Team:Freiburg/Model

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

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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

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 processes over time, predict the behavior of the desired circuit and also to support their further development such as optimizing for a desired output if enough data is available (Chen et al., 1999).

Fig. 1:

Finding the CARTEL^TM AND gate

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