"
Team:NYMU-Taipei/modeling/m6
From 2014.igem.org
| Line 9: | Line 9: | ||
We model this part to see how the circuit works if phage is unable to control the S. mutans quorum, so the initial state of comE, the molecule that triggers the nlmC promoter, has a certain amount, which means the S. mutans is out of control. </p> | We model this part to see how the circuit works if phage is unable to control the S. mutans quorum, so the initial state of comE, the molecule that triggers the nlmC promoter, has a certain amount, which means the S. mutans is out of control. </p> | ||
<h1>System</h1> | <h1>System</h1> | ||
| - | <p>(1)$$\frac{d[ | + | <p>(1)$$\frac{d[\text{luxI mRNA}]}{dt}=P_{nlmC} \frac{[\text{comE}]^{n1}}{K_{d1}+[\text{comE}]^{n1}} (1-a)^x - K_{deg\_mluxI} [\text{luxI mRNA}]$$ |
| - | $$\frac{d[luxI]}{dt}= K_{t1} [ | + | $$\frac{d[\text{luxI}]}{dt}= K_{t1} [\text{luxI mRNA}] - K_{deg\_luxI} [\text{luxI}]$$ |
1. $P_{nlmC}$:max nlmC promoter activity<br> | 1. $P_{nlmC}$:max nlmC promoter activity<br> | ||
2. $K_{d1}$:promoter-TF dissociation constant<br> | 2. $K_{d1}$:promoter-TF dissociation constant<br> | ||
| Line 18: | Line 18: | ||
6. $K_{deg\_luxI}$:luxI degredation<br> | 6. $K_{deg\_luxI}$:luxI degredation<br> | ||
7. $n1$:hill coefficient<br> | 7. $n1$:hill coefficient<br> | ||
| - | (2)$$\frac{d[ | + | (2)$$\frac{d[\text{luxR mRNA}]}{dt}=P_{const} - K_{deg\_mluxR} [\text{luxR mRNA}]$$ |
| - | $$\frac{d[luxR]}{dt}= K_{t2} [ | + | $$\frac{d[\text{luxR}]}{dt}= K_{t2} [\text{luxR mRNA}] - K_{deg\_luxR} [\text{luxR}]-K_{on}[\text{AHL}]^2[\text{luxR}]+K_{off}[\text{AHLluxR}]$$ |
1. $P_{const}$:constitutive promoter activity<br> | 1. $P_{const}$:constitutive promoter activity<br> | ||
2. $K_{deg\_mluxR}$:luxR mRNA degradation<br> | 2. $K_{deg\_mluxR}$:luxR mRNA degradation<br> | ||
3. $K_{t2}$:Translation efficiency<br> | 3. $K_{t2}$:Translation efficiency<br> | ||
4. $K_{deg\_luxR}$:luxR degredation<br> | 4. $K_{deg\_luxR}$:luxR degredation<br> | ||
| - | 5. $K_{on}$: reaction rate of $2AHL+luxR \rightarrow AHLluxR(complex)$<br> | + | 5. $K_{on}$: reaction rate of $\text{2AHL+luxR} \rightarrow \text{AHLluxR(complex)}$<br> |
| - | 6. $K_{off}$: reaction rate of $AHLluxR(complex) \rightarrow 2AHL+luxR $<br> | + | 6. $K_{off}$: reaction rate of $\text{AHLluxR(complex)} \rightarrow \text{2AHL+luxR}$<br> |
| - | (3)$$\frac{d[AHL]}{dt}= K_{AHL} [luxI] +2 K_{off}[AHLluxR] -2 K_{on}[AHL]^2[luxR] - K_{deg\_AHL}$$ | + | (3)$$\frac{d[\text{AHL}]}{dt}= K_{AHL} [\text{luxI}] +2 K_{off}[\text{AHLluxR}] -2 K_{on}[\text{AHL}]^2[\text{luxR}] - K_{deg\_AHL}$$ |
1. $K_{AHL}$:synthesis rate of AHL by LuxI<br> | 1. $K_{AHL}$:synthesis rate of AHL by LuxI<br> | ||
| - | (4)$$\frac{d[AHLluxR]}{dt}= K_{on}[AHL]^2[luxR] - K_{off}[AHLluxR]$$ | + | (4)$$\frac{d[\text{AHLluxR}]}{dt}= K_{on}[\text{AHL}]^2[\text{luxR}] - K_{off}[\text{AHLluxR}]$$ |
| - | 1. reaction of $2AHL+luxR \rightarrow AHLluxR(complex)$<br> | + | 1. reaction of $\text{2AHL+luxR} \rightarrow \text{AHLluxR(complex)}$<br> |
| - | (5)$$\frac{d[ | + | (5)$$\frac{d[\text{lysine gene mRNA}]}{dt}=P_{luxR} \frac{[\text{AHLluxR}]^{n2}}{K_{d2}+[\text{AHLluxR}]^{n2}} - K_{deg\_mlys} [\text{lysine gene mRNA}]$$ |
| - | $$\frac{d[ | + | $$\frac{d[\text{lysine protein}]}{dt}= K_{t2} [\text{lysine gene mRNA}] - K_{deg\_lys} [\text{lysine protein}]$$ |
1. $P_{luxR}$:max pluxR promoter activity<br> | 1. $P_{luxR}$:max pluxR promoter activity<br> | ||
2. $K_{d2}$:promoter-TF dissociation constant<br> | 2. $K_{d2}$:promoter-TF dissociation constant<br> | ||
Revision as of 15:38, 8 October 2014
Introduction
This part aims to simulate the circuit of the Target part, which will be turn on when S. mutans is too much or phage is unable to control the S. mutans quorum.
