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Journal of Mathematical Chemistry

, Volume 34, Issue 3–4, pp 227–242 | Cite as

Modelling of Amperometric Biosensors with Rough Surface of the Enzyme Membrane

  • R. Baronas
  • F. Ivanauskas
  • J. Kulys
  • M. Sapagovas
Article

Abstract

A two-dimensional-in-space mathematical model of amperometric biosensors has been developed. The model is based on the diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetic of the enzymatic reaction. The model takes into consideration two types of roughness of the upper surface (bulk solution/membrane interface) of the enzyme membrane, immobilised onto an electrode. Using digital simulation, the influence of the geometry of the roughness on the biosensor response was investigated. Digital simulation was carried out using the finite-difference technique.

reaction–diffusion modelling biosensor rough surface 

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]References

  1. [1]
    G.G. Guilbault, Analytical Uses of Immobilized Enzymes (Marcel Dekker, New York, 1984).Google Scholar
  2. [2]
    A.P.F. Turner, I. Karube and G.S. Wilson, Biosensors: Fundamentals and Applications (Oxford University Press, Oxford, 1987).Google Scholar
  3. [3]
    F. Scheller and F. Schubert, Biosensors (Elsevier, Amsterdam, 1992).Google Scholar
  4. [4]
    L.C. Clarc and C. Loys, Ann. N.Y. Acad. Sci. 102 (1962) 29.PubMedGoogle Scholar
  5. [5]
    K.R. Rogers, Biosens. Bioelectron. 10 (1995) 533.Google Scholar
  6. [6]
    U. Wollenberger, F. Lisdat and F.W. Scheller, Frontiers in Biosensorics 2: Practical Applications (Birkhäuser, Basel, 1997).Google Scholar
  7. [7]
    A. Chaubey and B.D. Malhotra, Biosens. Bioelectron. 17 (2002) 441.PubMedGoogle Scholar
  8. [8]
    G.G. Guilbault and G. Nagy, Anal. Chem. 45 (1973) 417.Google Scholar
  9. [9]
    C.D. Mell and J.T. Maloy, Anal. Chem. 47 (1975) 299.Google Scholar
  10. [10]
    C.D. Mell and J.T. Maloy, Anal. Chem. 48 (1976) 1597.PubMedGoogle Scholar
  11. [11]
    J.J. Kulys, V.V. Sorochinski and R.A. Vidziunaite, Biosensors 2 (1986) 135.PubMedGoogle Scholar
  12. [12]
    T. Schulmeister, J. Rose and F. Scheller, Biosens. Bioelectron. 12 (1997) 1021.Google Scholar
  13. [13]
    J. Crank, The Mathematics of Diffusion 2nd ed., (Clarendon Press, Oxford, 1975).Google Scholar
  14. [14]
    T. Schulmeister, Selective Electrode Rev. 12 (1990) 203.Google Scholar
  15. [15]
    R. Baronas, F. Ivanauskas and J. Kulys, Nonlinear Analysis: Modelling and Control 8 (2003) 3.Google Scholar
  16. [16]
    W.F. Ames, Numerical Methods for Partial Differential Equations 2nd ed., (Academic Press, New York, 1977).Google Scholar
  17. [17]
    D. Britz, Digital Simulation in Electrochemistry 2nd ed., (Springer, Berlin, 1988).Google Scholar
  18. [18]
    P.N. Bartlett and K.F.E. Pratt, Biosens. Bioelectron. 8 (1993) 451.Google Scholar
  19. [19]
    K. Yokoyama and Y. Kayanuma, Anal. Chem. 70 (1998) 3368.PubMedGoogle Scholar
  20. [20]
    EC RTD Project. INTELLISENS: Intelligent Signal Processing of Biosensor Arrays Using Pattern Recognition for Characterisation of Wastewater: Aiming Towards Alarm Systems, 2000–2003.Google Scholar
  21. [21]
    T. Gueshi, K. Tokuda and H. Matsuda, J. Electroanal. Chem. 89 (1978) 247.Google Scholar
  22. [22]
    C. Deslous, C. Gabrielli, M. Keddam, A. Khalil, R. Rosset, B. Trobollet and M. Zidoune, Electrochim. Acta 42 (1997) 1219.CrossRefGoogle Scholar
  23. [23]
    R. Baronas, F. Ivanauskas and A. Survila, J. Math. Chem. 27 (2000) 267.Google Scholar
  24. [24]
    J. Kulys, Enzyme Microbiol. Technol. 3 (1981) 344.Google Scholar
  25. [25]
    R. Baronas, F. Ivanauskas and J. Kulys, J. Math. Chem. 32 (2002) 225.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • R. Baronas
    • 1
  • F. Ivanauskas
    • 1
  • J. Kulys
    • 2
  • M. Sapagovas
    • 3
  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Institute of BiochemistryVilniusLithuania
  3. 3.Institute of Mathematics and InformaticsVilniusLithuania

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