Mathematical Modeling of Biosensors: An Introduction for Chemists and Mathematicians (Springer Series on Chemical Sensors and Biosensors Book 9)

Annotation This book presents biosensor development and modeling from both a chemical and a mathematical point of view. It contains unique modeling methods for catalytical (amperometric, potentiometer and optical) biosensors. It examines processes that occur in the sensors' layers and at their interface, and it provides analytical and numerical methods to solve enzymatic kinetic and diffusion equations. The action of single enzyme as well as polyenzyme biosensors is studied, and the modeling of biosensors that contain perforated membranes and multipart mass transport profiles is critically investigated. Furthermore, it is fully described how signals can be biochemically amplified, how cascades of enzymatic substrate conversion are triggered, and how signals are processed via a chemometric approach and artificial neuronal networks. The results of digital modeling are compared with both proximal analytical solutions and experimental data 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. Front Matter....Pages i-xix Front Matter....Pages 1-1 Biosensor Action....Pages 3-8 Modeling Biosensors at Steady State and Internal Diffusion Limitations....Pages 9-20 Modeling Biosensors at Steady State and External Diffusion Limitations....Pages 21-26 Modeling Biosensors Utilizing Microbial Cells....Pages 27-31 Modeling Nonstationary State of Biosensors....Pages 33-39 Front Matter....Pages 42-42 Mono-Layer Mono-Enzyme Models of Biosensors....Pages 43-111 One-Layer Multi-Enzyme Models of Biosensors....Pages 113-137 Multi-Layer Models of Biosensors....Pages 139-202 Modeling Biosensors of Complex Geometry....Pages 203-246 Front Matter....Pages 248-248 The Difference Schemes for the Diffusion Equation....Pages 249-291 The Difference Schemes for the Reaction–Diffusion Equations....Pages 293-315 Back Matter....Pages 317-334 Part I : Analytical modeling of biosensors Biosensor action Modeling biosensors at steady state and internal diffusion limitations Modeling biosensors at steady state and external diffusion limitations Modeling biosensors utilizing microbial cells Modeling nonstationary state of biosensors Part II : Numerical modeling of biosensors Mono-layer mono-enzyme models of biosensors One-layer multi-enzyme models of biosensors Multi layer models of biosensors Modeling biosensors of complex geometry Part III : Numerical methods for reaction-diffusion equations The difference schemes for the diffusion equation The difference schemes for the reaction-diffusion equations.