Advertisement

Computational and Applied Mathematics

, Volume 35, Issue 2, pp 405–421 | Cite as

Computational modelling of three-layered biosensor based on chemically modified electrode

  • Vytautas Ašeris
  • Romas Baronas
  • Karolis Petrauskas
Article

Abstract

This paper presents a mathematical model of a biosensor based on a chemically modified electrode. The model is solved numerically and results of the simulations are validated with analytical solutions for a specific set of parameter values. The mathematical model of the biosensor comprises three layers: an enzyme layer, a dialysis membrane and an outer diffusion layer. The dialysis membrane is merged with the diffusion layer in the mathematical model by introducing an effective diffusion coefficient. The main purpose of this work was to determine at which parameter values the three-layer model can be replaced with the two-layer model with desired accuracy. Additionally, a possibility to use the maximal gradient of the biosensor current density instead of the steady-state current density is investigated. Numerical experiments showed that using the maximal gradient of the output current density can be very attractive to improve biosensor sensitivity.

Keywords

Biosensor Mathematical modelling Effective diffusion coefficient  Finite difference scheme Maximal gradient value 

Notes

Acknowledgments

The authors of this work thank Professor Juozas Kulys and all the members of the Biomoda seminar in Vilnius University for their valuable remarks.

References

  1. Alkire R, Kolb D, Lipkowski J, Ross P (2011) Chemically modified electrodes. Wiley-VCH, WeinheimGoogle Scholar
  2. Aris R (1975) The mathematical theory of diffusion and reaction in permeable catalysts: the theory of the steady state. In: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts. Clarendon Press, OxfordGoogle Scholar
  3. Ašeris V (2013) Computational modelling of biosensors utilizing intermediate substances. Phd, Vilnius UniversityGoogle Scholar
  4. Ašeris V, Baronas R (2010) Using GRID computing to model biosensors acting in stirred and non-stirred solutions. In: Pereira CF, Sequeira A, Pereira JMC (eds) Proceedings of the 5th european conference on computational fluid dynamics (ECCOMAS CFD 2010), Lisbon, Portugal, pp 14–17Google Scholar
  5. Ašeris V, Baronas R, Kulys J (2012) Effect of diffusion limitations of the response of biosensors utilizing parallel substrates conversion. Proceedings of the 6th European congress on computational methods in applied sciences and engineering. Austria, Vienna, pp 1–10Google Scholar
  6. Banica F (2012) Chemical sensors and biosensors: fundamentals and applications. Wiley, Chichester, UKCrossRefGoogle Scholar
  7. Baronas R, Kulys J (2008) Modelling amperometric biosensors based on chemically modified electrodes. Sensors 8(8):4800–4820CrossRefGoogle Scholar
  8. Baronas R, Ivanauskas F, Kulys J (2010) Mathematical modeling of biosensors. In: Springer series on chemical sensors and biosesnsors, 1st edn. Springer, DordrechtGoogle Scholar
  9. Britz D (2005) Digital simulation in electrochemistry. In: Lecture Notes in Physics. Springer Science & Business Media, BerlinGoogle Scholar
  10. Chang H, Wu C, Ding S, Lin I, Sun I (2005) Measurement of diffusion and partition coefficients of ferrocyanide in protein-immobilized membranes. Analytica Chimica Acta 532(2):209–214CrossRefGoogle Scholar
  11. Cooper J, Cass A (2004) Biosensors: a practical approach. Practical Approach Series No 268, 2nd edn. Oxford University Press, OxfordGoogle Scholar
  12. Dabulyte-Bagdonavičiene J, Ivanauskas F, Razumas V (2011) The computational modelling of the kinetics of ascorbic acid palmitate hydrolysis by lipase considering diffusion. Cent Eur J Chem 9(4):712–719Google Scholar
  13. Gough DA, Leypoldt JK (1979) Membrane-covered, rotated disk electrode. Anal Chem 51(3):439–444CrossRefGoogle Scholar
  14. Grieshaber D, MacKenzie R, Vörös J, Reimhult E (2008) Electrochemical biosensors—sensor principles and architectures. Sensors 8(3):1400–1458CrossRefGoogle Scholar
  15. Marzocchia U, Revsbecha NP (2014) Electrophoretic sensitivity control applied on microscale NO\(_x^-\) biosensors with different membrane permeabilities. Sensor Actuat B-Chem 202(2014):307–313Google Scholar
  16. Murray RW (1980) Chemically modified electrodes. Acc Chem Res 117(1979):135–141CrossRefGoogle Scholar
  17. Petrauskas K, Baronas R (2009) Computational modelling of biosensors with an outer perforated membrane. Nonlinear Anal Model Control 14(1):85–102zbMATHGoogle Scholar
  18. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes, vol 29, 3rd edn. Cambridge University Press, New YorkGoogle Scholar
  19. Puida M, Ivanauskas F, Laurinavičius V (2010) Mathematical modeling of the action of biosensor possessing variable parameters. J Math Chem 47(1):191–200MathSciNetCrossRefzbMATHGoogle Scholar
  20. Sadana A, Sadana N (2010) Handbook of biosensors and biosensor kinetics. Elsevier, AmsterdamzbMATHGoogle Scholar
  21. Samarskij AA (2001) The theory of difference schemes. Marcel Dekker, New YorkCrossRefGoogle Scholar
  22. Sanghavi B, Mobin S, Mathur P, Lahiri G, Srivastava A (2013) Biomimetic sensor for certain catecholamines employing a copper(II) complex and silver nanoparticles modified glassy carbon paste electrode. Biosens Bioelectron 39:124–132CrossRefGoogle Scholar
  23. Scheller F, Schubert F (1992) Biosensors. Elsevier, AmsterdamGoogle Scholar
  24. Schulmeister T (1990) Mathematical modelling of the dynamic behaviour of amperometric enzyme electrodes. Select Electr Rev 12(2):203–260Google Scholar
  25. Šimelevičius D, Petrauskas K, Baronas R, Razumiene J (2014) Computational modeling of mediator oxidation by oxygen in an amperometric glucose biosensor. Sensors 14(2):2578–2594Google Scholar
  26. Turner AP, Karube I, Wilson GS (1987) Biosensors: fundamentals and applications. Oxford Science Publications, Oxford University Press, OxfordGoogle Scholar
  27. Čenas N, Kulys J (1981) Biocatalytic oxidation of glucose on the conductive charge transfer complexes. Bioelectrochem Bioenerg 8(1):103–113CrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014

Authors and Affiliations

  • Vytautas Ašeris
    • 1
  • Romas Baronas
    • 1
  • Karolis Petrauskas
    • 1
  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania

Personalised recommendations