Team:Ciencias-UNAM/Modeling

From 2012.igem.org

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The model is based on the next assumptions (represented en 1 and 2):
The model is based on the next assumptions (represented en 1 and 2):
<br/>
<br/>
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-The bicarbonate concentration is controlled in every moment, and it increments linearly.
+
-The bicarbonate concentration is controlled in every moment, and it increments linearly.<br/>
-
-The bicarbonate concentration will remain between two levels, [0,K], where K is the saturation concentration.  
+
-The bicarbonate concentration will remain between two levels, [0,K], where K is the saturation concentration. <br/>
-
-The GFP has a basal expression j.
+
-The GFP has a basal expression j.<br/>
-
-The GFP expression will remain too between the basal level, j, and the saturation J, (j,J].
+
-The GFP expression will remain too between the basal level, j, and the saturation J, (j,J].<br/>
-
<br/>
+
 
-
Where
+
<img src="https://static.igem.org/mediawiki/2012/9/98/F3_cu_mario.jpg" />.
<img src="https://static.igem.org/mediawiki/2012/9/98/F3_cu_mario.jpg" />.
-
Suppose that
+
<br/> Let's Suppose additionaly that
<img src="https://static.igem.org/mediawiki/2012/6/6b/F4_cu_mario.jpg" />
<img src="https://static.igem.org/mediawiki/2012/6/6b/F4_cu_mario.jpg" />
with
with
<img src="https://static.igem.org/mediawiki/2012/d/dd/F5_cu_mario.jpg" />
<img src="https://static.igem.org/mediawiki/2012/d/dd/F5_cu_mario.jpg" />
 +
<br/>
,then, we can define and solve the Differential Equation: <br /><br />
,then, we can define and solve the Differential Equation: <br /><br />
<img src="https://static.igem.org/mediawiki/2012/6/66/F6_cu_mario.jpg" /><br /><br />
<img src="https://static.igem.org/mediawiki/2012/6/66/F6_cu_mario.jpg" /><br /><br />

Revision as of 20:45, 26 September 2012

..:: CIENCIAS-UNAM ::..

MODELING

Introduction.

The usual approach in synthetic biology for modeling a genetic network is to describe the interaction of inducers and repressors with promoters. This description is very detailed and very difficult to implement because of the many unknown parameters involved in the differential equations.

We tried an approach called “keep it simple”, so the goal of our model is to describe the relation between the concentration of bicarbonate and the expression of the GFP but with the possibility of make useful predictions for lab.

The model.

In the description of the project, we introduced a CO2 induced biosensor with GFP as a reporter. The biosensor is designed to sense the concentration of bicarbonate on the media. There is a complex mechanism behind for the signaling of the bicarbonate concentration to the GFP expression. Some of the parameters required for a full described model of this signaling process were not available in the literature. For these reason we decided to model only the indirect expression of GFP by the induction of bicarbonate.


Let's represent the concentrations of bicarbonate and GFP as under the time constraint .


The model is based on the next assumptions (represented en 1 and 2):
-The bicarbonate concentration is controlled in every moment, and it increments linearly.
-The bicarbonate concentration will remain between two levels, [0,K], where K is the saturation concentration.
-The GFP has a basal expression j.
-The GFP expression will remain too between the basal level, j, and the saturation J, (j,J].
.
Let's Suppose additionaly that with
,then, we can define and solve the Differential Equation:



with .

Using initial values we have

so that: .

Then we have y and x in terms of t:







Here we have another expression of y in terms of x: