Team:UC Davis/Modeling

From 2010.igem.org

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<a name="impl"></a><p class="header">Implementation</p>
<a name="impl"></a><p class="header">Implementation</p>
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After we had derived the necessary equations, we implemented a computer program that would execute the appropriate calculations in order to depict our system at different time steps beginning with the initial stimulus of the system.<br/>
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After we had derived the necessary equations, we implemented a computer program that would execute the appropriate calculations in order to depict our system at different time steps beginning with the initial stimulus of the system.<br/><br/>
This computer program generated the simulation by treating the blank screen of pixels as a representation of the lawn of cells we wanted to construct.  Naturally, each pixel would then represent an individual cell in the system that has a certain degree of RFP expression.   
This computer program generated the simulation by treating the blank screen of pixels as a representation of the lawn of cells we wanted to construct.  Naturally, each pixel would then represent an individual cell in the system that has a certain degree of RFP expression.   
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In order to take into account the diffusion of the various substances in the system, we implemented a Gaussian blur at each pixel that would be recalculated at every time interval using the previous time interval's output as its input.  In this way, we could properly represent the step-by-step concentration of substances at each time step in each pixel by calculating the change in concentration at each time step using the Gaussian blur algorithm at each pixel.
In order to take into account the diffusion of the various substances in the system, we implemented a Gaussian blur at each pixel that would be recalculated at every time interval using the previous time interval's output as its input.  In this way, we could properly represent the step-by-step concentration of substances at each time step in each pixel by calculating the change in concentration at each time step using the Gaussian blur algorithm at each pixel.
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Pictured here is the initial output of the completed simulation.  In this particular run, we initialized the system with a vertical stimulus down the center of the plate, resulting in linear oscillation outwards towards the edges.
Pictured here is the initial output of the completed simulation.  In this particular run, we initialized the system with a vertical stimulus down the center of the plate, resulting in linear oscillation outwards towards the edges.
<br/><img src="https://static.igem.org/mediawiki/2010/1/19/UCD_SimuOP.png" width="680px" height="450px"><br/>From this, we can conclude that given our design, the system should function in accordance to our expectations.     
<br/><img src="https://static.igem.org/mediawiki/2010/1/19/UCD_SimuOP.png" width="680px" height="450px"><br/>From this, we can conclude that given our design, the system should function in accordance to our expectations.     
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<br/>To further test the simulation, we decided to try another type of initial stimulus and observe the results.  The stimulus we chose was seeding the oscillation at the four corners of the "plate".  The following is the result of this run, which again confirms the intended behavior of our system.
<br/>To further test the simulation, we decided to try another type of initial stimulus and observe the results.  The stimulus we chose was seeding the oscillation at the four corners of the "plate".  The following is the result of this run, which again confirms the intended behavior of our system.
<br/><img src="https://static.igem.org/mediawiki/2010/9/98/UCD_SimuOPCircles.png" width="680px" height="450px">                 
<br/><img src="https://static.igem.org/mediawiki/2010/9/98/UCD_SimuOPCircles.png" width="680px" height="450px">                 

Revision as of 01:05, 28 October 2010

Goals

Early on, we decided to create a computational model of our pattern generation system. This would allow us to accomplish several important goals:

  • Demonstrate that the circuit logic was sound
  • Test the viability of our construct given realistic parameters
  • Probe the effects that different parameters would have on the system
  • Identify potential failure modes, and the events that might trigger them
  • Evaluate alternative designs of the construct
With these goals in mind, we set about formalizing the system.

Equations

To start, we generate equations for all of the transcription reactions:



Implementation

After we had derived the necessary equations, we implemented a computer program that would execute the appropriate calculations in order to depict our system at different time steps beginning with the initial stimulus of the system.

This computer program generated the simulation by treating the blank screen of pixels as a representation of the lawn of cells we wanted to construct. Naturally, each pixel would then represent an individual cell in the system that has a certain degree of RFP expression.

In order to take into account the diffusion of the various substances in the system, we implemented a Gaussian blur at each pixel that would be recalculated at every time interval using the previous time interval's output as its input. In this way, we could properly represent the step-by-step concentration of substances at each time step in each pixel by calculating the change in concentration at each time step using the Gaussian blur algorithm at each pixel.

Results

Pictured here is the initial output of the completed simulation. In this particular run, we initialized the system with a vertical stimulus down the center of the plate, resulting in linear oscillation outwards towards the edges.

From this, we can conclude that given our design, the system should function in accordance to our expectations.

To further test the simulation, we decided to try another type of initial stimulus and observe the results. The stimulus we chose was seeding the oscillation at the four corners of the "plate". The following is the result of this run, which again confirms the intended behavior of our system.
We would like to take a moment to thank all of our sponsors for their very generous donations, as we could not have done this without your help!

We would also like to thank and acknowledge:
Our Advisors
Marc Facciotti
Ilias Tagkopoulos
Technical Guidance
David Larsen
Andrew Yao
Visiting iGEMer
Jia Li of Zhejiang University (TEAM ZJU-China)
cI Promoter Screen
Drew Endy - Stanford
Thomas Schneider - NIH
Want to sponsor us? Send an email to mtfacciotti@ucdavis.edu to discuss various ways you can help! :)

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