Team:CIDEB-UANL Mexico/math resistance

The resistance module is based in the use of IrrE gene. IrrE 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 IrrE gene length (986nt) and protein length (311aa) respectively.

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

But since IrrE half-life has not been determined yet, we decided to search about homologous proteins with the same function as IrrE (transcriptional factor) and according to Dibden and Green (2005) the average half-life for transcriptional factors in E. coli is 45 min. They tested FNR proteins (transcriptional factors) through thermo-induciblefnr expression observing that their half-life was 45min average.

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 IrrE was 4.45 min.

With all these information we could find the degradation rates for both transcription and translation of IrrE.

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.

We found that IrrE needs to have a positive charge to be functional, accepting one Zn2+ ion from E.coli (Vujicic, 2009). Vujicic’s team developed the structure of IrrE deducing it should have three domains; one specific is the zinc-binding site where the Zn2+ ion binds to make IrrE positive. It becomes positive what makes possible its binding to a substrate forming a substrate complex, but the substrate is unknown. For that reason we only take as a “f(post)” variable the Zn2+binding because the data for finding the affinity between IrrE and the unknown substrate was not possible to determine.

As we did not have the affinity between IrrE and Zn2+ we need to find the data from homologous proteins. In fact, we found that proteins with zinc binding domains have an affinity between 0.1 and 0.2 in E. coli (Vorackova, 2012). We used 0.15 as average in the equation for association constant which is defined as the following:

Where [C] is the complex formed, [S] is the substrate and [E] is the enzyme, ligand or ion. Substituting for IrrE it is expressed as below:

With the association constant we could use it in Simbiology for modelling the functional IrrE production. The results are shown next:

When we compared both graphs (Graph 1 and Graph 2) we realized that not all the IrrE production was functional. In fact from the total amount produce (about 2400), only about 1700 are functional. So it demonstrates that the rate at which Zn2+ ions binds to IrrE is slower than the rate at which IrrE is produced, leaving a nonfunctional IrrE.

Bibliography

● David Dibden, J. G. (2005). In vivo cycling of the Escherichia coli transcription factor FNR between active and inactive states. Microbiology, 4063-4070.

● Douglas Selinger, R. M. (2003). Global RNA Half-Life Analysis in Escherichia coli Reveals Positional Patterns of Transcript Degradation. Genome Research, 216-223.

● Vorackova Irena, S. S. (2011). Purification of proteins containing zinc finger domains using Immobilized Metal Ion Affinity Chromatography. Protein Expression and Purification, 88-95.