System Purpose and Summary
The genetic system created by the 2019 UNL iGEM team was designed to identify MRSA quorum sensing molecules, move towards their source, and produce a bacteriocin that will destroy MRSA cells. We modeled the protein production of our system using Simbiology in Matlab 2018b. The model was created using units of molecules over time.
To build the model, we relied upon the following assumptions:
- These reactions take place in a single E. coli cell of volume 1E-15 L.
- The cell has excess RNA polymerase, ribosomes, and tRNA.
- There are the maximum amount of plasmids for each plasmid count in the cell.
- There are 40 native AraC molecules in the cell. [1]
- The transcription rate is 40 nuc/s [2]
- The translation rate is 17 AA/s [3]
- The mRNA degradation rate is 0.139 min-1, based off of its degradation time of 5 minutes. [4]
- The protein degradation rate is half of the mRNA degradation rate at 0.070 min-1 [5]. This is because different proteins have different degradation rates, and they aren’t often found in literature. Since we know that proteins degrade far slower than mRNA, we’re using a conservative estimate that every protein whose degradation rate was not found in literature has a degradation rate of 10 minutes.
The model is broken up into two phases. The first phase begins when extracellular arabinose enters the cell. The arabinose binds with native AraC proteins, which dimerize and act as a transcription factor for the pBAD promoter. Once the AraC dimer binds to pBAD, transcription is able to initiate to produce a polycistronic mRNA strand encoding AgrA, AgrC, and SarA. This mRNA strand is then translated into the respective proteins through the three RBS sites located on the strand. AgrC then inserts itself into the cell membrane while AgrA and SarA remain in the cytoplasm.
In the second phase, AIP that is secreted from MRSA is introduced to our system by binding to the extracellular portion of AgrC, forming a complex. This complex then phosphorylates AgrA inside the cell. Once AgrA is phosphorylated, it is able to act as a transcription factor for the P2 promoter. A total of four AgrA proteins are needed to activate P2 transcription. Two AgrA proteins bind to P2 in two separate regions, and then two more AgrA proteins form dimers with the P2-bound AgrA. It is at this point that transcription is activated, but two SarA proteins can also bind to P2 to further enhance transcription.
There are three P2 promoters within our system. The first is upstream of the GFP gene, located on the sensing plasmid. The second is upstream of the cheZ gene with YbaQ degron sequence located on the motility plasmid. The third is upstream of gakA, gakB, and gakC, located on the killing plasmid. These genes are transcribed and translated once P2 becomes activated. GFP is a reporter protein with no further function. CheZ serves to inhibit CheY, forcing the E. coli cell to move forward instead of tumble. GakA, GakB, and GakC, once translated, will bind together to form garvicin KS (GarKS). GarKS is then secreted outside the cell and destroys any MRSA cells in the immediate vicinity of the cell.
Calculations
Transcription
We used a transcription rate of 40 nuc/s to calculate the transcription rate of each mRNA strand.
- Sensing_mRNA: 2621 nucleotides -> 0.916 mRNA / minute
- GFP_mRNA: 857 nucleotides -> 2.800 mRNA / minute
- Motility_mRNA: 838 nucleotides -> 2.864 mRNA / minute
- Killing_mRNA: 680 nucleotides -> 3.529 mRNA / minute
Translation
We used a translation rate of 17 AA/s to calculate the translation rate of each protein
- AgrA: 238 amino acids -> 4.284 AgrA / minute
- AgrC: 430 amino acids -> 2.372 AgrC / minute
- SarA: 124 amino acids -> 8.226 SarA / minute
- GFP: 240 amino acids -> 4.248 GFP / minute
- CheZ-YbaQ: 225 amino acids -> 4.533 CheZ-YbaQ / minute
- NSP4-GakA: 56 amino acids -> 18.216 NSP4-GakA / minute
- NSP4-GakB: 56 amino acids -> 18.216 NSP4-GakB / minute
- NSP4-GakC: 54 amino acids -> 18.888 NSP4-GakC / minute
Kd values
Since many equilibrium values are given as a Kd, we converted them to Kf and Kr based on the following equation:
- Kd = Kr⁄Kf, where Kf = 1
For AgrC dimerization and GarKS trimerization, there were no equilibrium values found in literature. Instead, we used conservative estimates of the Kd values.
