Team:HKUST-Hong Kong/modeling.html

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Modeling

In an attempt to illustrate and understand the dynamics of a mixed bacterial population once subjected to reduction of indole concentration, we have proposed a complete mathematical model which attempts to simulate the reduction of indole due to the activity of the T4MO enzyme complex.

Essentially, we make a few basic assumptions in order to formulate the model. Based on the evidences by Lee et. al. (2010) and Lee et. al. (2010), we expect that bacteria without antibiotic resistance gene will die due to loss of partial resistance conferred by the presence of indole. In addition, we assume that the indole production rate of the antibiotic-resistant bacteria remains constant and tied to the number of bacteria present in the culture. The same applies for the degradation rate by the bacteria producing the T4MO enzyme. In order for the model to work, we also assume that the degradation rate will surpass that of the production rate, creating a net reduction of indole in the culture (not mentioned explicitly in the paper).

Using the above as the basis, we hypothesize that there is a critical amount of indole that will confer partial antibiotic resistance to wild type bacteria, i.e. critical ratio. Once the amount of indole is too low, partial resistance would be lost, hence many wild type cells will die. This scenario would reflect our goal of preventing wild type cells from being able to obtain antibiotic resistance genes via horizontal gene transfer (HGT).

Even so, we revised our “Critical-Ratio model” due to one assumption (last assumption), where the death of the overall bacterial population is slow initially until we surpass the lower limits of the critical ratio (i.e. ratio of indole is lower than the critical ratio), in which the death increases significantly. One key reason is that we are unable to explain the sudden massive cell death (which includes resistant cells), as a gradual decrease of viable cells (all types) appears to be a more plausible scenario. The revision is done by removing the assumption that the reduction of bacterial population is tied to the presence of a critical ratio, but rather to a survival rate. With this, the model can illustrate the actual dynamics in an ideal manner.

The graphs in the diagram below is a rough illustration of a predicted outcome based on the two models mentioned above. It may not be very accurate as the Monte-Carlo method should be employed to illustrate the actual situation based on a wide array of random values for most parameters. Nonetheless, it is deemed adequate to represent our story well.

You can access our full modeling report here.

In addition, we have collaborated with the CUHK team to model the activity of E. coli bcr gene product (bcr multi-drug efflux pump) to understand the significance of the pump with relation to increasing the MIC of E. coli towards antibiotics (i.e. Kanamycin). The results unfortunately prove inconclusive for our understanding but we are grateful for their assistance.

You can access their collaboration page here.

References

Lee J. H. and Lee J. (2010). Indole as an intercellular signal in microbial communities. FEMS Microbiol Rev, Vol. 34, p. 426-444 .

Lee H. H., Molla M. N., Cantor C. R., and Collins, J. J. (2010). Bacterial charity work leads to population-wide resistance. Nature, Vol. 467, p. 82-85.

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