AM  Vol.6 No.7 , June 2015
Analytical Expression for the Concentration of Substrate and Product in Immobilized Enzyme System in Biofuel/Biosensor
Abstract: In this paper, an approximate analytical method to solve the non-linear differential equations in an immobilized enzyme film is presented. Analytical expressions for concentrations of substrate and product have been derived for all values of dimensionless parameter. Dimensionless numbers that can be used to study the effects of enzyme loading, enzymatic gel thickness, and oxidation/ reduction kinetics at the electrode in biosensor/biofuel cell performance were identified. Using the dimensionless numbers identified in this paper, and the plots representing the effects of these dimensionless numbers on concentrations and current in biosensor/biofuel cell are discussed. Analytical results are compared with simulation results and satisfactory agreement is noted.
Cite this paper: Devi, R. , Kirthiga, O. and Rajendran, L. (2015) Analytical Expression for the Concentration of Substrate and Product in Immobilized Enzyme System in Biofuel/Biosensor. Applied Mathematics, 6, 1148-1160. doi: 10.4236/am.2015.67105.

[1]   Wang, J., Krause, R., Block, K., Musameh, M., Mulchandani, A. and Schöning, M.J. (2003) Flow Injection Amperometric Detection of OP Nerve Agents Based on an Organophosphorus-Hydrolase Biosensor Detector. Biosensors and Bioelectronics, 18, 255-260.

[2]   Dennison, M.J., Hall, J.M. and Turner, A.P.F. (1996) Direct Monitoring of Formaldehyde Vapour and Detection of Ethanol Vapour Using Dehydrogenase-Based Biosensors. Analyst, 121, 1769-1773.

[3]   Wu, J., Cropek, D.M., West, A.C. and Banta, S. (2010) Development of a Troponin I Biosensor Using a Peptide Obtained through Phage Display. Analytical Chemistry, 82, 8235-8243.

[4]   Chen, X.J., West, A.C., Cropek, D.M. and Banta, S. (2008) Detection of the Superoxide Radical Anion Using Various Alkanethiol Monolayers and Immobilized Cytochrome c. Analytical Chemistry, 80, 9622-9629.

[5]   Lei, Y., Mulchandani, P., Wang, J., Chen, W. and Mulchandani, A. (2005) A Highly Sensitive and Selective Amperometric Microbial Biosensor for Direct Determination of p-Nitrophenyl-Substituted Organophosphate Nerve Agents. Environmental Science & Technology, 39, 8853-8857

[6]   Sahin, A., Dooley, K., Cropek, D.M., West, A.C. and Banta, S. (2011) A Dual Enzyme Electrochemical Assay for the Detection of Organophosphorus Compounds Using Organophosphorus Hydrolase and Horseradish Peroxidase. Sensors and Actuators B: Chemical, 158, 353-360.

[7]   Cass, A.E.G., Davis, G., Francis, G.D., Hill, H.A.O., Aston, W.J., Higgins, I.J., Plotkin, E.V., Scott, L.D.L. and Turner, A.P.F. (1984) Ferrocene-Mediated Enzyme Electrode for Amperometric Determination of Glucose. Analytical Chemistry, 56, 667-671.

[8]   Sheldon, R.A. (2007) Enzyme Immobilization: The Quest for Optimum Performance. Advanced Synthesis & Catalysis, 349, 1289-1307.

[9]   Bartlett, P.N. and Pratt, K.F.E. (1995) Theoretical Treatment of Diffusion and Kinetics in Amperometric Immobilized Enzyme Electrodes Part I: Redox Mediator Entrapped within the Film. Journal of Electroanalytical Chemistry, 397, 61-78.

[10]   Flexer, V., Pratt, K.F.E., Garay, F., Bartlett, P.N. and Calvo, E.J. (2008) Relaxation and Simplex Mathematical Algorithms Applied to the Study of Steady-State Electrochemical Responses of Immobilized Enzyme Biosensors: Comparison with Experiments. Journal of Electroanalytical Chemistry, 616, 87-98.

[11]   Lyons, M. (2006) Modelling the Transport and Kinetics of Electroenzymes at the Electrode/Solution Interface. Sensors, 6, 1765-1790.

[12]   Kartono, A., Sulistan, E. and Mamat, M. (2010) The Numerical Analysis of Enzyme Membrane Thickness on the Response of Amperometric Biosensor. Applied Mathematical Sciences, 4, 1299-1308.

