Modeling on the sensing device

In the mathematical modeling of quorum sensing, we formulated a system of ordinary equations representing the intracellular and extracellular interactions between the two Agr proteins and AIP (auto-inducing peptide) molecules. Along with numerical simulations, we performed an asymptotic analysis of the time-dependent model in order to characterize whether the AIP molecules produced by Staphylococcus aureus in the intestine would activate our sensing device.

To build the model, we first proposed the following assumptions:

• The agr mRNA contains all the information required for the translation of AgrC and AgrA. There are plentiful ribosomes for translation within the cells and the rates of translations of AgrC and AgrA are the same, and are proportional to the concentrations of their mRNA.
• Proteins and mRNA inside the cells are limited by natural degradation.
• Housekeeping phosphatases are able to dephosphorylate AgrA at rate αpidi.
• Receptor-bound AIP can dissociate spontaneously at rate α_unbind.
• When an AIP binds to AgrC, we assume that auto-phosphorylation of AgrC happens simultaneously because this process is sufficiently fast. When AgrC transfers its phosphate group to AgrA at rate α_pi, it is able to re-auto-phosphorylate.

The resulting equations, together with the definitions of the parameters and variables are shown below.

Modelling on peptide synthesis and cell lysis