Detailed description

Model development

To simulate the cell-cell communication system, we developed an ordinary differential equation model. The following segments describe in detail how the equations were developed with the mazEF system.

Fig.5-5-1. The mazEF system gene circuit

Differencial equations

Snow White

\begin{equation} \frac{d[mRNA_{RFP}]}{dt} = k - d[mRNA_{RFP}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{RFP}}})[mRNA_{RFP}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{RhlI}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{RhlI}] - F_{DiMazF}f[mRNA_{RhlI}][DiMazF] \end{equation} \begin{equation} \frac{d[RFP]}{dt} = \alpha [mRNA_{RFP}] - d_{RFP}[RFP] \end{equation} \begin{equation} \frac{d[RhlI]}{dt} = \alpha [mRNA_{RhlI}] - d_{RhlI}[RhlI] \end{equation} \begin{equation} \frac{d[C4]}{dt} = p_{C4}[RhlI]P_{Snow White} - d_{C4}[C4] \end{equation} \begin{equation} \frac{d[mRNA_{MazF}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}}+ [C12]^{n_{Lux}}} \\ 　　　　　　　- d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF] \end{equation} \begin{equation} \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{DiMazF}[MazF] + 2k_{-DiMazF}[DiMazF] - d_{MazF}[MazF] \end{equation} \begin{equation} \frac{d[DiMazF]}{dt} = k_{DiMazF}[MazF] - k_{-DiMazF}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] \end{equation} \begin{equation} \frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{DiMazE}[MazE] + 2k_{-DiMazE}[DiMazE] - d_{MazE}[MazE] \end{equation} \begin{equation} \frac{d[DiMazE]}{dt} = k_{DiMazE}[MazE] - k_{-DiMazE}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE] \end{equation} \begin{equation} \frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa] \end{equation} \begin{equation} \frac{dP_{Snow White}}{dt} = g \frac{E_{DiMazF}}{E_{DiMazF}+[DiMazF]}\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}} \right) P_{Snow White} \end{equation}

Queen

\begin{equation} \frac{d[mRNA_{GFP}]}{dt} = k - d[mRNA_{GFP}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{GFP}}})[mRNA_{GFP}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{LasI}]}{dt} = leak_{Prhl} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} \\ 　　　　　　　- d[mRNA_{LasI}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{LasI}}})[mRNA_{LasI}][DiMazF] \end{equation} \begin{equation} \frac{d[GFP]}{dt} = \alpha [mRNA_{GFP}] - d_{GFP}[GFP] \end{equation} \begin{equation} \frac{d[LasI]}{dt} = \alpha [mRNA_{LasI}] - d_{LasI}[LasI] \end{equation} \begin{equation} \frac{d[C12]}{dt} = p_{C12}[LasI]P_{Queen} - d_{C12}[C12] - D[C12][AmiE] \end{equation} \begin{equation} \frac{d[mRNA_{MazF}]}{dt} = leak_{Plux} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} \\ 　　　　　　　- d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF] \end{equation} \begin{equation} \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{DiMazF}[MazF] + 2k_{-DiMazF}[DiMazF] - d_{MazF}[MazF] \end{equation} \begin{equation} \frac{d[DiMazF]}{dt} = k_{DiMazF}[MazF] - k_{-DiMazF}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] \end{equation} \begin{equation} \frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{DiMazE}[MazE] + 2k_{-DiMazE}[DiMazE] - d_{MazE}[MazE] \end{equation} \begin{equation} \frac{d[DiMazE]}{dt} = k_{DiMazE}[MazE] - k_{-DiMazE}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE] \end{equation} \begin{equation} \frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa] \end{equation} \begin{equation} \frac{dP_{Queen}}{dt} = g \frac{E_{DiMazF}}{E_{DiMazF}+[DiMazF]}\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}}\right) P_{Queen}\\ \end{equation}

Prince

\begin{equation} \frac{d[mRNA_{AmiE}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{AmiE}] \end{equation} \begin{equation} \frac{d[AmiE]}{dt} = \alpha [mRNA_{AmiE}]P_{Prince} - d_{AmiE}[AmiE] \end{equation} \begin{equation} \frac{dP_{Prince}}{dt} = g\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}}\right) P_{Prince} \end{equation}

Explanation about parameters

Parameter	Description
$$g$$	Growth rate of each cells
$$P_{max}$$	Carrying capacity
$$E_{DiMazF}$$	Effect of MazF dimer on growth rate
$$k$$	Transcription rate of downstream of Pcon
$$leak_{Plux}$$	Leakage of Plux
$$leak_{Prhl}$$	Leakage of Prhl
$$\kappa_{Lux}$$	Maximum transcription rate of mRNA under Plux
$$\kappa_{Rhl}$$	Maximum transcription rate of downstream of Prhl
$$n_{Lux}$$	Hill coefficient for Plux
$$n_{Rhl}$$	Hill coefficient for Prhl
$$K_{mLux}$$	Lumped paremeter for the Lux System
$$K_{mRhl}$$	Lumped paremeter for the Rhl System
$$F_{DiMazF}$$	Cutting rate at ACA sequences on mRNA by MazF dimer
$$f$$	The probability of distinction of ACA sequencess in each mRNA
$$f_{mRNA_{RFP}}$$	The number of ACA sequences in $mRNA_{RFP}$
$$f_{mRNA_{GFP}}$$	The number of ACA sequences in $mRNA_{GFP}$
$$f_{mRNA_{RhlI}}$$	The number of ACA sequences in $mRNA_{RhlI}$
$$f_{mRNA_{LasI}}$$	The number of ACA sequences in $mRNA_{LasI}$
$$f_{mRNA_{MazF}}$$	The number of ACA sequences in $mRNA_{MazF}$
$$f_{mRNA_{MazE}}$$	The number of ACA sequences in $mRNA_{MazE}$
$$\alpha$$	Translation rate of Protein
$$k_{DiMazF}$$	Formation rate of MazF dimer
$$k_{-DiMazF}$$	Dissociation rate of MazF dimer
$$k_{DiMazE}$$	Formation rate of MazE dimer
$$k_{-DiMazE}$$	Dissociation rate of MazE dimer
$$k_{Hexa}$$	Formation rate of Maz hexamer
$$k_{-Hexa}$$	Dissociation rate of Maz hexamer
$$p_{C4}$$	Production rate of C4HSL by RhlI
$$p_{C12}$$	Production rate of 3OC12HSL by LuxI
$$D$$	Decomposition rate of 3OC12HSL by AmiE
$$d$$	Degradation rate of mRNA
$$d_{RFP}$$	Degradation rate of RFP
$$d_{GFP}$$	Degradation rate of GFP
$$d_{RhlI}$$	Degradation rate of RhlI
$$d_{LasI}$$	Degradation rate of LasI
$$d_{MazF}$$	Degradation rate of MazF
$$d_{DiMazF}$$	Degradation rate of MazF dimer
$$d_{MazE}$$	Degradation rate of MazE
$$d_{DiMazE}$$	Degradation rate of MazE dimer
$$d_{Hexa}$$	Degradation rate of Maz Hexamer
$$d_{C4}$$	Degradation rate of C4HSL
$$d_{C12}$$	Degradation rate of 3OC12HSL
$$d_{AmiE}$$	Degradation rate of AmiE

Expressions

1. Cell population

$$ \frac{dP_{Snow White}}{dt} = g \frac{E_{DiMazF}}{E_{DiMazF}+[DiMazF]}\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}} \right) P_{Snow White} $$
$$ \tag{1-1} $$

$$ \frac{dP_{Queen}}{dt} = g \frac{E_{DiMazF}}{E_{DiMazF}+[DiMazF]}\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}}\right) P_{Queen}$$
$$ \tag{1-2} $$

$$ \frac{dP_{Prince}}{dt} = g\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}}\right) P_{Prince} \tag{1-3} $$

Eq.1. Differential equation of cell population

The equations above describe how each cell grows in the culture. Equations (1-1), (1-2) and (1-3) describe the populations of Snow White coli, the Queen coli and the Prince coli. (1-3) is described by the logistic growth equation, but (1-1) and (1-2) are represented by the growth inhibition by MazF dimers. This factor is designed so that its value is small when the concentration of MazF dimers is high, and its value converges to 1 when the concentration of MazF dimers is low.
2. The mazEF system
- 2.1. Expression of the mazEF system
  
  After translation, MazE and MazF each form a dimer which can be activated to exert its function.
  
  Two MazF dimers sandwich a MazE dimer, forming MazF2-MazE2-MazF2 heterohexamers and suppressing the toxicity of the MazF dimers.
  
  Fig.5-5-2. Reaction of the mazEF system
  
  The mRNAs of Snow White coli and the Queen coli decrease because of their original degradation and the cleavage at ACA sequences by MazF dimers.
  Applying mass action kinetic laws, we obtain the following set of differential equations.
  
