Model

After binding to DNA, integrases can flip the fragment and thus compute the output of the XOR logic gate.

Principle

The fragment integrases can be flip is a terminator. Thus, the terminator can either be on or off.

• T_on: terminator is on, transcription is blocked.

• T_off: terminator is off, transcription is active. It corresponds to one flipping of the terminator.

In our design, we are interested in a double flipping. That is to say that two pairs of binding sites surrounds the fragment to be flipped. One pair of binding sites can be bound by DBxb1 and the other one by ΦC31.

Reactions

$$\begin{align*} SA_{Bxb1}+SA_{Bxb1}+T_{on,i}& \rightarrow T_{offBxb1}+ SF_{Bxb1}+SF_{Bxb1}\\ T_{offBxb1} &\rightarrow T_{offBxb1} + mRNA_{GFP} + mRNA_{LasI} \\ SA_{\phi C31}+SA_{\phi C31}+T_{on,i}& \rightarrow T_{off\phi C31}+SF_{\phi C31}+SF_{\phi C31}\\ T_{off\phi C31} &\rightarrow T_{off\phi C31} + mRNA_{GFP} + mRNA_{LasI} \\ SA_{Bxb1}+SA_{Bxb1}+T_{off,\phi C31}& \rightarrow T_{on,f}+SF_{Bxb1}+SF_{Bxb1}\\ SA_{\phi C31}+SA_{\phi C31}+T_{offBxb1}& \rightarrow T_{on,f}+SF_{\phi C31}+SF_{\phi C31}\\ mRNA_{GFP} &\rightarrow GFP\\ mRNA_{LasI} &\rightarrow LasI\\ mRNA_{GFP} &\rightarrow \emptyset\\ mRNA_{LasI}&\rightarrow \emptyset\\ GFP &\rightarrow \emptyset\\ LasI&\rightarrow \emptyset \end{align*}$$