Team:UC Berkeley/Modeling

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[[Image:cdb3.jpg]]  
[[Image:cdb3.jpg]]  
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Where $\Omega_H$, $\Omega_{AH}$ and $\phi$ are represented by the following collections of constants
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Where the system can be divided into three dimensionless parameters which describe the behavior of holin, antiholin and the holin-antiholin dimer
[[Image:cdb4.jpg]]  
[[Image:cdb4.jpg]]  
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Using MatLab, graphs of the system were produced
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Using MatLab, the following graph of the system was produced.
[[Image:image1.png]]
[[Image:image1.png]]
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The horizontal line at y=1 represents the critical holin concentration needed induce lysis.
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[[Image:image2.png]]
[[Image:image2.png]]
[[Image:image3.png]]
[[Image:image3.png]]

Revision as of 05:41, 25 October 2008


The kinetics of the Lambda phage lysis device was modeled to help our team gain an insight into the behavior of our system. The below equations describe our system


Cdb1.jpg


Where P1 and P2 approximate the mRNA promoter strength and /omega_mH and mH are the degradation rates for holin and antiholin respectively. kH , kAH and kc represent the rate constants for holin and antiholin formation and the coupling rate for the holin-antiholin dimer.

The literature indicates that at the time of lysis, cells infected with lambda phage have approximately 1000 holin proteins. Therefore, the critical concentration of holin (Hc) was set at 1000 holin proteins per cell.

At steady state,

Cdb2.jpg

The system can be simplified into the following transfer function

Cdb3.jpg

Where the system can be divided into three dimensionless parameters which describe the behavior of holin, antiholin and the holin-antiholin dimer

Cdb4.jpg

Using MatLab, the following graph of the system was produced.

Image1.png

The horizontal line at y=1 represents the critical holin concentration needed induce lysis.

Image2.png Image3.png