Journal of Mathematical Chemistry

, Volume 51, Issue 9, pp 2491–2502

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

• Feliksas Ivanauskas
• Valdas Laurinavicius
Original Paper

## Abstract

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.

## Notes

### Acknowledgments

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.

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