Advertisement

Basic Concepts in the Effects of Mass Transfer on Immobilized Enzyme Kinetics

  • Bruce K. Hamilton
  • Colin R. Gardner
  • C. K. Colton

Abstract

The observed kinetics of immobilized enzymes can often be influenced by mass transfer effects. To ensure straight-forward and useful analysis of data, these influences should be anticipated at the early stages of design and execution of kinetic experiments. With adequate care, it is then possible to interpret meaningfully values of commonly reported immobilized enzyme kinetic parameters, such as the “apparent Michaelis constant,” even if severe mass transfer effects are present when rate data are obtained.

Keywords

Immobilize Enzyme Mass Transfer Coefficient Effectiveness Factor External Mass Transfer Mass Transfer Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. Aris, R., “0n Shape Factors for Irregular Particles: I. The Steady-State Problem. Diffusion and Reaction,” Chem. Eng. Sci., 6, 262 (1957).CrossRefGoogle Scholar
  2. Aris, R., “Mobility, Permeability, and the Pseudo-Steady-State Hypothesis,” Math. Biosci., 13, 1 (1972).CrossRefGoogle Scholar
  3. Aris, R., The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Oxford at the Clarendon Press, London (1974).Google Scholar
  4. Atkinson, B., and S. Daoud, “The Analogy Between Microbiological “Reactions” and Heterogeneous Catalysis,” Trans. Instn. Chem. Engrs., 46, T19 (1968).Google Scholar
  5. Bischoff, K.B., “Effectiveness Factors for General Reaction Rate Forms,” AIChE J., 11, 351 (1965).CrossRefGoogle Scholar
  6. Blaedel, W.J., T.R. Kissel, and R.C. Boguslaski, “Kinetic Behavior of Enzymes Immobilized in Artificial Membranes,” Anal. Chem., 44, 2030 (1972).CrossRefGoogle Scholar
  7. Blum, J.J., and D.J. Jenden, “Rate Behavior and Concentration Profiles in Geometrically Constrained Enzyme Systems,” Arch. Biochem. Biophys., 66, 316 (1957).CrossRefGoogle Scholar
  8. Bunow, В., “Enzyme Kinetics in Cells,” J. Math. Biophys., in press (1974).Google Scholar
  9. Bunting, P.S., and K.J. Laidler, “Kinetic Studies on Solid-Supported ß-Galactosidase,” Biochemistry, 11, 4477 (1972).CrossRefGoogle Scholar
  10. Chu, С, and O.A. Hougen, “The Effect of Adsorption on the Effectiveness Factor of Catalyst Pellets,” Chem. Eng. Sci., 17, 167 (1962).CrossRefGoogle Scholar
  11. Cleland, W.W., “The Statistical Analysis of Enzyme Kinetic Data,” Adv. Enzymol. (edited by F.F. Nord), Vol. 29, Interscience, New York, page 1 (1967).Google Scholar
  12. Coleman, M.H., “Graphical Analysis of Enzyme Kinetic Data,” Nature, 205, 798 (1965).CrossRefGoogle Scholar
  13. Colton, C.K., K.A. Smith, E.W. Merrill, and P.C. Farrell, “Permeability Studies with Cellulosic Membranes,” J. Biomed. Mater. Res., 5_, 459 (1971).CrossRefGoogle Scholar
  14. Crank, J., The Mathematics of Diffusion, Oxford at Clarendon Press, London (1956).Google Scholar
  15. Desimone, J.A., and S.R. Caplan, “Symmetry and the Stationary State Behavior of Enzyme Membranes,” J. Theor. Biol., 39, 523 (1973).CrossRefGoogle Scholar
  16. Dixon, M., and E.C. Webb, Enzymes, Academic Press, New York (1964).Google Scholar
  17. Dowd, J.E., and D.S. Riggs, “A Comparison of Estimates of Michaelis-Menten Kinetic Constants from Various Linear Transformations,” J. Bio. Chem., 240, 863 (1965).Google Scholar
  18. Engasser, J., and C. Horvath, “Effect of Internal Diffusion in Heterogeneous Enzyme Systems: Evaluation of True Kinetic Parameters and Substrate Diffusivity,” J. Theor. Biol., 42, 137 (1973).CrossRefGoogle Scholar
