In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a
whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a
miniaturized electrochemical biosensor system was described using the equations for specific enzymatic
reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured
data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this
reason an analytical solution is demanded. The object of the present work is to provide such analytical
solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using
computer algebra software, specifically Maple. The method of solution is the Laplace transform, with
Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the
effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will
be very useful to predict further current variations in similar systems with different geometries, materials and
biological components. Beside of this the analytical solution that we provide is very useful to investigate the
relationship between different chamber parameters such as cell radius and height; and electrode radius.
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