A Mathemataical model for a modified micro- cylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reaction-diffusion Equations containing a non-linear term related to Michaelis Menten kinetics of the enzymatic reaction. Here a new analytical technique Homotopy Perturbation Method is used to solve the system of non-linear differential Equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Here we report an analytical expressions pretaining to the concentration of catechol and o-quinone and corresponding current in terms of dimensionless reaction-diffusion parameters in closed form. An excellent agreement with available limiting case is noticed.
Revzin, A.F., Sirkar, K., Simonian, A. and Pishko, M.V. (2002) Glucose, Lactate and Pyruvate Biosensor Arrays Based on Redox Polymer/Oxidoreductase Nanocomposite Thin Films Deposited on Photolithographically Patterned Gold Electrodes. Sensor and Actuators B, 81, 359. doi:org/10.1016/S0925-4005(01)00982-0
Shi, G., Liu, M., Zhu, M., Zhou, T., Chen, J., Jin, L. and Jin, J.-Y. (2002) The study of nafion/xanthine oxidase/au colloid chemically modified biosensor and its application in the determination of hypoxanthine in myocardial cells in vivo. Analyst, 127, 396. doi:org/10.1039/b108462n
Gue, A.-M., Tap, H., Gros, P. and Maury, F. (2002) A miniaturized silicon based enzymatic biosensor: towards a generic structure and technology for multi-analytes assays. Sensor and Actuators B, 82, 227. doi:org/10.1016/S0925-4005(01)01009-7
Gonon, F., Suaud-Changny, M.F. and Buda, M. (1992) Proceedings of satellite symposium on neu-roscience and technology, Lyon, 215.
Donnet, J.B. and Basal, R.C. (1984) International Fiber Science and Technology, Carbon Fibers, Dekker, New York, 3.
Decher, G. and Hong, J.D. (1991) Buildup of ultrathin multilayer films by a self-assembly process: II. Consecutive adsorption of anionic and cationic bipolar amphiphiles and polyelectrolytes on charged surfaces. Berichte der Bunsengesellschaft Für Physikalische Chemie, 95, 1430.
Hodak, J., Etchenique, R., Calvo, E.J., Singhal, K. and Bartlett, P.N. (1997) Layer by layer self assembly of glucose oxidase with a poly(allylmanine)-ferrocene redox mediator. Langmuir, 13, 2708. doi:org/10.1021/la962014h
Forzani, E.S., Solis, V.M. and Calvo, E.S. (2000) Electrochemical behavior of polyphenol oxidase immobilized in self-assembled structures layer by layer with cationic polyallylamine. Analytical Chemistry, 72, 5300. doi:org/10.1021/ac0003798
Coche-Guerante, L., Labbe, P. and Mengeand, V. (2001) Analytical Chemistry, 73, 3206. doi:org/10.1021/ac001534l
Lvov, Y. and Caruso, F. (2001) Biocolloids with Ordered Urease Multilayer Shells as Enzymatic Reactors. Analytical Chemistry, 73, 4212. doi:org/10.1021/ac010118d
Fang, M., Grant, P.S., McShane, M.J., Sukhorukov, G. B., Golub, V.O. and Lvov, Y. (2002) Magnetic bio/nanoreactor with multilayer shells of glucose oxidase and inorganic nanoparticles. Langmuir, 18, 6338. doi:org/10.1021/la025731m
Caruso, F. and Schuler, C. (2000) Enzyme multilayers on colloid particles: Assembly, stability, and enzymatic activity. Langmuir, 16, 9595. doi:org/10.1021/la000942h
Caruso, F., Fiedler, H. and Haage, K. (2000) Assembly of β-glucosidase multilayers on spherical colloidal particles and their use as active catalyst. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 169, 287. doi:org/10.1016/S0927-7757(00)00443-X
Sun, H. and Hu, N. (2004) 1. Voltammetric studies of hemoglobin-coated polystyrene latex bead films on pyrolytic graphite electrodes. Biophysical Chemistry, 110, 297. sdoi:org/10.1016/j.bpc.2004.03.005
Rijiravanich, P., Aoki, K. and Chen, J., Surareungchai, W., Somasundrum, M. (2006) Micro-cylinder biosensors for phenol and catechol based on layer-by-layer immobilization of tyrosinase on latex particles: Theory and experiment. Journal of Electroanalytical Chemistry, 589, 249-258. doi:org/10.1016/j.jelechem.2006.02.019
Wilcox, D.E., Porras, A.G., Hwang, Y.T., Lerch, K., Winkler, M.E. and Solomon, E.I. (1985) Substrate Analogue Binding to the Coupled Binuclear Copper Active Site in Tyrosinase. Journal of American Chemical Society, 107, 4015. doi:org/10.1021/ja00299a043
Carbanes, J., Garcia-Canovas, F., Lozano, J.A. and Garcia-Carmona. F (1987) A kinetic study of the melanization pathway between L-tyrosine and dopachrome. Biochimica et Biophysica Acta- General Subjects, 923, 187.
