AJAC  Vol.3 No.8 , August 2012
Analytical Expressions for Steady-State Concentrations of Substrate and Product in an Amperometric Biosensor with the Substrate Inhibition—The Adomian Decomposition Method
Abstract: A mathematical model of an amperometric biosensor with the substrate inhibition for steady-state condition is discussed. The model is based on the system of non-stationary diffusion equation containing a non-linear term related to non-Michaelis–Menten kinetics of the enzymatic reaction. This paper presents the analytical expression of concentrations and current for all values of parameters φ2s φ2s α and β . Here the Adomian decomposition method (ADM) is used to find the analytical expressions for substrate, product concentration and current. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.
Cite this paper: A. Anitha, S. Loghambal and L. Rajendran, "Analytical Expressions for Steady-State Concentrations of Substrate and Product in an Amperometric Biosensor with the Substrate Inhibition—The Adomian Decomposition Method," American Journal of Analytical Chemistry, Vol. 3 No. 8, 2012, pp. 495-502. doi: 10.4236/ajac.2012.38066.

[1]   P. Manimozhi, A. Subbiah and L. Rajendran, “Solution of Steady-State Substrate Concentration in the Action of Biosensor Response at Mixed Enzyme Kinetics,” Sensors and Actuators B: Chemical, Vol. 147, 2010, pp. 290-297. doi:10.1016/j.snb.2010.03.008

[2]   J. Kulys and R. Baronas, “Modeling of Amperometric Biosensors in the Case of Substrate Inhibition,” Sensors, Vol. 6, No. 11, 2006, pp. 1513-1522. doi:10.3390/s6111513

[3]   T. Schulmeister and D. Pfeiffer, “Mathematical Modeling of Amperometric Enzyme Electrodes with Perforated Membranes,” Biosensors and Bioelectronics, Vol. 8, No. 2, 1993, pp. 75-79. doi:10.1016/0956-5663(93)80055-T

[4]   A.J. Baeumner, C. Jones, C. Y. Wong and A. Price, “A Generic Sandwich-Type Biosensor with Nanomolar Detection Limits,” Analytical and Bioanalytical Chemistry, Vol. 378, No. 6, 2004, pp. 1587-1593. doi:10.1007/s00216-003-2466-0

[5]   R. Baronas, F. Ivanauska and J. Kulys, “The Influence of the Enzyme Membrane Thickness on the Response of Amperometric Biosensors,” Sensors, Vol. 3, No. 7, 2003, pp. 248-262. doi:10.3390/s30700248

[6]   G. C. Okpokwasili and C. O. Nweke, “Microbial Growth and Substrate Utilization Kinetics,” African Journal of Biotechnology, Vol. 5, No. 4, 2005, pp. 305-317.

[7]   V. Rangelova, A. Pandelova and N. Stoiyanov, “Acta Technica Corvinensis,” Bulletin of Engineering Tome IV, 2011.

[8]   S. E. Agarry, T. O. K. Audu and B. O. Solomon, “Substrate Inhibition Kinetics of Phenol Degradation by Pseu-domonas Fluorescence from Steady State and Wash-Out Data,” Internation Journal of Environmental Science and Technology, Vol. 6, No. 3, 2009, pp. 443-450.

[9]   A. Eswari, S. Usha and L. Rajendran, “Approximate Solution of Non-linear Reaction Diffusion Equations in Ho- mogeneous Processes Coupled to Electrode Reactions for CE Mechanism at a Spherical Electrode,” American Journal of Analytical Chemistry, Vol. 2, 2011, pp. 93-103. doi:10.4236/ajac.2011.22010

[10]   S. Anitha, A. Subbiah and L. Rajendran, “Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes,” ISRN Physical Chemistry, Vol. 2012, 2012, Article ID: 745616. doi:10.5402/2012/745616

[11]   M. V. Putz, “On the Reducible Character of Haldane- Radi? Enzyme Kinetics to Conventional and Logistic Michaelis-Menten Models,” Molecules, Vol. 16, No. 4, 2011, pp. 3128-3145. doi:10.3390/molecules16043128

[12]   M. C. Reed, A. Lieb and H. F. Nijhout, “The Biological Significance of Substrate Inhibition: A Mechanism with Diverse Functions,” Bioessays, Vol. 32, No. 5, 2010, pp. 422-429. doi:10.1002/bies.200900167

[13]   J. Kulys, “Biosensor Response at Mixed Enzyme Kinetics and External Diffusion Limitation in Case of Substrate Inhibition,” Nonlinear Analysis: Modelling and Control, Vol. 11, No. 4, 2006, pp. 385–392.

[14]   R. Baronas, F. Ivanauskas and J. Kulys, “Mathematical Modeling of Biosensors An Introduction for Chemists and Mathematicians,” Springer Series on Chemical Sensors and Biosensors, Vol. 9, 2010, p. 104 doi:10.1007/978-90-481-3243-0

[15]   M. A. Mohamed, “Comparison Differential Transformation Technique with Adomian Decomposition Method for Dispersive Long-Wave Equations in (2+1)-Dimensions,” Applications and Applied Mathematics, Vol. 5, No. 1, 2010, pp. 148-166.

[16]   O. K. Jaradat, “Adomian Decomposition Method for Solving Abelian Differential Equations,” Journal of Applied Sciences, Vol. 8, No. 10, 2008, pp. 1962-1966. doi:10.3923/jas.2008.1962.1966

[17]   A. M. Siddiqui, M. Hameed, B. M. Siddiqui and Q. K. Ghori, “Use of Adomian Decomposition Method in the Study of Parallel Plate Flow of a Third Grade Fluid,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 9, 2010, pp. 2388-2399. doi:10.1016/j.cnsns.2009.05.073

[18]   A. Majid Wazwaz and A. Gorguis, “An Analytic Study of Fisher’s Equation by Using Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 154, No. 3, 2004, pp. 609-620. doi:10.1016/S0096-3003(03)00738-0

[19]   H. Jafari and V. Daftardar-Gejji, “Solving Linear and Nonlinear Fractional Diffusion and Wave Equations by Adomian Decomposition,” Applied Mathematics and Com- putation, Vol. 180, No. 2, 2006, pp. 488-497. doi:10.1016/j.amc.2005.12.031

[20]   N. H. Sweilam and M. M. Khader, “Approximate Solutions to the Nonlinear Vibrations of Multiwalled Carbon Nanotubes Using Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 217, No. 2, 2010, pp. 495-505. doi:10.1016/j.amc.2010.05.082

[21]   G. Adomian, “Solving the Mathematical Models of Neurosciences and Medicine,” Mathematics and Computers in Simulation, Vol. 40, No. 1-2, 1995, pp. 107-114. doi:10.1016/0378-4754(95)00021-8

[22]   O. D. Makinde, “Adomian Decomposition Approach to a SIR Epidemic Model with Constant Vaccination Strategy,” Applied Mathematics and Computation, Vol. 184, No. 2, 2007, pp. 842-848. doi:10.1016/j.amc.2006.06.074

[23]   S. Loghambal and L. Rajendran, “Analytical Expressions for Steady-State Concentrations of Substrate, Oxidized and Reduced Mediator in an Amperometric Biosensor,” Kinetics and Catalysis, in press.