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\frac{d[mRNALacI]}{dt}= \frac{1-[ROSoxyR]^nROSoxyR }{ KdROSoxyR ^nROSoxyR + [ROSoxyR]^nROSoxyR} \times {PoPStrxC}\times\frac{N}{V}-KdegmRNA[mRNALacI]
In this equation, PoPStrxC represents the promoter strength of promotertrxC, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription; \frac{1-[ROSoxyR]^nROSoxyR }{ KdROSoxyR ^nROSoxyR + [ROSoxyR]^nROSoxyR} represents the hill effect of activator ROSoxyR to trxCpromoter.
For the section of the equation, \frac{1-[ROSoxyR]^nROSoxyR }{ KdROSoxyR ^nROSoxyR + [ROSoxyR]^nROSoxyR} \times {PoPStrxC}\times\frac{N}{V} represents the synthesizing rate of mRNALacI under the influence of activator ROSoxyR complex and trxC promoter; -kdegmRNA\times [mRNAlacI] represents the degrading rate of mRNALacI.