Species
| Initial Species | Initial Amount (Molecules) | Description |
| AraC | 40 | A native E. coli protein that binds to arabinose to promote pBAD transcription |
| Arabinose | 40 | An extracellular molecule that binds to AraC to promote pBAD transcription |
| AIP | 100 | A quorum sensing molecule secreted by MRSA, which our system detects |
| Sensing_DNA | 300 | The plasmid that contains the genetic code for AgrA, AgrC, and SarA |
| Motility_DNA | 5 | The plasmid that contains the genetic code for CheZ-YbaQ |
| Killing_DNA | 30 | The plasmid that contains the genetic code for GakA, GakB, and GakC |
| Other Species | Description |
| AraC_ara | The complex that is formed between AraC and Arabinose |
| AraC_dimer | The dimer that is formed between two AraC_ara complexes |
| AraC:Sensing_DNA | The complex that is formed between AraC and the pBAD promoter on the sensing plasmid |
| Sensing_mRNA | The transcript that is produced from the transcription of the pBAD promoter on the sensing plasmid |
| AgrA | One of the proteins translated from Sensing_mRNA. Is a precursor to the P2 transcription factor |
| AgrC | One of the proteins translated from Sensing_mRNA. Is a transmembrane protein that phosphorylates AgrA in the presence of AIP |
| SarA | One of the proteins translated from Sensing_mRNA. Is a transcriptional activator for P2, but only works if AgrA is already bound to P2. |
| AgrC_aip | The complex that is formed between AgrC and extracellular AIP |
| AgrA_phos | Phosphorylated AgrA, which is made possible by AgrC_aip |
| AgrA:Sensing_DNA | The complex that is formed on the sensing plasmid when two molecules of AgrA bind to the two regions on the P2 promoter |
| AgrA_2:Sensing_DNA | The complex that is formed on the sensing plasmid when two additional AgrA molecules form dimers with the initial AgrA complexes on the P2 promoter |
| SarA/AgrA_2:Sensing_DNA | The complex that is formed on the sensing plasmid when SarA binds to P2 after the AgrA dimers have already bound to the P2 promoter |
| AgrA:Motility_DNA | The complex that is formed on the motility plasmid when two molecules of AgrA bind to the two regions on the P2 promoter |
| AgrA_2:Motility_DNA | The complex that is formed on the motility plasmid when two additional AgrA molecules form dimers with the initial AgrA complexes on the P2 promoter |
| SarA/AgrA_2:Motility_DNA | The complex that is formed on the motility plasmid when SarA binds to P2 after the AgrA dimers have already bound to the P2 promoter |
| AgrA:Killing_DNA | The complex that is formed on the killing plasmid when two molecules of AgrA bind to the two regions on the P2 promoter |
| AgrA_2:Killing_DNA | The complex that is formed on the killing plasmid when two additional AgrA molecules form dimers with the initial AgrA complexes on the P2 promoter |
| SarA/AgrA_2:Killing_DNA | The complex that is formed on the killing plasmid when SarA binds to P2 after the AgrA dimers have already bound to the P2 promoter |
| GFP_mRNA | The transcript that is produced from the transcription of the P2 promoter on the sensing plasmid |
| Motility_mRNA | The transcript that is produced from the transcription of the P2 promoter on the motility plasmid |
| Killing_mRNA | The transcript that is produced from the transcription of the P2 promoter on the killing plasmid |
| GFP | The green fluorescence protein. Acts as a reporter protein to ensure that the system is detecting MRSA |
| CheZ-YbaQ | The motility protein. Acts by shutting off the E. coli’s native CheY protein, forcing the cell to move toward MRSA. Has a degron tag to prevent accumulation of CheZ, which could cause unwanted movement |
| NSP4-GakA | A precursor to GarKS. Has a secretion tag to ensure GarKS can be transported outside the cell |
| NSP4-GakB | A precursor to GarKS. Has a secretion tag to ensure GarKS can be transported outside the cell |
| NSP4-GakC | A precursor to GarKS. Has a secretion tag to ensure GarKS can be transported outside the cell |
| GarKS | The killing protein. While its mechanisms are unknown, it is able to destroy the MRSA virus. |
Parameters
| Reaction Name | Equation | Value (Molecules) | Source |
| AraC Activation | Arabinose + AraC <-> AraC_ara | kf: 1M / kr: 4E-4 M | [6] |
| AraC Dimerization | AraC_ara + AraC_ara <-> AraC_dimer | kf: 1M / kr: .5 M | Estimated |
| AraC Sensing DNA Binding | Sensing DNA + AraC_ara -> AraC:Sensing_DNA | kf: 1M / kr: 2E-13 M | [6] |
| Activated Sensing Transcription | AraC:Sensing_DNA -> Sensing_mRNA + AraC:Sensing_DNA | 1.26 minute-1 | [7] |
| AgrA Translation | Sensing_mRNA -> Sensing_mRNA + AgrA | 4.284 minute-1 | Calculated |
| AgrC Translation | Sensing_mRNA -> Sensing_mRNA + AgrC | 2.37 minute-1 | Calculated |
| SarA Translation | Sensing_mRNA -> Sensing_mRNA + SarA | 8.226 minute-1 | Calculated |
| Sensing_mRNA Degradation | Sensing_mRNA -> null | 0.139 minute-1 | Previous team |
| AgrA Degradation | AgrA -> null | 0.07 minute -1 | Estimated |
| AgrC Degradation | AgrC -> null | 0.07 minute -1 | Estimated |
| SarA Degradation | SarA -> null | 0.07 minute -1 | Estimated |
| AgrC Activation | AIP + AgrC <-> AgrC_aip | kf: 1M / kr: 6.3E-8 M | [8] |
| AgrA Phosphorylation | AgrC_aip + AgrA <-> AgrA_phos | kf: 1M / kr: 0.1M | [9] |
| AgrA_phos Degradation | AgrA_phos -> null | 0.0333 minute-1 | [10] |
| AgrA Sensing Binding_1 | 2 AgrA_phos + Sensing_DNA <-> AgrA:Sensing_DNA | kf: 1M / kr: 0M | [11] |
| AgrA Sensing Binding_2 | 2 AgrA_phos + AgrA:Sensing_DNA <-> AgrA_2:Sensing_DNA | kf: 1M / kr: 1.6E-10 M | [11] |
| SarA Sensing Binding | 2 SarA + AgrA_2:Sensing_DNA <-> SarA/AgrA_2:Sensing_DNA | kf: 1M / kr: 2E-7 M | [12] |
| AgrA Motility Binding_1 | 2 AgrA_phos + Motility_DNA <-> AgrA: Motility_DNA | kf: 1M / kr: 0M | [11] |
| AgrA Motility Binding_2 | 2 AgrA_phos + AgrA: Motility_DNA <-> AgrA_2: Motility_DNA | kf: 1M / kr: 1.6E-10 M | [11] |
| SarA Motility Binding | 2 SarA + AgrA_2: Motility_DNA <-> SarA/AgrA_2: Motility_DNA | kf: 1M / kr: 2E-7 M | [12] |
| AgrA Killing Binding_1 | 2 AgrA_phos + Killing_DNA <-> AgrA:Killing_DNA | kf: 1M / kr: 0M | [11] |
| AgrA Killing Binding_2 | 2 AgrA_phos + AgrA:Killing_DNA <-> AgrA_2:Killing_DNA | kf: 1M / kr: 1.6E-10 M | [11] |
| SarA Killing Binding | 2 SarA + AgrA_2:Killing_DNA <-> SarA/AgrA_2:Killing_DNA | kf: 1M / kr: 2E-7 M | [12] |
| Low GFP Transcription | AgrA_2:Sensing_DNA -> GFP_mRNA + AgrA_2:Sensing_DNA | 3.852 minute-1 | Calculated |
| High GFP Transcription | SarA/AgrA_2:Sensing_DNA -> GFP_mRNA + SarA/AgrA_2:Sensing_DNA | 3.852 minute-1 | Calculated |
| Low Motility Transcription | AgrA_2:Motility_DNA -> Motility_mRNA + AgrA_2:Motility_DNA | 3.936 minute-1 | Calculated |
| High Motility Transcription | SarA/AgrA_2:Motility_DNA -> Motility_mRNA + SarA/AgrA_2:Motility_DNA | 3.936 minute-1 | Calculated |
| Low Killing Transcription | AgrA_2:Killing_DNA -> Killing_mRNA + AgrA_2:Killing_DNA | 4.854 minute-1 | Calculated |
| High Killing Transcription | SarA/AgrA_2:Killing_DNA -> Killing_mRNA + SarA/AgrA_2:Killing_DNA | 4.854 minute-1 | Calculated |
| GFP Translation | GFP_mRNA -> GFP + GFP_mRNA | 4.248 minute-1 | Calculated |
| CheZ-YbaQ Translation | Motility_mRNA -> CheZ-YbaQ + Motility_mRNA | 4.554 minute-1 | Calculated |
| NSP4-GakA Translation | Killing_mRNA -> NSP4-GakA + Killing_mRNA | 18.216 minute-1 | Calculated |
| NSP4-GakB Translation | Killing_mRNA -> NSP4-GakB + Killing_mRNA | 18.216 minute-1 | Calculated |
| NSP4-GakC Translation | Killing_mRNA -> NSP4-GakC + Killing_mRNA | 18.888 minute-1 | Calculated |
| GarKS Trimerization | NSP4-GakA + NSP4-GakB + NSP4-GakC <-> GarKS | kf: 1M / kr: 0.5M | Estimated |
| GFP_mRNA Degradation | GFP_mRNA -> null | 0.139 minute-1 | Previous team |
| Motility_mRNA Degradation | Motility_mRNA -> null | 0.139 minute-1 | Previous team |
| Killing_mRNA Degradation | Killing_mRNA -> null | 0.139 minute-1 | Previous team |
| GFP Degradation | GFP -> null | 0.07 minute -1 | Estimated |
| CheZ-YbaQ Degradation | CheZ-YbaQ -> null | 0.9 minute -1 | [13] |
| GakA Degradation | NSP4-GakA -> null | 0.07 minute -1 | Estimated |
| GakB Degradation | NSP4-GakB -> null | 0.07 minute -1 | Estimated |
| GakC Degradation | NSP4-GakC -> null | 0.07 minute -1 | Estimated |
| GarKS Degradation | GarKS -> null | 0.07 minute -1 | Estimated |
Results
Steady State
In the absence of AIP, the three sensing proteins reach a steady state. Since translation is directly correlated with amino acid length, the proteins reach steady state at concentrations inversely proportional to their sequence length.
AIP Introduction at t=50
We designed the model so that AIP would be introduced to the system after 50 minutes. The three proteins of interest are GFP, CheZ-YbaQ, and GarKS.
Our model shows that GFP reaches a steady state around 350,000 molecules, GarKS reaches a steady state around 200,000 molecules, and CheZ-YbaQ reaches a steady state around 20,000 molecules. These concentrations seem to be due to the copy number of the plasmid each gene was cloned into. To corroborate this prediction, we adjusted the DNA levels so each plasmid had a high copy number of 300.
As predicted, CheZ-YbaQ and GFP are more similar in steady state concentration. However, GarKS has a much higher relative concentration. This is probably due to the fact that the NSP4-Gak proteins have a shorter amino acid sequence than GFP and CheZ-YbaQ, so more NSP4-Gak proteins are synthesized than GFP or CheZ-YbaQ during a given time.
Project Design
Arabinose Concentrations
Through modeling, we have found that the system can be turned on with relatively low concentrations of arabinose. Since we are assuming that there are around 40 monomers of AraC in E. coli at any given time, increasing arabinose concentrations past 40 molecules has negligible effects on the system.
