# Team:IIT Delhi/Modeling

iGEM IIT Delhi 2014  Synthetic Biology targets to design and create original biological systems. But the genetic systems involved are very intricate. Before going to lab and start working, one should first have a reasonable estimate of what they expect to do. And here mathematical modeling is useful.

Mathematical Model
The following assumptions were taken for modeling the system:
• ✔ All the cells behaves the same way in our system
• ✔Our consideration of the concentrations of mRNA and Protein starts from t=0, and there concentration is zero at t=0
• ✔ We have assumed the mRNA concentration to be "x" and protein concentration to be "y"

We chose a constitutive promoter so the input gene expression function do not involve any repression or activation term, So formulated the following set of differential equations of transcription and translation: The meaning of the respective symbols is given in the Parameter table below
We used some of the parameters developed by iGEM Team Aberdeen 2009 and for the maximal expression level of promoter J231119 we compared is RPU(Relative promoter unit) values with promoter J23101.
Parameters After putting values the set of differential equation becomes: After solving these in MATLAB we get the following curves:
The curve of mRNA concentration versus time  Conclusions
• ✔ Our design works as expected showing the work of a constitutive promoter
• ✔ Another important point is that by modeling our system, we are able to get an idea about the number of protein molecules present finally after 7200 s, the number is 12 x 10^4 , which is quite high compared to the total count of all proteins present in E Coli

• References:
• 1 http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf
• 2 http://www.jbc.org/content/277/26/23664.full.pdf
• 3 http://www.scielo.br/pdf/gmb/v27n3/a22v27n3.pdf
• 4 http://deepblue.lib.umich.edu/bitstream/handle/2027.42/22607/0000157.pdf?sequence=1