Team:Dundee Schools/Model
Dundee Schools
Modelling
Quorum sensing:
Most bacteria species coordinate their gene expression of virulence genes; they do this by sensing the density of their local population, and once they reach a certain density threshold they become harmful - a process known as quorum sensing.
The producing bacteria we designed can inhibit the growth of target bacteria; by slowing down its growth rate, we can make them less harmful to the human body.
Mathematical modelling can help us explain this concept.
Our producing bacteria produces an siRNA that targets a specific gene in the pathogen. In our project, the siRNA inhibits bacterial growth, and so we have to consider two modifications that can be made to the logistic growth to model this effect:
- the growth rate is affected, or
- the carrying capacity is altered
However, both modifications consider the same type of repression, as described here:
We have defined a value at which the level of bacteria can generate an infection. As the immune system has to generate a response in a given time, the goal of our system is to keep the bacteria below that threshold during a fixed period of time. This critical time is the moment in which the immune system can start fighting the pathogens.
As expected, two different behaviours are observed. If growth rate is affected, bacteria will grow slowly but reach their maximum level eventually. However, if the inhibition is strong enough, the bacteria will be below the threshold before the critical time, avoiding the infection. The second case is more reliable, as it can maintain the bacteria below the threshold for a long time.
It is expected this model can help us to understand how our system can inhibit bacterial growth and help to improve our biological device to make it more effective.
Some Equations:
Threshold – The minimum number of cells required for the target cells to become virulent and cause infection. The target cells must be below this line by the critical time in order for them to not be harmful (due to the body being prepared to fight off the bacteria).
Critical Time –The time at which the body is prepared to fight off the infection.