Of course, this only holds true in ideal systems where arabinose and AraC can readily react with each other. In practice, increasing arabinose concentrations will increase the likelihood of the reaction, but AraC’s low concentration acts as the limiting factor of the reaction; therefore, higher arabinose concentrations will have diminishing returns.
AIP Concentrations
The concentration of AIP does not appear to impact the reaction rates of the system. To test this, we simulated the model with concentrations of AIP at 1, 100, and 100000 molecules. We kept the input of arabinose at 40 molecules.
AIP = 1
AIP = 100
AIP = 100,000
We hypothesize that the impact of AIP is negligible because AgrC is an enzyme that phosphorylates AgrA. Within the context of a model, AgrC always functions as an excess reagent in the reaction. Therefore, adding more AIP to the system won’t increase the phosphorylation rate of AgrA.
GarKS
One paper demonstrated that 2560 BU of GarKS (equivalent to 5.120 µM) is required to neutralize 1 mL of S. aureus at OD = 0.5. This is the highest concentration of GarKS needed to kill any of 24 different species of Gram-positive bacteria tested, suggesting that this is among the highest concentrations required for therapeutic effect. [14] Using the following calculations, we have found that 6.166E9 molecules of GarKS are required to neutralize 1mL of S. aureus at OD = 0.5.
2560 BU⁄mL MRSA * 10nM GarKS⁄5 BU * 1M GarKS⁄1E9nM GarKS * 6.022E23 molecules GarKS⁄1M GarKS = 3.083E18 molecules GarKS ⁄ 1mL MRSA
Our simulations show that a maximum of 18,000 molecules of GarKS are produced in a single E. coli cell every minute. If we assume 1 mL of E. coli at OD = 1, then our system produces 3.6E13 molecules of GarKS per minute.
8,000 molecules GarKS⁄1 E. coli cell * 1 minute * 1E9 E. coli cells⁄1 OD * 1mL = 1.8E13 molecules GarKS / minute * mL
The goal of our system is to completely get rid of MRSA overnight, which is roughly 8 hours. Therefore, we calculated the amount of GarKS produced in 8 hours.
1.8E13 molecules GarKS⁄1 minute * 1 mL E.coli * 60 minutes⁄1 hour * 8 hours = 8.5E15 molecules GarKS / mL E. coli
Given these values, we calculated the amount of mL of our system at OD = 1 required to destroy 1mL of MRSA at OD = 0.5 in 8 hours.
3.083E18 molecules GarKS⁄1 mL MRSA * 1mL E.coli⁄8.5E15 molecules GarKS = 362.8mL of E. coli / 1mL of MRSA
Based on the modeling, we would need to use 362.8mL of our system to neutralize 1mL of concentrated OD 0.5 MRSA over a period of 8 hours. This assumes that our system reaches an OD of 1 in our solution and that the growth rates of both MRSA and E.coli are relatively the same. In a prctical setting, the concentration of MRSA present would be very minute and the volume of E. coli needed for treatment would be heavily reduced as such.
Plasmid Choice
Our design incorporates three plasmids, one with a high copy number (300), one with a medium copy number (30), and one with a low copy number (5). The high copy plasmid was cloned with the sensing strand and the medium copy and low copy plasmids were cloned with the killing and motility strands respectively. While the system works under this scheme, cloning the sensing strand into the low copy plasmid still allows the system to work. This would free up the high copy plasmid to be cloned with a more essential gene.
With this information, we could have designed our system more efficiently. If we cloned the low copy plasmid with the sensing strand, the medium copy plasmid with the motility strand, and the high copy plasmid with the killing strand, the system would still have effectively sensed AIP but would have produced higher concentrations of CheZ-YbaQ and GarKS.
This configuration is ideal for an in vitro broth design because motility is less essential to the success of our system.
However, if we were to do an in vivo application, then it might be more effective to clone the high copy plasmid with the motility strand since greater movement is required. In this case, the medium copy plasmid would be cloned with the killing strand.
One caveat is that since a surplus of CheZ is detrimental to the cell’s motility, this may be an overly simplistic solution. Further experimentation would be required.