  19. Fink, D.J., T. Na, and J.S. Schultz, “Effectiveness Factor Calculations for Immobilized Enzyme Catalysis,” Biotech. Bioeng., 15, 879 (1973).CrossRefGoogle Scholar
  20. Gavalas, G.R., Nonlinear Differential Equations of Chemically Reacting Systems, Springer-Verlag, New York (1968).Google Scholar
  21. Goldman, R.O., and E. Katchalski, “Kinetic Behavior of a Two-Enzyme Membrane Carrying Out a Consecutive Set of Reactions,” J. Theor. Biol., 32, 243 (1971).CrossRefGoogle Scholar
  22. Goldman, R., O. Kedem, and E. Katchalski, “Papain-Collodion Membranes. II. Analysis of the Kinetic Behavior of Enzymes Immobilized in Artificial Membranes,” Biochemistry, 7, 4518 (1968).CrossRefGoogle Scholar
  23. Goldstein, L., Y. Levin, and E. Katchalski, “A Water-insoluble Polyanionic Derivative of Trypsin. II. Effect of the Polyelectro-lyte Carrier on the Kinetic Behavior of the Bound Trypsin,” Biochemistry, 3, 1913 (1964).CrossRefGoogle Scholar
  24. Gondo, S., T. Sato, and K. Kusunoki, “Note on the Lineweaver-Burk Plots for the Immobilized Enzyme Particle,” Chem. Eng. Sci., 28, 1773 (1973).CrossRefGoogle Scholar
  25. Hamilton, В.K., L.J. Stockmeyer, and CK. Colton, “Comments on Diffusive and Electrostatic Effects with Immobilized Enzymes,” J. Theor. Biol., 41, 547 (1973).CrossRefGoogle Scholar
  26. Hamilton, B.K., C.R. Gardner, and CK. Colton, “Effect of Diffu-sional Limitations on Lineweaver-Burk Plots for Immobilized Enzymes,” AIChE J., in press (1974).Google Scholar
  27. Heineken, F.С., H. M. Tsuchiya, and R. Aris, “On the Mathematical Status of the Pseudo-steady State Hypothesis of Biochemical Kinetics,” Math. Biosci., 1, 95 (1967).CrossRefGoogle Scholar
  28. Hornby, W.E., M.D. Lilly, and E.M. Crook, “Some Changes in the Reactivity of Enzymes Resulting from their Chemical Attachment to Water-Insoluble Derivatives of Cellulose,” Biochem. J., 107, 669 (1968).Google Scholar
  29. Horvath, С. and J.M. Engasser, “Pellicular Heterogeneous Catalysts. A Theoretical Study of the Advantages of Shell Structured Immobilized Enzyme Particles,” Ind. Eng. Chem. Fund., 12, 229 (1973).CrossRefGoogle Scholar
  30. Kallen, R.C., T. Newirth, and M. Diegelman, “Consecutive Reactions with Immobilized Enzymes,” presented at 66th Annual AIChE Meeting, Philadelphia, Pa., Nov. 11–15, 1973.Google Scholar
  31. Kasche, V., H. Lundqvist, R. Bergman, and R. Axen, “A Theoretical Model Describing Steady-State Catalysis by Enzymes Immobilized in Spherical Gel Particles. Experimental Study of α-Chymotrypsin-Sepharose,” Biochem. Biophys. Res. Commun., 45, 615 (1971).CrossRefGoogle Scholar
  32. Kay, G., and M.D. Lilly, “The Chemical Attachment of Chymotrypsin to Water-Insoluble Polymers Using 2-Amino-4, 6-dichloro-5-triazine,” Biochem. Biophys. Acta, 198, 276 (1970).Google Scholar
  33. Kernevez, J.P., and D. Thomas, “Numerical Analysis of Immobilized Enzyme Systems,” Rapport de Recherche No. 28, Institute de Recherche d’Informatique et d’Automatique, Domaine de Voluceau, Rocquencort, Le Chesnay, France, Sept. 1973.Google Scholar
  34. Kobayashi, T., G. Van Dedem, and M. Moo-Young, “Oxygen Transfer into Mycelial Pellets,” Biotech. Bioeng., 15, 27 (1973).CrossRefGoogle Scholar
  35. Kobayashi, T., and K.J. Laidler, “Kinetic Analysis for Sodid-Supported Enzymes,” Biochem. Biophys. Acta, 302, 1 (1973).Google Scholar
