Team:UPO-Sevilla/Project/Improving Flip Flop/Modeling/Equations

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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:

Proteolysis Rate Law

Inhibition of translation

asRNA + mRNA → RNA complex

Rate law:

Inhibition of translation Rate Law