Team:Waterloo/Math Book

From 2014.igem.org

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      <h2>sRNA</h2>
 
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<p>Bacterial small RNAs (sRNA) are non-coding RNA molecules produced by bacteria. The role of sRNA in bacterial physiology is extremely diverse; they can either bind to protein targets, and modify the function of the bound protein, or bind to mRNA targets and regulate gene expression. Antisense sRNAs can be categorised as cis-encoded sRNAs, where there is an overlap between the antisense sRNA and the target gene, and trans-encoded sRNAs, where the antisense sRNA gene is separate from the target gene.</p>
 
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      <h3> Relevant Biology </h3>
 
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The model is based on sRNAs that bind to the chaperone protein, Hfq. Hfq binds to sRNA, forming a complex. This complex then binds to mRNA and promotes degradation of both the mRNA and sRNA in a stoichiometric manner. Mechanistically, the Hfq-mRNA-sRNA complex is broken down by a <b>degradosome</b>, a complex of proteins where the protein RNAse E is the centerpiece~\cite{aiba2007mechanism}. The important thing to note here is that the order is <b>compulsory</b>.</p>
 
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<p>We can also assume that binding of mRNA to sRNA doesn't happen on its own, which Professor Scott and myself talked about. Some papers seem to suggest that it does, others note the requirement for Hfq.</p>
 
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<p>In some cases Hfq is actually part of the degradosome, for example in SgrS regulation, and sometimes its not, in the case of RyhB. Both SrgS and RyhB are names for specific sRNA that regulate different metabolic pathways; RyhB is responsible for regulating iron metabolism in <em>E. coli</em>, SrgS is responsible for handling glucose-phosphate stress (a rapid increase in glucose-6-phosphate, a precursor to glycolysis). This changes the mechanism quite a bit, however, for the purposes of this model, I'm going to assume that our sRNA suppression style is more akin to RyhB - although we really should look into this.</p>
 
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<p>Our previous models haven't considered the fact that sRNA gets degraded with the mRNA by the degradosome simultaneously. This new formulation is that assumptions' reckoning.</p>
 
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      <h3> Model Formation </h3>
 
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<p>The model of chemical network is shown below. Before writing this out as a system of equations, I want to describe what's happening first. We are tracking the concentrations of seven species: <code>s, m, M, h, H, H<sub>s</sub> and H<sub>ms</sub></code>, representing the sRNA, the mRNA, the target protein, Hfq mRNA, Hfq, Hfq-sRNA complex, and Hfq-sRNA-mRNA complex respectively.</p>
 
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<!------------------- CONJUGATION SECTION --------------------------------->
<!------------------- CONJUGATION SECTION --------------------------------->

Revision as of 00:02, 18 October 2014

Math Book

Our Math Book is meant to be the mathematical modelling equivelent of a lab book, where we store everything another team might need to recreate our models. You can access code related to the models can be accessed from this github page.

We modelled three main aspects of the Staphylocide system: CRISPR Interference, silencing RNA and Conjugation.

We hope you enjoy learning more about our model on the subpages!

 

