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Sci-Phi 29

Overview - The Model

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 ... . 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 … . In our system the TALE protein binds to the promoter of a gene of interest and thus represses the expression of it. .... 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.

TALE system — Figure 1: Scheme of genetic circuit interactions

From this we can immediately derive the following system of ordinary differential equations: $\frac{dm_T}{dt}$ = $c\cdot a_T - y_m \cdot m_T$
$\frac{dT}{dt} = b_T \cdot m_T - y_T \cdot T - n \cdot k_{on}\cdot T^n \cdot P_G + n \cdot k_{off} \cdot P_{G.T} \cdot T^n$
$\frac{dP_G}{dt} = k_{off} \cdot P_{G.T} - n \cdot k_{on} \cdot T^n \cdot P_G + n \cdot y_T \cdot P_{G.T}$
$\frac{dP_{G.T}}{dt} = n \cdot k_{on} \cdot T^n \cdot P_G - k_{off} \cdot P_{G.T} - n \cdot y_T \cdot P_{G.T}$
$\frac{dm_G}{dt} = a_{Gmax} \cdot P_G + a_{Gmin} \cdot P_{G.T} - y_m \cdot m_G$
$\frac{dm_G}{dt}$ = $b_G \cdot m_G - y_G \cdot G$

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 <br>
 From this we can immediately derive the following system of ordinary differential equations:
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 <a href="https://www.codecogs.com/eqnedit.php?latex=\frac{dm_T}{dt}$&space;=&space;$c\cdot&space;a_T&space;-&space;y_m&space;\cdot&space;m_T" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{dm_T}{dt}$&space;=&space;$c\cdot&space;a_T&space;-&space;y_m&space;\cdot&space;m_T" title="\frac{dm_T}{dt}$ = $c\cdot a_T - y_m \cdot m_T" /></a>
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 <a href="https://www.codecogs.com/eqnedit.php?latex=\frac{dT}{dt}&space;=&space;b_T&space;\cdot&space;m_T&space;-&space;y_T&space;\cdot&space;T&space;-&space;n&space;\cdot&space;k_{on}\cdot&space;T^n&space;\cdot&space;P_G&space;&plus;&space;n&space;\cdot&space;k_{off}&space;\cdot&space;P_{G.T}&space;\cdot&space;T^n" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{dT}{dt}&space;=&space;b_T&space;\cdot&space;m_T&space;-&space;y_T&space;\cdot&space;T&space;-&space;n&space;\cdot&space;k_{on}\cdot&space;T^n&space;\cdot&space;P_G&space;&plus;&space;n&space;\cdot&space;k_{off}&space;\cdot&space;P_{G.T}&space;\cdot&space;T^n" title="\frac{dT}{dt} = b_T \cdot m_T - y_T \cdot T - n \cdot k_{on}\cdot T^n \cdot P_G + n \cdot k_{off} \cdot P_{G.T} \cdot T^n" /></a>
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 <a href="https://www.codecogs.com/eqnedit.php?latex=\frac{dP_G}{dt}&space;=&space;k_{off}&space;\cdot&space;P_{G.T}&space;-&space;n&space;\cdot&space;k_{on}&space;\cdot&space;T^n&space;\cdot&space;P_G&space;&plus;&space;n&space;\cdot&space;y_T&space;\cdot&space;P_{G.T}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{dP_G}{dt}&space;=&space;k_{off}&space;\cdot&space;P_{G.T}&space;-&space;n&space;\cdot&space;k_{on}&space;\cdot&space;T^n&space;\cdot&space;P_G&space;&plus;&space;n&space;\cdot&space;y_T&space;\cdot&space;P_{G.T}" title="\frac{dP_G}{dt} = k_{off} \cdot P_{G.T} - n \cdot k_{on} \cdot T^n \cdot P_G + n \cdot y_T \cdot P_{G.T}" /></a>
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 <a href="https://www.codecogs.com/eqnedit.php?latex=\frac{dP_{G.T}}{dt}&space;=&space;n&space;\cdot&space;k_{on}&space;\cdot&space;T^n&space;\cdot&space;P_G&space;-&space;k_{off}&space;\cdot&space;P_{G.T}&space;-&space;n&space;\cdot&space;y_T&space;\cdot&space;P_{G.T}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{dP_{G.T}}{dt}&space;=&space;n&space;\cdot&space;k_{on}&space;\cdot&space;T^n&space;\cdot&space;P_G&space;-&space;k_{off}&space;\cdot&space;P_{G.T}&space;-&space;n&space;\cdot&space;y_T&space;\cdot&space;P_{G.T}" title="\frac{dP_{G.T}}{dt} = n \cdot k_{on} \cdot T^n \cdot P_G - k_{off} \cdot P_{G.T} - n \cdot y_T \cdot P_{G.T}" /></a>
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 <a href="https://www.codecogs.com/eqnedit.php?latex=\frac{dm_G}{dt}&space;=&space;a_{Gmax}&space;\cdot&space;P_G&space;&plus;&space;a_{Gmin}&space;\cdot&space;P_{G.T}&space;-&space;y_m&space;\cdot&space;m_G" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{dm_G}{dt}&space;=&space;a_{Gmax}&space;\cdot&space;P_G&space;&plus;&space;a_{Gmin}&space;\cdot&space;P_{G.T}&space;-&space;y_m&space;\cdot&space;m_G" title="\frac{dm_G}{dt} = a_{Gmax} \cdot P_G + a_{Gmin} \cdot P_{G.T} - y_m \cdot m_G" /></a>
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 <a href="https://www.codecogs.com/eqnedit.php?latex=\frac{dm_G}{dt}$&space;=&space;$b_G&space;\cdot&space;m_G&space;-&space;y_G&space;\cdot&space;G" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{dm_G}{dt}$&space;=&space;$b_G&space;\cdot&space;m_G&space;-&space;y_G&space;\cdot&space;G" title="\frac{dm_G}{dt}$ = $b_G \cdot m_G - y_G \cdot G" /></a>
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