Team:BGU Israel/Model2.html



Modelling Results

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.

Strongest mechanism, Weakest leakage rate

Example 1: Strongest mechanism, weakest leakage rate. All experiments end with the entire population dying out. Cells experience a log phase of around 90 minutes, a maximum population of around 230 is reached, and the variance is small.

Intermediate combination. Mechanism strength=4, Leakage rate=0.4

Example 2: Intermediate parameters. Here, the stochasticity of the system takes an important role. Some of the experiments are trending down at the end of the timeframe, while others are trending up. Variance is much bigger. Log phase is about 200 minutes. A maximum population of around 410 is reached.

In order to compare all of the experiments, 3D surfaces projecting the data of all combinations were made. In each one of figures 4-6, a specific parameter was chosen to be compared between the combinations. The coefficient of variation (CV) of the 30 repeats was computed and is represented by the surface’s color:

Figure 3: 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, the bacteria symbol represents a non- reliable combination where less than 90% of the experiments died out within the model time frame, and the rest lived on.

The graph omits combinations in which the weakest mechanism strength 1 was used, because those combinations never died out. This parameter is robust and has a clear limit of around 2 as defined in the model.

The leakage is a more modular parameter, giving delicate tuning for high mechanism strengths, thus strengthening our hypothesis that leakage can provide nodularity for the system.

A time frame of around 300-750 minutes is seen, as the z-differential between the lowest combination and the highest one.

Figure 4: Z axis is the number of generations reached after 1000 minutes of simulation, in combinations that died out - a high number wasn’t reached

A generation frame of 13-32 generations within the effective combinations is seen in this model. This effects the chance of the system to transfer genes horizontally, and the chance for a mutation in the mechanism to occur.

Figure 5: Z axis is the time it took until population reached a 50% mark from initial conditions.

This parameter, the measurement of the half-life, can give an indication for the possible working time for the system. A time frame of 190-600 minutes has been calculated.

While inducer concentration usually doesn’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]. Therefore it is possible to induce P.A.S.E-containing bacteria to express only a partial percentage of the maximal protein expression capability, allowing for control of the overall population lifetime.

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[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