Behavior in Fixed-Bed Electrochemical Reactors: Akbari-Ganji’s Method, Electrochem. 3 (2022), 699–712. https://doi.org/10.3390/electrochem3040046.
  19. M.A. Attar, M. Roshani, Kh. Hosseinzadeh, D.D. Ganji, Analytical Solution of Fractional Differential Equations by Akbari-Ganji’s Method, Part. Differ. Equ. Appl. Math. 6 (2022), 100450. https://doi.org/10.1016/j.padiff.2022.100450.
  20. M. Mallikarjuna, R. Senthamarai, An Amperometric Biosensor and Its Steady State Current in the Case of Substrate and Product Inhibition: Taylors Series Method and Adomian Decomposition Method, J. Electroanal. Chem. 946 (2023), 117699. https://doi.org/10.1016/j.jelechem.2023.117699.
  21. C.H. He, Y. Shen, F.Y. Ji, J.H. He, Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process, Fractals. 28 (2020), 2050011. https://doi.org/10.1142/s0218348x20500115.
  22. A. Afreen, A. Raheem, Study of a Nonlinear System of Fractional Differential Equations with Deviated Arguments Via Adomian Decomposition Method, Int. J. Appl. Comput. Math. 8 (2022), 269. https://doi.org/10.1007/s40819-022-01464-5.
  23. M. Mallikarjuna, R. Senthamarai, Analytical Solution of Enzyme Catalysis in Calcium Alginate Beads, AIP Conf. Proc. 2516 (2022), 250007. https://doi.org/10.1063/5.0108653.
  24. T. Vijayalakshmi, R. Senthamarai, Application of Homotopy Perturbation and Variational Iteration Methods for Nonlinear Imprecise Prey–predator Model With Stability Analysis, J. Supercomput. 78 (2021), 2477–2502. https://doi.org/10.1007/s11227-021-03956-5.
  25. G.H. Ibraheem, M. Turkyilmazoglu, M.A. AL-Jawary, Novel Approximate Solution for Fractional Differential Equations by the Optimal Variational Iteration Method, J. Comput. Sci. 64 (2022), 101841. https://doi.org/10.1016/j.jocs.2022.101841.