Utilize este identificador para referenciar este registo: http://elartu.tntu.edu.ua/handle/lib/31716

Título: Identification of parameters and investigation of stability of the mathematical model biosensor formeasuring α-chaconine
Outros títulos: Ідентифікація параметрів та дослідження стійкості математичної моделі біосенсору для визначення
Autor: Марценюк, Василь Петрович
Сверстюк, Андрій Степанович
Дзядевич, Сергій
Martsenyuk, Vasyl
Sverstiuk, Andrii
Dzyadevych, Sergei
Affiliation: Університет в Бєльсько-Бялій, Бєльсько-Бяла, Польща
Тернопільський національний медичний університет імені І. Я. Горбачевського, Тернопіль, Україна
Інститут молекулярної біології та генетики НАН України, Київ, Україна
University of Bielsko-Biala, Bielsko-Biala, Poland
Ternopil National Medical University, Ternopil, Ukraine
Department of of Biomolecular Electronics, Institute of Molecular Biology and Genetics, NAS of Ukraine, Kyiv, Ukraine
Bibliographic description (Ukraine): Martsenyuk V. Identification of parameters and investigation of stability of the mathematical model biosensor formeasuring α-chaconine / Vasyl Martsenyuk, Andrii Sverstiuk, Sergei Dzyadevych // Scientific Journal of TNTU. — Ternopil : TNTU, 2019. — Vol 96. — No 4. — P. 101–111.
Bibliographic description (International): Martsenyuk V., Sverstiuk A., Dzyadevych S. (2019) Identification of parameters and investigation of stability of the mathematical model biosensor formeasuring α-chaconine. Scientific Journal of TNTU (Ternopil), vol. 96, no 4, pp. 101-111.
Is part of: Вісник Тернопільського національного технічного університету, 4 (96), 2019
Scientific Journal of the Ternopil National Technical University, 4 (96), 2019
Journal/Collection: Вісник Тернопільського національного технічного університету
Issue: 4
Volume: 96
Data: 28-Jan-2020
Submitted date: 20-Dez-2019
Date of entry: 21-Mai-2020
Editora: ТНТУ
TNTU
Place of the edition/event: Тернопіль
Ternopil
DOI: https://doi.org/10.33108/visnyk_tntu2019.04.101
UDC: 004
94
53
616-073
Palavras-chave: математична модель
біосенсор
дослідження стійкості α-чаконін
чисельне моделювання
mathematical model
biosensor
investigation of stability
α-chaconine
numerical modeling
Number of pages: 11
Page range: 101-111
Start page: 101
End page: 111
Resumo: Присвячено проблемі вдосконалення існуючих математичних і обчислювальних засобів для отримання та аналізу результатів чисельного моделювання при проектуванні біосенсорів. Ідентифіковано параметри, досліджено стійкість та проведено верифікацію математичної моделі потенціометричного біосенсору на основі зворотного інгібування бутирихолінестерази для визначення α-чаконіну. Математична модель досліджуваного біосенсору представлена системою семи лінійних диференціальних рівнянь, які описують динаміку біохімічних реакцій під час повного циклу вимірювання концентрації α-чаконіну. При цьому кожне із диференціальних рівнянь описує концентрації ферменту, субстрату, інгібітора, продукту, фермент-субстратного, фермент-інгібіторного, фермент-субстрат-інгібіторного комплексів залежно від часу. Математична модель біосенсора для визначення α-чаконіну розв’язана чисельно за допомогою пакета R. Вхідними параметрами системи є початкові концентрації ферменту, субстрату та інгібітора (5,8×10-4 М бутирихолінестерази, 1×10-3 М бутирихолін хлориду та 1×10−6; 2×10−6; 5×10−6; 10×10−6 М α-чаконіну відповідно), які експериментально розраховані. Для верифікації моделі та порівняння з експериментальним відгуком використано існуючий потенціометричний біосенсор на основі іммобілізованої бутирихолінестерази. Прямі та зворотні константи швидкостей ферментативних реакцій підібрані таким чином, щоб результат чисельного моделювання максимально відповідав експериментальному відгуку досліджуваного біосенсора. За результатами порівняльного аналізу встановлено залежність відхилення змодельованого та експериментального відгуків біосенсора для визначення α-чаконіну. Встановлено, що абсолютна похибка не перевищує 0,045 ум.од. На основі отриманих результатів чисельного моделювання зроблено висновок, що розроблена кінетична модель потенціометричного біосенсора дає змогу адекватно визначати усі основні складові компартментних компонент біохімічних реакцій при вимірюванні концентрації α-чаконіну
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
URI: http://elartu.tntu.edu.ua/handle/lib/31716
ISSN: 2522-4433
Copyright owner: © Тернопільський національний технічний університет імені Івана Пулюя, 2019
URL for reference material: https://doi.org/10.3390/foods3030491
https://doi.org/10.14232/ejqtde.2018.1.27
https://doi.org/10.1615/JAutomatInfScien.v50.i6.50
https://doi.org/10.1615/JAutomatInfScien.v51.i2.70
https://doi.org/10.1007/s10559-019-00171-2
https://doi.org/10.1021/ac60352a006
https://doi.org/10.1021/ac9806355
https://doi.org/10.1016/j.snb.2011.12.079
https://doi.org/10.1016/j.electacta.2010.04.050
https://doi.org/10.1016/j.memsci.2011.02.033
https://doi.org/10.1016/j.jelechem.2010.03.027
https://doi.org/10.1016/j.electacta.2014.08.125
https://doi.org/10.1016/j.jelechem.2012.06.025
https://doi.org/10.1007/10_2013_224
https://doi.org/10.1080/00032719.2012.713069
https://doi.org/10.1016/j.aca.2014.11.027
