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Team:ETH Zurich/modeling/int
From 2014.igem.org
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|k<sub>SABxb1</sub> | |k<sub>SABxb1</sub> | ||
| - | |Rate of formation of | + | |Rate of formation of SA<sub>Bxb1</sub> from DBxb1 and SI<sub>Bxb1</sub> |
|Unknown | |Unknown | ||
|- | |- | ||
|k<sub>-SABxb1</sub> | |k<sub>-SABxb1</sub> | ||
| - | |Dissociation rate of | + | |Dissociation rate of SA<sub>Bxb1</sub> |
|Unknown | |Unknown | ||
|- | |- | ||
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|Unknown | |Unknown | ||
|} | |} | ||
| - | Remplacing every occurence of Bxb1 by ΦC31 gives the set of parameters for ΦC31. The same | + | |
| + | Remplacing every occurence of Bxb1 by ΦC31 gives the set of parameters for ΦC31. The same status can be applied to those parameters. | ||
| + | |||
| + | Even if degradation rates were not determined specifically for the serine integrases and their dimerized form, degradation rates of proteins in ''E. coli'' are available. To characterize integrases behavior, we focus on finding the parameters for dimerization and DNA-binding. | ||
=== Differential Equations === | === Differential Equations === | ||
Revision as of 09:05, 12 October 2014
Integrases
Model
In our design, integrases compute the output of the logic gates. Integrases allow to flip one fragment of DNA. The model we developped is described here.
Chemical Species
| Name | Description |
|---|---|
| Bxb1 | Serine integrase that can fold into two conformations called Bxb1a and Bxb1b. Even if those conformations have the same sequence of amino acids, their tertiary structure is different. As it is experimentally difficult to differentiate these two conformations, we chose to to use a common notation for both conformations. |
| ΦC31 | Serine integrase that can fold into two conformations called ΦC31a and ΦC31b. Similarly to Bxb1, we chose to use a common notation for both conformations. |
| DBxb1 | Dimer of Bxb1. Bxb1a (respectively Bxb1b) forms a dimer DBxb1a (respectively DBxb1b). To be coherent, dimers are not differentiated depending on their spatial configuration. |
| DΦC31 | Dimer of ΦC31. ΦC31a (respectively ΦC31b) forms a dimer DΦC31a (respectively DΦC31b). The different spatial configuration are not taken into account. |
Modeling DNA-binding sites
Each dimer of integrases can specifically bind to a DNA binding site. As the flipping is irreversible, these DNA binding sites can be three possible states:
- SIIntegraseName: inactive DNA binding site. No dimer is bound to this site, which has never been flipped.
- SAIntegraseName: active DNA binding site. A dimer is to this site.
- SFIntegraseName: flipped DNA binding site. This DNA binding site has been used by a flipping.
Reactions
- For Bxb1
$$ \begin{align} Bxb1 + Bxb1 &\leftrightarrow DBxb1 \\ DBxb1 + SI_{Bxb1} & \leftrightarrow SA_{Bxb1}\\ Bxb1 &\rightarrow \\ DBxb1 &\rightarrow \end{align}$$
- 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}
Parameters
| Name | Description | Status |
|---|---|---|
| kDBxb1 | Dimerization rate of Bxb1 | Unknown |
| k`-DBxb1 | Dissociation rate of DBxb1 | Unknown |
| kSABxb1 | Rate of formation of SABxb1 from DBxb1 and SIBxb1 | Unknown |
| k-SABxb1 | Dissociation rate of SABxb1 | Unknown |
| dBxb1 | Degradation rate of Bxb1 | Unknown |
| dDBxb1 | Degradation rate of DBxb1 | Unknown |
Remplacing every occurence of Bxb1 by ΦC31 gives the set of parameters for ΦC31. The same status can be applied to those parameters.
Even if degradation rates were not determined specifically for the serine integrases and their dimerized form, degradation rates of proteins in E. coli are available. To characterize integrases behavior, we focus on finding the parameters for dimerization and DNA-binding.
Differential Equations
Applying mass action kinetic laws, we obtain the following set of differential equations for Bxb1.
$$\frac{d[Bxb1]}{dt}=-2 k_{DBxb1}[Bxb1]^2+ 2 k_{-DBxb1}[DBxb1]-d_{Bxb1}[Bxb1]$$
$$\frac{d[DBxb1]}{dt}=-k_{SABxb1}[DBxb1][SI_{Bxb1}]+k_{-SABxb1}[SA_{Bxb1}]+k_{DBxb1}[Bxb1]^2-k_{-DBxb1}[DBxb1]-d_{DBxb1}[DBxb1]$$
$$\frac{d[SA_{Bxb1}]}{dt}=k_{SABxb1}[DBxb1][SI_{Bxb1}]-k_{-SABxb1}[SA_{Bxb1}]$$
Remplacing every occurence of Bxb1 by ΦC31 gives the set of differential equations for ΦC31.
Characterization
Data
Assumptions
Parameter fitting
Range of validity of the assumptions
Characterization
Data
Assumptions
Parameter fitting
Range of validity of the assumptions
