In order to have a closer math with the real life situation, we released some of our assumptions...
First, let's see whether an equilibrium can still be achieved if assumption 10 is released
Assumption 10: The probability of phenotype switching from F (green) to R (red) was the same as from R to F.
Solution: Consider different probabilities of phenotype switching. pF represents the probability from F (green) to R (red) while pR represents the probability from R to F.
tf=10, tr=20, pf=0.03, pr=0.01
tf=10, tr=30, pf=0.01, pr=0.03
As shown, even if the probability of flipping for the forward and reverse phenotypes are different, an equilibrium of the two phenotypes can still be achieved
It also shows that the probability of flipping is one of the major factor affecting the final ratio
Hence, we can add another level of control by adjusting the arabinose concentration for promoter induction of the Cre gene. With different levels of Cre-enzymes, we can adjust the final equilibrium position as more frequent flipping brings us closer the desired ratio.
Then, let's take a look at what will happen if assumption 1 is also released~
Assumption 1: Cells do not die or get inactivated throughout the process.
Solution: Consider a model which accounts for cell mutations over time. A kill switch model has also been created to counter the effects of mutant cells in the population.
tf = 20, tr = 20, tm =15
If we set the division time of mutant cells (tm) to be 25% shorter than normal cells, they can take over the system very quickly!! What can we do?
What can we do?
It's OK! We have the kill switch model!