Team:Dundee Schools/Model
Dundee Schools
Modelling
Bacterial infections:
Bacteria inhabit all exposed surfaces of our bodies and yet they rarely make us ill. Only pathogenic bacteria can cause infections and only when they are present in sufficient numbers to overcome our immune system's defences. This threshold will be unique to each pathogen in each environment it encounters, and may be influenced by the bacteria's ability to communicate and the strength of the host individual's immune function among other things.
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 a siRNA that targets a gene in the pathogen, this could be a gene that codes a nutrient uptake protein that would slow down growth when targeted. We have to consider two modifications 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:
- the growth rate is affected, or
- the carrying capacity is altered
However, both modifications consider the same type of repression, as described here:
where R is a measure of the abundance of siRNA.
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 marks the period in which the immune system is sifficiently prepared to fight the infection.
As expected, two different behaviours are observed. If only growth rate is repressed by the presence of siRNA, 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 case in which the pathogen’s carrying capacity is repressed by siRNA 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 period during which the body can fight off subcritical the infection loads.
Using this model we could calculate the effective time window of our spiRNA for a number of different infections using data specific to both the pathogen and to the gene targeted. As such, it could be used as a tool for finding the optimal gene to target, given the correct data.
