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

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 136.42 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.

Complex behavior

Intracellular AHL behavior

Extracellular AHL behavior

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.

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