The change of the species concentrations in time is given by non-linear ordinary differential equations (ODEs), most of which follow Hill kinetics. The parameters we used in the model are derived from literature.

Mine Cells

Equation system 1: ODE for Mine Cells.

The Mine Cells lead to the synthesis the signalling molecule, by constitutive expression of luxI gene. To reveal the nature of the cells, a coloured-substrate reaction is triggered upon addition of 5-Bromo-4-chloro-3-indoxyl-N-acetyl-beta-D-glucosaminide; given that the glycoside hydrolase NagZ is expressed constitutively.

The ODEs for the states involved in the sender module are given below:

Biosensors

Equation system 1: ODE for Mine Cells.

Our Biosensor cells are engineered to respond differently to high and medium concentrations of AHL. This cells are capable of discriminate between the presence of 1 or 2 mine cells around them in the immediate vicinity. To accomplish this task, the enzymes involved in the coloured-substrate reaction are sensitive to different concentrations of the dimer LuxR-AHL (denoted as R).