Mathematical Modeling of Biosensors

1. Front Matter

   Pages i-xix

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2. Analytical Modeling of Biosensors

   1. Front Matter

      Pages 1-1

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   2. Biosensor Action

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 3-8

   3. Modeling Biosensors at Steady State and Internal Diffusion Limitations

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 9-20

   4. Modeling Biosensors at Steady State and External Diffusion Limitations

      • Romas Baronas, Feliksas Ivanauskas, Juozas Kulys

      Pages 21-26

   5. Modeling Biosensors Utilizing Microbial Cells

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 27-31

   6. Modeling Nonstationary State of Biosensors

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 33-39

3. Numerical Modeling of Biosensors

   1. Front Matter

      Pages 42-42

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   2. Mono-Layer Mono-Enzyme Models of Biosensors

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 43-111

   3. One-Layer Multi-Enzyme Models of Biosensors

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 113-137

   4. Multi-Layer Models of Biosensors

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 139-202

   5. Modeling Biosensors of Complex Geometry

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 203-246

4. Numerical Methods for Reaction-Diffusion Equations

   1. Front Matter

      Pages 248-248

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   2. The Difference Schemes for the Diffusion Equation

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 249-291

   3. The Difference Schemes for the Reaction–Diffusion Equations

      • Romas Baronas, Ivanauskas Feliksas, Juozas Kulys

      Pages 293-315

5. Back Matter

   Pages 317-334

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Biosensors are analytical devices in which speci?c recognition of the chemical substances is performed by biological material. The biological material that serves as recognition element is used in combination with a transducer. The transducer transforms concentration of substrate or product to electrical signal that is amp- ?ed and further processed. The biosensors may utilize enzymes, antibodies, nucleic acids, organelles, plant and animal tissue, whole organism or organs. Biosensors containing biological catalysts (enzymes) are called catalytical biosensors. These type of biosensors are the most abundant, and they found the largest application in medicine, ecology, and environmental monitoring. The action of catalytical biosensors is associated with substrate diffusion into biocatalytical membrane and it conversion to a product. The modeling of bios- sors involves solving the diffusion equations for substrate and product with a term containing a rate of biocatalytical transformation of substrate. The complications of modeling arise due to solving of partially differential equations with non-linear biocatalytical term and with complex boundary and initial conditions. The book starts with the modeling biosensors by analytical solution of partial differential equations. Historically this method was used to describe fundamental features of biosensors action though it is limited by substrate concentration, and is applicable for simple biocatalytical processes. Using this method the action of biosensors was analyzed at critical concentrations of substrate and enzyme activity.

• Biochemical A
• Biosensor
• Biosensors
• Catalytical Biosensors
• Diffusion Equation
• Digital Modeling
• Enzymatic Kinetic Equation
• Enzyme
• Fractal Kinetics
• Mathematical Model
• Modeling
• Numerical Method
• cells
• enzymes
• mathematical modeling

• Dept. Mathematics & Informatics, Vilnius University, Vilnius, Lithuania

  Romas Baronas, Feliksas Ivanauskas

• Fac. Fundamental Sciences, Vilnius Gediminas Technical University, Vilnius, Lithuania

  Juozas Kulys

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