MATHEMATICAL MODEL OF BIOSENSOR WITH MULTILAYER CHARGED MEMBRANES
N.Rossokhata, V.Rossokhaty
Kiev National University,
P.O.Box 493, 253222 Kiev - 222,
Ukraine,
E-mail: nross@nv.kiev.ua
Biosensors combining the basic principals of microelectronics,
chemistry and biotechnology attract considerable attention in such
fields as medicine, environmental monitoring, pharmaceutics and food
quality control. In this work we develop a mathematical model of
enzyme potentiometric biosensor for glucose determination with charged
multilayer membrane. Biosensor consists of two parts: solid-state
transducer linearly transforming the concentration of protons near
membrane-transducer interface into electrical signal and 3-layer
membrane, with each layer involving uniformly distributed both enzyme
and charged encapsulated molecules of given concentrations with
various combinations. Test solution is considered to be infinite source
of five types of species, namely, glucose, oxygen, protons, buffer and
its conjugate base.
Mathematically the model is reduced to a transmission problem with
two interface points for a system of five one-dimensional nonlinear
parabolic partial differential equations for concentrations and
Poisson equation for charge. In order to find the numerical solution,
we use the techniques known from semiconductor modeling literature and
receive an explicit difference scheme. Because of concentration
profiles change most rapidly at the beginning of the intervals
corresponding to the enzyme layer(s), we use irregular space grid,
which nodes are chosen automatically in
dependence on physical data of the problem. To find charge and
concentration distributions, we get uncoupled systems of linear
algebraic equations with threediagonal matrix with diagonal prevalence.
To solve them, we use effective iterative algorithms.
To carry out a numerical experiment, the developed model of the
biosensor was adopted to the experimental multilayer membrane system
with the inner layer being enzyme one and the outer layer containing
the uniformly distributed negative charge. The results of computer
simulation give opportunity to optimize performances of enzyme
potentiometric biosensors by varying combinations of physical and
biochemical parameters of the membrane layers.