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.