Team:CIDEB-UANL Mexico/math union

Binding module

The binding module is based in the use of a fusion protein composed by L2 and AIDA. L2+AIDA is a protein which is not affected by external factors during its transcription as well as its translation, so we need to use the stablished parameters but with the data we obtained from it:

We used the parameters for translation and transcription rate from Singapore 2008 iGEM team as well as the speeds at which E. coli carry out transcription and translation assuming a transcription speed of 70nt/s and a translation speed of 40aa/s. So we used them in the equations below with the L2+AIDA gene length (2620nt) and protein length (856aa) respectively:

Then, we use the parameters for degradation rates for proteins and mRNAs from Beijing PKU 2009 iGEM team:

As the protein was the fusion of two we need to search for each half-life. The half-life of membrane proteins range between 2 to 20 hours in E. coli (Hare, 1991), and as AIDA-I is a membrane protein its half-life must be between that range since it is not determined the specific half-life of AIDA. To find the half-life of L2 we assumed it was 7.8 hours (Bergant, 2010). Bergant’s team made test with a homologous protein but found in the minor capsid of the Human Papillomavirus (HPV). Although the function of the L2 strand in HPV is viral, and in E. coli is ribosomal, both share similar structures and sequences. Once we have decided to use the half-life from the homologous L2 we determined to use it as the half-life for the fusion protein because it was between the range of AIDA-I, and also because it was the lower half-life assuming as E. coli start the L2 degradation, it would degrade the whole protein.

For determining the degradation rate of average mRNA we used the information from Selinger’s team (2003). They carried several experiments for finding average mRNA half-life in E. coli. They used mRNAs about 1100 bp concluding they have an average half-life of 5min. So with this we found the average mRNA half-life of L2+AIDA was 11.9 min.

With all these information we could find the degradation rates for both transcription and translation ofL2+AIDA:

For the simulation we used Simbiology using the previous data in the equations for finding the amount of proteins E.coli would produce at certain time. The simulation find out the next graph as the result.

But for translation there was another factor we had to consider, the “f(post) which were the posttranslational variables affecting the production of the functional protein:

As the fusion protein needs to be expressed in the membrane of E. coli, we needed to find the average velocity at which E. coli exports its proteins. The process by which bacteria exports its proteins are divided into three phases, the “breathing” between translation and the second phase, which is movement of a protein to the membrane and translocation; in this phase the protein attaches to the membrane of bacteria (Peskin, 1991). Using this information, we found E. coli completes these phases in an average of 5 to 6 min depending on the protein size (Driessen, 1990). We determined to use 5.5min because L2+AIDA are not too small or too big in length (2620nt).