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Biosensors Based on Microreactors

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Mathematical Modeling of Biosensors

Part of the book series: Springer Series on Chemical Sensors and Biosensors ((SSSENSORS,volume 9))

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Abstract

The reduction of the device size, reagents and sample consumption is among the most important advantages of miniaturization of analytical systems. An integration of the systems with enzymatic microreactors proved to be a very suitable approach to the biosensor miniaturization. In this chapter, three types of amperometric biosensors are mathematically and numerically modeled in a two-dimensional space at transient conditions. The biosensing systems are modeled by reaction–diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetics of an enzymatic reaction. A biosensor based on a carbon paste electrode encrusted with a single microreactor is modeled by a two-compartment model . The constructed biosensor explores an idea to separate the enzyme and the electron transfer components in a microreactor, the silica particle, and use the well-established carbon paste electrode. Then, a biosensing system based on an array of enzyme microreactors immobilized on a single electrode is modeled. Carbon paste porous electrodes are also modeled and investigated by applying a plate–gap model . Using the numerical simulation, the influence of the geometry of the microreactors as well as of the diffusion region on the output current and sensitivity is investigated.

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References

  1. Amatore C, Oleinick AI, Svir I (2006) Construction of optimal quasi-conformal mappings for the 2D-numerical simulation of diffusion at microelectrodes. Part 1: principle of the method and its application to the inlaid disk microelectrode. J Electroanal Chem 597(1):69–76

    Article  Google Scholar 

  2. Amine A, Kauffmann J, Patriarche G, Kaifer A (1991) Long-term operational stability of a mixed glucose oxidase-redox mediator-carbon paste electrode. Anal Lett 24(8):1293–1315

    Article  Google Scholar 

  3. Amine A, Kauffmann J, Guilbault G (1993) Characterization of mixed enzyme-mediator-carbon paste electrodes. Anal Lett 26(7):1281–1299

    Article  Google Scholar 

  4. Bailey R, Jones F, Fisher B, Elmore B (2005) Enhancing design of immobilized enzymatic microbioreactors using computational simulation. Appl Biochem Biotechnol 122(1–3):639–652

    Article  Google Scholar 

  5. Bakhvalov N, Panasenko G (1989) Homogenization: averaging processes in periodic media. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  6. Baronas R, Ivanauskas F, Kulys J (1998) Modeling of a microreactor on heterogeneous surface and an influence of geometry to microreactor operation. Nonlinear Anal Model Control 3:19–30

    Article  MATH  Google Scholar 

  7. Baronas R, Ivanauskas F, Kulys J (1999) Modeling a biosensor based on the heterogeneous microreactor. J Math Chem 25(3–4):245–252

    Article  MATH  Google Scholar 

  8. Baronas R, Ivanauskas F, Survila A (2000) Simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep conditions. J Math Chem 27(4):267–278

    Article  MATH  Google Scholar 

  9. Baronas R, Ivanauskas F, Kulys J (2003) Computer simulation of the response of amperometric biosensors in stirred and non stirred solution. Nonlinear Anal Model Control 8(1):3–18

    Article  MATH  Google Scholar 

  10. Baronas R, Ivanauskas F, Kulys J, Sapagovas M (2003) Modeling of amperometric biosensors with rough surface of the enzyme membrane. J Math Chem 34(3–4):227–242

    Article  MathSciNet  MATH  Google Scholar 

  11. Baronas R, Ivanauskas F, Kulys J, Sapagovas M (2004) Computational modeling of a sensor based on an array of enzyme microreactors. Nonlinear Anal Model Control 9(1):203–218

    Article  MATH  Google Scholar 

  12. Baronas R, Ivanauskas F, Kaunietis I, Laurinavicius V (2006) Mathematical modeling of plate-gap biosensors with an outer porous membrane. Sensors 6(7):727–745

    Article  Google Scholar 

  13. Baronas R, Ivanauskas F, Kulys J (2006) Mathematical modeling of biosensors based on an array of enzyme microreactors. Sensors 6(4):453–465

    Article  Google Scholar 

  14. Baronas R, Ivanauskas F, Kulys J (2010) Mathematical modeling of biosensors. Springer, Dordrecht

    Book  MATH  Google Scholar 

  15. Baronas R, Kulys J, Petkevičius L (2018) Modelling the enzyme catalysed substrate conversion in a microbioreactor acting in continuous flow mode. Nonlinear Anal Model Control 23(3):437–456

    Article  MathSciNet  MATH  Google Scholar 

  16. Baronas R, Kulys J, Petkevičius L (2019) Computational modeling of batch stirred tank reactor based on spherical catalyst particles. J Math Chem 57(1):327–342

    Article  MathSciNet  MATH  Google Scholar 

  17. Bertram R, Pernarowski M (1998) Glucose diffusion in pancreatic islets of Langerhans. Biophys J 74:1722–1731

    Article  Google Scholar 

  18. Britz D (2005) Digital simulation in electrochemistry, 3rd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  19. Britz D, Strutwolf J (2016) Digital simulation in electrochemistry. Monographs in Electrochemistry, 4th edn. Springer, Cham

    Google Scholar 

  20. Boujtita M, El Murr N (2006) Biosensors for analysis of ethanol in foods. J Food Sci 60(1):201–204

    Article  Google Scholar 

  21. Crank J (1975) The mathematics of diffusion. Oxford University Press, London

    MATH  Google Scholar 

  22. Deslous C, Gabrielli C, Keddam M, Khalil A, Rosset R, Trobollet B, Zidoune M (1997) Impedance techniques at partially blocked electrodes by scale deposition. Electrochim Acta 42(8):1219–1233

    Article  Google Scholar 

  23. Dormieux L, Lemarchand E (2001) Homogenization approach of advection and diffusion in cracked porous material. J Eng Mech ASCE 127:1267–1274

    Article  Google Scholar 

  24. Eggins B (2002) Chemical sensors and biosensors. Analytical Techniques in the Sciences. Wiley, Chichester

    Google Scholar 

  25. Ehrfeld W, Hessel V, Löwe H (2000) Microreactors: new technology for modern chemistry. Wiley-VCH, New York

    Book  Google Scholar 

  26. Forrow N, Bayliff S (2005) A commercial whole blood glucose biosensor with a low sensitivity to hematocrit based on an impregnated porous carbon electrode. Biosens Bioelectron 21(4):3581–3587

    Article  Google Scholar 

  27. Fraser D (1997): Biosensors in the body: continuous in vivo monitoring. Wiley, Chichester

    Google Scholar 

  28. Garboczi EJ (1990) Permeability, diffusivity and microstructural parameters: a critical review. Cem Concr Res 20(4):591–601

    Article  Google Scholar 

  29. Gorton L (1995) Carbon paste electrodes modified with enzymes, tissues, and cells. Electroanal 7(1):23–45

    Article  Google Scholar 

  30. Gueshi T, Tokuda K, Matsuda H (1978) Voltammetry at partially covered electrodes: part I. Chronopotentiometry and chronoamperometry at model electrodes. J Electroanal Chem 89(2):247–260

    Article  Google Scholar 

  31. Guilbault G (1970) Enzymatic methods of analysis. Pergamon Press, Oxford

    Google Scholar 

  32. Guilbault G (1984) Analytical uses of immobilized enzymes. Marcel Dekker, New York

    Google Scholar 

  33. Hale P, Lan H, Boguslavsky L, Karan H, Okamoto Y, Skotheim T (1991) Amperometric glucose sensors based on ferrocene-modified poly(ethylene oxide) and glucose oxidase. Anal Chim Acta 251(1–2):121–128

    Article  Google Scholar 

  34. Hobbs D (1999) Aggregate influence on chloride ion diffusion into concrete. Cem Concr Res 29(12):1995–1998

    Article  Google Scholar 

  35. Ikeda T (1995) Enzyme-modified electrodes with bioelectrocatalytic function (Review). Bunsuki Kagaku 44(5):333–354

    Article  Google Scholar 

  36. Ispas C, Sokolov I, Andreescu S (2009) Enzyme-functionalized mesoporous silica for bioanalytical applications. Anal Bioanal Chem 393(2):543–554

    Article  Google Scholar 

  37. Ivanauskas F, Baronas R (2008) Numerical simulation of a plate-gap biosensor with an outer porous membrane. Simul Model Pract Th 16(8):962–970

