Team:Tec-Chihuahua/Model

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Results

To summerize

REACTIONS

Based on the law of mass action that states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants, the whole modified ecosystem is represented in the next chemical reaction network

EQUATIONS SYSTEM

PARAMETERS

MATLAB

To be able to visualize the numbers obtained from modeling, we simulated the behavior described before, on the MathWorks® platform MATLAB. Thanks to these simulations we were able to compare the graphs between the variables concentrations inside a Wild Erwinia amylovora and a Modified one. The results were the following

Wild Cell

Modified Cell

EamI gene behavior

In the graphic of the wild cell (graph 1) we observed that the EamI gene expression is not significant until the cell density reaches a critical value, around 1800 in this particular scenario. Considering a time horizon of 300 minutes and a range of values of cell density from 0 to 5000 we obtained an increasing EamI concentration from zero to an stationary value of 136.4 nM. In contrast, in the graphic of the modified cell (graph 2), we observed that in the same horizon of time and with the same range of cell density, there is not enough time and density to reach quorum sensing, sustaining the hypothesis that the aiiA will help to inhibit the virulence gene expression. The EamI protein will reach a concentration equal to 0.9525 nM, 99.30% less than the observed in the wild cell.

Graph 1. Cell density against EamI concentration (Wild).

Graph 2. Cell density against EamI concentration (Modified).

Complex behavior

Graph 3. Cell density against Complex concentration (Wild).

Graph 4. Cell density against Complex concentration (Modified).

Intracellular AHL behavior

Graph 5. Cell density against Intracellular AHL concentration (Wild).

Graph 6. Cell density against Intracellular AHL concentration (Modified).

Extracellular AHL behavior

Graph 7. Cell density against Extracellular AHL concentration (Wild).

Graph 8. Cell density against Extracellular AHL concentration (Modified).

AQUI EXPLICAR QUE AHORA SE ESTAN ODELANDO TODAS CONTRA EL TIEMPO

Behavior through time

Graph 9. Time against EamI, Complex, Intracellular and Extracellular AHL concentrations (Wild).

Graph 10. Time against EamI, Complex, Intracellular and Extracellular AHL concentrations (Modified).

CONCLUSIONS

After analyzing the contrast between the wild and modified cell we concluded that under the same conditions (time and cell density) the modified cell will have a significant inhibition in reaching the critical value for the QS activation and therefore the virulence expression because of the aiiA capacity to delay the growing behavior of all variables (EamI, AHL-EamR complex, intracellular and extracellular AHL). Nevertheless, if the horizon of time and the range of cell density are expanded strategically, the modified cell, in fact, can reach the QS. In this particular scenario, the QS was not completely eradicated but remarkably delayed. The modified cell needs around four times the time and cell density of the wild cell to be able to reach the critical value that triggers the QS. Noticing that a basal state value of the EamI protein was taken under consideration which influenced in the synthesis of EamI, it did not matter that this value was as small as we wanted, the concentration of EamI in the media always existed. This is the reason why a predisposition of reaching QS inevitably remains, but always depending on the intrinsic characteristics of Erwinia amylovora. It is important to conclude that the activity of only one enzyme will not inhibit the virulence by itself, reason why the project revolves around the interaction of the three enzymes: aiiA,epsE,yhjH, to counteract the virulence in an integral way.

Graph 11. Quorm sensing conditions for a Modified cell.

If you are interested in learning and understanding a little bit more of our model simulations, you can check-out our MATLAB codes with just a click.

Wild cell

Modified cell

OPEN PROBLEMS

Through the model we described the E. amylovra's behavior changes caused by the aiiA enzyme insertion. Nevertheless, the project is based on the combination of three enzymes to reach our goal and inhibit the E. amylovra's virulence factors. We are aware that there is more to do, so with a little help from our friends from IONIS Paris, the yhjH enzyme model is now a future project. They helped us to 3D model the yhjH enzyme (shown below) and to take certain conditions under consideration to its proper activity. Thanks to this edition model, the unregulated gene inhibition over a regulated one can be taken as a basis, and together with the 3D simulation, a second model could be achieved.

References

Ingalls, B. (2013) Modeling of Chemical Reaction Networks & Gene Regulatory Networks. From Mathematical Modeling in Systems Biology(pp. 21-314 ). England: MIT press.

Frederick K. Balagaddé et al. (2008) A synthetic Escherichia coli predator–prey ecosystem, EMBO, 187, pp. 1-26.

James, S. et al. (2000) Luminescence Control in the Marine Bacterium Vibrio fischeri: An Analysis of the Dynamics of lux Regulation., JMB, 296, pp. 1127-1137.

Koczan JM, McGrath MJ, Zhao Y, Sundin GW (2009) Contribution of Erwinia amylovora exopolysaccharides amylovoran and levan to biofilm formation: implications in pathogenicity. Phytopathology 99:1237-1244

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