Substrates' concentration profile was studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis was performed by using an analytical method called Least Square Method, and the results were compared with numerical solution. Effects of effective diffusivity, Michael's constant, maximum reaction rate and initial substrate concentration were studied on Soluble Starch and Dextrin concentration in the spherical support. The outcomes revealed that Least Square Method has an excellent agreement with numerical solution, and in the center of support, substrate concentration is minimum. Increasing of effective diffusivity and Michael's constant reduced the Soluble Starch and Dextrin profile gradient.
Bullock C. Immobilized enzymes. Sci Progress. 1995;
Fchaplin M, Bucke C. Enzyme technology: Cambridge
University Press, 1990; 35-45.
Kennedy JF, Cabral JMS. Solid-phase biochemistry:
Analytical and synthetic aspects. John Wiley & Sons.
USA. 1983; 790-800.
Woodley JM. Immobilized biocatalysts. Solid Supports
Catal Org Synth. 1992; 21: 254-271.
Kobayaslh T, Moo-Young M. Backmixing and mass
transfer in the design of immobilized-enzyme reactors.
Biotechnol Bioeng. 1971; 13: 893-910.
Lilly MD, Hornby WE, Crook EM. The kinetics of
carboxymethylcellulose-ficin in packed beds. Biochem J.
; 100: 718-723.
Silman IH, Katchalski E. Water-insoluble derivatives of
enzymes, antigens, and antibodies. Annu Rev Biochem.
; 35: 873-908.
Scouten HW, Tluong JH, Brown RS. Enzyme or protein
immobilization techniques for applications in biosensor
design. Trends Biotechnol. 1995; 13:178-185.
Tischer W, Wedekind F. Immobilized enzymes: methods
and applications. Top Curr Chem. 1999; 200: 95-126.
Clark DS, Bailey JE, Do DD. A mathematical model for
restricted diffusion effects on macromolecule impregnation
in porous supports. Biotechnol Bioeng. 1985; 27:
Dennis KE, Clark DS, Bailey JE, Cho YK, Park. YM.
Immobilization of enzymes in porous supports: effects of
support-enzyme solution contacting. Biotechnol Bioeng.
; 26: 892-900.
Hossain MM, Do DD, Bailey JE. Immobilization of
enzyme in porous solids under restricted diffusion
conditions. AIChE J. 1986; 32(7): 1088-1098.
Park TG, Hoffman AS. Immobilization and characterization
of β-galactosidase in thermally reversible
hydrogel beads. J Biomed Mater Res. 1990; 24: 21-38.
Moo-Young M, Kobayashi T. Effectiveness factors for immobilized enzyme reactions. Can J Chem Eng. 1972; 50 (2): 162-167.
Carleysmith SW, Eames MB, Lilly MD. Staining method for determination of the penetration of immobilized enzyme into a porous support. Biotechnol Bioeng. 1980; 22: 957-967.
Pedersen H, Furler L, Venkatasubramanian K, Prenosil J, Stuker E. Enzyme adsorption in porous supports: Local thermodynamic equilibrium model. Biotechnol Bioeng. 1985; 27: 961-971.
Manjon A, Iborra JL, Gornez JL, Gornez E, Bastida J, Bodalo A. Evaluation of the effectiveness factor along immobilized enzyme fixed-bed reactors: Design of a reactor with naringinase covalently immobilized into glycophase-coated porous glass. Biotechnol Bioeng. 1986; 30(4): 491-497.
Mireshghi SA, Kheirolomoom A, Khorasheh F. Application of an optimization algorithm for estimation of substrate mass transfer parameters for immobilized enzyme reactions. Scientia Iranica. 2001; 3: 189-196.
Do DD, Clark DS, Bailey JE. Modeling enzyme immobilization in porous solid supports. Biotechnol Bioeng. 1982; 24 (7): 1527-1546.
Shuler ML, Kargi F. Bioprocess engineering: basic concepts, 2nd Edition. Prentice-Hall, USA. 2002; 70-85.
Fink DJ. Effectiveness factor calculations for immob-ilized enzyme catalysts. Biotechnol Bioeng. 1973; 15(5): 879-888.
Lee Gk, Lesch RA, Reilly PG. Estimation of intrinsic kinetic constants for pore diffusion-limited immobilized enzyme reaction. Biotechnol Bioeng. 1981; 23: 487-497.
Shiraishi F. Experimental evaluation of the usefulness of equations describing the apparent maximum reaction rate and apparent Michaelis constant for an immobilized enzyme reaction. Enzy Microb Technol. 1993; 15: 150-154.
Hatami M, Ganji DD. Thermal performance of circular convective-radiative porous fins with different section shapes and materials. Energ Convers Manage. 2013; 76: 185-193.
Hatami M, Ganji DD. Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu–water nanofluid using porous media approach and least square method. Energ Convers Manage. 2014; 78: 347-358.
Nelson DL, Cox MM. Lehninger principles of biochemistry. 5th Edition, W.H. Freeman and Company. USA. 2008; 1090-1100.
Bird RB, Stewart WE, Lightfoot EN. Transport phenomena. 2nd edition, John Wiley & Sons. USA. 2006; 900-905.