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Multi-Layer Models of Biosensors

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

Abstract

There are various reasons for applying a multi-layer approach to the modeling of biosensors. Multi-layer models are usually used in the following cases [35, 119, 235, 236]:

  • The bulk solution is assumed to be slightly-stirred or non-stirred. This assumption leads to two-compartment models [51, 60, 102, 120, 286].

  • The enzyme layer is covered with an inert outer membrane [234]. The membrane stabilizes the enzyme layer and creates a diffusion limitation to the substrate, i.e. lowers the substrate concentration in the enzymatic layer and thereby prolongs the calibration curve of the biosensor [152, 166, 229, 238, 258].

  • The electrode is covered with a selective membrane [236]. Selective membranes are usually impermeable to certain molecules and permeable to a desired substance. This arrangement can notably increase the biosensor selectivity. The selective layer can also protect the metal interface of the electrode [16, 47, 91, 157].

  • In multienzyme systems, enzymes are often immobilized separately in different active layers packed in a sandwich-like multi-layer arrangement [13, 14, 15, 113, 184, 242]. This approach seems to be a rather fast and cheap method to design biosensors for different purposes.

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References

  1. Amatore C, Szunerits S, Thouin L, Warkocz J-S (2001) The real meaning of Nernst’s steady diffusion layer concept under non-forced hydrodynamic conditions. A simple model based on Levich’s seminal view of convection. J Electroanal Chem 500:62

    CAS  Google Scholar 

  2. 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 597:69

    Google Scholar 

  3. Amine A, Kauffmann JM, Patriarche GJ (1991) Long-term operational stability of a mixed glucose oxidase-redox mediator-carbon paste electrode. Anal Lett 24:1293

    CAS  Google Scholar 

  4. Antiochia R, Lavagnini I, Magno F (2004) Amperometric mediated carbon nanotube paste biosensor for fructose determination. Anal Let 37:1657

    CAS  Google Scholar 

  5. Aris R (1975) The mathematical theory of diffusion and reaction in permeable catalysts. The theory of the steady state. Clarendon, Oxford

    Google Scholar 

  6. Bacha S, Bergel A, Comtat M (1995) Transient response of multilayer electroenzymic biosensors. Anal Chem 67:1669

    CAS  Google Scholar 

  7. Baeumner AJ, Jones C, Wong CY, Price A (2004) A generic sandwich-type biosensor with nanomolar detection limits. Anal Bioanal Chem 378:1587

    CAS  Google Scholar 

  8. Baldini F, Chester AN, Homola J, Martellucci S (2006) Optical chemical sensors. Springer, Amsterdam

    Google Scholar 

  9. Bakhvalov NS, Panasenko GP (1989) Homogenization: averaging processes in periodic media. Kluwer, Dordrecht

    Google Scholar 

  10. Baronas V, Ivanauskas F, Kulys J (1999) Modeling a biosensor based on the heterogeneous microreactor. J Math Chem 25:245

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  12. Baronas R, Ivanauskas F, Kulys J (2003) The influence of the enzyme membrane thickness on the response of amperometric biosensors. Sensors 3:248

    CAS  Google Scholar 

  13. Baronas R, Ivanauskas F, Kulys J (2004) The effect of diffusion limitations on the response of amperometric biosensors with substrate cyclic conversion. J Math Chem 35:199

    CAS  Google Scholar 

  14. Baronas R, Kulys J, Ivanauskas F (2006) Computational modeling of biosensors with perforated and selective membranes. J Math Chem 39:345

    CAS  Google Scholar 

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

    Google Scholar 

  16. Baronas R, Gaidamauskaite E, Kulys J (2007) Modeling a peroxidase-based optical biosensor. Sensors 7:2723

    CAS  Google Scholar 

  17. Baronas R, Kulys J (2008) Modeling amperometric biosensors based on chemically modified electrodes. Sensors 8:4845

    Google Scholar 

  18. Bartlett PN, Pratt KFE (1995) Theoretical treatment of diffusion and kinetics in amperometric immobilized enzyme electrodes Part I: Redox mediator entrapped within the film. J Electroanal Chem 397:61

    Google Scholar 

  19. Bergel A, Comtat M (1984) Theoretical evaluation of transient responses of an amperometric enzyme electrode. Anal Chem 56:2904

    CAS  Google Scholar 

  20. Bindra DS, Zhang Y, Wilson GS et al (1991) Design and in vitro studies of a needle-type glucose sensor for subcutaneous monitoring. Anal Chem 63:1692

    CAS  Google Scholar 

  21. Blaedel WJ, Kissel TR, Boguslaski RC (1972) Kinetic behavior of enzymes immobilized in artificial membranes. Anal Chem 44:2030

    CAS  Google Scholar 

  22. Bosch ME, Sánchez AJR, Rojas FS, Ojeda CB (2007) Recent development in optical fiber biosensors. Sensors 7:797

    CAS  Google Scholar 

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

    Google Scholar 

  24. Cenas NK, Kulys JJ (1981) Biocatalytic oxidation of glucose on the conductive charge transfer complexes. Bioelectrochem Bioenerg 8:103

    CAS  Google Scholar 

  25. Corcuera JRD, Cavalieri R, Powers J, Tang J (2004) Amperometric enzyme biosensor optimization using mathematical modeling. In: Proceedings of the 2004 ASAE/Csae Annual International Meeting, Paper No. 047030 American Society of Agricultural Engineers, Ottawa

    Google Scholar 

  26. Crank J (1975) The mathematics of diffusion, 2nd edn. Clarendon, Oxford

    Google Scholar 

  27. Forrow NJ, Bayliff SW (2005) A commercial whole blood glucose biosensor with a low sensitivity to hematocrit based on an impregnated porous carbon electrode. Biosens Bioelectron 21:3581

    Google Scholar 

  28. Fraser DM (ed) (1997) Biosensors in the body: continuous in vivo monitoring. Wiley, Chichester

    Google Scholar 

  29. Ivanauskas F, Baronas R (2008) Modeling an amperometric biosensor acting in a flowing liquid. Int J Numer Meth Fluids 56:1313

    Google Scholar 

  30. Kulys J, Samalius AS, Svirmickas G-JS (1980) Electron exchange between the enzyme active center and organic metal. FEBS Lett 114:7

    CAS  Google Scholar 

  31. Kulys J, Razumas V (1986) Bioamperometry. Mokslas, Vilnius (in Lithuanian)

    Google Scholar 

  32. Laurinavicius VA, Kulys JJ, Gureviciene VV, Simonavicius KJ (1989) Flow through and cateter biosensors with an extended concentration range. Biomed Biochem Acta 48:905

    CAS  Google Scholar 

  33. Leatherbarrow RJ, Edwards PR (1999) Analysis of molecular recognition using optical biosensors. Curr Opin Chem Biol 3:544

    CAS  Google Scholar 

  34. Ligler FS, Taitt CR (2002) Optical biosensors: present and future Elsevier, Amsterdam

    Google Scholar 

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

    CAS  Google Scholar 

  36. Merino S, Grinfeld M, McKee S (1998) A degenerate reaction diffusion system modeling an optical biosensor. Z Angew Math Phys 49:46

    CAS  Google Scholar 

  37. Özisik MN (1980) Heat conduction. Wiley, New York

    Google Scholar 

  38. Ojeda CB, Rojas FS (2006) Recent development in optical chemical sensors coupling with flow injection analysis. Sensors 6:1245

    CAS  Google Scholar 

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

    Google Scholar 

  40. Scheller F, Schubert F (1992) Biosensors. Elsevier, Amsterdam

    Google Scholar 

  41. Schulmeister T (1987) Mathematical treatment of concentration profiles and anodic current of amperometric enzyme electrodes with chemically amplified response. Anal Chim Acta 201:305

    CAS  Google Scholar 

  42. Schulmeister T (1990) Mathematical modeling of the dynamic behavior of amperometric enzyme electrodes. Selective Electrode Rev 12:203

    Google Scholar 

  43. Schulmeister T, Pfeiffer D (1993) Mathematical modelling of amperometric enzyme electrodes with perforated membranes. Biosens Bioelectron 8:75

    CAS  Google Scholar 

  44. Vo-Dinh T (2003) Biomedical photonics handbook. CRC Press, New York

    Google Scholar 

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

    Google Scholar 

  46. Wollenberger U, Lisdat F, Scheller FW (1997) Frontiers in biosensorics 2. Practical applications. Birkhauser Verlag, Basel

    Google Scholar 

  47. Zhao W, Xu JJ, Chen HY (2006) Electrochemical biosensors based on layer-by-layer assemblies. Electroanal 18:1737

    CAS  Google Scholar 

  48. Ivanauskas F, Baronas R (2008) Modeling an amperometric biosensor acting in a flowing liquid. Int J Numer Meth Fluids 56:1313

    Google Scholar 

  49. Hameka HF, Rechnitz GA (1983) Theory of the biocatalytic membrane electrode. J Phys Chem 87:1235

    CAS  Google Scholar 

  50. Jochum P, Kowalski BR (1982) A coupled two-compartment model for immobilized enzyme electrodes. Anal Chim Acta 144:25

    CAS  Google Scholar 

  51. Ylilammi M, Lehtinen L (1988) Numerical analysis of a theoretical one-dimensional amperometric enzyme sensor. Med Biol Eng Comput 26:81

    CAS  Google Scholar 

  52. Blaedel WJ, Kissel TR, Boguslaski RC (1972) Kinetic behavior of enzymes immobilized in artificial membranes. Anal Chem 44:2030

    CAS  Google Scholar 

  53. Cambiaso A, Delfino L, Grattarola M et al (1996) Modeling and simulation of a diffusion limited glucose biosensor. Sensor Actuat B-Chem 33:203

    Google Scholar 

  54. Laurinavicius VA, Kulys JJ, Gureviciene VV, Simonavicius KJ (1989) Flow through and cateter biosensors with an extended concentration range. Biomed Biochem Acta 48:905

    CAS  Google Scholar 

  55. Lyons MEG, Murphy J, Rebouillat S (2000) Theoretical analysis of time dependent diffusion, reaction and electromigration in membranes. J Solid State Electrochem 4:458

    CAS  Google Scholar 

  56. Scheller F, Schubert F (1992) Biosensors. Elsevier, Amsterdam

    Google Scholar 

  57. Senda M, Ikeda T, Miki K, Hiasa H (1886) Amperometric biosensors based on a biocatalyst electrode with entrapped mediator. Anal Sci 2:501

    Google Scholar 

  58. Turner APF, Karube I, Wilson GS (1987) Biosensors: fundamentals and applications. Oxford University Press, Oxford

    Google Scholar 

  59. Schulmeister T, Pfeiffer D (1993) Mathematical modelling of amperometric enzyme electrodes with perforated membranes. Biosens Bioelectron 8:75

    CAS  Google Scholar 

  60. Frew JE, Hill HO (1987) Electrochemical biosensors. Anal Chem 59:933A

    CAS  Google Scholar 

  61. Lemke K (1988) Mathematical simulation of an amperometric enzyme-substrate electrode with a pO2 basic sensor. Part 2. Mathematical simulation of the glucose oxidase glucose electrode. Med Biol Eng Comput 26:533

    Google Scholar 

  62. Iliev I, Atanasov P, Gamburzev S et al (1992) Transient response of electrochemical biosensors with asymmetrical sandwich membranes. Sensor Actuat B-Chem 8:65

    Google Scholar 

  63. Meyerhoff ME, Duan CM, Meusel M (1995) Novel nonseparation sandwich-type electrochemical enzyme immunoassay system for detecting marker proteins in undiluted blood. Clin Chem 41:1378

    CAS  Google Scholar 

  64. Sorochinskii VV, Kurganov BI (1996) Amperometric biosensors with a laminated distribution of enzymes in their coating. Steady state kinetics. Biosens Bioelectron 11:45

    CAS  Google Scholar 

  65. Schulmeister T (1987) Mathematical treatment of concentration profiles and anodic current of amperometric enzyme electrodes with chemically amplified response. Anal Chim Acta 201:305

    CAS  Google Scholar 

  66. Schulmeister T (1990) Mathematical modeling of the dynamic behavior of amperometric enzyme electrodes. Selective Electrode Rev 12:203

    Google Scholar 

  67. Ha J, Engler CR, Lee SJ (2008) Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-Alginate gel beads. Biotechnol Bioeng 100:698

    CAS  Google Scholar 

  68. Hassan MM, Atiqullah M, Beg SA, Chowdhury MHM (1995) Analysis of non-isothermal tubular reactor packed with immobilized enzyme systems. Chem Eng J Biochem Eng J 58:275

    CAS  Google Scholar 

  69. Lyons MEG, Bannon T, Hinds G, Rebouillat S (1998) Reaction/diffusion with Michaelis-Menten kinetics in electroactive polymer films. Part 2. The transient amperometric response. Analyst 123:1947

    Google Scholar 

  70. Yang HM (2000) Mathematical model for liquid-liquid phase-transfer catalysis. Chem Eng Comm 179:117

    CAS  Google Scholar 

  71. Hart JP, Crew A, Crouch E et al (2004) Some recent designs and developments of screen-printed carbon electrochemical sensors/biosensors for biomedical, environmental, and industrial analyses. Anal Lett 37:789

    CAS  Google Scholar 

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

    Google Scholar 

  73. Jobst G, Moser I, Urban G (1996) Numerical simulation of multi-layered enzymatic sensors. Biosens Bioelectron 11:111

    CAS  Google Scholar 

  74. Kernevez JP (1980) Enzyme mathematics. Studies in mathematics and its applications. Elsevier, Amsterdam

    Google Scholar 

  75. Knopf GK, Bassi AS (2007) Smart biosensor technology. CRC Press, New York

    Google Scholar 

  76. Kulys J, Samalius AS, Svirmickas G-JS (1980) Electron exchange between the enzyme active center and organic metal. FEBS Lett 114:7

    CAS  Google Scholar 

  77. Kulys J, Razumas V (1986) Bioamperometry. Mokslas, Vilnius (in Lithuanian)

    Google Scholar 

  78. Kulys J, Tetianec L (2005) Synergistic substrates determination with biosensors. Biosens Bioelectron 21:152

    CAS  Google Scholar 

  79. Lyons MEG (2001) Mediated electron transfer at redox active monolayers. Sensors 1:215

    CAS  Google Scholar 

  80. Naujikas R, Malinauskas A, Ivanauskas F (2007) Modeling of electrocatalytic processes at conducting polymer modified electrodes. J Math Chem 42:1069

    CAS  Google Scholar 

  81. Yokoyama K, Koide S, Kayanuma Y (2002) Cyclic voltammetric simulation of electrochemically mediated enzyme reaction and elucidation of biosensor behaviors. Anal Bioanal Chem 372:248

    CAS  Google Scholar 

  82. Leatherbarrow RJ, Edwards PR (1999) Analysis of molecular recognition using optical biosensors. Curr Opin Chem Biol 3:544

    CAS  Google Scholar 

  83. Passaro VMN, Dell’olio F, Casamassima B, Leonardis FD (2007) Guided-wave optical biosensors. Sensors 7:508

    CAS  Google Scholar 

  84. Sanz V, de Marcos S, Galbán J (2007) Direct glucose determination in blood using a reagentless optical biosensor. Biosens Bioelectron 22:2876

    CAS  Google Scholar 

  85. Stefano LD, Arcari P, Lamberti A et al (2007) DNA optical detection based on porous silicon technology: from biosensors to biochips. Sensors 7:214

    Google Scholar 

  86. Wu B, Wang Y, Li J, Song Z, Huang J et al (2006) An optical biosensor for kinetic analysis of soluble interleukin-1 receptor I binding to immobilized interleukin-1α.Talanta 70:485

