Journal of Mathematical Chemistry

, Volume 51, Issue 9, pp 2491–2502 | Cite as

Degradation of substrate and/or product: mathematical modeling of biosensor action

  • Tadas MeškauskasEmail author
  • Feliksas Ivanauskas
  • Valdas Laurinavicius
Original Paper


Mathematical model for evaluation of the multilayer heterogeneous biocatalytic system has been elaborated. The model consists of nonlinear system of partial differential equations with initial values and boundary conditions. An algorithm for computing the numerical solution of the mathematical model has been applied. Two cases: when product diffuses out of the biosensor and when the outer membrane is impermeable for product (product is trapped inside the biosensor) have been dealt with by adjusting boundary conditions in the mathematical model. Profiles of the impact of the substrate and product degradation rates on the biosensor response have been constructed in both cases. Value of the degradation impact has been analyzed as a function of the outer membrane thickness. The initial substrate concentration also affects influence of the degradation rates on the biosensor response. Analytical formulae, defining approximate values of relationships between the degradation rates and the outer membrane thickness or the initial substrate concentration, have been obtained. These formulae can be employed for monitoring of the biosensor response.


Biosensor modeling Enzyme electrode Substrate degradation Product degradation Michaelis–Menten kinetics 



This work has been supported by the project “Theoretical and engineering aspects of e-service technology development and application in high-performance computing platforms” (No. VP1-3.1-ŠMM-08-K-01-010) funded by the European Social Fund.


  1. 1.
    A.P.F. Turner, I. Karube, G.S. Wilson (eds.), Biosensors: Fundamentals and Applications (Oxford University Press, Oxford, 1987)Google Scholar
  2. 2.
    D.M. Fraser (ed.), Biosensors in the Body: Continuous in vivo Monitoring. Wiley Series in Biomaterials Science and Engineering (Wiley, New York, 1997)Google Scholar
  3. 3.
    T. Schulmeister, Anal. Chim. Acta 201, 305 (1987)CrossRefGoogle Scholar
  4. 4.
    R. Baronas, F. Ivanauskas, J. Kulys, J. Math. Chem. 32, 225 (2002)CrossRefGoogle Scholar
  5. 5.
    R. Baronas, F. Ivanauskas, J. Kulys, M. Sapagovas, J. Math. Chem. 34, 227 (2003)CrossRefGoogle Scholar
  6. 6.
    R. Baronas, J. Kulys, F. Ivanauskas, Biosens. Bioelectron. 19, 915 (2004)CrossRefGoogle Scholar
  7. 7.
    R. Baronas, F. Ivanauskas, J. Kulys, J. Math. Chem. 42, 321 (2007)CrossRefGoogle Scholar
  8. 8.
    R. Baronas, F. Ivanauskas, J. Kulys, Mathematical Modeling of Biosensors: An Introduction for Chemists and Mathematicians, Springer Series on Chemical Sensors and Biosensors, vol. 9 (Springer, Berlin, 2010)Google Scholar
  9. 9.
    O. Štikoniene, F. Ivanauskas, V. Laurinavicius, Talanta 81, 1245 (2010)CrossRefGoogle Scholar
  10. 10.
    S. Poorahong, C. Thammakhet, P. Thavarungkul, P. Kanatharana, Pure Appl. Chem. 84, 2055 (2012)CrossRefGoogle Scholar
  11. 11.
    S. Demirci, F.B. Emre, F. Ekiz, F. O\(\tilde{{\rm g}}\)uzkaya, S. Timur, C. Tanyeli, L. Toppare, Analyst 137, 4254 (2012)Google Scholar
  12. 12.
    V.A. Laurinavicius, J.J. Kulys, V.V. Gureviciene, K.J. Simonavicius, Biomed. Biochim. Acta 48, 905 (1989)Google Scholar
  13. 13.
    D. Britz, Digital Simulation in Electrochemistry, 3rd ed, Lecture Notes in Physics, vol. 666 (Springer, Berlin, 2005)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tadas Meškauskas
    • 1
    Email author
  • Feliksas Ivanauskas
    • 1
  • Valdas Laurinavicius
    • 1
  1. 1.Vilnius UniversityUniversiteto 3VilniusLithuania

Personalised recommendations