    Article  Google Scholar 

  38. Ivanauskas F, Kaunietis I, Laurinavičius V, Razumienė J, Šimkus R (2005) Computer simulation of the steady state currents at enzyme doped carbon paste electrode. J Math Chem 38(3):355–366

    Article  MATH  Google Scholar 

  39. Ivanauskas F, Kaunietis I, Laurinavičius V, Razumienė J, Šimkus R (2008) Apparent Michaelis constant of the enzyme modified porous electrode. J Math Chem 43(4):1516–1526

    Article  MathSciNet  MATH  Google Scholar 

  40. Jȩdrzak A, Rȩbiś T, Klapiszewski Ł, Zdarta J, Milczarek G, Jesionowski T (2018) Carbon paste electrode based on functional GOx/silica-lignin system to prepare an amperometric glucose biosensor. Sens Actuator B Chem 256:176–185

    Google Scholar 

  41. Kalnin J, Kotomin E, Maier J (2002) Calculations of the effective diffusion coefficient for inhomogeneous media. J Phys Chem Solids 63(3):449–456

    Article  Google Scholar 

  42. Kirthiga O, Rajendran L (2016) Superior performance of a carbon-paste electrode based glucose biosensor containing glucose oxidase enzyme in mesoporous silica powder. Adv Powder Technol 27(1):85–92

    Article  Google Scholar 

  43. Konti A, Mamma D, Hatzinikolaou DG, Kekos D (2016) 3-Chloro-1,2-propanediol biodegradation by Ca-alginate immobilized Pseudomonas putida DSM 437 cells applying different processes: mass transfer effects. Bioprocess Biosyst Eng 39(10):1597–1609

    Article  Google Scholar 

  44. Kricka LJ (1998) Miniaturization of analytical systems. Clin Chem 44(9):2008–2014

    Article  Google Scholar 

  45. Kulys J (1999) The carbon paste electrode encrusted with a microreactor as glucose biosensor. Biosens Bioelectron 14(5):473–479

    Article  Google Scholar 

  46. Kulys J, Hansen H (1994) Carbon-paste biosensors array for long-term glucose measurement. Biosens Bioelectron 9(7):491–500

    Article  Google Scholar 

  47. Kulys J, Hansen H (1995) Long-term response of an integrated carbon paste based glucose biosensor. Anal Chim Acta 303(3):285–294

    Article  Google Scholar 

  48. Kulys J, Razumas V (1986) Bioamperometry. Mokslas, Vilnius

    Google Scholar 

  49. Kulys J, Hansen HE, Buch-Rasmussen T, Wang J, Ozsoz M (1994) Glucose biosensor based on the incorporation of Meldola Blue and glucose oxidase within carbon paste. Anal Chim Acta 288(3):193–196

    Article  Google Scholar 

  50. Laurinavicius V, Razumiene J, Kurtinaitiene B, Lapenaite I, Bachmatova, I, Marcinkeviciene L, Meskys R, Ramanavicius A (2002) Bioelectrochemical application of some PQQ-dependent enzymes. Bioelectrochem 55(1–2):29–32

    Article  Google Scholar 

  51. Laurinavicius V, Razumiene J, Ramanavicius A, Ryabov A (2004) Wiring of PQQ-dehydrogenases. Biosens Bioelectron 20(6):1217–1222

    Article  Google Scholar 

  52. Lawrence NS, Deo RP, Wang J (2004) Biocatalytic carbon paste sensors based on a mediator pasting liquid. Anal Chem 76(13):3735–3739

    Article  Google Scholar 

  53. Levich V (1962) Physicochemical hydrodynamics. Prentice-Hall, London

    Google Scholar 

  54. Liang J, Li Y, Yang V (2000) Biomedical application of immobilized enzymes. J Pharm Sci 89(8):979–990

    Article  Google Scholar 

  55. Lide D (ed) (2008) Handbook of chemistry and physics, 88th edn. CRC Press, Boca Raton

    Google Scholar 

  56. Luckarift HR (2008) Silica-immobilized enzyme reactors. J Liq Chromatogr R T 31(11–12):1568–1592

    Article  Google Scholar 

  57. Manz A, Graber N, Widmer H (1990) Miniaturised total chemical analysis systems: a novel concept for chemical sensing. Sensor Actuat B-Chem 1(1–6):244–248

