Difference between revisions of "Team:ETH Zurich/Model/Environment Sensing/parameter space"
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&\simeq \frac{\left(\frac{[\text{Lac}]}{K_{\text{Lac}}} \right)^{n_{\text{Lac}}}}{1 + \left(\frac{[\text{Lac}]}{K_{\text{Lac}}} \right)^{n_{\text{Lac}}}}\end{aligned}\]</span> | &\simeq \frac{\left(\frac{[\text{Lac}]}{K_{\text{Lac}}} \right)^{n_{\text{Lac}}}}{1 + \left(\frac{[\text{Lac}]}{K_{\text{Lac}}} \right)^{n_{\text{Lac}}}}\end{aligned}\]</span> | ||
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| + | <p>As a result, the schematics of the circuit can be simplified this way: | ||
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| + | <img style="{width:400px;}" src="https://static.igem.org/mediawiki/2017/7/73/T--ETH_Zurich--tumor_sensing_lactate_highlight.png" | ||
| + | alt="Modeling process principle" | ||
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| + | <img style="{width:400px;}" src="https://static.igem.org/mediawiki/2017/9/9e/T--ETH_Zurich--tumor_sensing_lactate_simplified.png" | ||
| + | alt="Modeling process principle" | ||
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Revision as of 10:27, 23 October 2017
Parameter search
Model of our circuit
The tumor sensing circuit is composed of several proteins interacting with small molecules (AHL and lactate) and DNA (at the transcription factors binding sites). To establish a model describing the behavior of our circuit, we first had to understand the way these interactions are happening inside of the cell. BLABLA references DAVID. Here is a detailed overview of the tumor sensing circuit:
Simplification of the lactate sensing
Let us first focus on the lactate sensing part of the circuit. In the cell, two proteins are produced:
- LldP: a transmembrane protein enabling the transport of extracellular lactate into E. coli.
- LldR: a transcription factor, repressing the expression of the hybride transcription factor when unbound to lactate, and deactivated when bound to it.
To model precisely the regulation of the hybrid promoter by lactate, it would be necessary to take into account all the following points:
- How the intracellular lactate concentration behaves in regards to the expression level of LldP and the extracellular lactate concentration
- What is the binding constant between LldR and the lactate
- What is the binding dynamics of Lldr to the operon, and how it affects the transcription rate downstream
In an effort to simplify our model to reduce it to the most meaningful parameters, and because it has already extensively been studied and characterized by previous iGEM teams, we have chosen not to take into account the complexity of the lactate sensing pathway and rather use a phenomenological model to describe its influence. We rely on the characterization of the lactate sensor using several expression regulation sequences done by the ETH 2015 iGEM team. We consider therefore that lactate sensing follows a Hill function as following:
\[\begin{aligned} P_{\text{Lac}} &\simeq \frac{\left(\frac{[\text{Lac}]}{K_{\text{Lac}}} \right)^{n_{\text{Lac}}}}{1 + \left(\frac{[\text{Lac}]}{K_{\text{Lac}}} \right)^{n_{\text{Lac}}}}\end{aligned}\]
As a result, the schematics of the circuit can be simplified this way:
