Team:BIOSINT Mexico/Modeling

Modeling

This year we designed a construct where a lot of different genes interact in several ways. Eight sets of genes were constructed, using five distinctive kinds of genetic expression. They can be classified under the following categories:
a) Genes constitutively expressed
b) Genes that form a protein complex
c) Auto regulated networks
d) Simply induced sequences
e) Complex induced sequences

Equations for Phytochrome-PIF6 complex
In order to produce proteins, in the cell, two main reactions happen. First, DNA is transcripted to mRNA and then it is translated to a peptide sequence, it could be represented in the reaction by:
http://i1379.photobucket.com/albums/ah147/juanjoquispe/modelo/ec1_zpsec1a4694.png
All these reactions are mediated by two specific enzymes, which are RNA polymerase (transcription) and ribosome (translation). These reactions have been well described in literature and can be modeled to a Ordinary Differential Equation system.
The rate of production of the PhyB construct is given by the rate of transcription of the protein from the mRNA molecule and the degradation of the messenger. Therefore:
http://i1379.photobucket.com/albums/ah147/juanjoquispe/modelo/ec2_zpsa7b38e69.png
Where γ is the translation rate of the cell, and α is the degradation of the degradation rate of the protein.
Also, the concentration of the messenger molecule is given by the equation
http://i1379.photobucket.com/albums/ah147/juanjoquispe/modelo/ec3_zpsf3178124.png
Where a represents the activity of the promoter, that is related to the capacity of being activated or suppressed by a transcription factor; β is the maximal production rate of the CaMV promoter (which is attached upstream to PhyB) and is a linear function dependent on the time of the reaction; as in the last equation, α is the degradation rate.

Also, since PCaMV is a constitutive promoter, the value of its activity is equal to 1. So the equation is reduced to
http://i1379.photobucket.com/albums/ah147/juanjoquispe/modelo/ec4_zps89bad846.png

As PIF6 construct is connected to the same promoter, the equations of its expression are deduced by the same way, so:
http://i1379.photobucket.com/albums/ah147/juanjoquispe/modelo/ec5_zpscd0dee12.png
http://i1379.photobucket.com/albums/ah147/juanjoquispe/modelo/ec6_zpsc569b44d.png

In our system, both expressed gene constructs are part of another reaction in presence of deep red light (660 nm lightwave). When photoreceptor protein (PhyB construct) detects deep red light, it fuses to its interaction factor (PIF6 construct) and form a protein complex that in later steps, serves as the activator of another promoter.