Mathematical Modeling of Biosensors: An Introduction for Chemists and Mathematicians
Springer Science & Business Media, Nov 12, 2009 - Technology & Engineering - 334 pages
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.
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ˇ ˇ ˇ ˇ ˇ xD0 amperometric biosensor ampliﬁcation approximation biocatalytical biosen biosensor acting biosensor action biosensor based biosensor current biosensor operation biosensor response biosensor sensitivity boundary conditions boundary-value problem buffer solution bulk solution calculated concentration proﬁles corresponding curves decrease deﬁned density dependence difference equation diffusion coefﬁcients diffusion layer diffusion module dimensionless electrode surface enzymatic rate Vmax enzyme activity enzyme kinetics enzyme layer external diffusion layer Faraday constant ﬁnite difference ﬁrst function GCCE GCEC glucose glucose oxidase grid hydrogen peroxide increase initial conditions kinetics mass transport mathematical model maximal enzymatic rate mediator Michaelis constant microreactors Modeling of Biosensors numerical simulation numerical solution parameters perforated membrane porous membrane reaction product S0 KM Sensors Springer Science+Business Media stationary current steady state biosensor steady state current substrate concentration S0 substrate inhibition thickness ı transducer transport by diffusion versus zero