# Team:Tuebingen/Modeling

### From 2013.igem.org

### Motivation

The aim of our modeling approach is the formal description of the biosensor system. We look from an engineering viewpoint and want to create a technical specification for our device similar to the specifications often found in electrical engineering.

The basis for the mathematical formulation has to be an abstract representation. The underlying network we used for our modeling tasks is structured as follows:

Another aspect we want to consider with a computational model are the benefits for both the model and the biological system. Through several iterations of analyses of the computational model and data generation with the biological system, we can verify the model and find interesting characteristics of the biological system.

### Model equations

In essence, the computational model consists of the following three equations. The all specify the concentrations for the key components of the system: (1) for the active receptor (ligand-receptor-complex), (2) for the repressor protein and (3) for the reporter protein.

This approach combines the transcription and translation processes into a single production process. There is also only one degradation process. Through this simplification, the number of parameters is reduced to 8. Some parameters are available from literature, others are estimated based on similar, known interactions.

The binding characteristic of the membrane progesterone receptor and the hormone progesterone has been fitted using the non-linear least squares method approach and yields the half-maximal concentration.

### Results

Two important simulations using the model have been conducted. The first one describes the dependence of the output signal (the reporter concentration) on the input signal (the hormone concentration). The second one tries to identify sensitive parts of the system.

The general behavior of the system is shown in the following plot. Two simulations are shown which differ slithly because of random parameter variations.

The detection range is clearly in the range of nanomolar concentrations of progesterone. This renders the biosensor suitable because the physiological active levels of progesterone are covered.

A sensitivity analysis has uncovered that only two of the eight parameters have a significant effect on strength of the output signal: (1) the maximal concentraion of the repressor protein and (2) the binding affinity of the fet3 promoter.

### Outlook

Using the model and the specific results above, we hope to provide a suitable theoretical description of the biosensor system. We also want to use to model to find parts of the system which can be modified to improve the sensitivity, the detection range and the output signal strength.

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