Spatial Structures Evolving from Homogeneous Media in Immobilized Enzyme Systems

Sang Hwan Kim; Jun-Bong Kim; Hyung-Sang Park

Korean Journal of Chemical Engineering, Vol.18, No.1, 14-20, January, 2001

DOI10.1007/BF02707192 Export Citation

Spatial Structures Evolving from Homogeneous Media in Immobilized Enzyme Systems

Sang Hwan Kim^†, Jun-Bong Kim, and Hyung-Sang Park¹

Department of Chemical Engineering, Konkuk University, Seoul 143-701, Korea
¹Department of Chemical Engineering, Sogang University, Seoul 121-742, Korea

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The detailed pattern of spatial structures for the reaction-diffusion system involving substrate-inhibited reactions on immobilized uricase enzyme was studied. Depending on the governing parameters, three basic solutions may exist and there are two kinds of possible branching, either successive primary bifurcation from a basic trivial branch or consecutive secondary bifurcation. In both cases the branching follows the sequence of symmetric --> asymmetric --> symmetric, and so forth. The emergence of subsequently more complex spatial structures with the increasing length of systems suggests a close similarity to gradual buildup of complex morphogenetic patterns in developmental biology.

Keywords:Spatial Structures;Thomas Model;Immobilized Enzyme Systems;Bifurcation;Multiple Steady States

[References]

Catalano G, Physica, 3D, 439 (1981)
Chandrasekhar S, "Hydrodynamics and Hydromagnetic Stability," Dover Publications, New York (1981)
Doedel E, "Auto: A Program for Automatic Bifurication Analysis of Autonomous Systems," Proc. 10th Manitoba Conference on Numerical Mathematics and Computing, Winnipeg, Canada (1980)
Erk HF, Ducukovic MP, Ind. Eng. Chem. Fundam., 22, 55 (1983)
Erneux T, Herschkowitz-Kaufman M, Bull. Math. Biol., 41, 21 (1979)
Gierer A, Phil. Trans. Roy. Soc., B295, 429 (1981)
Glansdorff P, Prigogine T, "Thermodynamics of Structures, Stability and Fluctuations," Interscience, New York (1971)
Goldbeter A, Proc. Natl. Acad. Sci., 70, 3255 (1973)
Goodwin BC, J. Theor. Biol., 25, 49 (1969)
Herschkowitz-Kaufman M, J. Chem. Phys., 56, 1890 (1972)
Herschkowitz-Kaufman M, Nicolis G, Bull. Math. Biol., 37, 589 (1975)
Hildebrand FB, "Finite-Difference Equations and Simulations," Prentice Hall, Englewood Cliffs, New Jersey (1968)
Janssen R, Hlavacek V, Rompay P, Z. Naturforch, 38, 487 (1983)
Kernevez JP, Joly G, Duban MC, Bunow B, Thomas D, J. Theor. Biol., 7, 143 (1982)
Kim SH, "Application of Nonlinear Dynamic Analysis to Chemically Reacting Systems," Ph.D. Dissertation, State University of New York at Buffalo, Buffalo (1988)
Kim SH, Korean J. Chem. Eng., 6(3), 165 (1989)
Kubicek M, Ryzler V, Marek M, Biophys. Chem., 8, 235 (1978)
Murray JD, J. Theor. Biol., 98, 143 (1982)
Prigogine I, Lefever R, J. Chem. Phys., 48, 1695 (1968)
Schmitz RA, Tsotsis TT, "On the Possibility of Spatially Patterned States in Systems of Interacting Catalyst Particles," 72nd Annual Meeting of AIChE, San Francisco, U.S.A (1971)
Schmitz RA, Tsotsis TT, Chem. Eng. Sci., 38, 1431 (1983)
Turing AM, Phill. Trans. Roy. Soc., B237, 37 (1952)

[Related Articles]

[1] Catalano G, Physica, 3D, 439 (1981)

[2] Chandrasekhar S, "Hydrodynamics and Hydromagnetic Stability," Dover Publications, New York (1981)

[3] Doedel E, "Auto: A Program for Automatic Bifurication Analysis of Autonomous Systems," Proc. 10th Manitoba Conference on Numerical Mathematics and Computing, Winnipeg, Canada (1980)

[4] Erk HF, Ducukovic MP, Ind. Eng. Chem. Fundam., 22, 55 (1983)

[5] Erneux T, Herschkowitz-Kaufman M, Bull. Math. Biol., 41, 21 (1979)

[6] Gierer A, Phil. Trans. Roy. Soc., B295, 429 (1981)

[7] Glansdorff P, Prigogine T, "Thermodynamics of Structures, Stability and Fluctuations," Interscience, New York (1971)

[8] Goldbeter A, Proc. Natl. Acad. Sci., 70, 3255 (1973)

[9] Goodwin BC, J. Theor. Biol., 25, 49 (1969)

[10] Herschkowitz-Kaufman M, J. Chem. Phys., 56, 1890 (1972)

[11] Herschkowitz-Kaufman M, Nicolis G, Bull. Math. Biol., 37, 589 (1975)

[12] Hildebrand FB, "Finite-Difference Equations and Simulations," Prentice Hall, Englewood Cliffs, New Jersey (1968)

[13] Janssen R, Hlavacek V, Rompay P, Z. Naturforch, 38, 487 (1983)

[14] Kernevez JP, Joly G, Duban MC, Bunow B, Thomas D, J. Theor. Biol., 7, 143 (1982)

[15] Kim SH, "Application of Nonlinear Dynamic Analysis to Chemically Reacting Systems," Ph.D. Dissertation, State University of New York at Buffalo, Buffalo (1988)

[16] Kim SH, Korean J. Chem. Eng., 6(3), 165 (1989)

[17] Kubicek M, Ryzler V, Marek M, Biophys. Chem., 8, 235 (1978)

[18] Murray JD, J. Theor. Biol., 98, 143 (1982)

[19] Prigogine I, Lefever R, J. Chem. Phys., 48, 1695 (1968)

[20] Schmitz RA, Tsotsis TT, "On the Possibility of Spatially Patterned States in Systems of Interacting Catalyst Particles," 72nd Annual Meeting of AIChE, San Francisco, U.S.A (1971)

[21] Schmitz RA, Tsotsis TT, Chem. Eng. Sci., 38, 1431 (1983)

[22] Turing AM, Phill. Trans. Roy. Soc., B237, 37 (1952)