Modeling Biosensors Utilizing Microbial Cells

Abstract

The biocatalytical system of microbial cells can be used as biocatalyzers for the biosensor preparation [127, 130]. They can show very high specificity for some substrates. For example, yeast cells Hansenula anomala grown in lactate reach breeding media induce cytochrome b ₂, and shows high specificity to L-lactate [125]. The scheme of substrates distribution in a microbial biosensor is depicted in Fig. 1.

The peculiarity of the modeling of the microbial biosensors is a slow substrate and product transport through the microbial cell wall. If the substrate transport is slower than the diffusion through the bulk solution and the semipermeable membrane the substrate and the product concentration change in the cell can be written:

$$\begin{array}{rcl} & & \frac{\mathrm{d}{S}_{c}} {\mathrm{d}t} = k({S}_{0} - {S}_{c}) - {V }_{c}\,, \\ & & \frac{\mathrm{d}{P}_{c}} {\mathrm{d}t} = {V }_{c} - k'{P}_{c}\,, \end{array}$$

(1)

where S _c and P _c are the concentrations of the substrate and the product in the cell, respectively, k and k′ are constants of substrate transport into the cell and the product transport from the cell, respectively, and V _c is the rate of the enzymatic process in the cell. The constants k and k′ are related to permeability (h) of the cell wall, that can be expressed as

$$\begin{array}{rcl} & & k = {h}_{s}/l\,, \\ & & k' = {h}_{p}{\mathit{sur}}_{c}/{\mathit{vol}}_{c}\end{array}$$

(2)

where sur _c and vol _c are the surface and the volume of the microbial cell, respectively.