  Snow White
  
  $$\frac{d[mRNA_{MazF}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}}+ [C12]^{n_{Lux}}} \\ 　　　　　　　- d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] $$
  $$ \tag{2-1} $$
  
  $$ \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{DiMazF}[MazF] + 2k_{-DiMazF}[DiMazF] - d_{MazF}[MazF] $$
  $$\tag{2-2}$$
  
  $$ \frac{d[DiMazF]}{dt} = k_{DiMazF}[MazF] - k_{-DiMazF}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] $$
  $$ \tag{2-3} $$
  
  $$ \frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF] $$
  $$ \tag{2-4} $$
  
  $$\frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{DiMazE}[MazE] + 2k_{-DiMazE}[DiMazE] - d_{MazE}[MazE]$$
  $$\tag{2-5}$$
  
  $$ \frac{d[DiMazE]}{dt} = k_{DiMazE}[MazE] - k_{-DiMazE}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE]$$
  $$\tag{2-6} $$
  
  $$\frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa]$$
  $$ \tag{2-7}$$
  
  Queen
  
  $$ \frac{d[mRNA_{MazF}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}}+ [C12]^{n_{Lux}}} \\ 　　　　　　　- d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] $$
  $$ \tag{2-8} $$
  
  $$ \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{DiMazF}[MazF] + 2k_{-DiMazF}[DiMazF] - d_{MazF}[MazF] $$
  $$\tag{2-9}$$
  
  $$ \frac{d[DiMazF]}{dt} = k_{DiMazF}[MazF] - k_{-DiMazF}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] $$
  $$ \tag{2-10} $$
  
  $$ \frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF] $$
  $$ \tag{2-11} $$
  
  $$\frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{DiMazE}[MazE] + 2k_{-DiMazE}[DiMazE] - d_{MazE}[MazE]$$
  $$\tag{2-12}$$
  
  $$ \frac{d[DiMazE]}{dt} = k_{DiMazE}[MazE] - k_{-DiMazE}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2 \\ 　　　　　　　+ k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE]$$
  $$\tag{2-13} $$
  
  $$\frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa]$$
  $$ \tag{2-14}$$
  
  Eq. 2. Differential equations of the mazEF system
  
  Equations (2-1) and (2-8) describe the concentration of mRNAs under AHL-inducible promoters. Thus, they comprise terms of production by leaky expression of promoters, terms of production by Hill function dependent on the concentration of C4HSL (C4) and 3OC12HSL (C12), terms of original degradation and terms of degradation from cleavage at ACA sequences by MazF dimers.
  Since equations (2-2), (2-3), (2-5), (2-6), (2-7), (2-9), (2-10), (2-12), (2-13) and (2-14) describe the concentrations of complexes, mainly they comprise terms of production and terms of binding and dissociation.
- 2.2. Cleavage by MazF dimers
  
  MazF dimers recognize and cleave ACA sequences in mRNAs, thus acting as a toxin.We estimated the rate of recognitions of ACA sequences by MazF dimers at $$ 1-(1-f)^n $$ where n is the number of ACA sequences in mRNA and f is the probability of distinction of ACA sequences on each mRNA. Then, we expressed the rate of degradation by MazF dimers in $$ F(1-(1-f)^{f_{mRNA}}) $$ and obtain the following set of differential equations.
  
  Snow White
  
  $$\frac{d[mRNA_{RFP}]}{dt} = k - d[mRNA_{RFP}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{RFP}}})[mRNA_{RFP}][DiMazF] $$
  $$ \tag{3-1} $$
  
  $$\frac{d[mRNA_{RhlI}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{RhlI}] - F_{DiMazF}$$
  $$ \tag{3-2} $$
  
  $$\frac{d[mRNA_{MazF}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}}+ [C12]^{n_{Lux}}} \\ 　　　　　　　- d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] $$
  $$\tag{3-3}$$
  
  $$\frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF]$$
  $$ \tag{3-4} $$
  
  Queen
  
  $$\frac{d[mRNA_{GFP}]}{dt} = k - d[mRNA_{GFP}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{GFP}}})[mRNA_{GFP}][DiMazF] $$
  $$ \tag{3-5} $$
  
  $$ \frac{d[mRNA_{LasI}]}{dt} = leak_{Prhl} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} \\ 　　　　　　　- d[mRNA_{LasI}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{LasI}}})[mRNA_{LasI}][DiMazF] $$
  $$ \tag{3-6} $$
  
  $$\frac{d[mRNA_{MazF}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}}+ [C12]^{n_{Lux}}} \\ 　　　　　　　- d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] $$
  $$\tag{3-7}$$
  
  $$\frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF]$$
  $$ \tag{3-8} $$
  
  Eq. 3. Differential equations of mRNA concentrations
  
  The equations above comprise terms of production, terms of only original degradation and terms of degradation from cleavage at ACA sequences by MazF dimers.
3. Signaling molecules

