004:94:53:616-073

mathematical model, biosensor, investigation of stability, α-chaconine, numerical modeling

The article is devoted to the problem of improving the existing mathematical and computational tools for obtaining and analyzing the results of numerical modeling in the design of biosensors. Parameters are identified in the work, stability is investigated and mathematical model is verified of a potentiometric biosensor based on the inverse inhibition of butyricolinesterase to determine α-chaconin is substantiated. The mathematical model of the biosensor under study is represented by a system of seven linear differential equations that describe the dynamics of biochemical reactions during a complete cycle of measurement of α-chaconine concentration. In this case, each of the differential equations describes the concentration of enzyme, substrate, inhibitor, product, enzyme-substrate, enzyme-inhibitory, enzyme-substrate-inhibitory complexes depending on time. A mathematical model of the biosensor for the determination of α-chaconine is numerically solved using Wolfram Mathematica software. The initial parameters of the system are the initial concentrations of the enzyme, substrate and inhibitor (5.8×10^-4 M butyricholinesterase, 1×10^-3 M butyrylcholine chloride and 1×10^-6; 2×10^-6; 5×10^-6; 10×10^-6 M α-chaconine, respectively), which are experimentally calculated. An existing potentiometric biosensor based on immobilized butyrylcholinesterase was used to verify the model and compare it with the experimental response. The forward and reverse rate constants of the enzymatic reactions are chosen so that the result of the numerical simulation is as consistent as possible with the experimental response of the biosensor under study. According to the results of the comparative analysis, the dependence of the deviation of the simulated and experimental responses of the biosensor to determine α-chaconine is established. It is found that the absolute error does not exceed 0.045 conventional units. Based on the results of numerical simulation, it is concluded that the developed kinetic model of the potentiometric biosensor allows to adequately determine all the main components of the compartment components of biochemical reactions when measuring the concentration of α-chaconine.

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7. Martsenyuk V. P., Sverstiuk A. S., Andrushchak I. Ye. Approach to the Study of Global Asymptotic Stability of Lattice Differential Equations with Delay for Modeling of Immunosensors. Journal of Automation and Information Sciences. 2019. Vol. 48 (8). P. 58–71.
8. Martsenyuk V., Sverstiuk А., Gvozdetska I. Using Differential Equations with Time Delay on a Hexagonal Lattice for Modeling Immunosensors. Cybernetics and Systems Analysis. 2019. Vol. 55 (4).
   P. 625–636.
9. Martsenyuk V. P., Klos-Witkowska A., Sverstiuk A. S. Stability, bifurcation and transition to chaos in a model of immunosensor based on lattice differential equations with delay. Electronic Journal of Qualitative Theory of Differential Equations. 2018. No. 27. P. 1–31.
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    P. 299–307.
12. Gajovic N., Warsinke A., Huang T., Schulmeister T., Scheller F. W. Characterization and Mathematical Modeling of a Bienzyme Electrode for l-Malate with Cofactor Recycling. Analytical Chemistry. 1999.
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13. Romero M. R., Baruzzi A. M., Garay F. Mathematical modeling and experimental results of a sandwich-type amperometric biosensor. Sensors Actuators, B Chemistry. 2012. Vol. 162. No. 1. P. 284–291.
14. Loghambal S., Rajendran L. Mathematical modeling of diffusion and kinetics in amperometric immobilized enzyme electrodes. Electrochimica Acta. 2010. Vol. 55. No. 18. P. 5230–5238.
15. Loghambal S., Rajendran L. Mathematical modeling in amperometric oxidase enzyme-membrane electrodes. Journal of Membrane Science. Vol. 373. No. 1–2. 2011. P. 20–28.
16. Meena A., Rajendran L. Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations – Homotopy perturbation approach. Journal of Electroanalytical Chemistry. 2010. Vol. 644. No. 1. P. 50–59.
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19. Arduini F., Amine A. Biosensors Based on Enzyme Inhibition. Advances in Biochemical Engineering. 2014. Vol. 140. P. 299–326.
20. Upadhyay L. S., Verma N. Enzyme Inhibition Based Biosensors: A Review. Analytical Letters. 2012.
    Vol. 46. P. 225–241.
