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National Yang Ming University

Explanation:

\frac{d[mRNAOxyR]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA[mRNAOxyR]

In this equation, PoPSconstitutive represents the promoter strength of promoter J23102, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription.

For the section of the equation, PoPSconstitutive\times\frac{N}{V} represents the synthesizing rate of mRNAOxyR ; -KdegmRNA[mRNAOxyR] represents the degrading rate of mRNAOxyR .

\frac{d[OxyR]}{dt}=RBS\times[mRNAOxyR]-KdegOxyR[OxyR]

In this equation, RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA.

For the section of the equation, RBS×[mRNAoxyR] represents the synthesizing rate of OxyR; KdegOxyR[xyR] represents the degrading rate of OxyR .

[OxyR*]=KOxyR*\times[ROS]\times[OxyR]

This equation shows the equilibrium of ROS + OxyR → OxyR* (KOxyR* is the rate constant of ROS + OxyR → OxyR*)

\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.