    Article  Google Scholar 

  58. Matuszewski W, Trojanowicz M (1988) Graphite paste-based enzymatic glucose electrode for flow-injection analysis. Analyst 113(5):735–738

    Article  Google Scholar 

  59. Mello LD, Kubota LT (2002) Review of the use of biosensors as analytical tools in the food and drink industries. Food Chem 77(2):237–256

    Article  Google Scholar 

  60. Miscoria S, Barrera G, Rivas G (2005) Enzymatic biosensor based on carbon paste electrodes modified with gold nanoparticles and polyphenol oxidase. Electroanal 17(17):1578–1582

    Article  Google Scholar 

  61. Mizutani F (1999) Application of enzyme-modified electrodes to biosensors. Bunseki Kagaku 48(9):809–822

    Article  Google Scholar 

  62. Mizutani F, Yabuki S, Okuda A, Katsura T (1991) Glucose-sensing electrode based on carbon paste containing ferrocene and polyethylene glycol-modified enzyme. Bull Chem Soc Jpn 64(9):2849–2851

    Article  Google Scholar 

  63. Moreira JE, Midkiff SP, Gupta M, Artigas PV, Snir M, Lawrence RD (2000) Java programming for high-performance numerical computing. IBM Syst J 39(1):21–56

    Article  Google Scholar 

  64. Mulchandani A, Rogers K (1998) Enzyme & microbial biosensors: techniques and protocols (methods in biotechnology). Humana Press, Totowa, New Jersey

    Book  Google Scholar 

  65. Nernst W (1904) Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen. Z Phys Chem 47(1):52–55

    Google Scholar 

  66. Nguyen HH, Lee SH, Lee UJ, Fermin CD, Kim M (2019) Immobilized enzymes in biosensor applications. Materials 12(1):121

    Article  Google Scholar 

  67. Pandey P, Kayastha A, Pandey V (1992) Amperometric enzyme sensor for glucose based on graphite paste-modified electrodes. Appl Bioch Biotech 33(2):139–144

    Article  Google Scholar 

  68. Popovtzer R, Neufeld T, Ron E, Rishpon J, Shacham-Diamand Y (2006) Electrochemical detection of biological reactions using a novel nano-bio-chip array. Sensor Actuat B-Chem 119(2):664–672

    Article  Google Scholar 

  69. Reyes DR, Iossifidis D, Auroux PA, Manz A (2002) Micro total analysis systems. 1. Introduction. theory, and technology. Anal Chem 74(12):2623–2636

    Article  Google Scholar 

  70. Rinas U, El-Enshasy H, Emmler M, Hille A, Hempel DC, Horn H (2005) Model-based prediction of substrate conversion and protein synthesis and excretion in recombinant Aspergillus niger biopellets. Chem Eng Sci 60(10):2729–2739

    Article  Google Scholar 

  71. Sakura S, Buck R (1992) Amperometric processes with glucose oxidase embedded in the electrode. Bioelect Bioenerg 28(3):387–400

    Article  Google Scholar 

  72. Samarskii A (2001) The theory of difference schemes. Marcel Dekker, New York-Basel

    Book  MATH  Google Scholar 

  73. Schachl K, Turkušić E, Komersová A, Bartoš M, Moderegger H, Švancara I, Alemu H, Vytřas K, Jimenez-Castro M, Kalcher K (2002) Amperometric determination of glucose with a carbon paste biosensor. Collect Czech Chem Commun 67(3):302–313

    Article  Google Scholar 

  74. Scheller FW, Schubert F (1992) Biosensors. Elsevier Science, Amsterdam

    Google Scholar 

  75. Schulmeister T (1990) Mathematical modelling of the dynamic behaviour of amperometric enzyme electrodes. Sel Electrode Rev 12(2):203–260

    Google Scholar 

  76. Soleymani L, Li F (2017) Mechanistic challenges and advantages of biosensor miniaturization into the nanoscale. ACS Sens 2(4):458–467

    Article  Google Scholar 

  77. Somasundrum M, Aoki K (2002) The steady-state current at microcylinder electrodes modified by enzymes immobilized in conducting or non-conducting material. J Electroanal Chem 530(1–2):40–46

