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### From 2013.igem.org

In this equation, PoPStrxC,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-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^n ROSoxyR I} represents the hill effect of activator ROSoxyR complex to trxCpromoter; \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-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^n ROSoxyR I} \times PoPStrxC\times\frac{N}{V} represents the synthesizing rate of mRNALuxI under the influence of activator ROSoxyR complex and trxC promoter; \frac{1-[ LuxRAHL]^nLuxRAHL}{ KdLuxRAHL ^nLuxRAHL + [LuxRAHL]^nLuxRAHL}\times\frac{1-{1-[CI leak]^nCI}}{ KdCI^nCI+[CI]^nCI}\times PoPSLuxCI\times\frac{N}{V} represents the synthesizing rate of mRNALuxI under the influence of LuxRAHL complex, CI repression and leaking, and LuxcI hybrid promoter; -kdegmRNA\times [mRNAluxI]represents the degrading rate of mRNAluxI.