Mathematical model
From 2007.igem.org
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- | In the equations SA and SB | + | In the equations SA and SB are function of oleate concentration and represent the transcriptional activity of the promoters. Notice that the second assumption is used to obtain this equations form. [Pho4free]is the Pho4 concentration (''the output from protein-protein interaction'') that participates to transcription factor interaction. To get this value we write the equation for protein-protein interaction,: |
[[Image:igemmodeling4.jpg|300px|center]] | [[Image:igemmodeling4.jpg|300px|center]] | ||
Using the first assumption and the mass conservation law (since [Pho4]=[Pho4free]+[Pho4P] )we can obtain an expression for [Pho4free] in terms of [Pho80Pho85] and [PhO4] using steady state solution. The third equation in the ODEs system will become: | Using the first assumption and the mass conservation law (since [Pho4]=[Pho4free]+[Pho4P] )we can obtain an expression for [Pho4free] in terms of [Pho80Pho85] and [PhO4] using steady state solution. The third equation in the ODEs system will become: | ||
[[Image:igemmodeling5.jpg|300px|center]] | [[Image:igemmodeling5.jpg|300px|center]] |
Latest revision as of 11:28, 23 October 2007
We modeled the transcriptions factor interactions as Hill-like functions, while the protein-protein interactions are represented through a typical prey-predator model. All the hypotesis were used to get the ODE model. For the transcription factor level we have the following equations:
In the equations SA and SB are function of oleate concentration and represent the transcriptional activity of the promoters. Notice that the second assumption is used to obtain this equations form. [Pho4free]is the Pho4 concentration (the output from protein-protein interaction) that participates to transcription factor interaction. To get this value we write the equation for protein-protein interaction,:
Using the first assumption and the mass conservation law (since [Pho4]=[Pho4free]+[Pho4P] )we can obtain an expression for [Pho4free] in terms of [Pho80Pho85] and [PhO4] using steady state solution. The third equation in the ODEs system will become: