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\frac{d[mRNALacI]}{dt}=\frac{ [mRNALuxI] }{dt}=\frac{ [mRNALuxR] }{dt}
=\frac{ {[OxyR*]} ^{{n}^{OxyR*}}}{{{KdOxyR*}^{{n}^{OxyR*}}}+{[OxyR*]}^{{n}^{OxyR*}}}\times{PoPSTrxC}\times\frac{N}{V}
In this equation, PoPSTrxC represents the promoter strength of promoter TrxC, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription; \frac{ {[OxyR*]} ^{{n}^{OxyR*}}}{{{KdOxyR*}^{{n}^{OxyR*}}}+{[OxyR*]}^{{n}^{OxyR*}}}
represents the hill effect of activator OxyR* to TrxC promoter.
The production rate of mRNATetR, mRNALuxI, mRNALuxR can be written as \frac{d[mRNALacI]}{dt}=\frac{ [mRNALuxI] }{dt}=\frac{ [mRNALuxR] }{dt} =\frac{ {[OxyR*]} ^{{n}^{OxyR*}}}{{{KdOxyR*}^{{n}^{OxyR*}}}+{[OxyR*]}^{{n}^{OxyR*}}}\times{PoPSTrxC}\times\frac{N}{V}
, which is under the influence of activator OxyR* binding to TrxC promoter.
