Call for Paper - March 2022 Edition
IJCA solicits original research papers for the March 2022 Edition. Last date of manuscript submission is February 22, 2022. Read More

Analytical Expression Pertaining to Concentration of Substrate and Effectiveness Factor for Immobilized Enzymes with Reversible Michaelis Menten Kinetics

International Journal of Computer Applications
© 2011 by IJCA Journal
Volume 33 - Number 3
Year of Publication: 2011
S. Sevukaperumal
A. Eswari
L. Rajendran

S Sevukaperumal, A Eswari and L Rajendran. Article: Analytical Expression Pertaining to Concentration of Substrate and Effectiveness Factor for Immobilized Enzymes with Reversible Michaelis Menten Kinetics. International Journal of Computer Applications 33(3):46-53, November 2011. Full text available. BibTeX

	author = {S. Sevukaperumal and A. Eswari and L. Rajendran},
	title = {Article: Analytical Expression Pertaining to Concentration of Substrate and Effectiveness Factor for Immobilized Enzymes with Reversible Michaelis Menten Kinetics},
	journal = {International Journal of Computer Applications},
	year = {2011},
	volume = {33},
	number = {3},
	pages = {46-53},
	month = {November},
	note = {Full text available}


The mathematical model of immobilized enzyme system in porous spherical particle is presented. The model is based on non-stationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. A general and closed form of an analytical expression pertaining to the substrate concentration profile and effectiveness factor are reported for all possible values of dimensionless modules and . Moreover, herein we have employed “Homotopy Perturbation Method” (HPM) to solve the non-linear reaction/diffusion equation in immobilized enzymes system. These analytical results were found to be in good agreement with simulation result.