    Google Scholar 

  87. Corcuera JRD, Cavalieri R, Powers J, Tang J (2004) Amperometric enzyme biosensor optimization using mathematical modeling. In: Proceedings of the 2004 ASAE/Csae Annual International Meeting, Paper No. 047030 American Society of Agricultural Engineers, Ottawa

    Google Scholar 

  88. Ferreira LS, Souza MBD, Trierweiler JO et al (2003) Aspects concerning the use of biosensors for process control: experimental and simulation investigations.Comp Chem Eng 27:1165

    Google Scholar 

  89. Stamatin I, Berlic C, Vaseashta A (2006) On the computer-aided modeling of analyte-receptor interactions for an efficient sensor design. Thin Solid Films 495:312

    CAS  Google Scholar 

  90. Cenas NK, Kulys JJ (1981) Biocatalytic oxidation of glucose on the conductive charge transfer complexes. Bioelectrochem Bioenerg 8:103

    CAS  Google Scholar 

  91. Sapelnikova S, Dock E, Solna R et al (2003) Screen-printed multienzyme arrays for use in amperometric batch and flow systems. Anal Bioanal Chem 376:1098

    CAS  Google Scholar 

  92. Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, London

    Google Scholar 

  93. Ligler FS, Taitt CR (2002) Optical biosensors: present and future Elsevier, Amsterdam

    Google Scholar 

  94. Wollenberger U, Lisdat F, Scheller FW (1997) Frontiers in biosensorics 2. Practical applications. Birkhauser Verlag, Basel

    Google Scholar 

  95. Ojeda CB, Rojas FS (2006) Recent development in optical chemical sensors coupling with flow injection analysis. Sensors 6:1245

    CAS  Google Scholar 

  96. Lyons MEG, Greer JC, Fitzgerald CA et al (1996) Reaction/diffusion with Michaelis-Menten kinetics in electroactive polymer films. Part 1. The steady-state amperometric response. Analyst 121:715

    Google Scholar 

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

    CAS  Google Scholar 

  98. Mizutani F (1999) Application of enzyme-modified electrodes to biosensors. Bunseki Kagaku 48:809

    CAS  Google Scholar 

  99. Murray RW (1980) Chemically modified electrodes. Accts Chem Res 13:135

    CAS  Google Scholar 

  100. Svancara I, Vytras K, Barek J, Zima J (2001) Carbon paste electrodes in modern electroanalysis. Crit Rev Anal Chem 31:311

    CAS  Google Scholar 

  101. Merino S, Grinfeld M, McKee S (1998) A degenerate reaction diffusion system modeling an optical biosensor. Z Angew Math Phys 49:46

    CAS  Google Scholar 

  102. Rickus JL (2005) Impact of coenzyme regeneration on the performance of an enzyme based optical biosensor: a computational study. Biosens Bioelectron 21:965

    CAS  Google Scholar 

  103. Mullen WH, Keedy FH, Churchouse SJ, Vadgama PM (1986) Glucose enzyme electrode with extended linearity: application to undiluted blood measurements. Anal Chim Acta 183:59

    CAS  Google Scholar 

  104. Tang LX, Koochaki ZB, Vadgama PM (1990) Composite liquid membrane for enzyme electrode construction. Anal Chim Acta 232:357

    CAS  Google Scholar 

  105. Fraser DM (ed) (1997) Biosensors in the body: continuous in vivo monitoring. Wiley, Chichester

    Google Scholar 

  106. Nernst W (1904) Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen. Z Phys Chem 47:52

    CAS  Google Scholar 

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

    Google Scholar 

  108. Özisik MN (1980) Heat conduction. Wiley, New York

    Google Scholar 

  109. Pfeiffer D, Scheller FW, Setz K, Schubert F (1993) Amperometric enzyme electrodes for lactate and glucose determinations in highly diluted and undiluted media. Anal Chim Acta 281:489

    CAS  Google Scholar 

  110. Scheller FW, Pfeiffer D (1978) Enzyme electrodes. Z Chem 18:50

    CAS  Google Scholar 

  111. Renedo OD, Alonso-Lomillo MA, Martinez MJA (2007) Recent developments in the field of screen-printed electrodes and their related applications. Talanta 73:202

    CAS  Google Scholar 

  112. Rong ZM, Cheema U, Vadgama P (2006) Needle enzyme electrode based glucose diffusive transport measurement in a collagen gel and validation of a simulation model. Analyst 131:816

    CAS  Google Scholar 

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

    Google Scholar 

  114. Schöning MJ (2005) “Playing around” with field-effect sensors on the basis of EIS structures, LAPS and ISFETs. Sensors 5:126

    Google Scholar 

  115. Treloar PH, Christie IM, Vadgama PM (1995) Engineering the right membranes for electrodes at the biological interface; solvent cast and electropolymerised. Biosens Bioelectron 10:195

    CAS  Google Scholar 

  116. Takoh K, Ishibashi T, Matsue T, Nishizawa M (2005) Localized chemical stimulation of cellular micropatterns using a porous membrane-based culture substrate. Sensor Actuat B-Chem 108:683

    Google Scholar 

  117. Tudorache M, Bala C (2007) Biosensors based on screen-printing technology, and their applications in environmental and food analysis. Anal Bioanal Chem 388:565

    CAS  Google Scholar 

  118. Vo-Dinh T (2003) Biomedical photonics handbook. CRC Press, New York

    Google Scholar 

  119. Whitaker S (1999) The method of volume averaging. Kluwer, Boston

    Google Scholar 

  120. Wu X, Detzel CJ, Van Wie BJ, Haarsma SJ, Kidwel DA (2004) Model-based optimization of a conductive matrix enzyme electrode. Biotechnol Bioeng 88:135

    Google Scholar 

  121. Zhao W, Xu JJ, Chen HY (2006) Electrochemical biosensors based on layer-by-layer assemblies. Electroanal 18:1737

    CAS  Google Scholar 

  122. Bindra DS, Zhang Y, Wilson GS et al (1991) Design and in vitro studies of a needle-type glucose sensor for subcutaneous monitoring. Anal Chem 63:1692

    CAS  Google Scholar 

  123. Bosch ME, Sánchez AJR, Rojas FS, Ojeda CB (2007) Recent development in optical fiber biosensors. Sensors 7:797

    CAS  Google Scholar 

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

    Google Scholar 

  125. Carr PW, Bowers LD (1980) Immobilized enzymes in analytical and clinical chemistry. Wiley, New York

    Google Scholar 

  126. Chen LC, Tseng KS, Ho KC (2006) General kinetic model for amperometric sensors based on Prussian blue mediator and its analogs: Application to cysteine detection. Electroanal 18:1313

    CAS  Google Scholar 

  127. Choi MMF (2004) Progress in enzyme-based biosensors using optical transducers. Microchimica Acta 148:107

    CAS  Google Scholar 

  128. Crank J (1975) The mathematics of diffusion, 2nd edn. Clarendon, Oxford

    Google Scholar 

  129. Dohnal M (1992) Qualitative partial differential equations and their realistic applications. Comput Ind 20:209

    Google Scholar 

  130. Forrow NJ, Bayliff SW (2005) A commercial whole blood glucose biosensor with a low sensitivity to hematocrit based on an impregnated porous carbon electrode. Biosens Bioelectron 21:3581

    Google Scholar 

  131. Gaidamauskaite E, Baronas R Modeling a peroxide-based fluorescent biosensor. In: Louca LS, Chrysanthou Y, Oplatkova Z, Al-Begain K (eds) Proceedings, 22nd European Conference on modeling and Simulation ECMS 2008, 3–6 June 2008, Nicosia, Cyprus. EMCS 2008, Nicosia 2008

    Google Scholar 

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Baronas, R., Ivanauskas, F., Kulys, J. (2010). Multi-Layer Models of Biosensors. In: Mathematical Modeling of Biosensors. Springer Series on Chemical Sensors and Biosensors, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3243-0_8

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