Modeling
It is of interest to model the amplification of the signal at steady-state through the use of quorum sensing. The model system used is induced by IPTG through the Plac promoter. We analyze the model at steady-state while varying IPTG. Thus IPTG can be assigned a rate so that it increases as time goes on.
This equation is used to describe the dynamics of LuxR production and dimerization, LuxI and its production of AHL, as well as the binding of AHL to LuxR dimers. These are all lumped together in this equation. The first term describes the production of AHL as a function of IPTG from the Plac promoter, the second term describes the positive feedback of AHL production through the Plux promoter, the last term is for degradation.
This equation is used to model the output signal (CFP in this case) from the system hooked onto the quorum sensing system. The first term describes the production of CFP as function of AHL through the Plux promoter, the last term is for degradation.
This equation is used to model the response from a system that does not have a quorum sensing system attached to it. The first term describes the production of CFP as function of IPTG through the Plac promoter, the last term is for degradation.
Performing a steady-state analysis on these equations, with logically assigned parameters, we get the following result.
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