LuxI coding sequence is controlled by nlmC promoter and threshold terminator. When the quorum of S. mutans is too much, the LuxI will be expressed and generate AHL-synthase. LuxR, on the other hand, is generated by E. coli constitutively. The LuxR and AHL can form a complex that can activate the pLuxR promoter. In our design, pLuxR promoter in E. coli can activate the lysine protein that can kill S. mutans only.
We model this part to see how the circuit works if phage is unable to control the S. mutans quorum, so the initial state of comE, the molecule that triggers the nlmC promoter, has a certain amount, which means the S. mutans is out of control.
System
(1)$$\frac{d[\text{luxI mRNA}]}{dt}=P_{nlmC} \frac{[\text{comE}]^{n1}}{K_{d1}+[\text{comE}]^{n1}} (1-a)^x - K_{deg\_mluxI} [\text{luxI mRNA}]$$
$$\frac{d[\text{luxI}]}{dt}= K_{t1} [\text{luxI mRNA}] - K_{deg\_luxI} [\text{luxI}]$$
1. $P_{nlmC}$:max nlmC promoter activity
2. $K_{d1}$:promoter-TF dissociation constant
3. $K_{deg\_mluxI}$:luxI mRNA degradation
4. $(1-a)^x$:terminator effect
5. $K_{t1}$:Translation efficiency
6. $K_{deg\_luxI}$:luxI degredation
7. $n1$:hill coefficient
(2)$$\frac{d[\text{luxR mRNA}]}{dt}=P_{const} - K_{deg\_mluxR} [\text{luxR mRNA}]$$
$$\frac{d[\text{luxR}]}{dt}= K_{t2} [\text{luxR mRNA}] - K_{deg\_luxR} [\text{luxR}]-K_{on}[\text{AHL}]^2[\text{luxR}]+K_{off}[\text{AHLluxR}]$$
1. $P_{const}$:constitutive promoter activity
2. $K_{deg\_mluxR}$:luxR mRNA degradation
3. $K_{t2}$:Translation efficiency
4. $K_{deg\_luxR}$:luxR degredation
5. $K_{on}$: reaction rate of $\text{2AHL+luxR} \rightarrow \text{AHLluxR(complex)}$
6. $K_{off}$: reaction rate of $\text{AHLluxR(complex)} \rightarrow \text{2AHL+luxR}$
(3)$$\frac{d[\text{AHL}]}{dt}= K_{AHL} [\text{luxI}] +2 K_{off}[\text{AHLluxR}] -2 K_{on}[\text{AHL}]^2[\text{luxR}] - K_{deg\_AHL}$$
1. $K_{AHL}$:synthesis rate of AHL by LuxI
(4)$$\frac{d[\text{AHLluxR}]}{dt}= K_{on}[\text{AHL}]^2[\text{luxR}] - K_{off}[\text{AHLluxR}]$$
1. reaction of $\text{2AHL+luxR} \rightarrow \text{AHLluxR(complex)}$
(5)$$\frac{d[\text{lysine gene mRNA}]}{dt}=P_{luxR} \frac{[\text{AHLluxR}]^{n2}}{K_{d2}+[\text{AHLluxR}]^{n2}} - K_{deg\_mlys} [\text{lysine gene mRNA}]$$
$$\frac{d[\text{lysine protein}]}{dt}= K_{t2} [\text{lysine gene mRNA}] - K_{deg\_lys} [\text{lysine protein}]$$
1. $P_{luxR}$:max pluxR promoter activity
2. $K_{d2}$:promoter-TF dissociation constant
3. $K_{deg\_mlyx}$:lysine gene mRNA degradation
4. $K_{t2}$:Translation efficiency
5. $K_{deg\_lys}$:lysine protein degredation
6. $n2$:hill coefficient
Result
Reference
method
result
Reference
