Team:BGU Israel/Model2.html

As explained in the theoretical section on the stochastic birth-death model, 25 combinations of protein leakage and mechanism strength were simulated in-silico. For each combination, 30 repeats ("experiments") were performed.

Leakage rate was set between 0.1-0.5, and mechanism strengths were given numbers between 1-5, representing the 'a' parameter: protein concentrations functions.

Model Results

1. Die-out timeframe: 300-750 minutes.
2. Working timeframe: 190-600 minutes.
3. Generation range: 13-32 generations.

What does a simulation of one of these combinations of protein leakage and mechanism strength look like? In each example below, 5 experiments out of the 30 are marked in grey, an average curve is red, and standard deviation curves are black.

Figure 1: 5 curves represent 5 repeats of the experiment with same initial conditions.

In this one it is visible that when the mechanism is weak and the protein is leakage rate is high, the population behaves exponentially, variance is visible, though not major.

Strongest mechanism, weakest leakage:

Figure 2

We can see that although variance is bigger, all experiments end up with all the population dying out. Cells experience a log phase of around 100 minutes, and at low count some of them survive around 100 minutes more.

Intermediate:

Figure 3

In intermediate parameters the stochasticity of the system takes important role. While 4 experiments are trending down, on is trending up. Variance is much bigger. Log phase is about 200 minutes.

In order to show a complete comparable picture, 3d surfaces projecting the data of all combinations were made, in each one of figures 4-6 one specific parameter was chosen to be compared for each combination, the variance between the 5 repeats was computed and normalized to the mean and is represented by the surfaces color:

Figure 4: Z axis shows the time it took for 95% of the population to die out, X and Y are the values for the tested parameters.



Figure 5: Z axis is the number of generations reached after 1000 minutes of simulation, for combinations that died out a high number wasn’t reached.



Figure 6: Z axis is the time it took until population reached a 50% mark from initial conditions.

In the threshold surfaces, combinations reaching the 1000 minutes plateau never died out.

It is important to estimate number of generations because the higher it gets, the higher the probability is for a mutation to happen. Another thing to think about is the working time of the GEM, effective combinations reached the 50% threshold after between 200-500 minutes.

While inducer concentration usually don’t provide adequate control of the system because of the promoter’s bimodality[1] (all or nothing behavior when induced), some control can be achieved from different inducer combinations [2], it is possible to release the P.A.S.E after being induced to express only partial percentage of the maximal protein expression capability.

[1] [1] J Biotechnol. 2007 Feb 1;128(2):362-75. Epub 2006 Oct 17. Cell population heterogeneity in expression of a gene-switching network with fluorescent markers of different half-lives. Portle S, Causey TB, Wolf K, Bennett GN, San KY, Mantzaris N. View Source
[2] R. Lutz, H. Bujard. Independent and tight regulation of transcriptional units in Escherichia coli via the LacR/O, the TetR/O and AraC/I1-I2 regulatory elements. Nucleic Acids Research 25(6), 1203–1210 (1997). View Source