References
[1] Kolodrubetz, D., & Schleif, R. (1981). Identification of araC protein on two-dimensional gels, its in vivo instability and normal level. Journal of Molecular Biology, 149(1), 133–139. doi: 10.1016/0022-2836(81)90265-5
[2] Koš, M., & Tollervey, D. (2010). Yeast Pre-rRNA Processing and Modification Occur Cotranscriptionally. Molecular Cell, 37(6), 809–820. doi: 10.1016/j.molcel.2010.02.024
[3] Young, R., & Bremer, H. (1976). Polypeptide-chain-elongation rate in Escherichia coli B/r as a function of growth rate. Biochemical Journal, 160(2), 185–194. doi: 10.1042/bj1600185
[4] Young, R., & Bremer, H. (1976). Polypeptide-chain-elongation rate in Escherichia coli B/r as a function of growth rate. Biochemical Journal, 160(2), 185–194. doi: 10.1042/bj1600185
[5] Milo, R., & Philips, R. (n.d.). " How fast do RNAs and proteins degrade? Retrieved from http://book.bionumbers.org/how-fast-do-rnas-and-proteins-degrade/.
[6] Schleif, R. (2010). AraC protein, regulation of the l-arabinose operon inEscherichia coli, and the light switch mechanism of AraC action. FEMS Microbiology Reviews, 34(5), 779–796. doi: 10.1111/j.1574-6976.2010.00226.x
[7] Zhang, X., Reeder, T., & Schleif, R. (1996). Transcription Activation Parameters atara pBAD. Journal of Molecular Biology, 258(1), 14–24. doi: 10.1006/jmbi.1996.0230
[8] Wang, B., Zhao, A., Novick, R. P., & Muir, T. W. (2014). Activation and Inhibition of the Receptor Histidine Kinase AgrC Occurs through Opposite Helical Transduction Motions. Molecular Cell, 53(6), 929–940. doi: 10.1016/j.molcel.2014.02.029
[9] Srivastava, S. K., Rajasree, K., Fasim, A., Arakere, G., & Gopal, B. (2014). Influence of the AgrC-AgrA Complex on the Response Time of Staphylococcus aureus Quorum Sensing. Journal of Bacteriology, 196(15), 2876–2888. doi: 10.1128/jb.01530-14
[10] Zeng X. et al. (2013) A Simulation of Synthetic agr System in E.coli. In: Cai Z., Eulenstein O., Janies D., Schwartz D. (eds) Bioinformatics Research and Applications. ISBRA 2013. Lecture Notes in Computer Science, vol 7875. Springer, Berlin, Heidelberg
[11] Koenig, R. L., Ray, J. L., Maleki, S. J., Smeltzer, M. S., & Hurlburt, B. K. (2004). Staphylococcus aureus AgrA Binding to the RNAIII-agr Regulatory Region. Journal of Bacteriology, 186(22), 7549–7555. doi: 10.1128/jb.186.22.7549-7555.2004
[12] Reyes, D., Andrey, D. O., Monod, A., Kelley, W. L., Zhang, G., & Cheung, A. L. (2011). Coordinated Regulation by AgrA, SarA, and SarR To Control agr Expression in Staphylococcus aureus. Journal of Bacteriology, 193(21), 6020–6031. doi: 10.1128/jb.05436-11
[13] Flynn, J. M., Neher, S. B., Kim, Y.-I., Sauer, R. T., & Baker, T. A. (2003). Proteomic Discovery of Cellular Substrates of the ClpXP Protease Reveals Five Classes of ClpX-Recognition Signals. Molecular Cell, 11(3), 671–683. doi: 10.1016/s1097-2765(03)00060-1
[14] Chi, H., & Holo, H. (2017). Synergistic Antimicrobial Activity Between the Broad Spectrum Bacteriocin Garvicin KS and Nisin, Farnesol and Polymyxin B Against Gram-Positive and Gram-Negative Bacteria. Current Microbiology, 75(3), 272–277. doi: 10.1007/s00284-017-1375-y
