Team:University College London/Module 2/Modelling

From 2012.igem.org

(Difference between revisions)
(Modelling)
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== Modelling ==
== Modelling ==
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In addition to our gene network model for this module, we have come up with a system of equations which describe the strength of our adhesive biofilms under shear force stress.
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Our cell model for aggregation describes the pathways through which the proteins CsgA and CsgB, which make up curli fibrils, are produced on detection of microplastics.  Using this we aim to find out how many curlis each cell might express, which we could then use to estimate the binding strength of our bacteria.
[[File:aggnet.png]]
[[File:aggnet.png]]
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[[File:agggraph.png]]
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As with our [[Team:University_College_London/Module_3/Modelling|degradation model]], this SimBiology model is divided into three compartments:
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Outside1: in this compartment we see the association, adherence, and dissociation of persistent organic pollutants (POPs) from polyethylene (PE) (R1). We rely on the POPs to induce our degradation system, increasing by (10<sup>5</sup> to 10<sup>6</sup> the specificity to our system.
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Cell: NahR is a constitutively produced mRNA product (R9) of which around 3% degrades (R10). When POP diffuses into the cell (R2), it forms a complex with intact NahR (R3) which then binds to the pSal promoter (R4) to induce the curli gene cluster (R5).  This starts translation of five proteins which make up curli fibrils.  Here we focus on those controlled by the CsgAB operon, CsgA (R7) and CsgB (R6), as these are the most important in curli synthesis as described on our [[https://2012.igem.org/Team:University_College_London/Module_2 | research page]].  The CsgA and CsgB that do not degrade (R11, R12) diffuse out of the cell. 
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Outside2: Outside of the cell the polymerization of CsgA by CsgB takes place (R8) to make a curli fibril.
==Species ==
==Species ==
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| POPinNahRpSal || 0.0 || Complex of the above molecule and pSal (promoter that induces laccase transcription)
| POPinNahRpSal || 0.0 || Complex of the above molecule and pSal (promoter that induces laccase transcription)
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|-
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| mRNACurli || 0.0 || Polycistronic mRNA as it codes for more than one protein, in reality curli cluster contains five or more proteins, in our model mRNA is present as ??CsgE??<sup>5</sup>
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| mRNACurli || 0.0 || Polycistronic mRNA as it codes for more than one protein, in reality curli cluster contains five or more proteins, in our model mRNA is present as CsgE<sup>5</sup>
|-
|-
| CsgA || 0.0 || One of the polypeptides that is coded for in curli cluster, it is a structural component secreted in subunits outside of the cell
| CsgA || 0.0 || One of the polypeptides that is coded for in curli cluster, it is a structural component secreted in subunits outside of the cell
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| CsgB || 0.0 || One of the polypeptides that is coded for in curli cluster, it is secreted outside of the cell allowing polymerization of CsgA
| CsgB || 0.0 || One of the polypeptides that is coded for in curli cluster, it is secreted outside of the cell allowing polymerization of CsgA
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|-
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| Fibril || Result of CsgA and CsgB interaction
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| Fibril || 0.0 || Result of CsgA and CsgB interaction
|}
|}
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| R2 || POPex ↔ POPin || Forward: 0.6 <br /> Backward: 0.4 || Based on membrane permeability<sup>4</sup>: diffusion gradient
| R2 || POPex ↔ POPin || Forward: 0.6 <br /> Backward: 0.4 || Based on membrane permeability<sup>4</sup>: diffusion gradient
|-
|-
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| R3 || POPin + mRNA.Nahr → POPin.mRNA.Nahr || Forward: 1 <br /> Backward: 0.0001 || Based on the assumption that the chemical structure/size of POPs is similar to salycilate<sup>6</sup>.  Salycilate binds to the NahR mRNA product, which complex then binds to the pSal promoter.
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| R3 || POPin + mRNA.Nahr → POPin.mRNA.Nahr || Forward: 1 <br /> Backward: 0.0001 || Based on the assumption that the chemical structure/size of POPs is similar to salycilate<sup>7</sup>.  Salycilate binds to the NahR mRNA product, which complex then binds to the pSal promoter.
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|-
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| R7 || 0 → mRNA.Nahr || Forward: 0.088 <br /> Backward: 0.6 || Transcription rate of NahR in molecules/sec (for NahR size 909 bp<sup>7</sup>, transcription rate in E.coli 80bp/sec<sup>8</sup>) under constitutive promoter control
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| R9 || 0 → mRNA.Nahr || Forward: 0.088 <br /> Backward: 0.6 || Transcription rate of NahR in molecules/sec (for NahR size 909 bp<sup>8</sup>, transcription rate in E.coli 80bp/sec<sup>9</sup>) under constitutive promoter control
