Team:ETH Zurich/Modeling/Analysis

Sensitivity Analysis

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

Since we consider the sensing molecules (acetaldehyde and unbound xylene) as a parameters in our models, we did 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 acetaldehyde concentrations when GFP rises and falls.

Parameter sweeps

For the parameters included in the band detector module, we explored the parameter space around their values which we found in the literature and used for the simuations in order to see how they can affect the band width and height. As we varied each parameter (while keeping the rest constant), we varied also the acetaldehyde input and monitored the GFP output. We analysed the parameter space only for the model that uses acetaldehyde as an input parameter.

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

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

Protein Synthesis Rates

Repression Coefficients

Protein Degradation Rates