Conjugation

ABM

ABM 0h ABM 6h ABM 12h ABM 18h ABM 24h ABM Plot n=10 ABM Plot n=100

References

[1]D. Bikard et al. “Programmable repression and activation of bacterial gene expression using an engineered CRISPR-Cas system”. In: Nucleic Acids Res. 41.15 (Aug. 2013), pp. 7429–7437.
[2]Florian Brandt et al. “The Native 3D Organization of Bacterial Polysomes”. In: Cell 136.2 (2009), pp. 261 –271. issn: 0092-8674. doi: 10.1016/j.cell.2008.11.016.
[3]A. G. Cheng, D. Missiakas, and O. Schneewind. “The giant protein Ebh is a determinant of Staphylococcus aureus cell size and complement resistance”. In: J. Bacteriol. 196.5 (2014), pp. 971–981.
[4]A. L. Cheung, K. Nishina, and A. C. Manna. “SarA of Staphylococcus aureus binds to the sarA promoter to regulate gene expression”. In: J. Bacteriol. 190.6 (Mar. 2008), pp. 2239–2243.
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[6]S. Michalik et al. “Life and death of proteins: a case study of glucose-starved Staphylococcus aureus”. In: Mol. Cell Proteomics 11.9 (Sept. 2012), pp. 558–570.
[7]R. Milo et al. “BioNumbers-the database of key numbers in molecular and cell biology”. In: Nucleic Acids Res. 30 (Jan. 2010), pp. D750–D753. url: http://bionumbers.hms.harvard.edu/bionumber.aspx?id=107869}.
[8]L. S. Qi et al. “Repurposing CRISPR as an RNA-guided platform for sequence-specific control of gene expression”. In: Cell 152.5 (Feb. 2013), pp. 1173–1183.
[9]C. Roberts et al. “Characterizing the effect of the Staphylococcus aureus virulence factor regulator, SarA, on log-phase mRNA half-lives”. In: J. Bacteriol. 188.7 (Apr. 2006), pp. 2593–2603. doi: 10.1128/JB.188.7.2593-2603.2006
[10]Marlena Siwiak and Piotr Zielenkiewicz. “Transimulation - Protein Biosynthesis Web Service”. In: PLoS ONE 8.9 (Sept. 2013), e73943. doi: 10.1371/journal.pone.0073943.
[11]S.H. Sternberg et al. “DNA interrogation by the CRISPR RNA-guided endonuclease Cas9”. In: Nature 7490 (2014), 6267. doi: 10.1038/nature13011. url: http://www.nature.com/nature/journal/v507/n7490/full/nature13011.html.
[12]Freiburg iGEM Team. dCas9. BBa K1150000 Standard Biological Part. 2013. url: http://parts.igem.org/Part:BBa_K1150000.
[13]UCSF iGEM Team. Operation CRISPR: Decision Making Circuit Model. 2013. url: https://2013.igem.org/Team:UCSF/Modeling.
[14]Jian-Qiu Wu and Thomas D. Pollard. “Counting Cytokinesis Proteins Globally and Locally in Fission Yeast”. In: Science 310.5746 (2005), pp. 310–314. doi: 10.1126/science.1113230.
[15]Jianfang Jia and Hong Yue. “Sensitivity Analysis and Parameter Estimation of Signal Transduction Pathways Model”. In: Proceedings of the 7th Asian Control Conference (Aug. 2009), pp. 1357–1362.
[16]Fi-John Chang and J. W. Delleur. “Systematic Parameter Estimation Of Watershed Acidification Model”. In: Hydrological Processes 6. (1992), pp. 29–44. doi: 10.1002/hyp.3360060104.
[17]Aiba, H. (2007). Mechanism of RNA silencing by Hfq-binding small RNAs. Current opinion in microbiology, 10 (2), 134-139.
[18]Horstmann, N., Orans, J., Valentin-Hansen, P., Shelburne, S. A., & Brennan, R. G. (2012). Structural mechanism of Staphylococcus aureus Hfq binding to an RNA A-tract. Nucleic acids research, gks809.
[19]Eyraud, A., Tattevin, P., Chabelskaya, S., & Felden, B. (2014). A small RNA controls a protein regulator involved in antibiotic resistance in Staphylococcus aureus. Nucleic acids research, gku149.
[20]Shimoni, Y., Friedlander, G., Hetzroni, G., Niv, G., Altuvia, S., Biham, O., & Margalit, H. (2007). Regulation of gene expression by small non‐coding RNAs: a quantitative view. Molecular Systems Biology, 3 (1)
[21]Fender, A., Elf, J., Hampel, K., Zimmermann, B., & Wagner, E. G. H. (2010). RNAs actively cycle on the Sm-like protein Hfq. Genes & Development, 24 (23),2621-2626.
[22] Swain, P. S. (2004). Efficient attenuation of stochasticity in gene expression through post-transcriptional control. Journal of molecular biology, 344 (4),965-976.
[23] Hussein, R., & Lim, H. N. (2012). Direct comparison of small RNA and transcription factor signaling. Nucleic acids research, 40 (15), 7269-7279.
[24] Levin, B.R., Stewart, F.M. and Rice, V.A. 1979. “The Kinetics of Conjugative Plasmid Transmission: Fit of a Simple Mass Action Model.” In: Plasmid. 2. pp. 247-260.
[25]Projan, S.J. and Archer, G.L. 1989. “Mobilization of the Relaxable Staphylococcus aureus Plasmid pC221 by the Conjugative Plasmid pGO1 Involves Three pC221 Loci.” In: Journal of Bacteriology. pp. 1841-1845.
[26]Phornphisutthimas, S., Thamchaipenet, A., and Panijpan, B. 2007. “Conjugation in Escherichia coli.” In: The International Union of Biochemistry and Molecular Biology. 35. 6. pp. 440-445.
[27]Phornphisutthimas, S., Thamchaipenet, A., and Panijpan, B. 2007. “Conjugation in Escherichia coli.” In: The International Union of Biochemistry and Molecular Biology. 35. 6. pp. 440-445.
[28]P Chung P., McNamara P.J., Campion J.J., Evans M.E. 2006. “Mechanism-based pharmacodynamic models of fluoroquinolone resistance in Staphylococcus aureus.” In: In: Antimicrobial Agents Chemotherapy. 50. pp. 2957-2965.
[29] Chang H., Wang L. “A Simple Proof of Thue's Theorem on Circle Packing” In: arXiv:1009.4322v1.

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