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Team:HKUST-Hong Kong/modeling.html
From 2011.igem.org
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. (2009) 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 graph illustration of the diagrams 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.
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 our full modeling report here.
