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Team:ETH Zurich/modeling/qs
From 2014.igem.org
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* ΦC31: serine integrase that can fold into two conformations- ΦC31a and ΦC31b. We chose to use a common connotation for both conformations - ΦC31. | * ΦC31: serine integrase that can fold into two conformations- ΦC31a and ΦC31b. We chose to use a common connotation for both conformations - ΦC31. | ||
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=== Reactions === | === Reactions === | ||
| - | ;For | + | ;For the Lux system: |
$$ \begin{align} | $$ \begin{align} | ||
| - | + | &\rightarrow LuxR \\ | |
| - | + | Lux-AHL+LuxR & \leftrightarrow RLux\\ | |
| - | Bxb1 &\rightarrow \\ | + | RLux}+RLux & \leftrightarrow DRLux\\ |
| - | + | DRLux}+P_{luxOFF} & \leftrightarrow P_{luxON}\\ | |
| + | P_{luxON}&\rightarrow P_{luxON}+mRNA_{Bxb1}\\ | ||
| + | mRNA_{Bxb1}&\rightarrow Bxb1\\ | ||
| + | AHL &\rightarrow \\ | ||
| + | LuxR &\rightarrow \\ | ||
| + | R_{Lux} &\rightarrow\\ | ||
| + | DR_{Lux} &\rightarrow\\ | ||
| + | mRNA_{Bxb1} &\rightarrow\\ | ||
| + | Bxb1 &\rightarrow | ||
\end{align}$$ | \end{align}$$ | ||
Revision as of 16:34, 11 October 2014
Modeling quorum sensing
Model
The Quorum sensing module is mainly involved in receiving signals from the sender cells. The sender cells secrete some signalling molecules (inducers) which bind to the regulator molecules in the receiver cells, thus activating the transcription of certain genes. The model for this module is presented below.
Chemical Species
- Lux-AHL: 30C6HSL is an acyl homoserine lactone which mainly binds to LuxR.
- LuxR: constitutively expressed regulator protein that can bind Lux-AHL and stimulate transcription of Bxb1.
- RLux: LuxR and Lux-AHL complex which can dimerise.
- DRLux: Dimerised form of RLux.
- Bxb1: serine integrase that can fold into two conformations- Bxb1a and Bxb1b. We chose to use a common connotation for both conformations - Bxb1.
- Las-AHL: 30C12HSL is an acyl homoserine lactone which mainly binds to LasR.
- LasR: constitutively expressed regulator protein that can bind Las-AHL and stimulate transcription of ΦC31.
- RLas: LasR and Las-AHL complex which can dimerise.
- DRLas: Dimerised form of RLas.
- ΦC31: serine integrase that can fold into two conformations- ΦC31a and ΦC31b. We chose to use a common connotation for both conformations - ΦC31.
Reactions
- For the Lux system
$$ \begin{align} &\rightarrow LuxR \\ Lux-AHL+LuxR & \leftrightarrow RLux\\ RLux}+RLux & \leftrightarrow DRLux\\ DRLux}+P_{luxOFF} & \leftrightarrow P_{luxON}\\ P_{luxON}&\rightarrow P_{luxON}+mRNA_{Bxb1}\\ mRNA_{Bxb1}&\rightarrow Bxb1\\ AHL &\rightarrow \\ LuxR &\rightarrow \\ R_{Lux} &\rightarrow\\ DR_{Lux} &\rightarrow\\ mRNA_{Bxb1} &\rightarrow\\ Bxb1 &\rightarrow \end{align}$$
- For ΦC31
\begin{align} \phi C31 + \phi C31 &\leftrightarrow D\phi C 31 \\ D\phi C 31 + SI_{\phi C31} & \leftrightarrow SA_{\phi C31}\\ \phi C31 &\rightarrow \\ D\phi C31 &\rightarrow \end{align}
Differential Equations
Applying mass action kinetic laws, we obtain the following set of differential equations.
$$\frac{d[Bxb1]}{dt}=-2 k_{dimBxb1}[Bxb1]^2+ 2 k_{-dimBxb1}[DBxb1]-d_{Bxb1}[Bxb1]$$
$$\frac{d[DBxb1]}{dt}=-k_{DNABxb1}[DBxb1][SI_{Bxb1}]+k_{-DNABxb1}[SA_{Bxb1}]+k_{dimBxb1}[Bxb1]^2-k_{-dimBxb1}[DBxb1a]-d_{DBxb1}[DBxb1]$$
$$\frac{d[SA_{Bxb1}]}{dt}=k_{DNABxb1}[DBxb1][SI_{Bxb1}]-k_{-DNABxb1}[SA_{Bxb1}]$$
Characterization
Data
Assumptions
Parameter fitting
Range of validity of the assumptions
Characterization
Data
Assumptions
Parameter fitting
Range of validity of the assumptions