    Article  Google Scholar 

  78. Song MJ, Yun DH, Jin JH, Min NK, Hong SI (2006) Comparison of effective working electrode areas on planar and porous silicon substrates for cholesterol biosensor. Jpn J Appl Phys 45(9A):7197–7202

    Article  Google Scholar 

  79. Suzuki H (2000) Advances in the microfabrication of electrochemical sensors and systems. Electroanal 12(9):703–715

    Article  Google Scholar 

  80. Suzuki H, Arakawa H, Karube I (2001) Fabrication of a sensing module using micromachined biosensors. Biosens Bioelectron 16(9–12):725–733

    Article  Google Scholar 

  81. Talaei S, van der Wal PD, Ahmed S, de Rooij MLNF (2015) Enzyme SU-8 microreactors: simple tools for cell-culture monitoring. Microfluid Nanofluid 19(2):351–361

    Article  Google Scholar 

  82. Urban P, Goodall D, Bruce N (2001) Biosensor microsystems. Sens Update 8(1):189–214

    Article  Google Scholar 

  83. Urban P, Goodall D, Bruce N (2006) Enzymatic microreactors in chemical analysis and kinetic studies. Biotechnol Adv 24(1):42–57

    Article  Google Scholar 

  84. Vashist SK, Zheng D, Al-Rubeaan K, Luong JH, Sheu FS (2011) Technology behind commercial devices for blood glucose monitoring in diabetes management: a review. Anal Chim Acta 703(2):124–136

    Article  Google Scholar 

  85. Velkovsky M, Snider R, Cliffel DE, Wikswo JP (2011) Modeling the measurements of cellular fluxes in microbioreactor devices using thin enzyme electrodes. J Math Chem 49(1):251–275

    Article  MathSciNet  MATH  Google Scholar 

  86. Vojinovic V, Esteves F, Cabral J, Fonseca L (2006) Bienzymatic analytical microreactors for glucose, lactate, ethanol, galactose and l-amino acid monitoring in cell culture media. Anal Chim Acta 565(2):240–249

    Article  Google Scholar 

  87. Wanekaya A, Chen W, Mulchandani A (2008) Recent biosensing developments in environmental security. J Environ Monitor 10(6):703–712

    Article  Google Scholar 

  88. Wang J (2000) Analytical electrochemistry, 2nd edn. Wiley, New-York

    Book  Google Scholar 

  89. Wang J (2001) Glucose biosensors: 40 years of advances and challenges. Electroanal 13(12):983–988

    Article  Google Scholar 

  90. Wang J, Liu J, Cepra G (1997) Thermal stabilization of enzymes immobilized within carbon paste electrodes. Anal Chem 69(15):3124–3127

    Article  Google Scholar 

  91. Weibel M, Bright H (1971) The glucose oxidase mechanism. J Biol Chem 246:2734–2744

    Article  Google Scholar 

  92. Whitaker S (1999) The method of volume averaging. Theory and Applications of Transport in Porous Media. Kluwer, Boston

    Google Scholar 

  93. Wu B, Zhang G, Zhang Y, Shuang S, Choi M (2005) Measurement of glucose concentrations in human plasma using a glucose biosensor. Anal Biochem 340(1):181–183

    Article  Google Scholar 

  94. Xi Y, Bazant Z (1999) Modeling chloride penetration in saturated concrete. J Mater Civil Eng 11(1):58–65

    Article  Google Scholar 

  95. Zhang Q, Xu J, Chen H (2006) Glucose microfluidic biosensors based on immobilizing glucose oxidase in poly(dimethylsiloxane) electrophoretic microchips. J Chromatogr A 1135(1):122–126

    Article  Google Scholar 

  96. Zhu Z, Zhang J, Zhu J (2005) An overview of Si-based biosensors. Sensor Lett 3(2):71–88

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics & Informatics, Institute of Computer Science, Vilnius University, Vilnius, Lithuania

    Romas Baronas & Feliksas Ivanauskas

  2. Life Sciences Center, Vilnius University, Vilnius, Lithuania

    Juozas Kulys

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  1. Romas Baronas
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  2. Feliksas Ivanauskas
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  3. Juozas Kulys
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Baronas, R., Ivanauskas, F., Kulys, J. (2021). Biosensors Based on Microreactors. In: Mathematical Modeling of Biosensors. Springer Series on Chemical Sensors and Biosensors, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-65505-1_10

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