Since our project is divided into two main categories being binding and treatment, we have decided to create two models. Thanks to iGEM we were able to download and use MATLAB’s simbiology for free in their making. However, our ineptitude in the area caused us a lot of trouble and we ended up using a lot of premade equations and parameters provided by previous years’ iGEM teams whom we are grateful to.
FimH, TetR-LVA and Antiholin Production
Our first model involves the production of FimH and it also has our holin-antiholin kill switch as an addition. We decided not to limit ourselves in the space provided and used two separate schemes for this model.
The scheme below shows what we expect to see happen in the presence of arabinose.
We have assumed here that there is sufficient amounts of arabinose in the cell and started off by showing the transcription of FimH, TetR-LVA and Antiholin mRNAs. After we were done adding their degradation and translation rates by using the equations and parameters below we got a satisfying graph.
Total mRNA Concentration: [Promoter strength]*[Copy number]-[Degradation rate]*mRNA
The strenght of the promoter was assumed to be the same as the medium-strength promoter J23100(2.80 microPoPs) and the copy number was assumed to be 300.
Antiholin Concentration: [Translation rate of Antiholin]*mRNA-[Degradation rate of Antiholin]*Antiholin
TetR-LVA Concentration: [Translation rate of TetR-LVA]*mRNA-[Degradation rate of TetR-LVA]*Antiholin
The graph below shows the increase in molar concentrations of FimH, TetR-LVA, Antiholin and mRNA in 10 seconds. All of our species were given an initial amount of 0 and showed an increase as time went on. The results supported our goal of producing FimH and showed that the first part of our kill switch is functional.
Our Kill Switch in Action
The scheme below shows what we want to see happen in the absence of arabinose.
The assumption here was that there isn’t a sufficient amount of arabinose to increase antiholin levels. We have used the value given by Team TU-Delft in 2013 where they estimated 190 molecules of holin to be lethal and assumed antiholin to have the initial value of 190 molecules. Then we forced them to form dimers with holin until there was none left which would eventually lead to a lethal amount of Holin molecules being present in the cell. The equations and parameters below were used in our model.
Holin mRNA Concentration: [Copy number]*[Strength]-([Dilution rate]*[Holin mRNA]+[Degradation rate of Holin]*[Holin mRNA])
Holin Concentration: [Translation coefficient]*[Holin mRNA]-[Dilution constant of protein]*[Holin]
Endolysin mRNA Concentration: [Copy number]*[Strength] ]-([Dilution rate]*[Endolysin mRNA]+[Degradation rate of Endolysin]*[Endolysin mRNA])
Endolysin Concentration: [Translation coefficient]*[Endolysin mRNA] ]-[Dilution constant of protein]*[Endolysin]
Dimer complex concentration: [Forward rate]*[Holin]*[Antiholin] -[Reverse rate]*[Dimer complex]
The graph below shows the change in molecule concentrations of Holin mRNA, Holin, Endolysin mRNA, Endolysin, Antiholin and dimer complexes over 10 seconds. All of our species except for Antiholin had the initial amount of 0. The decrease of Antiholin from 190 molecules as the amount of dimer complexes increases until Antiholin is completely depleted can be seen while Holin molecules increase. This means that the second part of our kill switch is functional.
Knowing that our bacteria are now able to bind to cancerous cells in theory, we moved on to the treatment section of our project.
Our main goal while making the butyrate model was to show an increase in the concentrations of both butyrate and But-CoAT. The scheme below was used the provide us with graphs.
We started off by diffusing arabinose into our cell and used the equations below. The equations and parameters for the reactions from Tfactor Concentration to PBAD formation were taken from Team UC_Davis 2013’s wiki page.
Arabinose concentration: [Extracellular arab] – [Extracellular arabinose]/[Diffusion rate]
TFactor Concentration: [Transcription factor]*[Arabinose concentration]/(Kd+[Arabinose concentration])
Final concentration:-[Total concentration]+slope*[TFactor concentration]
Active complex concentration: (K1+K2*[TFactor concentration])/(A+K4+K5*[TFactor concentration]+K3*[Final concentration])
mRNA Concentration: [Transcription rate]*PBAD-[Degradation rate]*mRNA
ButCoAT Concentration: [Rate of translation]*mRNA-[ButCoAT Degradation rate]*ButCoAT
Butyrate concentration: vm*[Acetate Concentration]/(km+[Acetate Concentration])
The acetate concentration here was assumed to be 8.0E-5 moles.
The graph below shows the change in molecule concentration of ButCoAT over 10 seconds. It was given the initial amount of 0 and showed an increase as time went on.
The second graph shows the increase in the molar concentrations of butyrate over ten seconds with Acetate having the initial amount of 8.0E-5 moles. Butyrate alike ButCoAT was given the initial amount of 0 and showed an increase as time went on. Being able to show an increase in Butyrate concentration allowed us to consider the treatment part of our model complete.
1. TU_Delft, 2013 http://2013.igem.org/Team:TU-Delft/Timer-Sumo-KillSwitch
2. METU_HS Ankara, 2015 http://2015.igem.org/Team:METU_HS_Ankara/Modeling
3. St_Andrews, 2011 http://2011.igem.org/Team:St_Andrews/modelling
4. UC_Davis, 2013 http://2013.igem.org/Team:UC_Davis/Modeling
5. Charrier, Cédric et al., “A novel class of CoA-transferase involved in shortchain fatty acid metabolism in butyrate-producing human colonic bacteria”, Microbiology 152, 182 (2006)
6. "Key Numbers for Cell Biologists." Bionumbers: The Database of Useful Biological Numbers