  36. Knudsen, C.W., G.W. Roberts, and C.N. Satterfield, “Effect of Geometry on Catalyst Effectiveness Factor: Langmuir-Hinshelwood Kinetics,” Ind. Eng. Chem. Fund., 5, 325 (1966).CrossRefGoogle Scholar
  37. Krasuk, J.H., and J.M. Smith, “Effectiveness Factors with Surface Diffusion,” Ind. Eng. Chem. Fund., 4, 102 (1965).CrossRefGoogle Scholar
  38. Laidler, K.J., and P.V. Sundaram, “The Kinetics of Supported Enzyme Systems,” in Chemistry of the Cell Interface (edited by H.D. Brown), Academic Press, New York (1971).Google Scholar
  39. Lasch, J., “Theoretical Analysis of the Kinetics of Enzymes Immobilized in Spherical Pellets,” in Analysis and Simulation of Biochemical Systems, edited by H.C. Henker and B. Hess, American Elsevier, New York, page 295 (1972).Google Scholar
  40. Lawrence, R.L., and V. Okay, “Diffusion and Reaction in a Double Enzyme Supported Catalyst,” Biotech. Bioeng., 15, 217 (1973).CrossRefGoogle Scholar
  41. Lilly, M.D., and A.K. Sharp, “The Kinetics of Enzymes Attached to Water-Insoluble Polymers,” The Chemical Engineer, Jan/Feb, CE12 (1968).Google Scholar
  42. Marsh, D.R., Y.Y. Lee, and G.T. Tsao, “Immobilized Glucoamylase on Porous Glass,” Biotech. Bioeng., 15, 483 (1973).CrossRefGoogle Scholar
  43. Meyer, J., F. Sauer, and D. Woermann, “Study of a First Order Diffusion Controlled Chemical Reaction Occuring Inside Catalytically Active Membranes,” Berichte der Bunsen-Gesellschaft, 74, 245 (1970).Google Scholar
  44. Miyamoto, К., T. Fujii, N. Tamaoki, M. Okazaki, and Y. Miura, “Intraparticle Diffusion in the Reaction Catalyzed by Immobilized Glucoamylase,” J. Ferment. Technol., 51, 566 (1973).Google Scholar
  45. Moo-Young, M., and T. Kobayashi, “Effectiveness Factors for Immobilized-Enzyme Reactions,” Can. J. Chem. Eng., 50, 162 (1972).CrossRefGoogle Scholar
  46. O’Neill, S.P., “External Diffusional Resistance in Immobilized Enzyme Catalysis,” Biotech. Bioeng., 14, 675 (1972).CrossRefGoogle Scholar
  47. Petersen, E.E., Chemical Reaction Analysis, Prentice-Hall, Englewood Cliffs (1965).Google Scholar
  48. Plowman, K.M., Enzyme Kinetics, McGraw-Hill, New York (1972).Google Scholar
  49. Prater, CD., and R.M. Lago, “The Kinetics of the Cracking of Cumene by Silica-Alumina Catalysts,” in Adv. in Cat, (edited by W.G. Frandenburg and V.l. Domarensky), Vol. 8, Academic Press, New York (1956).Google Scholar
  50. Roberts, G.W., “I. Kinetics of Thiophene Hydrogenolysis. II. Effectiveness Factors for Porous Catalysts,” Sc.D. Thesis, Mass. Inst, of Technology, Cambridge (1965).Google Scholar
  51. Roberts, G.W., and C.N. Satterfield, “Effectiveness Factor for Porous Catalysts,” Ind. Eng. Chem. Fund., 4, 289 (1965).CrossRefGoogle Scholar
  52. Rony, P.R., “Multiphase Catalysis. II. Hollow Fiber Catalysts,” Biotech. Bioeng., 13, 431 (1971).CrossRefGoogle Scholar
  53. Roughton, F.J.W., “Diffusion and Chemical Reaction Velocity as Joint Factors in Determining the Rate of Uptake of Oxygen and Carbon Monoxide by the Red Blood Corpuscle,” Proc. Roy. Soc. B, 111, 1 (1932).CrossRefGoogle Scholar
  54. Roughton, F.J.W., “Diffusion and Chemical Reaction Velocity in Cylindrical and Spherical Systems of Physiological Interest,” Proc. Roy. Soc. B, 140, 203 (1952).CrossRefGoogle Scholar
  55. Roughton, F.J.W., “Diffusion and Simultaneous Chemical Reaction Velocity in Haemoglobin Solutions and Red Cell Suspensions,” Prog. Biophys. Mol. Biol., 9, 55 (1959).Google Scholar
