Team:KAIST Korea/Project Modeling
From 2012.igem.org
![](https://static.igem.org/mediawiki/2012/5/59/Logopart_Kaist.png)
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2012 KAIST Korea
Mail : kaist.igem.2012@gmail.com
Twitter : twitter.com/KAIST_iGEM_2012
Facebook : www.facebook.com/KAISTiGEM2012
Project : Modeling
![](https://static.igem.org/mediawiki/2012/7/7f/Horizontal_line_kaist.png)
Cell Growth Curve
Proof of concept
Auto Regulation
And we plot the result using 3D bar graph. As graph represents, some parameters are critical to change the output of our system and some are not.
![](https://static.igem.org/mediawiki/2012/9/95/Starter_gradient_kaist.png)
Modeling
Computational modeling of our project
Cell Growth Curve
Cell growth can be modeled using Logistic differential equation as shown below.
When we solve this equation with appropriate parameters(using MATLAB), we can get solution curve as shown below. This curve matches with our knowledge about cell growth.
![](https://static.igem.org/mediawiki/2012/a/a2/KAIST_Logistic_equation.png)
![](https://static.igem.org/mediawiki/2012/4/4a/KAIST_Cell_growth_curve.png)
Proof of concept
Using these reaction, we constructed mathematical model of our system as shown below. Pg(gene probability), in our model, represents the number of plasmid which is inverted. And the rate of producing inverted gene is reduced as the remaining non-inverted gene is reduced.
Using MATLAB we can solve these set of differential equations and get solution curve like below.
We also consider concentration of GFP/RFP of cell colony. The solution curve shown below represents that result.
- Mathematical model
![](https://static.igem.org/mediawiki/2012/d/d7/KAIST_Gfprfp.png)
![](https://static.igem.org/mediawiki/2012/b/b0/KAIST_Gfprfp2.png)
![](https://static.igem.org/mediawiki/2012/1/13/Result_graph_gfprfp1.png)
![](https://static.igem.org/mediawiki/2012/b/b8/KAIST_Result_graph_gfprfp2.png)
- Parameter Sensitivity Analysis
![](https://static.igem.org/mediawiki/2012/d/d3/KAIST_Sensitivity_coeff.png)
![](https://static.igem.org/mediawiki/2012/1/1d/KAIST_Sensitivityresult.png)
![](https://static.igem.org/mediawiki/2012/c/c8/Sensitivityresult2.png)
Auto Regulation
Based on the reaction above, we constructed our mathematical model like this.
Using MATLAB we can solve these set of differential equations and get solution curve like below.
When we consider the cell colony instead of one cell, we simply multiply cell growth curve to original result. And derived curve is like below.
- Mathematical model
![](https://static.igem.org/mediawiki/2012/thumb/1/1b/KAIST_ReactionofbFMO.png/623px-KAIST_ReactionofbFMO.png)
![](https://static.igem.org/mediawiki/2012/e/ed/KAIST_ODEbFMO.png)
![](https://static.igem.org/mediawiki/2012/8/8e/KAIST_Result_graph_bFMO1.png)
![](https://static.igem.org/mediawiki/2012/7/77/KAIST_Result_graph_bFMO2.png)
- Parameter Sensitivity Analysis
![](https://static.igem.org/mediawiki/2012/6/60/KAIST_sensitivityresult3.png)