[13]   Baronas, R., Ivanauskas, F. and Kulys, J. (2009) Mathematical Modeling of Biosensors: An Introduction for Chemists and Mathematicians. Springer, Dordrecht.

[14]   Shunmugham, L. and Rajendran, L. (2013) Analytical Expressions for Steady-State Concentrations of Substrate and Oxidized and Reduced Mediator in an Amperometric Biosensor. International Journal of Electrochemistry, 2013, 1-12.

[15]   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.

[16]   Cambiaso, A., Delfino, L., Grattarola, M., Verreschi, G., Ashworth, D., Maines, A. and Vadgama, P. (1996) Modelling and Simulation of a Diffusion Limited Glucose Biosensor. Sensors and Actuators B: Chemical, 33, 203-207.

[17]   Mell, L.D. and Maloy, J.T. (1975) Model for the Amperometric Enzyme Electrode Obtained through Digital Simulation and Applied to the Immobilized Glucose Oxidase System. Analytical Chemistry, 47, 299-307.

[18]   Mell, L.D. and Maloy, J.T. (1976) Amperometric Response Enhancement of the Immobilized Glucose Oxidase Enzyme Electrode. Analytical Chemistry, 48, 1597-1601.

[19]   Simelevicius, D. and Baronas, R. (2010) Computational Modelling of Amperometric Biosensors in the Case of Substrate and Product Inhibition. Journal of Mathematical Chemistry, 47, 430-445.

[20]   Puida, M., Ivanauskas, F. and Laurinavicius, V. (2010) Mathematical Modeling of the Action of Biosensor Possessing Variable Parameters. Journal of Mathematical Chemistry, 47, 191-200.

[21]   Schulmeister, T. and Pfeiffer, D. (1993) Mathematical Modelling of Amperometric Enzyme Electrodes with Perforated Membranes. Biosensors and Bioelectronics, 8, 75-79.

[22]   Rinken, T. (2003) Determination of Kinetic Constants and Enzyme Activity from a Biosensor Transient Signal. Analytical Letters, 36, 1535-1545.

[23]   Sachin, A. (2012) Development of Electrochemical Methods for Detection of Pesticides and Biofuel Production. Columbia University, New York.

[24]   He, J.H. (1999) Homotopy Perturbation Technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262.

[25]   He, J.H. (2003) Homotopy Perturbation Method: A New Nonlinear Analytical Technique. Applied Mathematics and Computation, 135, 73-79.

[26]   He, J.H. (2003) A Simple Perturbation Approach to Blasius Equation. Applied Mathematics and Computation, 140, 217-222.

[27]   He, J.H. (2006) Homotopy Perturbation Method for Solving Boundary Value Problems. Physics Letters A, 350, 87-88.

[28]   Ghori, Q.K., Ahmed, M. and Siddiqui, A.M. (2007) Application of Homotopy Perturbation Method to Squeezing Flow of a Newtonian Fluid. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 179-184.

[29]   Ozis, T. and Yildirim, A. (2007) Relation of a Nonlinear Oscillator with Discontinuities. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 243-248.

[30]   Li, S.J. and Liu, Y.X. (2006) An Improved Approach to Nonlinear Dynamical System Identification Using PID Neural Networks. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 177-182.

[31]   Mousa, M.M. and Ragab, S.F. (2008) Application of the Homotopy Perturbation Method to Linear and Nonlinear Schrodinger Equations. Zeitschrift für Naturforschung A, 63, 140-144.

[32]   Golbabai, A. and Keramati, B. (2008) Modified Homotopy Perturbation Method for Solving Fredholm Integral Equations. Chaos, Solitons & Fractals, 37, 1528-1537.

[33]   Ghasemi, M., Kajani, T.M. and Babolian, E. (2007) Numerical Solutions of the Nonlinear Volterra-Fredholm Integral Equations by Using Homotopy Perturbation Method. Applied Mathematics and Computation, 188, 446-449.

[34]   Biazar, J. and Ghazvini, H. (2009) He’s Homotopy Perturbation Method for Solving System of Volterra Integral Equations of the Second Kind. Chaos, Solitons & Fractals, 39, 770-777.

[35]   Odibat, Z., Momani, S., Odibat, Z. and Momani, S. (2007) A Reliable Treatment of Homotopy Perturbation Method for Klein-Gordon Equations. Physics Letters A, 365, 351-357.

[36]   Chowdhury, M.S.H. and Hashim, I. (2007) Solutions of Time-Dependent Emden-Fowler Type Equations by Homotopy-Perturbation Method. Physics Letters A, 368, 305-313.