  56. Rovito, B.J., and J.R. Kittrell, “Film and Pore Diffusion Studies with Immobilized Glucose Oxidase,” Biotech. Bioeng., 15, 143 (1973).CrossRefGoogle Scholar
  57. Satterfield, C.N., Mass Transfer in Heterogeneous Catalysis, MIT Press, Cambridge (1970).Google Scholar
  58. Schneider, P., and P. Mitschka, “Effect of Internal Diffusion on Catalytic Reaction,” Collection Czechoslov. Chem. Commun., 30, 146 (1965).Google Scholar
  59. Schneider, P., and P. Mitschka, “Effect of Internal Diffusion on Catalytic Reactions. III. Effect of Particle Shape on Reaction with Langmuir-Hinshelwood Type of Kinetics,” Collection Czechoslov. Chem. Commun., 31, 1205 (1966).Google Scholar
  60. Segel, I.H., Biochemical Calculations, Wiley, New York (1968).Google Scholar
  61. Selegny, E., G. Brown, J. Geffroy, and D. Thomas, “Méthode de Determination de Км Réel d’un Enzyme par le Régime Stationnaire d’une Membrane en Activité Enzymatique,” J. Chem. Phys. et Physico-Chimie Bio., 66, 391 (1969).Google Scholar
  62. Shuler, M.L., H.M. Tsuchiya, and R. Aris, “Diffusive and Electrostatic Effects with Insolubilized Enzymes,” J. Theor. Biol., 35, 67 (1972).CrossRefGoogle Scholar
  63. Shuler, M.L., H.M. Tsuchiya, and R. Aris, “Diffusive and Electrostatic Effects with Insolubilized Enzymes Subject to Substrate Inhibition,” J. Theor. Biol., 41. 347 (1973).CrossRefGoogle Scholar
  64. Sundaram, P.V., A. Tweedale, and K.J. Laidler, “Kinetic Laws for Solid-Supported Enzymes,” Can. Jour. Chem., 48, 1498 (1970).CrossRefGoogle Scholar
  65. Sundaram, P.V., E.K. Pye, T.M.S. Chang, V.H. Edwards, E.A. Humphrey, N.O. Kaplan, E. Katchalski, Y. Levin, M.D. Lilly, G. Manecke, K. Mosbach, A. Patchornik, J. Porath, H.H. Weetall, and L.B. Wingard, Jr., “Recommendations for Standardization of Nomenclature in Enzyme Technology,” Enzyme Engineering (edited by L.B. Wingard, Jr.), Wiley-Interscience, page 15 (1972).Google Scholar
  66. Thomas, D., G. Brown, and E. Selegny, “Monoenzymatic Model Membranes: Diffusion-Reaction Kinetics and Phenomena,” Biochimie, 54, 229 (1972).CrossRefGoogle Scholar
  67. Van Duijn, P., E. Pascoe, and M. Van der Ploeg, “Theoretical and Experimental Aspects of Enzyme Determination in a Cytochemical Model System of Polyacrylamide Films Containing Alkaline Phosphatase,” J. Hist. Cytochem., 15, 631 (1967).CrossRefGoogle Scholar
  68. Vieth, W.R., A.K. Mendiratta, A.O. Mogensen, R. Saini, and K. Venkatasubramanian, “Mass Transfer and Biochemical Reaction in Enzyme Membrane Reactor Systems. I. Single Enzyme Reactions,” Chem. Eng. Sci., 28, 1013 (1973).CrossRefGoogle Scholar
  69. Wagner, С, “Über das Zusammenwinker von Strömung, Diffusion und chemischer Reaktion bei der heterogenen Katalyse,” Z. Phys. Chem., 193, 1 (1943).Google Scholar
  70. Weisz, P.B., and CD. Prater, “Interpretation of Measurements in Experimental Catalysts,” Adv. Catalysis, 6, 143 (1954).CrossRefGoogle Scholar
  71. Wharton, C.W., E.M. Crook, and K. Brocklehurst, “The Nature of the Perturbation of the Michaelis Constant of the Bromelain-Catalyzed Hydrolysis of a-N-Benzoyl-L-Arginine Ethyl Ester Consequent upon Attachment of Bromelain to O-(Carboxymethyl)-Cellulose,” Eur. J. Biochem., 6, 572 (1968).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • Bruce K. Hamilton
    • 1
  • Colin R. Gardner
    • 1
  • C. K. Colton
    • 1
  1. 1.Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations