Rutgers modelling

Diff Eq's using Matlab and Simulink

Our goal is essentially to understand and observe the changes associated with Acyl Homoserine Lactone, or AHL, within the confines of a cell and how it is affected by concentrations of AHL from the surrounding cells. This is done using differential equations derived using Michaelis-Menten kinetics as a way of describing the rate of enzymatic reactions involved. The Hill function, represented by equation five, allows us to model the time delay associated with protein production, including protein transcription, translation and overall synthesis. External AHL is represented by the fourth equation which takes into account the diffusivity and the overall flux of the overall AHL entering the cell. Similarly, internal AHL is portrayed using the third equation. The equation is absent of flux because internal AHL is formed in the Lux operon. Quorum sensing is done using the Lux operon, specifically LuxI, represented by the second equation. Quorum degradation occurs through the degradation protein qsdA. The different outputs correlate to the different rates of diffusivities portraying the flux of AHL. The results show that degradation of AHL occurs primarily during increases in concentrations of qsdA as depicted by the third figure. Figures one and two show the fluctuations of internal and external AHL respectively and their oscillations to a constant value lower than the original concentration. Overall, the model proves to be a valid representation of quorum sensing and degradation.