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

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