21. Stepurska K. V., Soldatkin О. О., Kucherenko I. S., Arkhypova V. M., Dzyadevych S. V., Soldatkin A. P. Feasibility of application of conductometric biosensor based on acetylcholinesterase for the inhibitory analysis of toxic compounds of different nature. Analytica Chimica Acta. 2015. Vol. 854. P. 161–168.
22. Dhull V., Gahlaut A., Dilbaghi N., Hooda V. Acetylcholinesterase biosensors for electrochemical detection of organophosphorus compounds: A review. Biochemistry Research International.
    2013. P. 1–18.
23. Achi F., Bourouina-Bacha S., Bourouina M., Amine A. Mathematical model and numerical simulation of inhibition based biosensor for the detection of Hg(II). Sensors & Actuators, B: Chemical. 2015. Vol. 207.
    P. 413–423.
24. Arkhypova V. N, Dzyadevych S. V., Soldatkin A. P., El’skaya A. V., Martelet C., Jaffrezic-Renault N. Development and optimisation of biosensors based on pH-sensitive field effect transistor and cholinesterase for sensitive detection of solanaceous glycoalkaloids. Biosensors & Bioelectronics. 2003.
    Vol. 18. P. 1047–1053.
25. Arkhypova V. N., Dzyadevych S. V., Soldatkin A. P., Korpan Y. I., El’skaya A. V., Gravoueille J.-M., Martelet C., Jaffrezic-Renault N. Application of enzyme field effect transistors for fast detection of total glycoalkaloids content in potatoes. Sensors and Actuators B. 2004. Vol. 103. P. 416–422.
26. Arrowsmith D. K., Place C. M. The Linearization Theorem. Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour. London: Chapman & Hall. 1992. P. 77–81.

1. Mosinska L., Fabisiak K., Paprocki K., Kowalska M., Popielarski P., Szybowicz M., Stasiak A. Diamond as a transducer material for the production of biosensors. Przemysl Chemiczny. 2013. Vol. 92. No. 6.
   Р. 919–923.
2. Adley C. Past, present and future of sensors in food production. Foods. 2014. Vol. 3. No. 3. P. 491–510.
   Doi: 10.3390/foods3030491.
3. Martsenyuk V. P., Klos-Witkowska A., Sverstiuk A. S. Study of classification of immunosensors from viewpoint of medical tasks. Medical informatics and engineering. 2018. № 1 (41). Р. 13–19.
4. Martsenyuk V. P., Klos-Witkowska A., Sverstiuk A. S., Bihunyak T. V. On principles, methods and areas of medical and biological application of optical immunosensors. Medical informatics and engineering. 2018. № 2 (42). Р. 28–36.
5. Martsenyuk V., Klos–Witkowska A., Sverstiuk A. Stability, bifurcation and transition to chaos in a model of immunosensor based on lattice differential equations with delay. Electronic Journal of Qualitative Theory of Differential Equations. 2018. No. 27. Р. 1–31.
6. Martsenyuk V. P., Andrushchak I. Ye., Zinko P. M., Sverstiuk A. S. On Application of Latticed Differential Equations with a Delay for Immunosensor Modeling. Journal of Automation and Information Sciences. 2018. Vol. 50 (6). P. 55–65.
7. Martsenyuk V. P., Sverstiuk A. S., Andrushchak I. Ye. Approach to the Study of Global Asymptotic Stability of Lattice Differential Equations with Delay for Modeling of Immunosensors. Journal of Automation and Information Sciences. 2019. Vol. 48 (8). P. 58–71.
8. Martsenyuk V., Sverstiuk А., Gvozdetska I. Using Differential Equations with Time Delay on a Hexagonal Lattice for Modeling Immunosensors. Cybernetics and Systems Analysis. 2019. Vol. 55 (4).
   P. 625–636.
9. Martsenyuk V. P., Klos-Witkowska A., Sverstiuk A. S. Stability, bifurcation and transition to chaos in a model of immunosensor based on lattice differential equations with delay. Electronic Journal of Qualitative Theory of Differential Equations. 2018. No. 27. P. 1–31.
