2.1 Modelling results

The WITS-CSIR_SA iGEM team intend to use a riboswitch to reprogram the chemotactic behavior of E. coli. The project includes engineering the attraction of the bacteria to theophylline[1]. CheZ is an important protein controlling the chemotaxis of bacteria, and WITS-CSIR_SA have used a theophylline riboswitch to control the expression of CheZ in CheZ mutants in order to engineer the bacterial movement towards theophylline[1]. They are using a riboswitch sensitive to theophylline to control the expression of CheZ. In the absence of theophylline, the start codon is covered so the translation cannot occur. In the presence of theophylline, the shape of the aptamer (riboswitch) changes and the start codon is exposed[1]. Thus, the higher the concentration of the theophylline, the more will enter the cell and the higher the expression of CheZ and the higher the level of directed movement[1]. The theophylline riboswitch can be modelled in three differential equations (Equation 1)[2].

M, CheZ and T respectively stands for the concentration of CheZ mRNA, the concentration of protein CheZ and the concentration of theophylline. The constants α,β,γ,ξ and δ are all positive, and respectively denote the CheZ-promoter transcription rate, the CheZ-mRNA translation rate and the mRNA, CheZ and theophylline degradation-plus-dilution-rates. ζ(Text) is the theophylline transport rate per unit CheZ concentration. It is a function of number of theophylline receptors and external theophylline concentration. The function ϕ(T) and Θ(T) denote the theophylline-governed regulation at the transcription and translation levels respectively (Equation 2 below [2]). K_Φ is the equilibrium constant at transcriptional level and K_Θ is the equilibrium constant at translation level [2].

Varying the parameter ζ(Text) of above model could help us to understand how the number of receptors and external theophylline concentration effect the intracellular concentration of theothyline and hence the expression level of CheZ. The results are shown in Figure 3(a) and Figure 3(b) below. In addition, the response curve of CheZ against theophylline concentration with different theophylline transport rate was illustrated in Figure 3(c).

Fig.3: Expression of CheZ vs. timeThe expression of CheZ increases with increase of transport rate. With higher theophyline transport rate bacteria will produce more CheZ and therefore a higher level of directed movement.

Fig.4: Intracellular theophylline vs. time The intracellular theophylline level increases with transport rate. It means we can enhance CheZ expression with increasing theophylline chemoreceptors.

Fig.5: Response curve of CheZ vs. intracellular theophylline. The CheZ response curve shows that the transport rate can be used to tune CheZ response, the threshold intracellular concentration of theophylline required to trigger CheZ response increases with transport rate.

In conclusion, from modelling we know that the concentration of CheZ and intracellular theophylline increase with increasing theophylline transport rate. Also, the expression of CheZ can be tuned by this transport rate. Therefore, it is believed that the CheZ level and the level of directed movement of bacteria can be increased by expressing more theophylline transporter in the cell membrane.

2.2 Parameters

2.3 Matlab code

2.4 References

[1] Topp S, Gallivan JP (2007) Guiding bacteria with small molecules and RNA. J Am Chem Soc 129(21): 6807-6811.

[2] Santillan M, Mackey MC (2005) Dynamic behavior of the B12 riboswitch. Phys Biol 2: 29-35, Doi: 10.1088/1478-3967/2/1/004.

[3] Beisel CL and Smolke CD (2009) Design principles for riboswitch function. PLoS Comput Biol 5(4): e1000363, doi:10.1371/journal.pcbi.1000363.