  • Bailey, J. E., Ollis, D. F. (1986) Biochemical Engineering Fundamentals (2nd ed). McGraw-Hill, New York.
  • Engasser, J. M., & Horvath, C. (1973) Effect of internal diffusion in heterogeneous enzymatic systems: evaluation of true kinetic parameters and substrate diffusivity, J. Theor. Biol. 42, 137-155.
  • Tuncel, A. (1999) A diffusion-reaction model for -chymotrypsin carrying uniform thermosensitive gel beads, J. Appl. Polym. Sci. 74, 1025-1034.
  • Paiva, A. L., & Malcata, F. X. (1997) Reversible reaction and diffusion within a porous catalyst slab, Chem. Eng. Sci. 52 (23), 4429-4432.
  • 5 Xiu, G., Jiang, L. & Li, P. (2000) Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a batch reactor, Ind. Eng Chem. Res. 39, 4054-4062.
  • 6 Engasser, J. M. & Hisland, P. (1979) Diffusional effects on the heterogeneous kinetics of two-substrate enzymic reactions, J. Theor. Biol. 77 (1979), 427-440.
  • Rony, P. R. Multiphase catalysis. II. Hollow fiber catalysts, Biotechnol. Bioeng. 13, 431-447.
  • Moo-Young, M. and Kobayashi, T. (1972) Effectiveness factors for immobilized enzyme reactions, J. Can. Chem. Eng. 50, 162-167.
  • Kobayashi, T. and Laidler, K. J. (1973) Effectiveness factor calculations for immobilized enzyme catalysts, Biochim. et Biophys. Acta. 1, 302-311.
  • Fink, D. J., Na, T. Y., and Suchltz, J. S. (1973) Effectiveness factor calculations for immobilized enzyme catalysts, Biotechnol. Bioeng, 15, 879-888.
  • Engasser, J. M., Horvath, J. C. (1973) Metabolism: Interplay of Membrane Transport and Consecutive Enzymic Reaction, Theor. Biol. 42, 137-155.
  • Marsh, D. R., Lee, Y. Y. and Tsao, G.T. (1973) Immobilized glucoamylase on porous glass, Biotechnol. Bioeng. 15, 483-492.
  • Hamilton, B. K., Cardner, C. R. and Colton. C. K. (1974) Effect of Diffusional Limitations on. Lineweaver-Burk Plots for Immobilized Enzymes, AICHE J. 20, 503-510.
  • Rovito, B. J., and Kittrell, J. R. (1973) Film and pore diffusion studies with immobilized glucose Oxidase, Biotechnol. Bioeng. 15, 143-161.
  • Engasser. J. M. (1978) The experimental results accorded quantitatively with the theory of diffusion limitation, Biochim. Biophys. Acta. 526, 301-310.
  • Marc, A. and Engasser, J. M. (1982) Influence of substrate and product diffusion on the heterogeneous kinetics of enzymic reversible reactions, J. Theor. Biol. 94, 179-189.
  • Goldman, R., Keden, O., Silman, I. H., Caplan, S. R. and Katchalski, E. (1968) Papain-collodion membranes. I. Preparation and properties, Biochemistry. 7, 486-500.
  • Engasser, J. M. and Horvath, C. (1974) Inhibition of Bound Enzymes. II. Characterization of Product Inhibition and Accumulation, Biochemistry. 13, 3849-3854.
  • Ramachandran, P. A. (1975) Solution of immobilized enzyme problems by collocation methods, Biotechnol. Bioeng. 17, 211-226
  • Manjon, A., Iborra, J.L., Gomez, J.L., Gomez, E., Bastida, J., Bodalo, A. (1987) Evaluation of the effectiveness factor along immobilized enzyme fixed-bed reactors: design for a reactor with naringinase covalently immobilized into glycophase-coated porous glass, Biotechnol. Bioeng. 30, 491-497.
  • Bodalo Santoyo, A., G´omez Carrasco, J.L., G´omez G´omez, E., Bastida Rodr´ıguez, J., Mart´ınez Morales, E. (1993) Transient stirred tank reactors operating with immobilized enzyme systems: analysis and simulation models and their experimental checking, Biotechnol. Progr. 9, 166–173.
  • Bodalo, A., G´omez, J.L., G´omez, E., Bastida, J., M´aximo, M.F. (1995) Fluidized bed reactors operating with immobilized enzyme systems: design model and its experimental verification, Enzyme Microb. Technol. 17, 915–922.
  • AL-Muftah, A.E., Abu-Reesh, I.M. (2005) Effects of internal mass transfer and product inhibition on a simulated immobilized enzyme-catalyzed reactor for lactose hydrolysis, Biochem. Eng. J. 23, 139–153.
  • AL-Muftah, A.E., Abu-Reesh, I.M. (2005) Effects of simultaneous internal and external mass transfer and product inhibition on immobilized enzymecatalyzed reactor, Biochem. Eng. J. 27, 167–178.
  • Keegan, S.D., Mariani, N.J. Bressa, S.P., Mazza, G.D., Barreto, G.F. (2003) Approximation of the effectiveness factor in catalytic pellets, Chem. Eng. J. 94, 107–112.
  • Szukiewicz, M., Petrus, R. (2004) Approximate model for diffusion and reaction in a porous pellet and an effectiveness factor, Chem. Eng. Sci. 59, 479–483.
  • Li, X., Chen, X.D., Chen, N. (2004) A third-order approximate solution of the reaction-diffusion process in an immobilized biocatalyst particle, Biochem. Eng. J. 17, 65–69.
  • Carnahan, B., Luther, H.A., Wilkes, J.O. (1969) Applied Numerical Methods, Wiley, New York.
  • Villadsen, J., Michelsen, M.L. (1978) Solution of Differential Equation Models by Polynomial Approximation., New York: Prentice-Hall, Englewood Cliffs.
  • Chen., X. B., Sui, Y., Lee, H. P., Bai, H. X., Yu, P., Winoto, S. H. and Low, H. T. (2010) Mass transport in a microchannel bioreactor with a porous wall, ASME J. Biomech. Engrg. 132(6), 061001.
  • Chen., X. B., Sui., Y., Cheng., Y. P., Lee., H. P., Yu., P., Winoto, S. H. and Low, H. T. (2010) Mass transport in a microchannel enzyme reactor with a porous wall: Hydrodynamic modeling and applications, Biochem. Eng. J. 52, 227-235.
  • Gomez Carrasco, J. L., Bodalo Santoyo, A., Gomez Gomez, E., Bastida Rodriguez, J., Maximo Martin, M. F., Gomez Gomez, M. (2008) A short recursive procedure for evaluating effectiveness factors for immobilized enzymes with reversible Michaelis-Menten kinetics, Biochem. Eng. J. 39, 58-65.
  • Bodalo, A., Gomez, J. L., Gomez., E., Bastida, J., Iborra, J. L. & Manjon, A. (1986) Analysis of diffusion effects on immobilized enzyme on porous supports with reversible Michaelis-Menten kinetics, Enzyme Microb. Technol. 8, 433-438.
  • He, J. H. (2008) An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Modern. Physics. B. 22, 3487-3578.
  • He, J. H. (1998) Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods. Appl. Mech. Engrg. 167, 57.
  • He, J. H. (2005) Application of homotopy perturbation method to nonlinear wave equations, Appl. Math. Comput. 26, 695.
  • He, J. H. (2006) Homotopy perturbation method for solving boundary value problems, Phys. Lett. A. 350, 87.
  • Eswari, A., Rajendran, L. (2010) Analytical solution of steady state current at a micro disk biosensor, J. Electroanal. Chem. 641, 35-44.
  • Meena, A., Rajendran, L. (2010) Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations-Homotopy perturbation approach, J. Electroanal. Chem. 644, 50-59.
  • Meena, A., Rajendran, L. (2010) Analytical solution of system of coupled non-linear reaction diffusion equations. Part I: Mediated electron transfer at conducting polymer ultramicroelectrodes, J. Electroanal. Chem. 647, 103-116.