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|-
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| R4 || POPinmRNANahr POPinmRNANahr.Psal || Forward: 78200 <br /> Backward: 0.191 <sup>9</sup> || NahR to pSal binding based on the assumption that POP-NahR binding has no effect on NahR-pSal binding
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| R10 || mRNA.Nahr 0 || 0.03 || Degradation rate of NahR mRNA product<sup>14</sup>  
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|-
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| R5 || POPexmRNANahr.Psal → GFP.mRNA|| 0.11 || Transcription rate of GFP in molecules/sec (for GFP size 720bp<sup>10</sup>, transcription rate in E.coli 80bp/sec<sup>8</sup>)
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| R4 || POPinmRNANahr → POPinmRNANahr.Psal || Forward: 78200 <br /> Backward: 0.191 <sup>10</sup> || NahR to pSal binding based on the assumption that POP-NahR binding has no effect on NahR-pSal binding
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|-
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| R6 || GFP.mRNA GFP|| 0.084 || Translation rate of GFP in molecules/sec (for GFP size 240aa<sup>10</sup>, translation rate in E.coli 20aa/sec<sup>8</sup>)
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| R5 || POPexmRNANahr.Psal mRNAcurli || 0.054 || Transcription rate of curli cluster in molecules/sec (for cluster size 1500bp<sup>11</sup>, transcription rate in E.coli 80bp/sec<sup>9</sup>)
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|-
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| R9 || GFP.mRNA → 0 || 0.03 || Degradation rate of GFP mRNA product<sup>11</sup> must be taken into account due to suboptimal conditions
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| R6 || mRNAcurli → CsgB || 0.13 || Translation rate of CsgB in molecules/sec (for CsgB size 151aa<sup>12</sup>, translation rate in E.coli 20aa/sec<sup>9</sup>)
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|-
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| R7 || mRNAcurli → CsgA || 0.13 || Translation rate of CsgA in molecules/sec (for CsgA size 151aa<sup>13</sup>, translation rate in E.coli 20aa/sec<sup>9</sup>)
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|-
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| R11 || CsgA → 0 || 0.03 || Degradation rate of CsgA <sup>14</sup> must be taken into account due to suboptimal conditions
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|-
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| R12 || CsgB → 0 || 0.03 || Degradation rate of CsgB <sup>14</sup> must be taken into account due to suboptimal conditions
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|-
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| R8 || CsgB + CsgA -> fibril || ARGH || ARGH
|}
|}
== Results ==
== Results ==
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To follow
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[[File:agggraph.png]]
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The graph shows that fibrils are produced at a rate of around 1 fibril per second.
== References ==
== References ==
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6. Mato Y, Isobe T, Takada H, Kanehiro H, Ohtake C, Kaminuma T (2001) Plastic Resin Pellets as a Transport Medium for Toxic Chemicals in the Marine Environment. Environ. Sci. Technol. 35: 318-324
6. Mato Y, Isobe T, Takada H, Kanehiro H, Ohtake C, Kaminuma T (2001) Plastic Resin Pellets as a Transport Medium for Toxic Chemicals in the Marine Environment. Environ. Sci. Technol. 35: 318-324
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7.  https://2011.igem.org/Team:Peking_S/project/wire/harvest
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 +
8. http://www.xbase.ac.uk/genome/azoarcus-sp-bh72/NC_008702/azo2419;nahR1/viewer
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9. http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf
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10. Park H, Lim W, Shin H (2005) In vitro binding of purified NahR regulatory protein with promoter Psal. <i>Biochimica et Biophysica Acta</i> 1775: 247-255
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11. Shala AA, Restrepo S, Gonzalez Barrios AF (2011) A network model for biofilm development in Escherichia coli K-12.  <i> Theoretical Biology and Medical Modelling </i> 8: 34 doi:10.1186/1742-4682-8-34
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12. http://www.ecogene.org//?q=gene/EG12621
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 +
13. http://www.ecogene.org/?q=gene/EG11489
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Walsh DM, Lomakin A, Benedek GB, Condron MM, Teplow DB (1997) Amyloid b-Protein Fibrillogenesis: Detection of a protofibrillar intermediate. <i> The Journal of Biological Chemistry </i> 272: 22364–22372
+
14. Kushner S (2002) mRNA Decay in <i>Escherichia coli</i> Comes of Age. <i>J Bacteriol.</i> 184: 4658-4665
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Shala AA, Restrepo S, Gonzalez Barrios AF (2011) A network model for biofilm development in Escherichia coli K-12.  <i> Theoretical Biology and Medical Modelling </i> 8: 34 doi:10.1186/1742-4682-8-34
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Where does this go? Walsh DM, Lomakin A, Benedek GB, Condron MM, Teplow DB (1997) Amyloid b-Protein Fibrillogenesis: Detection of a protofibrillar intermediate.  <i> The Journal of Biological Chemistry </i> 272: 22364–22372

Revision as of 13:53, 25 September 2012

Contents

Module 2: Aggregation

Description | Design | Construction | Characterisation | Shear Device | Modelling | Results | Conclusions

Modelling

Our cell model for aggregation describes the pathways through which the proteins CsgA and CsgB, which make up curli fibrils, are produced on detection of microplastics. Using this we aim to find out how many curlis each cell might express, which we could then use to estimate the binding strength of our bacteria.

Aggnet.png

As with our degradation model, this SimBiology model is divided into three compartments:

Outside1: in this compartment we see the association, adherence, and dissociation of persistent organic pollutants (POPs) from polyethylene (PE) (R1). We rely on the POPs to induce our degradation system, increasing by (105 to 106 the specificity to our system.

Cell: NahR is a constitutively produced mRNA product (R9) of which around 3% degrades (R10). When POP diffuses into the cell (R2), it forms a complex with intact NahR (R3) which then binds to the pSal promoter (R4) to induce the curli gene cluster (R5). This starts translation of five proteins which make up curli fibrils. Here we focus on those controlled by the CsgAB operon, CsgA (R7) and CsgB (R6), as these are the most important in curli synthesis as described on our [| research page]. The CsgA and CsgB that do not degrade (R11, R12) diffuse out of the cell.

Outside2: Outside of the cell the polymerization of CsgA by CsgB takes place (R8) to make a curli fibril.

Species

Species Initial value (molecules) Notes
PE 0.044 Polyethylene found in North Pacific Gyre (value per cubic metre)1,2
POPex 0.0 Persistent organic pollutants (ex = extracellular) that are not adhered to plastic surface
PEPOPex 9.24E-5 Persistent organic pollutants (ex = extracellular) that are adhered to the plastic surface3
POPin 0.5 Persistent organic pollutants (in = intracellular) assumed from E. coli membrane permeability 4
mRNANahR 0.0 NahR mRNA product
POPinNahR 0.0 Complex of the above two molecules
POPinNahRpSal 0.0 Complex of the above molecule and pSal (promoter that induces laccase transcription)
mRNACurli 0.0 Polycistronic mRNA as it codes for more than one protein, in reality curli cluster contains five or more proteins, in our model mRNA is present as CsgE5
CsgA 0.0 One of the polypeptides that is coded for in curli cluster, it is a structural component secreted in subunits outside of the cell
CsgB 0.0 One of the polypeptides that is coded for in curli cluster, it is secreted outside of the cell allowing polymerization of CsgA
Fibril 0.0 Result of CsgA and CsgB interaction

Reactions taking place in the model

Number Reaction Reaction rate (molecules/sec) Notes
R1 PE + POPex ↔ PEPOPex Forward: 1000
Backward: 1
Pops have 1000 to 10000 times greater tendency to adhere to plastic than float free in the ocean6
R2 POPex ↔ POPin Forward: 0.6
Backward: 0.4
Based on membrane permeability4: diffusion gradient
R3 POPin + mRNA.Nahr → POPin.mRNA.Nahr Forward: 1
Backward: 0.0001
Based on the assumption that the chemical structure/size of POPs is similar to salycilate7. Salycilate binds to the NahR mRNA product, which complex then binds to the pSal promoter.
R9 0 → mRNA.Nahr Forward: 0.088
Backward: 0.6
Transcription rate of NahR in molecules/sec (for NahR size 909 bp8, transcription rate in E.coli 80bp/sec9) under constitutive promoter control
R10 mRNA.Nahr → 0 0.03 Degradation rate of NahR mRNA product14
R4 POPinmRNANahr → POPinmRNANahr.Psal Forward: 78200
Backward: 0.191 10
NahR to pSal binding based on the assumption that POP-NahR binding has no effect on NahR-pSal binding
R5 POPexmRNANahr.Psal → mRNAcurli 0.054 Transcription rate of curli cluster in molecules/sec (for cluster size 1500bp11, transcription rate in E.coli 80bp/sec9)
R6 mRNAcurli → CsgB 0.13 Translation rate of CsgB in molecules/sec (for CsgB size 151aa12, translation rate in E.coli 20aa/sec9)
R7 mRNAcurli → CsgA 0.13 Translation rate of CsgA in molecules/sec (for CsgA size 151aa13, translation rate in E.coli 20aa/sec9)
R11 CsgA → 0 0.03 Degradation rate of CsgA 14 must be taken into account due to suboptimal conditions
R12 CsgB → 0 0.03 Degradation rate of CsgB 14 must be taken into account due to suboptimal conditions
R8 CsgB + CsgA -> fibril ARGH ARGH

Results

Agggraph.png

The graph shows that fibrils are produced at a rate of around 1 fibril per second.

References

1. Goldstein M, Rosenberg M, Cheng L (2012) Increased oceanic microplastic debris enhances oviposition in an endemic pelagic insect. Biology Letters 10.1098

2. Andrady AL (2011) Microplastics in the marine environment. Marine Pollution Bulletin 62: 1596-1605

3. To follow

4. To follow

5. Nenninger AA, Robinson LS, Hammer ND, Epstein EA, Badtke MP, Hultgren SJ, Chapman MR (2011) CsgE is a curli secretion specificity factor that prevents amyloid fibre aggregation. Mol Microbiol 81: 486-499

6. Mato Y, Isobe T, Takada H, Kanehiro H, Ohtake C, Kaminuma T (2001) Plastic Resin Pellets as a Transport Medium for Toxic Chemicals in the Marine Environment. Environ. Sci. Technol. 35: 318-324

7. https://2011.igem.org/Team:Peking_S/project/wire/harvest

8. http://www.xbase.ac.uk/genome/azoarcus-sp-bh72/NC_008702/azo2419;nahR1/viewer

9. http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf

10. Park H, Lim W, Shin H (2005) In vitro binding of purified NahR regulatory protein with promoter Psal. Biochimica et Biophysica Acta 1775: 247-255

11. Shala AA, Restrepo S, Gonzalez Barrios AF (2011) A network model for biofilm development in Escherichia coli K-12. Theoretical Biology and Medical Modelling 8: 34 doi:10.1186/1742-4682-8-34

12. http://www.ecogene.org//?q=gene/EG12621

13. http://www.ecogene.org/?q=gene/EG11489

14. Kushner S (2002) mRNA Decay in Escherichia coli Comes of Age. J Bacteriol. 184: 4658-4665

Where does this go? Walsh DM, Lomakin A, Benedek GB, Condron MM, Teplow DB (1997) Amyloid b-Protein Fibrillogenesis: Detection of a protofibrillar intermediate. The Journal of Biological Chemistry 272: 22364–22372