# Decoy Sites

To tune the level of protein expression, we used decoy sites. Decoy sites are tandem repeats of DNA where transcriptional factor can bind to but don't promote gene expression. Therefore it competes with promoter sites and lowers the gene expression rate. LeeDecoyTek-Hyung Lee and Narendra Maheshri, A regulatory role for repeated decoy transcription factor binding sites in target gene expression. Molecular Systems Biology 8, 576 (2012)

## The Model

### Decoy Sites

DecoyModelSchematics Schematic of the Decoy model
The model of decoy sites consists of two reactions, i.e., the transcriptional factor binding to decoy sites and to promoter sites. The schematic graph of this model is illustrated in . The reactions are:
\eqalignno{ \ce{T + N\, &<=>[\text{Kn-on}][\text{Kn-off}] TN} & (1) \\ \ce{T + P\, &<=>[\text{Kp-on}][\text{Kp-off}] TP} & (2) \\ }

The T is the transcriptional factor, which is FNR. It can binds to either the decoy sites(N) or the promoter(P). The production and degradation of T is included in the FNR model.

### Copy Number

The copy numbers refers to the number of certain plasmids in E.coli. In this project we used the derivative of pBR322. So the copy number is between 15 to 20.CopyNr, Growth of Bacterial Cultures. www.qiagen.com/Knowledge-and-Support/Spotlight/Plasmid-Resource-Center/Growth%20of%20bacterial%20cultures/ , () As the plasmid has a low copy number, we take the average of copy number and multiply it with the amount of promoter and decoy sites.

### Protein Expression Rate

The protein expression rate was assumed to be linear to the promoter binding ratio in Tek-Hyung Lee and Narendra MaheshriLeeDecoy. As we have only one promoter in each plasmid, we have either the 'on-state' plasmid or the 'off-state' plasmid. So we take the idea of linearity and convert the assumption to that the protein expression rate is linear to the proportion of 'on-state' plasmid.

## Simulation Result

This model will later on be used for simulations of the complete system we designed. Some results of solely the decoy site model are shown below. and show the binding ratios calculated by either one or multiple stochastic simulations. The simulated result of decoy site binding ratio:

decoyBindingRatio The decoy site and promotor site binding ratios simulated using the stochastic version of the decoy sites model.
decoyBindingRatioMultiple The decoy site binding ratio using simulated 50 times using the stochastic version of the decoy sites model.

These simulation results comply with the original article, so we can go on adapting and extending this model. For these extended models see the complex FNR promoter and the integral model.

## References

The source code of all models can be found here.