# Team:IIT Delhi/Modeling

### From 2014.igem.org

- 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:
- ✔ 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
- 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

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.

After putting values the set of differential equation becomes:

After solving these in MATLAB we get the following curves:

- References: