The input dependant model

For this model, we no longer assume a trivial process of repression of lacI being liften and QS being turned on. The LacI repression is now a repression / induction hill function with a K_d of 1200 molecules per cell for IPGT forming IPGT lacI complexes. We assume IPGT leaks into the cell from outside. We only set the outside concentration of IPGT. For quorum sensing all we set is an elevated HSL concentration outside which is free to defuse in. We now include a feedback loop into the QS mechanism. To do this we attach a lux box onto the plasmid for producing luxR and luxI, like so:

However, we are taking the production strengths of this lux box to be reduced in comparison to our lux box for producing X, Y and cI. The strengths are

Production max for X, Y and cI = 0.44 pops

Production min for X Y and cI = 0.013 pops

Production max for QS feedback = 0.002 pops

Production min for QS feedback = 0.00015 pops

These values are taken from the paper “ FIOADAOIDFJAOFJASDIOJASOIJADOAJSDAFOJAFOAJSD”

An important new parameter is K_P. This is the dissociation constant for “P” activating the lux boxes. P is the luxR/HSL complex . To take a break from the wordy descriptions we will now show some small sections of results for this model, which should be easily interpretable after following the section about the Monte Carlo analysis