Team:Freiburg/Model

Overview Motivation CAR T Cells Tumor Microenvironment AND Gate Outlook Achievements References

Members Attributions Partners Contact

Main Project Modeling Applied Design Proof of Concept BioBricks Basic Part BioBrick Improvement Interlab Study

Safety Cloning HIF1A Knockdown Cell Culture Lab Book

Human Practice Integrated Human Practice Collaborations

Modeling

Modeling of the CARTEL^TM AND gate

In synthetic biology, modeling can be applied to a wide range of topics, for example, modeling of genetic circuits. In this subfield of mathematical and computational biology, ordinary differential equations (ODEs) are used to describe the transcriptional and translational process and predict the behavior of the desired circuit and also to support, if enough data is available, their further development such as optimizing for a desired output (Chen et al., 1999).

As already stated, the hypoxia response element (HRE), cAMP response element (CRE) and CTLA4 promoter could be utilized for more specific CAR expression. Combining 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. Using endogenous systems came with the drawback, we had to generate a knockout or knockdown of either HIF1, VEGFR-2 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.

Figure 1: Schematic depiction of the the workflow
T cells are first collected from a patient via apheresis, then cultured and engineered in the laboratory. These engineered T cells express CAR constitutively and are then infused into the patient.

Finding the CARTEL^TM AND gate

The ODEs, that have been used to describe the different AND gate possibilities, 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.

$f^{\text{'}}\left(t\right)=y\left(z\right)-k1*f\left(t\right)$

(1)

$z\text{'}\left(x\right)=k2*f\left(t\right)-k3*z\left(t\right)$

(2)

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.

Rate constant	Description
$k1$	mRNA degradation rate
$k2$	Translation rate
$k3$	Protein degradation rate

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.

Rate constant	Description
$k4$	Basal expression rate
$k5$	Maximal expression rate
$k6$	Degradation rate