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National Yang Ming University

\frac{d[kill]}{dt}={RBS}\times{[mRNAkill]} –Kdegkill\times{[kill]}

After trxC promoter is turned on by ROSoxyR complex and the downstream genes – LacI, LuxI, and LuxR starts to produce, which blocks the CI promoter and turns on the LuxCI hybrid promoter. After that, the gene encoded with kill protein downstream LuxCI hybrid promoter also begins to transcribe.

This equation shows production rate of mRNAkill. PoPSLuxcI represents the promoter strength of promoter trxC and LuxcI hybrid promoter, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription; \frac{1-[ LuxRAHL]^nLuxRAHL}{ KdLuxRAHL ^nLuxRAHL + [LuxRAHL]^nLuxRAHL} represents the hill effect of activator LuxRAHL to LuxcI hybrid promoter; \ frac{1-[CI leak]^nCI}{ KdCI^nCI+[CI]^nCI} represents the hill effect of repressor CI, while frac{1-{1-[CI leak]^nCI}}{ KdCI^nCI+[CI]^nCI} takes CI leaking into consideration (promoter pLac will not close thoroughly even though CI exists).

For the section of the equation, \frac{1-[ LuxRAHL]^nLuxRAHL}{ KdLuxRAHL ^nLuxRAHL + [LuxRAHL]^nLuxRAHL}\times \frac {1-[CI leak]^nCI}{ KdCI^nCI+[CI]^nCI}\times {PoPSLuxcI} \times \frac{N}{V}

represents the synthesizing rate of mRNAkill under the influence of LuxRAHLCI repression and leaking, and LuxcI hybrid promoter; -kdegmRNA\times [mRNALuxR] represents the degrading rate of mRNAkill.