Team:TUDelft/DennisModelFull
Overview - The Model
There are many variables that play a role in the behavior of synthetic circuits. Many (if not all) of these variables can greatly change when transferring a genetic circuit between organisms. We adopted a system developed by Sontag et al. (2018) which has shown to result in independence of copy number for the production of a gene of interest. This system contains unexplored properties which enable us to take away the uncertainty of changing variables when transferring genetic constructs between organisms.
The kinetics
In our system we exploit a commonly applied control system known as an Incoherent Feed-Forward Loop (iFFL), in which an activator regulates both a gene and a repressor of the gene (Goentoro, Shoval et al. 2009) . This control system is established through the expression of a Transcription activator-like effector (TALE) protein. TALE proteins recognize DNA by a simple DNA-binding mechanism which can be altered to recognize any sequence you want (Doyle 2013). In our system, the TALE protein binds to the promoter of a gene of interest and thus represses the expression of it. Sontag et al. (2018) has previously described this system and showed how it results in independence of copy number for a gene of interest. Our further analyzation of this system has revealed the system to be independent of many other variables. We exploit this robustness of the system to show how it can yield predictable expression when transferring your genetic circuit between prokaryotes.
Visit our page on TALE to learn more!
In order to model our system we have to identify all interactions and subsequently define the rate equations. Figure 1 depicts a scheme of all interactions.
From these interactions we can derive the following system of ordinary differential equations:
| Parameter | Explanation |
|---|---|
| $a_T$ | Transcription rate TALE |
| c | copy number plasmid |
| $y_m$ | degradation rate mRNA |
| $b_T$ | Translation rate TALE |
| $y_T$ | Degradation rate TALE |
| n | Cooperativity of binding |
| $k_{on} /k_{off}$ | (un)Binding of TALE to promoter |
| $a_{Gmax}/a_{Gmin}$ | Maximum and minimum transcription of GFP |
| $b_G$ | Translation rate GFP |
| $y_G$ | Degradation rate GFP |
Simplification of the system
This system can be simplified by making a few assumptions:
- Amount of TALE protein is much larger than binding sites for TALE
- TALE binding and unbinding occurs much more rapidly than protein production and degradation
- There is negligable expression when the promoter is repressed
$G = (\frac{c}{c^n}) (\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m})$
In the case of $n = 1$, this system is independent of copy number. However, maybe more notably the system also appears to be dependent only on the ratios of the remaining variables. The dependence on the ratio of these variables has not been explored by other research groups. This allows us to ensure stable expression across different bacterial species and has not been described, we will elaborate on this more in the section "Sensitivity to different environments".
Copy number independence
Broad host range plasmids are often used when using different hosts however, they do not guarantee the same copy number in every organism Jain and Srivastava 2013. In some organisms, it is not common practice to use a plasmid but rather insert into the genome. The need for consistent expression at a wide range of copy number is thus a desirable feature of any synthetic circuit. We, therefore, have simulated this system from a range of 1 to 600 (genome integration to high-copy number plasmid).
As predicted by our model simplification the system has no variation in steady-state protein levels.
Sensitivity to different environments
As stated before, there are many variables that influence the expression of a gene of interest. However, according to the steady-state model solution, the final level of the gene of interest is only dependent on the ratio of transcription, translation and degradation rates. We can use this to ensure stable expression across different bacterial species if we make the following assumptions:- Transcription rates will change in a similar way for both the TALE gene as the gene of interest.
- Translation initiation rate will change in a similar way for both the TALE gene as the gene of interest if the same ribosome binding site is used for both.
- Translation elongation rate will change in a similar way for both the TALE gene as the gene of interest, if both proteins are similarly codon-optimized.