Picard Iteration Method to Kinetic Analysis of Thermal Inactivation of Enzyme as Applied in Biotechnology
الموضوعات :
A. Olurotimi Adeleye
1
(Department of System Engineering,
University of Lagos, Nigeria)
M. Gbeminiyi Sobamowo
2
(Department of Mechanical Engineering,
University of Lagos, Nigeria)
الکلمات المفتاحية: Picard, Enzyme, Jack Bean Urease, Iteration Method, Kinetics, Thermal Activation,
ملخص المقالة :
In this work, Picard iteration method is used to obtain analytical expressions for the prediction of molar concentration of native and denatured jack bean urease (EC 3.5.1.5) through the three-reaction steps kinetic model of thermal inactivation of the urease. The obtained solutions are used to study the kinetics of thermal inactivation of the enzyme as applied in biotechnology. The analytical solutions are verified with numerical solutions using Runge –Kutta with shooting method and good agreements are established between the solutions. From the parametric studies using the iterative method, the molar concentration of native enzyme decreases as the time increases while the molar concentration of the denatured enzyme increases as the time increases. The time taken to reach the maximum value of the molar concentration of native enzyme is the same as the time taken to reach the minimum value of the molar concentration of the denature enzyme. The information given in this theoretical investigation will assist in the kinetic analysis of the experimental results over handling rate constants and molar concentrations.
[1] Zimmer, M., Molecular Mechanics Evaluation of the Proposed Mechanisms for the Degradation of Urea by Urease, J., Biomol Struct Dyn, Vol. 17, No. 5, 2000, pp. 787–97.
[2] Quin, Y., Cabral, J. Properties and Applications of Urease, Biocatal. Biotransform, Vol. 20, 2002, pp. 227–236.
[3] Krajewska, B., Van Eldik, R., and Brindell, M., Temperature and Pressure Dependent Stopped Flow Kinetic Studies of Jack Bean Urease, Implications for the Catalytic Mechanism, JBIC Journal of Biological Inorganic Chemistry, Vol. 17, No. 7, 2012, pp. 1123–1134.
[4] Dixon, N. E., Gazzola, C., Blakeley, R. L., and Zerner, B., Jack Bean Urease (E.C.3.5.1.5), A Metalloenzyme, A Simple Biological Role for Nickel, J. Am. Chem. Soc., Vol. 97, 1975, pp. 4131–4133.
[5] Winquist, F., Lundstroem, L., and Danielsson, B., Trace Level Analysis for Mercury Using Urease in Combination with an Ammonia Gas Sensitive Semiconductor Structure, Anal. Lett. B, Vol. 21, 1988, pp. 1801–1816.
[6] Miyagawa, K., Sumida, M., Nakao, M., Harada, M., Yamamoto, H., Kusumi, T., Yoshizawa, K., and Amachi, T., Purification, Characterization and Application of an Acid Urease from Arthrobacter Mobilis, J. Biotechnol, Vol. 68, 1999, pp. 227–236.
[7] Sansubrino, A., Mascini, M., Development of an Optical Fbre Sensor for Ammonia, Urea, Urease and IgG. Biosens. Bioelectron, Vol. 9, 1994, pp. 207–216.
[8] Godjevargova, T., A. Dimov, Immobilization of Urease Onto Membranes of Modified Acrylonitrile Copolymer, J. Membr. Sci., Vol. 135, 1997, pp. 93–98.
[9] Rejikumar, S., Devi, S., Preparation and Characterization of Urease Bound on Crosslinked Poly (vinyl alcohol), J. Mol. Catal. B, Vol. 4, 1998, pp. 61–66.
[10] Chen, J. P., Chiu, S. H., A Poly (n-Sopropylacrylamide-Co-Nacroloxysuccinimide-Co-2-Hydroxyetyl Methacrylate) Composite Hydrogel Membrane for Urease Immobilization to Enhance Urea Hydrolysis Rate by Temperature Swing. Enzyme Microb, Technol, Vol. 26, 2000, pp. 359–367.
[11] Omar, S., Beauregard, M., Dissociation and Unfolding of Jack Bean Urease Studied by Fuorescence Emission Spectroscopy, J. Biotechnol, Vol. 39, 1995, pp. 221–228.
[12] Mobley, H. L. T., Hausinger, R. P., Microbial Ureases: Significance, Regulation, and Molecular Characterization, Microbiological Reviews, Vol. 53, No. 1, 1989, pp. 85–108.
[13] Summner, J.B, “The isolation and crystallization of the enzyme urease,” The Journal of Biological Chemistry, 69, 435–441, 1926.
[14] Dixon, N. E., Gazzola, C., Blakeley, R. L., and Zerner, B., Jack Bean Urease (EC 3.5.1.5), A Metalloenzyme, A Simple Biological Role for Nickel?, Journal of the American Chemical Society, Vol. 97, No. 14, 1975, pp. 4131–4133.
[15] Winquist, F., Lundstrom, I., and Danielsson, B., Trace Level Analysis of Mercury Using Urease in Combination with an Ammonia Gas Sensitive Semiconductor Structure, Analytical Letters, Vol. 21, No. 10, 1988, pp. 1801–1816.
[16] Prakash, O., Bhushan, G., Isolation, Purification and Partial Characterisation of Urease from Seeds of Water Melon (Citrullus Vulgaris), Journal of Plant Biochemistry and Biotechnology, Vol. 6, No. 1, 1997, pp. 45–47.
[17] Hirai, M., Kawai-Hirai, R., Hirai, T., and Ueki, T., Structural Change of Jack Bean Urease Induced by Addition of Surfactants Studied with Synchrotron-Radiation Small-Angle X-Ray Scattering, European Journal of Biochemistry, Vol. 215, No. 1, 1993, pp. 55–61.
[18] Illeova, V., Polakovic, M., Stefuca, V., Acai, P., and Juma, M., Experimental Modelling of Thermal Inactivation of Urease, Journal of Biotechnology, Vol. 105, No. 3, 2003, pp. 235–243.
[19] Ananthi, S. P., Manimozhi, P., Praveen, T., Eswari, A., and Rajendran, L., Mathematical Modeling and Analysis of the Kinetics of Thermal Inactivation of Enzyme. International Journal of Engineering Mathematics, Volume 2013, Article ID 132827, 8 pages, 2013.
