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. Lactose is the inducing compound involved in the freeze system, which can result in the production of ice nucleating protein (INP), while antifreeze system is repressed by lactose. On the other hand, L-arabinose is repressing the system by inducing the production of LuxI, and yet, in the antifreeze model, AFP production is induced by it.

The results reveal that the kinetics of synthesis of AFP and CeaB are much higher than that of INP formation, for example, the difference of the concentrations of AFP and INP can reach 10E15 in Fig. 1. The main reason is the efficiency of the formation of AHL complex. From mathematical modeling, we can find INP gene functions after AHL complex, and they are in same series reaction. Therefore, the low activity of AHL directly leads to the limited amount of INP formation.

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 dramatically increases by 10E14.

FIG1.JPG

FIG2.JPG

4. Sensitivity Analysis and parameter scan

5. Kinetic Constants

ODE.PDF

The parameters used in this model are: