# SIMPLE CIRCUIT MODEL

“The dream of every cell is to become two cells”

- François Jacob, 1965 Nobel Prize Laureate in Physiology or Medicine

What will happen when we have cells which periodically change their phenotypes and pursue their “dreams” of replicating at different rates? Can cells perform multiple tasks?

We carried out several simulations to test whether the cre-based recombinase system allows cells to differentiate into an equilirbium of multiple phenotypes over time.

### CHAOTIC BEGINNINGS

tf:tr=1:2

tf:tr=1:1.1

If cells express phenotype F have less metabolic burden, it divides faster than cell with phenotype
R

- if the difference in division time created has a mere 10% difference, the culture will still be
dominated by the F phenotype in an exponential speed

--> due to nutrient competition, R phenotype will soon die out

### RESOLVING THE CHAOS WITH OUR GENETIC CIRCUIT

With our cre-lox system, an equilibrium can be achieved over time regardless of the difference of tf and tr caused by metabolic burden:

tf:tr=1:2

By implementing the Cre-based recombinase system, the population can reach an equilibrium between the two states at the ratio of around 3:1 when F cells divide twice as fast as R cells.

tf:tr=1:10

Even if F cells divide ten times as fast as R cells, the population will still reach an equilibrium with F:R cell ratio slightly higher than 4:1.

As metabolic burden has a positive correlation with the cell division time, our system can be adopted in any conditions when you want to achieve a constant ratio of two phenotypes with different metabolic burdens.

tf=10; tr=100

tf=10; tr=20

If CV is closer to 0, the system is more stable, as the values deviate less from the average
value at
each time point.

As shown from the two graphs above, CV approaches very close to 0 (at around 0.015 to
0.013)

Hence, we can conclude that our cre-lox system is stable over time.

nf0=1000; nr0=1000 (1:1)

nf0=100; nr0=1000 (1:10)

nf0=1000; nr0=100 (10:1)

An equilibrium can be achieved over time despite the difference in original concentrations of cells expressing the two phenotypes.

ps=0.05

ps=0.01

ps=0

All trials displayed above are with tf:tr = 1:3

Larger ps = higher probability of flipping

More frequent flipping allows us to achieve an equilibrium closer to the desired ratio

- Cells do not die or get inactivated throughout the process
- Cells were assumed to have four possible states, namely F state, F-transition (Ft) state, R state, and R-transition (Rt) state. Within each state, cells could possess substates representing the cell age, i.e. the time each cell has been in their cell cycle.
- The phenotype switching events in cells were independent events which can be modelled using binomial distribution.
- For cells undergoing phenotype switching during their cell cycles, they would enter the transition state of the other phenotype which the division time adopts that of the original phenotype (e.g. F state → Rt state, division time = tf).
- Cells in transition state would switch to the new phenotype upon cell division.
- Cells in transition state would return to their original phenotype upon phenotype switching event (e.g. Rt state → F state)
- For cells undergoing phenotype switching during cell division, they would turn into the new phenotype directly (e.g. F state → R state)
- Time of division for each phenotype remained constant throughout the process regardless of the phenotype.
- The probability that a cell would switch phenotype remained constant throughout the cell cycle.
- The probability of phenotype switching from F to R was the same as from R to F.