Coely, A., et al. (2001) Backlund and Darboux Transformation. American Mathematical Society, Providence, RI.
Wadati, M., Sanuki, H. and Konno, K. (1975) Relationships among Inverse Method, B?cklund Transformation and an Infinite Number of Conservation Laws. Progress of Theoretical Physics, 53, 419. doi:org/10.1143/PTP.53.419
Gardener, C.S., Green, J.M., Kruskal, M.D. and Miura, R.M. (1967) Method for solving the Korteweg–de Vries Equation. Physical Review Letter, 19, 1095. doi:org/10.1103/PhysRevLett.19.1095
Hirota, R. (1971) Exact solutions to the Equation describing cylindrical solitons. Physical Review Letter, 27, 1192. doi:org/10.1103/PhysRevLett.27.1192
Malfliet, W. (1992) Solitary wave solutions of nonlinear wave Equations. American Journal of Physics, 60, 650. doi:org/10.1119/1.17120
He, J.H. (1998) Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering, 167, 57. doi:org/10.1016/S0045-7825(98)00108-X
He, J.H. (2005) Approximate solution of nonlinear differential Equations with convolution product nonlinearities. Computer Methods in Applied Mechanics and Engineering, 26, 695-700.
He, J.H. (2006) Homotopy perturbation method for solving boundary value problems. Physical Letter A, 350, 87-88. doi:org/10.1016/j.physleta.2005.10.005
Ariel, P.D. (2010) Homotopy perturbation method and the natural convection flow of a third grade fluid through a circular tube. Nonlinear Science Letters A, 1, 43-52.
Ganji, D.D. and Rafei, M. (2006) Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV Equation by homotopy perturbation Method. Physical Letter A, 356, 131-137. doi:org/10.1016/j.physleta.2006.03.039
Meena, A. and Rajendran, L. (2010) Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear Equations-Homotopy perturbation approach. Journal of Electroanalytical Chemistry, 644, 50-59. doi:org/10.1016/j.jelechem.2010.03.027
Anitha, S., Subbiah, A., Rajendran, L. and Ashok K.J. (2010) Solutions of the coupled reaction and diffusion equations within polymer-modified ultramicroelectrodes. Physical Chemistry C, 114, 7030-7037.
Manimozhi, P., Subbiah, A. and Rajendran, L. (2010) Solution of steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics. Sensor and Actuators B, 147, 290-297. doi:org/10.1016/j.snb.2010.03.008
Eswari, A. and Rajendran, L. (2010) Analytical solution of steady state current at a microdisk biosensor. Journal of Electroanalytical Chemistry, 641, 35-44. doi:org/10.1016/j.jelechem.2010.01.015
Eswari, A. and Rajendran, L. (2010) Analytical solution of steady-state current an enzyme-modified microcylinder electrodes. Journal of Electroanalytical Chemistry, 648, 36-46. doi:org/10.1016/j.jelechem.2010.07.002