Team:KULeuven/Modeling

Modeling Overview

1. Description of the whole system

Lactose induces the freeze system, resulting in the production of the ice nucleating protein (INP). In addition, lactose will repress the antifreeze system, preventing the formation of the antifreeze protein (AFP). On the other hand, L-arabinose is the inducing compound of the antifreeze system and the repressing compound of the freeze system. Upon application in the environment at low temperatures, a cell death mechanism will kill off the cells.

To make predictions for the E.D-Frosti system, a structured segregated model is designed in Simbiology. A graphical representation of the model was build in the block diagram editor. Afterwards reaction equations and parameters were added to mathematically describe the biological system. For the reactions, a PDF with ordinary differential equations (ODE) is created [13]. There are in total three different kinetic equations we used in the model: Hill equation [14], Mass equation, Assimiliation reaction. For the parameters, a PDF with parameter values is given below. Also for every subsystem, there are PDF’s with ODE’s. However the equations and parameters used for the full model, should be the most accurate.

We designed one model for the whole system and 3 models for 3 subsystems. The 3 subsystems are antifreeze, freeze and cell death. For more information about these 3 subsystems, we refer to the extended project description and the 3 modelling pages: freeze, antifreeze and cell death.

FULL MODEL SCHEME.JPG

2. Full Model

There are in total 5 different kinetic equations we used in the model Transcription equation For most promoters, hill kinetics is used, it is a way of quantitatively describing cooperative binding processes, it was developed for hemoglobin in 1913. A Hill coefficient (n) is a measure for the cooperativity. Translation equation RNA degradation Protein degration Assimiliation

FULL MODEL FIGURE.PNG

Click here to download the full model (FULL MODEL.SBPROJ)

3. Simulation tests

Different amounts of lactose and arabinose are used to check the efficiency of the model. The results reveal that the production rate of AFP and CeaB are much higher than that of INP formation, for example, the difference between the concentrations of AFP and INP can reach 1015 in Fig. 1. In this figure the amounts for lactose/arabinose are taken 1/1.

The main reason for the difference in protein production is the formation of LuxR-AHL complex. This complex stimulates AFP production and inhibits INP production. The assimilation reaction is a fast reaction compared to other reactions in the system. Therefore the rate of AFP production is much higher than the rate of INP production also the inhibition of AFP production is much lower than the inhibition of INP production. The dual inhibition system enlarges the difference in reaction rates, because it works at two sides.

To stimulate the INP production, we can increase the amount of lactose, e.g. 100 for lactose and 1 for arabinose (Fig.2). As a result, the INP production increases by 1014 when the time interval is 100 seconds in stead of 1 second! This is a very small increase of production compared to increase of stimulus lactose.

To improve the system, it would be better to use a more symmetric system, especially because we are working with a dual inhibition system which enlarges the differences between the two parallel subsystems: freeze and antifreeze. The previous simulation is not a problem for the proper working of the system. We never want to create AFP and INP at the same time. The only disadvantage of such an assymetrical system is the much higher amount of lactose compared to arabinose which will be recquired to produce INP.

FIG1.JPG

Figure 1: amount of lactose-arabinose 1-1, huge difference between production of AFP and INP

FIG2.JPG

Figure 2: amount of lactose-arabinose 100-1 after 100 second

4. Sensitivity Analysis and parameter scan

In our works, sensitivity analysis (SA) is used to examine how the activity of the gene expression in the output of each model can be attributed to different kinetic parameters in the inputs of the model. We can also use this technique to determine the effects of changing variable in the models. The results of sensitivity analysis for each model are shown in subsystem pages.

In the model of cell death, we do the simulation test with each parameter changing within the certain range with the value incremented by the certain interval.

5. Kinetic Constants

KINETIC PARAMETER.PDF