Difference between revisions of "Team:XJTLU-CHINA/Model"
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<img class="img-responsive center-block" src="https://static.igem.org/mediawiki/2017/9/9e/State_values.png" height=600 width=600> | <img class="img-responsive center-block" src="https://static.igem.org/mediawiki/2017/9/9e/State_values.png" height=600 width=600> | ||
<p class="form"><b>Fig 1.</b> State values of AgrA, Cbind, AgrC, Cp, Api and sfGFP.</p> | <p class="form"><b>Fig 1.</b> State values of AgrA, Cbind, AgrC, Cp, Api and sfGFP.</p> | ||
| − | <img class="img-responsive center-block" src="https://static.igem.org/mediawiki/2017/b/be/Individual_display_of_6_variables.png" height= | + | <img class="img-responsive center-block" src="https://static.igem.org/mediawiki/2017/b/be/Individual_display_of_6_variables.png" height=700 width=700> |
<p class="form"><b>Fig 2.</b> Individual display of 6 variables</p> | <p class="form"><b>Fig 2.</b> Individual display of 6 variables</p> | ||
Revision as of 21:40, 22 October 2017
Modeling
Modeling on the sensing device
In the mathematical modeling of quorum sensing, we formulated a system of ordinary equations representing the intracellular and extracellular interactions between the two Agr proteins and AIP (auto-inducing peptide) molecules. Along with numerical simulations, we performed an asymptotic analysis of the time-dependent model in order to characterize whether the AIP molecules produced by Staphylococcus aureus in the intestine would activate our sensing device.
To build the model, we first proposed the following assumptions:
- The agr mRNA contains all the information required for the translation of AgrC and AgrA. There are plentiful ribosomes for translation within the cells and the rates of translations of AgrC and AgrA are the same, and are proportional to the concentrations of their mRNA.
- Proteins and mRNA inside the cells are limited by natural degradation.
- Housekeeping phosphatases are able to dephosphorylate AgrA at rate α
pidi. - Receptor-bound AIP can dissociate spontaneously at rate αunbind.
- When an AIP binds to AgrC, we assume that auto-phosphorylation of AgrC happens simultaneously because this process is sufficiently fast. When AgrC transfers its phosphate group to AgrA at rate αpi, it is able to re-auto-phosphorylate.
The resulting equations, together with the definitions of the parameters and variables are shown below.
Table 1 Definitions of the parameters
| Parameters | Pate constant for | Value | Units | Note |
|---|---|---|---|---|
| αpi | Phosphorylation of AgrA | 10[1] | μmol-1 ml-1 h-1 | |
| αpidi | Dephosphorylation of AgrA | 1[1] | h-1 | |
| μx | Degradation and dilution | 2[1] | h-1 | |
| αcbind | AgrC that anchors to the cell membrane | 10 | μmol-1 ml-1 h-1 | Assume the same as αpi |
| αbind | Binding of AIP to AgrC | 1[1] | μmol-1 ml-1 h-1 | |
| αunbind | Separation of AIP from AgrC | 0.1[1] | h-1 |
| Parameters | Definitions | Value | Units | Note |
|---|---|---|---|---|
| X | Nisin | 1.42×10-7[2] | μmol ml-1 | |
| k2 | The Phosphorylated AgrA concentration required for half-maximal transcription rate of P2 | 1[1] | μmol ml-1 | |
| β1 | Maximum transcription rate of pnisA | 10 | μmol h-1 | Assume the same as β2 |
| β2 | Maximum transcription rate of P2 | 10[1] | μmol h-1 |
Table 2 Definitions of the variables
| Variables | Concentration of | Units |
|---|---|---|
| A | AgrA | μmol ml-1 |
| C | AgrC | μmol ml-1 |
| Cbind | AgrC that anchors to the cell membrane | μmol ml-1 |
| AIP | Free AIP molecules | μmol ml-1 |
| Cp | AIP-bound AgrC | μmol ml-1 |
| Api | The phosphorylated AgrA | μmol ml-1 |
| sfGFP | The product of P2 promoter | μmol ml-1 |
The three Hill equations represent the rates of translation of AgrA, AgrC and sfGFP. Β1 is the highest efficiency for the promoter pnisA to initiate the transcription of the agrC and agrA genes, and β2 is the highest efficiency for the promoter P2 to initiate the transcription of the sfGFP gene. X is the concentration of nisin which is needed to activate the promoter pnisA, to this extent, k1 equals to the concentration of Api when the rate of reaction is up to half of Vmax. K2, which is controlled by another regulatory factor, is the concentration of phosphorylated AgrA when the rate of reaction is up to half of Vmax.
By assuming that 0.25 μM of AIP molecules is present in the intestine, we run the MATLAB script to check whether AIP molecules can successfully activate the promoter P2 by binding to AgrC and phosphorylating AgrA. We set the threshold concentration of sfGFP to be 0.5 μM, and at this point, we consider the promoter P2 is activated. The results are shown below.
Fig 1. State values of AgrA, Cbind, AgrC, Cp, Api and sfGFP.
Fig 2. Individual display of 6 variables
Modelling on peptide synthesis and cell lysis
Collaborators and Supporters
