The ordinary differential equation model for small ribonucleic acid (sRNA) gene silencing was formulated for the purpose of:

1. Model Formation
2. Model Reductions and Steady State Behaviour
3. Parameters
4. Results
5. Sensitivity Analysis
6. Conclusion

Model Formation

Inspiration for the model came from the metabolic pathway reported in the literature by Abia in 2007 [17]. In the network, sRNA binds to by Hfq, a chaperone protein which increases the binding rate between sRNA and its target mRNA substantially. Once bound, the Hfq-sRNA-mRNA complex is broken down by a degradosome, a specialized quaternary structure in sRNA-regulated gene expression.

At least, this is how the pathway works in E. coli. A major difficulty is that Hfq in S. aures doesn’t seem to play any major physiological role [18]. To make matters more difficult, the existence of a chaperone protein for sRNA in S. aures has yet to be discovered [19]. Additionally, the proteins that make up the degradosome in E. coli are not present in S. aures..

Our solution to these problems was to simple provide Staphylococcus aures the Hfq present in E. coli. In this way, a model of sRNA gene-regulation could be implemented to aid with laboratory design, and respond to the purposes of the model. Since Hfq would need to be expressed in the target cell, the reaction network took the form of Figure X.

Applying the usual mass action to the reaction network in Figure X, we arrive at the model equations:

Model Reduction and Steady State Behaviour

In our model equations presented previously, if we define the total amount of Hfq present in the cell as H_T=H+H_s+H_ms, we find: