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National Yang Ming University

\frac{d[LuxI]}{dt}={RBS}\times{[mRNA LuxI]} -KAHL\times{[LuxI]} -Kdeg {[LuxI]} \times{[LuxI]}

In this equation, RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA; KAHL represents the rate constant of AHL to LuxI. For the section of the equation, {RBS}\times {[mRNALuxI]} represents the synthesizing rate of LuxI; KAHL[LuxI] represents the transforming rate of AHL to LuxI; -KdegLuxI\times [LuxI] represents the degrading rate of LuxI.

LacI will repress pLac promoter, which leads to no production of CI. Without CI, LuxCI hybrid promoter will no longer be repressed, and kill protein can thus be generated. This situation happens when Nosema exist, and when the sensor promoter is turned on.