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Equations

We define the reactions and the parameters involved in the system.

First we show a summary of the species:

Species:

• Promoter1
• Promoter2
• mRNA1
• mRNA2
• Repressor1/r1
• Repressor2
• Ribosomes
• IPTG
• asRNA
• Protease

Parameters:

• Km : Michaelis constant of transcription
• Kmu: Michaelis constant of translation
• δ: mRNA rate of degradation
• λ: mRNA maximum rate of synthesis
• k: Repressor rate of synthesis
• Kiu: Dissociation constant of repression
• γ: Cooperativity of inhibition by the repressor
• Ki: Binding constant for IPTG to the repressor
• K: Multimerization constant
• η: Maximum number of bound IPTG molecule per repressor
• ktemp: Degradation constant due to the temperature effect
• kprs: Rate constant for proteolysis kinetic
• kinh: Rate constant for inhibition of translation
• δ₃: Degradation rate of asRNA
• kptsa: Degradation rate of Protease

Proteolysis

Protease + repressor → Protease

Rate law:

Inhibition of translation

asRNA + mRNA → RNA complex

Rate law: