Team:ETH Zurich/Modeling/Analysis

Parameter Sweeps

For the parameters that belong to the band detector module, we explored their parameter spaces to quantify how they affect the features of the GFP band . As we varied each parameter (while keeping the rest constant), we varied also the acetaldehyde input and monitored the GFP output. We analyzed the parameter space only for the model that uses acetaldehyde as an input parameter.

In both models the band is affected in the same way by the parameters of the band detector module. The sensor mechanism can only cause shifts in the band but the band detector module itself is unaffected by the input of the system. The parameter sweeps for the xylene model would therefore be similar to the acetaldehyde model, with differences only for the parameters involved in the sensor mechanism.

The following figures show how the band changes with the variation of protein production rates, repression coefficients and degradation rates.

Protein Synthesis Rates

Figure 1: Exploring the parameter space of TetR production rate	Figure 2: Exploring the parameter space of CI production rate
We see that the existence of the GFP band is not affected by the TetR and CI production rates, thus as soon as the values go above a treshold the band is present and the peak stays at a constant amplitude. TetR only affects the width and position of the band which widens and shifts to higher acetaldehyde values as TetR increases. The GFP band is however very robust to the CI production rate, all its characteristics being preserved.
Figure 3: Exploring the parameter space of LacI production rate	Figure 4: Exploring the parameter space of LacIM1 production rate
The LacI and LacIM1 production rates have a more pronounced effect on the GFP band. When the values are very small the band seems to be wide and bounded only on one side. For larger values the desired band appears but its amplitude and width are decreasing with the further increase of the parameter values, up to the point where the band dissapears completely.
Figure 5: Exploring the parameter space of GFP production rate
For the GFP production rate, the band evolves as expected - it is absent for very small values and only its amplitude increases with increasing production rate.

Repression Coefficients

Figure 6: Exploring the parameter space of TetR repression coefficient	Figure 7: Exploring the parameter space of TetR repression coefficient
Figure 8: Exploring the parameter space of TetR repression coefficient	Figure 9: Exploring the parameter space of TetR repression coefficient

Protein Degradation Rates

Sensitivity Analysis

Sensitivity analysis is a technique that studies the change of the output (or any observable) of a certain function with the variation of a certain parameter. It gives us an overview of how sensitive the model is with respect to the parameter, i.e. what the impact of the parameter is. The sensitivity is defined as the partial differential equation of the observable with respect to a certain parameter.

We performed sensitivity analysis with respect to acetaldehyde or xylene. For different input concentrations we monitored the change in the GFP output (dGFP/dAcetaldehyde or dGFP/dXylene.

For the acetaldehyde model, it can be seen from the figure below that the sensitivity is highest when GFP rises. For the peak itself (at [AA] = 1000uM), the sensitivity drops down and then rises again once GFP concentration starts decreasing. This tells us that the GFP concentration level is most sensitive to acetaldehyde at those concentrations where GFP rises and falls.