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

Modelling 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:

• SI_{IntegraseName}: inactive DNA binding site. No dimer is bound to this site, which has never been flipped.

• SA_{IntegraseName}: active DNA binding site. A dimer is to this site.

• SF_{IntegraseName}: flipped DNA binding site. This DNA binding site has been used by a flipping.

The three different states of DBxb1-DNA binding sites.

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}

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