Modeling in synthetic biology and iGEM Freiburg 2017

In synthetic biology, modeling can be applied to a wide range of topics, for example modeling of genetic circuits to predict their outcome and to support, if enough data is available, further development such as optimizing genetic circuits for a desired outcome.

In this subfield of mathematical and computational biology, ordinary differential equations (ODEs) are used to describe the transcriptional and translational process (Chen et al., 1999). ODEs consist of a set of parameters and a system of functions and their derivatives. How they can be set up in their simplest form is shown below.

The variables are functions of time t where $f\left(t\right)$ describes the mRNA concentration, $y\left(z\right)$ the transcription function and $z\left(t\right)$ the protein concentration. Rate constants are enlisted in the following table.

This system of ODEs can now be solved via numerical integration, but to obtain constants like $k1$, $k2$, $k3$, experimental data has to be produced that is suitable for a nonlinear regression (Ingalls et al., 2012).

The obtained model is to be compared with new experimental data in order to verify the parameter sets. If necessary, parameters or assumptions have to be corrected.

Why did we choose an AND gate?

As already stated the hypoxia response element (HRE), cAMP response element (CRE) and NFAT binding site are enhancers, that could be utilized for more specific CAR expression. But the combination of these three enhancers in an AND gate to even further boost the specificity of the CAR expression (Brophy et al., 2014) proved to be quite challenging, because using endogenes systems came with the drawback. This was that we had to generate a knockout or knockdown of either HIF1, VEGF-R, or TDAG8.

Generating a single knockout or knockdown is challenging enough but generating three to test all possibilities seemed quite impossible in six months. So using modeling to find the best combination of enhancers and knockout was an attractive option instead of choosing a random AND gate design. This was carried out and is described below.