Fig.5-5-3. Reaction of signaling molecules

Snow White coli expresses RhlI under Plux induced by C12, the Queen coli expresses LasI under Prhl induced by C4 and the Prince coli expresses AmiE under Plux induced by C12.
The mRNAs of Snow White coli and the Queen coli decrease from original degradation and the cleavage at ACA sequences by MazF dimers. On the other hand, those of the Prince coli don’t have any MazF genes so they decrease from original degradation only.
After translation, C4 and C12 are enzymatically synthesized by LasI and RhlI from some substrates respectively.
For simplicity, we assumed that the amount of substrates is sufficient so that the C4 and C12 synthesis rate per cell is estimated to be proportional to the LasI and RhlI concentrations.C4 decreases from original degradation only meanwhile C12 decreases from both original degradation and degradation by AmiE, which the Prince coli produces.
Applying mass action kinetic laws, we obtain the following set of differential equations.

$$ \frac{d[mRNA_{RhlI}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{RhlI}] - F_{DiMazF}f[mRNA_{RhlI}][DiMazF] $$
$$\tag{4-1}$$

$$\frac{d[RhlI]}{dt} = \alpha [mRNA_{RhlI}] - d_{RhlI}[RhlI] \tag{4-2}$$

$$ \frac{d[C4]}{dt} = p_{Rhl}[RhlI]P_{Snowwhite} - d_{C4}[C4] \tag{4-3} $$

$$ \frac{d[mRNA_{LasI}]}{dt} = leak_{Prhl} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} - d[mRNA_{LasI}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{LasI}}})[mRNA_{LasI}][DiMazF] $$
$$\tag{4-4}$$

$$\frac{d[LasI]}{dt} = \alpha [mRNA_{LasI}] - d_{LasI}[LasI] \tag{4-5}$$

$$\frac{d[C12]}{dt} = p_{C12}[LasI]P_{Stepmother} - d_{C12}[C12] - D[C12][AmiE]$$
$$\tag{4-6}$$

$$\frac{d[mRNA_{AmiE}]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{AmiE}]$$
$$\tag{4-7}$$

$$\frac{d[AmiE]}{dt} = \alpha [mRNA_{AmiE}]P_{Prince} - d_{AmiE}[AmiE] \tag{4-8} $$

Eq. 4. Differential equations of signaling molecules

Equations (4-1), (4-4) and (4-7) describe the concentrations of mRNAs under the AHL-inducible promoters.Thus, they comprise terms of production by leaky expression of promoters, terms of production by Hill function depending on the concentration of C4 and C12, terms of original degradation and terms of degradation from cleavage at ACA sequences by MazF dimers.
The other ODEs describe how the concentrations of materials change in individuals, on the other hand (4-3), (4-6) describe the concentrations of C4 and C12 in the whole culture medium.

Back to Model page.

Parameters

Parameter	Value	Description	Reference
$$ g $$	$$ 0.0123 $$	Growth rate of each cells	Fitted to experimental data
$$ P_{max} $$	$$3.3 $$	Carrying capacity	Fitted to experimental data
$$ E_{DiMazF} $$	$$ 0.462234 nM^{-1} min^{-1} $$	Effect of MazF dimer on growth rate of each cells	Fitted to experimental data
$$ k $$	$$5 min^{-1}$$	Transcription rate of downstream of Ptet	Reference[1]
$$ leak_{Plux} $$	$$ 2.26 min^{-1} $$	Leakage of Plux	Fitted to experimental data
$$ leak_{Prhl} $$	$$ 4.654 min^{-1} $$	Leakage of Prhl	Fitted to experimental data
$$ κ_{Lux} $$	$$ 6.984 nM^{-1} min^{-1} $$	Maximum transcription rate of under streams of Plux	Fitted to experimental data
$$ κ_{Rhl} $$	$$ 14.95 nM^{-1} min^{-1} $$	Maximum transcription rate of understreams of Prhl	Fitted to experimental data
$$ n_{Lux} $$	$$ 0.76 $$	Hill coefficient for Plux	Fitted to experimental data
$$ n_{Rhl} $$	$$ 5 $$	Hill cofficient for Prhl	Fitted to experimental data
$$ K_{mLux} $$	$$ 116.24nM $$	Lumped parameter for the Lux system	Fitted to experimental data
$$ K_{mRhl} $$	$$ 1000 nM $$	Lumped parameter for the Rhl system	Fitted to experimental data
$$ F_{DiMazF} $$	$$ 5 nM^{-1} min^{-1} $$	Cutting rate at ACA sequences on mRNA by MazF dimers	Assumption
$$ f $$	$$ 0.299 $$	The probability of distinction of ACA sequences on each mRNA	Fitted to experimental data
$$ f_{mRNA_{RFP}} $$	$$ 10 $$	The number of ACA sequences on mRNA_{RFP}	Extraction of data
$$ f_{mRNA_{GFP}} $$	$$ 23 $$	The number of ACA sequences on mRNA_{GFP}	Extraction of data
$$ f_{mRNA_{RhlI}} $$	$$ 1 $$	The number of ACA sequences on mRNA_{RhlI}	Extraction of data
$$ f_{mRNA_{LasI}} $$	$$ 10 $$	The number of ACA sequences on mRNA_{LasI}	Extraction of data
$$ f_{mRNA_{MazF}} $$	$$2$$	The number of ACA sequences on mRNA_{MazF}	Extraction of data
$$ f_{mRNA_{MazE}} $$	$$2$$	The number of ACA sequences on mRNA_{MazE}	Extraction of data
$$ α $$	$$ 0.04 min_{-1} $$	Translation rate of	Assumption
$$ k_{DiMazF}$$	$$ 6.82 nM_{-1} min_{-1} $$	Formation rate of MazF dimer	Fitted to experimental data
$$ k_{-Di_{MazF}}$$	$$ 6.24 nM^{-1} min^{-1} $$	Formation rate of MazF dimer	Fitted to experimental data
$$ k_{Di_{MazE}}$$	$$ 3.46 nM^{-1} min^{-1} $$	Formation rate of MazF dimer	Fitted to experimental data
$$ k_{-Di_{MazE}}$$	$$ 7.25 min^{-1} $$	Dissociation rate of MazF dimer	Fitted to experimental data
$$ k_{Hexa}$$	$$ 4.51 nM^{-1} min^{-1} $$	Formation rate of Maz hexamer	Fitted to experimental data
$$ k_{-Hexa}$$	$$ 4.05 min^{-1} $$	Dissociation rate of Maz hexamer	Fitted to experimental data
$$ p_{C4}$$	$$ 0.07 min^{-1} $$	Production rate of C4HSL by RhlI	Assumption
$$ p_{C12}$$	$$ 0.07 min^{-1} $$	Production rate of 3OC12HSL by LasI	Assumption
$$ D $$	$$ 0.1 nM^{-1} min^{-1} $$	Decomposition rate of 3OC12HSL by AmiE	Assumption
$$ d $$	$$ 0.2773 min^{-1} $$	Degradation rate of mRNA	Leference[2]
$$ d_{RFP} $$	$$ 0.005 min^{-1} $$	Degradation rate of RFP	Assumption
$$ d_{GFP} $$	$$ 0.005 min^{-1} $$	Degradation rate of GFP	Assumption
$$ d_{RhlI} $$	$$ 0.0167 min^{-1} $$	Degradation rate of RhlI	Leference[1]
$$ d_{LasI} $$	$$ 0.0167 min^{-1} $$	Degradation rate of LasI	Leference[1]
$$ d_{MazF} $$	$$ 0.7 min^{-1} $$	Degradation rate of MazF	Fitted to experimental data
$$ d_{DiMazF} $$	$$ 0.17 min^{-1} $$	Degradation rate of MazF dimer	Fitted to experimental data
$$ d_{MazE} $$	$$ 0.55 min^{-1} $$	Degradation rate of MazE	Fitted to experimental data
$$ d_{DiMazE} $$	$$ 0.416 min^{-1} $$	Degradation rate of MazE dimer	Fitted to experimental data
$$ d_{Hexa} $$	$$ 0.511 min^{-1} $$	Degradation rate of Maz hexameter	Fitted to experimental data
$$ d_{C4} $$	$$ 0.000222 min^{-1} $$	Degradation rate of C4HSL	Literature[3]
$$ d_{C12} $$	$$ 0.004 min^{-1} $$	Degradation rate of 3OC12HSL	Literature[4]
$$ d_{AmiE} $$	$$ 0.001 min^{-1} $$	Degradation rate of AmiE	Assumption