Analytical Solution of Substrate Concentration in the Biosensor Response

Author(s)
Seyed Ali Madani Tonekaboni,
Ali Shahbazi Mastan Abad,
Amin Afshari,
Ali Khalilzadeh,
Shahab Karimi,
Mitra Shabanisamghabady

Affiliation(s)

School of Mechanical Engineering, University of Waterloo, Waterloo, Canada.

School of Mechanical Engineering, University of Tehran, Tehran, Iran.

School of Mechanical Engineering, University of Waterloo, Waterloo, Canada.

School of Mechanical Engineering, University of Tehran, Tehran, Iran.

ABSTRACT

Homotopy analysis method (HAM) is employed to investigate amperometric biosensor at mixed enzyme kinetics and diffusion limitation. Mathematical modeling of the problem is developed utilizing non-Michaelis-Menten kinetics of the enzymatic reaction. Different results of the problem are obtained for different values of the dimensionless parameters. Accuracy of the obtained results is verified by comparing them with the available actual and simulated ones. It is concluded that the obtained solution can be considered as a promising one to investigate different aspects of the phenomena.

Cite this paper

Tonekaboni, S. , Abad, A. , Afshari, A. , Khalilzadeh, A. , Karimi, S. and Shabanisamghabady, M. (2013) Analytical Solution of Substrate Concentration in the Biosensor Response.*Applied Mathematics*, **4**, 1603-1608. doi: 10.4236/am.2013.412217.

Tonekaboni, S. , Abad, A. , Afshari, A. , Khalilzadeh, A. , Karimi, S. and Shabanisamghabady, M. (2013) Analytical Solution of Substrate Concentration in the Biosensor Response.

References

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http://dx.doi.org/10.1080/01480540701375232

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http://dx.doi.org/10.1007/s00216-003-2466-0

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http://dx.doi.org/10.1016/j.snb.2010.03.008

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http://dx.doi.org/10.1016/j.cnsns.2009.01.030

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http://dx.doi.org/10.1016/j.cnsns.2008.07.010

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http://dx.doi.org/10.1016/j.mbs.2008.09.001

[24] M. S. H. Chowdhury, T. H. Hassan and S. Mawa, “A New Application of Homotopy Perturbation Method to the Reaction-diffusion Brusselator Model,” Procedia— Social and Behavioral Sciences, Vol. 8, 2010, pp. 648653. http://dx.doi.org/10.1016/j.sbspro.2010.12.090

[25] D. M. Dunlavy and C. Prospectus, “A Homotopy Method for Predicting the Lowest Energy Conformations of Proteins,” 18 April 2003.

[26] R. Baronas, F. Ivanauskas, J. Kulys and M. Sapagovas, “Modeling of Amperometri Biosensors with Rough Surface of the Enzyme Membrane,” Journal of Mathematical Chemistry, Vol. 34, No. 3-4, 2003, pp. 227-242.

http://dx.doi.org/10.1023/B:JOMC.0000004072.97338.12

[27] C. V. Pao, “Mathematical Analysis of Enzyme-Substrate Reaction Diffusion Insomebiochemical Systems,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 4, No. 2, 1979, pp. 369-392.

http://dx.doi.org/10.1016/0362-546X(80)90061-9

[28] 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, Vol. 147, 2010, pp. 290-297.

http://dx.doi.org/10.1016/j.snb.2010.03.008

[1] F. Scheller and F. Schubert, “Biosensors,” Elsevier, Amsterdam, 1988.

[2] U. Wollenberger, F. Lisdat and F. W. Scheller, “Enzymatic Substrate Recycling Electrodes,” Frontiers in Biosensorics II, Vol. 81, 1997, pp. 45-70.

[3] M. Pohanka, P. Skladal and M. Kroca, “Biosensors for Biological Warfare Agent Detection,” Defense Science Journal, Vol. 57, No. 3, 2007, pp. 185-193.

[4] M. Pohanka, D. Jun and K. Kuca, “Mycotoxin Assay Using Biosensor Technology: A Review,” Drug and Chemical Toxicology, Vol. 30, No. 3, 2007, pp. 253-261.

http://dx.doi.org/10.1080/01480540701375232

[5] S. Haron and A. K. Ray, “Optical Biodetection of Cadmium and Lead Ions in Water,” Medical Engineering and Physics, Vol. 28, No. 10, 2006, pp. 978-981.

http://dx.doi.org/10.1016/j.medengphy.2006.04.004

[6] 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.

http://dx.doi.org/10.1007/s00216-003-2466-0

[7] K. R. Rogers, “Biosensors for Environmental Applications,” Biosensors and Bioelectronics, Vol. 10, No. 6-7, 1995, pp. 533-541.

http://dx.doi.org/10.1016/0956-5663(95)96929-S

[8] A. P. F. Turner, I. Karube and G. S. Wilson, “Biosensors: Fundamentals and Applications,” Oxford University Press, Oxford, 1987.

[9] U. Wollenberger, F. Lisdat and F. W. Scheller, “Frontiers in Biosensorics 2. Practical Applications,” Birkhauser Verlag, Basel, 1997.

[10] A. Chaubey and B. D. Malhotra, “Mediated Biosensors,” Biosensors and Bioelectronics, Vol. 17, No. 6-7, 2002, pp. 441-456. http://dx.doi.org/10.1016/S0956-5663(01)00313-X

[11] G. G. Guilbault and G. Nagy, “An Improved Urea Electrode,” Analytical Chemistry, Vol. 45, No. 2, 1973, pp. 417-419. http://dx.doi.org/10.1021/ac60324a053

[12] L. D. Mell and J. T. Maloy, “A Model for the Amperometric Enzyme Electrode Obtained through Digital Simulation and Applied to the Glucose Oxidase System,” Analytical Chemistry, Vol. 47, No. 2, 1975, pp. 299-307.

http://dx.doi.org/10.1021/ac60352a006

[13] J. D. Hoffman, “Numerical Methods for Engineers and Scientists,” McGraw-Hill, New York, 1992.

[14] T. Schulmeister, “Mathematical Modeling of the Dynamic Behavior of Ampero-Metric Enzyme Electrodes,” Selective Electrode Reviews, Vol. 12, 1990, pp. 203-260.

[15] R. Aris, “The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts: The Theory of the Steady State,” Clarendon Press, Oxford, 1975.

[16] L. K. Bieniasz and D. Britz, “Recent Developments in Digital Simulation of Electroan-Alytical Experiments,” Polish Journal of Chemistry, Vol. 78, 2004, pp. 11951219.

[17] S. J. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method,” Chapman and Hall/CRC Press, Boca Raton, 2003.

http://dx.doi.org/10.1201/9780203491164

[18] A. H. Nayfeh, “Problems in Perturbation,” 2nd Edition, Wiley, New York, 1993.

[19] S. J. Liao, “The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,” Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, 1992.

[20] 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, Vol. 147, No. 1, 2010, pp. 290-297.

http://dx.doi.org/10.1016/j.snb.2010.03.008

[21] S. Abbasbandy, T. Hayat, “Solution of the MHD FalknerSkan Flow by Homotopy Analysis Method,” Communications in Nonlinear Science and Numerical, Vol. 14, No. 9-10, 2009, pp. 3591-3598.

http://dx.doi.org/10.1016/j.cnsns.2009.01.030

[22] Y. M. Chen and J. K. Liu, “A Study of Homotopy Analysis Method for Limit Cycle of Van Der Pol Equation,” Communications in Nonlinear Science and Numerical, Vol. 14, No. 5, 2009, pp. 1816-1821.

http://dx.doi.org/10.1016/j.cnsns.2008.07.010

[23] G. Craciun, J. W. Helton and R. J. Williams, “Homotopy Methods for Counting Reaction Network Equilibria,” Mathematical Biosciences, Vol. 216, No. 2, 2008, pp. 140-149.

http://dx.doi.org/10.1016/j.mbs.2008.09.001

[24] M. S. H. Chowdhury, T. H. Hassan and S. Mawa, “A New Application of Homotopy Perturbation Method to the Reaction-diffusion Brusselator Model,” Procedia— Social and Behavioral Sciences, Vol. 8, 2010, pp. 648653. http://dx.doi.org/10.1016/j.sbspro.2010.12.090

[25] D. M. Dunlavy and C. Prospectus, “A Homotopy Method for Predicting the Lowest Energy Conformations of Proteins,” 18 April 2003.

[26] R. Baronas, F. Ivanauskas, J. Kulys and M. Sapagovas, “Modeling of Amperometri Biosensors with Rough Surface of the Enzyme Membrane,” Journal of Mathematical Chemistry, Vol. 34, No. 3-4, 2003, pp. 227-242.

http://dx.doi.org/10.1023/B:JOMC.0000004072.97338.12

[27] C. V. Pao, “Mathematical Analysis of Enzyme-Substrate Reaction Diffusion Insomebiochemical Systems,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 4, No. 2, 1979, pp. 369-392.

http://dx.doi.org/10.1016/0362-546X(80)90061-9

[28] 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, Vol. 147, 2010, pp. 290-297.

http://dx.doi.org/10.1016/j.snb.2010.03.008