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\frac{d[mRNACI]}{dt}= \frac{1-[LacI]^nLacI}{ KdLacI^nLacI+ [LacI]^nLacI} \times PoPSconstitutive\times\frac{N}{V}-KdegmRNA\times [mRNACI]
In this equation, PoPSpLac represents the promoter strength of LacI promoter, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription; \frac{1-[LacI]^nLacI }{ KdLacI^nLacI+[LacI]^nLacI } represents the hill effect of repressor LacI to LacI promoter. Because LacI is a repressor, the numerator is {1-[LacI]^nLacI } . For the section of the equation, \frac{1-[LacI]^nLacI}{ KdLacI^nLacI+ [LacI]^nLacI} \times PoPSconstitutive\times\frac{N}{V}represents the synthesizing rate of mRNACI under the influence of LacI and LacI promoter; -{kdegmRNA}\times {[mRNACI]} represents the degrading rate of mRNA
