Team:KULeuven/Freeze

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Modeling Freeze

1. Description of the freeze system

Here we will describe the freeze system briefly. The pLac-Lux promoter (BBa_K091100), of the freeze system is negatively regulated through LuxR-AHL complex and positively regulated through lactose. LuxR-AHL production is induced by L-arabinose. When the promoter is positively regulated, four proteins will be transcribed. The first three proteins are responsible for the production of a red lycopene color, while the fourth protein is the ice nucleating protein (INP).

In the freeze model, the following simplification is made: The association of LuxR and HSL is not included. The pLac_lux hybrid promoter (BBa_K091100), of the freeze subsystem is negatively regulated through LuxI and positively regulated through lactose. LuxI production is induced by L-arabinose.

However in the full model the LuxR-HSL association is included.

ODE

2. Freeze Model

Click here to download the Freeze model

3. Simulations

In figures 1 till 4, simulations are performed with different amounts of lactose and L-arabinose to check the overall working of the system. As expected, lactose is inducing the freeze system resulting in the production of ice nucleating protein (INP). On the other hand, L-arabinose is repressing the system by inducing the production of LuxI. When both lactose and L-arabinose are present in the cellular environment, INP is initially produced but after a while the concentration of LuxI becomes more significant which will repress the production of INP. The more L-arabinose is added, the faster the production of INP is inhibited resulting in a lower amount of INP produced. These simulations were all performed with estimated values, because accurate values are hard to find. We will investigate the importance of finding more accurate values for some parameters with sensitivity analysis. Sensitivity analysis will give idea about the influence of a parameter on the output results.


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Fig.A State profile of INP and LuxI

4. Sensitivity analysis

As output for the sensitivity analysis, we take the concentration of INP because it is the final purpose of this subsystem. As inputparameters we check all the parameters used in the model of this subsystem. Also the concentration of CrtB, CrtE and CrtI can be checked as output, but they will behave identical to INP because we chose the same estimated parameter values as for INP for the transcription, translation and degradation reaction of these proteins.

The sensitivity analysis for INP reveals that in the beginning, shown in figure 5, the transcription parameter has more influence on the output than other parameters. When the time interval is bigger, the sensitivity of degradation parameters is more important than the sensitivity of the transcription parameter. This is shown in figure 6.

Transcription k forward 2 is here unimportant because the only input here is lactose, thus L-arabinose cannot inhibit the system.

Fig.B Sensitivity analysis of INP gene

Figures 7 till 9 make clear the role of different amounts of lactose and arabinose to the sensitivity of the parameters. When only lactose is present, is the sensitivity of INP transcription kforward1 most important. When both lactose and arabinose are present, the sensitivity of both INP transcription parameters and luxI transcription are important. When only arabinose is present, only INP transcription kforward2 and luxI transcription sensitivities are important. When sensitivity of a parameter is important, then we need to search for accurate value of this parameter. Only then our model, would have good predictive value.

Fig.C Another sensitivity analysis of INP gene