"
Team:St Andrews/project/modelling/model 3
Model 3: Pseudo Multi Cell One Dimension
Theory & assumptions
The results produced from both of our previous models were unsatisfactory, since neither gave us quantifiable data from which experimental comparisons could be made, although the switching on was clearly visible in both. Therefore it was decided that in order to properly capture the mechanism of bistability it was essential to have some element of cell number, and as such we must simulate the growth of a cell colony rather than artificially increase the amount of HSL in our external environment. Several crucial elements were added to the model to incorporate this new outlook:
i. A new variable 'Number of cells' was added
ii. Two new functions which simulate cell growth and cell death
iii. A new paramter 'Volume'
The number of cells is set at the beginning of the simulation by the user. Based on a doubling time of 20 minutes, the variable is increased every increment by the cell growth function. In order to simulate the increase in HSL due to these new cells, each new cell is accompanied by an increase in HSL which is equal to that being contributed by the cells already present in the system. (VOLUME THING IN DIFFERENTIALS). Similarly we included a cell death function which decreases the number of cells at a halving rate of 20 minutes in tandem to the growth rate.
Results
On running the model through the cell growth, stationary and cell death phases, the first example of ‘true bistability’ is produced, see figure . Since this model contains spatial dimensions we are able to determine a specific cell density at which the switch happens, and this is comparable to the value predicted by other models and by experimental evidence. There is also a clear difference between the switch-on and switch-off thresholds which we hypothesise is caused by…
Figure 1: Graph showing change in GFP concentration against cell density