10. Martsenyuk V. P., Andrushchak I. Ye., Zinko P. M., Sverstiuk A. S. On Application of Latticed Differential Equations with a Delay for Immunosensor Modeling. Journal of Automation and Information Sciences. Vol. 50 (6). 2018. P. 55–65.
11. Mell L. D., Maloy J. T. A model for the amperometric enzyme electrode obtained through digital simulation and applied to the immobilized glucose oxidase system. Anal. Chem. 1975. Vol. 47. No. 2.
    P. 299–307.
12. Gajovic N., Warsinke A., Huang T., Schulmeister T., Scheller F. W. Characterization and Mathematical Modeling of a Bienzyme Electrode for l-Malate with Cofactor Recycling. Analytical Chemistry. 1999.
    Vol. 71. No. 20. P. 4657–4662.
13. Romero M. R., Baruzzi A. M., Garay F. Mathematical modeling and experimental results of a sandwich-type amperometric biosensor. Sensors Actuators, B Chemistry. 2012. Vol. 162. No. 1. P. 284–291.
14. Loghambal S., Rajendran L. Mathematical modeling of diffusion and kinetics in amperometric immobilized enzyme electrodes. Electrochimica Acta. 2010. Vol. 55. No. 18. P. 5230–5238.
15. Loghambal S., Rajendran L. Mathematical modeling in amperometric oxidase enzyme-membrane electrodes. Journal of Membrane Science. Vol. 373. No. 1–2. 2011. P. 20–28.
16. Meena A., Rajendran L. Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations – Homotopy perturbation approach. Journal of Electroanalytical Chemistry. 2010. Vol. 644. No. 1. P. 50–59.
17. Ašeris V., Gaidamauskaitė E., Kulys J., Baronas R. Modelling glucose dehydrogenase-based amperometric biosensor utilizing synergistic substrates conversion. Electrochimica Acta. 2014. Vol. 146.
    P. 752–758.
18. Ašeris V., Baronas R., Kulys J. Modelling the biosensor utilising parallel substrates conversion. Journal of Electroanalytical Chemistry. 2012. Vol. 685. P. 63–71.
19. Arduini F., Amine A. Biosensors Based on Enzyme Inhibition. Advances in Biochemical Engineering. 2014. Vol. 140. P. 299–326.
20. Upadhyay L. S., Verma N. Enzyme Inhibition Based Biosensors: A Review. Analytical Letters. 2012.
    Vol. 46. P. 225–241.
21. Stepurska K. V., Soldatkin О. О., Kucherenko I. S., Arkhypova V. M., Dzyadevych S. V., Soldatkin A. P. Feasibility of application of conductometric biosensor based on acetylcholinesterase for the inhibitory analysis of toxic compounds of different nature. Analytica Chimica Acta. 2015. Vol. 854. P. 161–168.
22. Dhull V., Gahlaut A., Dilbaghi N., Hooda V. Acetylcholinesterase biosensors for electrochemical detection of organophosphorus compounds: A review. Biochemistry Research International.
    2013. P. 1–18.
23. Achi F., Bourouina-Bacha S., Bourouina M., Amine A. Mathematical model and numerical simulation of inhibition based biosensor for the detection of Hg(II). Sensors & Actuators, B: Chemical. 2015. Vol. 207.
    P. 413–423.
24. Arkhypova V. N, Dzyadevych S. V., Soldatkin A. P., El’skaya A. V., Martelet C., Jaffrezic-Renault N. Development and optimisation of biosensors based on pH-sensitive field effect transistor and cholinesterase for sensitive detection of solanaceous glycoalkaloids. Biosensors & Bioelectronics. 2003.
    Vol. 18. P. 1047–1053.
25. Arkhypova V. N., Dzyadevych S. V., Soldatkin A. P., Korpan Y. I., El’skaya A. V., Gravoueille J.-M., Martelet C., Jaffrezic-Renault N. Application of enzyme field effect transistors for fast detection of total glycoalkaloids content in potatoes. Sensors and Actuators B. 2004. Vol. 103. P. 416–422.
26. Arrowsmith D. K., Place C. M. The Linearization Theorem. Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour. London: Chapman & Hall. 1992. P. 77–81.