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\frac{d[LuxR]}{dt}={RBS}\times{[mRNA LuxR]} – {KmAHL}\times{[AHL]}
- {Kdeg LuxR} \times{[LuxR]} \times {KmAHL}\{times[AHL]^{2}} \times{[LuxR]}- KdegAHL\times{[AHL]}
In this equation, RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA; KmAHL represents the rate constant of AHLLuxI; KonAHL represents the rate constant of 2AHL+LuxR to AHL2LuxR complex.
For the section of the equation, { RBS}\times{ [mRNALuxR]} represents the synthesizing rate of LuxR; { -KmAHL}\times{ [AHL]} represents the transforming rate of AHL to LuxI; {-KdegLuxR}\times {[LuxR]} represents the degrading rate of LuxR; { -KonAHL}\times{ [AHL]^2}\times{ [LuxR]} represents the transforming rate of 2AHL+LuxR to AHL2LuxR complex; {-KdegLuxI}\times {[AHL]} represents the degrading rate of AHL.