https://doi.org/10.1155/2013/731501
https://doi.org/10.1016/j.snb.2014.10.033
https://doi.org/10.1016/S0956-5663(02)00222-1
https://doi.org/10.1016/j.snb.2004.04.070
References (Ukraine): 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. https://doi.org/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. https://doi.org/10.14232/ejqtde.2018.1.27
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. https://doi.org/10.1615/JAutomatInfScien.v50.i6.50
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. https://doi.org/10.1615/JAutomatInfScien.v51.i2.70
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. https://doi.org/10.1007/s10559-019-00171-2
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. https://doi.org/10.14232/ejqtde.2018.1.27
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. https://doi.org/10.1615/JAutomatInfScien.v50.i6.50
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. https://doi.org/10.1021/ac60352a006
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. https://doi.org/10.1021/ac9806355
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. https://doi.org/10.1016/j.snb.2011.12.079
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. https://doi.org/10.1016/j.electacta.2010.04.050
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. https://doi.org/10.1016/j.memsci.2011.02.033
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. https://doi.org/10.1016/j.jelechem.2010.03.027
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. https://doi.org/10.1016/j.electacta.2014.08.125
18. Ašeris V., Baronas R., Kulys J. Modelling the biosensor utilising parallel substrates conversion. Journal of Electroanalytical Chemistry. 2012. Vol. 685. P. 63–71. https://doi.org/10.1016/j.jelechem.2012.06.025
19. Arduini F., Amine A. Biosensors Based on Enzyme Inhibition. Advances in Biochemical Engineering. 2014. Vol. 140. P. 299–326. https://doi.org/10.1007/10_2013_224
20. Upadhyay L. S., Verma N. Enzyme Inhibition Based Biosensors: A Review. Analytical Letters. 2012.Vol. 46. P. 225–241. https://doi.org/10.1080/00032719.2012.713069
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. https://doi.org/10.1016/j.aca.2014.11.027
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. https://doi.org/10.1155/2013/731501
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. https://doi.org/10.1016/j.snb.2014.10.033
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. https://doi.org/10.1016/S0956-5663(02)00222-1
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. https://doi.org/10.1016/j.snb.2004.04.070
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.
References (International): 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. https://doi.org/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. https://doi.org/10.14232/ejqtde.2018.1.27
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. https://doi.org/10.1615/JAutomatInfScien.v50.i6.50
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. https://doi.org/10.1615/JAutomatInfScien.v51.i2.70
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. https://doi.org/10.1007/s10559-019-00171-2
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. https://doi.org/10.14232/ejqtde.2018.1.27
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. https://doi.org/10.1615/JAutomatInfScien.v50.i6.50
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. https://doi.org/10.1021/ac60352a006
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. https://doi.org/10.1021/ac9806355
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. https://doi.org/10.1016/j.snb.2011.12.079
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. https://doi.org/10.1016/j.electacta.2010.04.050
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. https://doi.org/10.1016/j.memsci.2011.02.033
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. https://doi.org/10.1016/j.jelechem.2010.03.027
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. https://doi.org/10.1016/j.electacta.2014.08.125
18. Ašeris V., Baronas R., Kulys J. Modelling the biosensor utilising parallel substrates conversion. Journal of Electroanalytical Chemistry. 2012. Vol. 685. P. 63–71. https://doi.org/10.1016/j.jelechem.2012.06.025
19. Arduini F., Amine A. Biosensors Based on Enzyme Inhibition. Advances in Biochemical Engineering. 2014. Vol. 140. P. 299–326. https://doi.org/10.1007/10_2013_224
20. Upadhyay L. S., Verma N. Enzyme Inhibition Based Biosensors: A Review. Analytical Letters. 2012.Vol. 46. P. 225–241. https://doi.org/10.1080/00032719.2012.713069
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. https://doi.org/10.1016/j.aca.2014.11.027
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. https://doi.org/10.1155/2013/731501
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. https://doi.org/10.1016/j.snb.2014.10.033
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. https://doi.org/10.1016/S0956-5663(02)00222-1
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. https://doi.org/10.1016/j.snb.2004.04.070
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.
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