To model how the system works and to check if it can function in reality, and to obtain data of how many target eforRed chromoprotein would be generated in our system with a varying DSF, we conducted simulation modeling for the system. We concerned about whether the results obtained in the simulation consistent with those obtained in the wet lab, and aim at providing references for the selection of the wet-lab scheme by changes of the relative concentration of diffusable signal factor in the simulated system, and further verify the correctness and feasibility of the cascade.

Objectives:

(1) To model the system under mRNA level

(2) To characterize the efficiency of promoter PspA

Background

Figure 1 shows our Engineered E. coli with RpfC-RpfG system.

We constructed models for design and calibrate the signal-response behaviour of the DSF system. Our model took account of the following processes:

(1) phosphorylation of RpfG is induced by DSF binding to cell-surface receptor RpfC;

(2) RpfG[P] then degrades c-di-GMP which relieves the inhibition of Clp-PspF;

(3) Clp-PspF then activates the expression of CBSI-CBSII-PspA-eforRED via the overexpressed Sigma54 transcription factor. In the absence of the DSF signal, it is proven with our wet lab data that

(4) RpfG was remained in its unphosphorylated form, and no eforRED would express, under T7 promoter.

Our model is written as followings:

Figure 2 shows chemical equations in the system.

Assumption:

(1) Clp-PspF has the same association rate and dissociation rate with c-di-GMP as Clp.

(2) Clp-PspF has the same association rate with CBSI-CBSII-PspA-eforRed as PspA.

(3) Sigma54/polymerase will have no effect on mRNA formation of fusion protein.

Our model, therefore, is rewritten with following chemical equations.

Figure 3 is the chemical equations in the modified system with assumptions taken.

Hypothesis:

(1) Our system would detect 100uM of DSF (with 100uM DSF indicated late phase infection).

(2) The expression of eforRed was dependent on signal-independent phosphorylation of RpfG.

(A) The overall system

From the assumptions and settings above, we constructed our MatLab model as follows and present in figure 4.

Figure 4 is the system set in SynBiology system in Matlab.

We constructed our model to model the formation of mRNA transcript of our system only, as (1) under the quasi-state approximation, the binding and dissociation of of a complex occurs faster than the synthesis of a protein and such that the rate of protein folding is assumed as zero and (2)the formation of eforRed chromoprotein recruits Sigma 54 and RNA polymerase to "crush" onto our mRNA transcript to proceed the formation, and would be hard to calculate the collision frequency. It would be done as a future plan.

For the parameters used in the model, they are presented in figure 5.

Figure 5: Parameters taken in calculations and model construction.

ODE equation is established with the system by Mass-Action Kinetics law and is represented in the diagram.

Figure 6: ODE equation of change of intensity in each components in the system.

Figure 7: Concentration of components under 100uM DSF.

Under our modeling, mRNA transcript of eforRed increased under 100uM DSF. It is demonstrated that the phospho-relay system of our bio-brick functions properly, and Clp-PspF would bind onto CBSI-CBSII-PspA-eforRed. Our wet lab data also indicated the increase of gene expression level of CBSI-CBSII-PspA-eforRed, which matches with the dry lab result.

In our wet lab result, the gene expression increased but not red signal was found. It is suggested that (1) the promoter (pspA) used was not as strong as T7 promoter, such that not enough Sigma54 and RNA polymerase were recruited by the Clp-PspF fusion protein to pspA promoter for sufficient mRNA transcription. Hence, another model would be built to model the difference of efficiency of pspA and T7 promoter in terms of strength to recruit Clp-PspF at the part of "Promoter Activity".

(B) Effect of concentration of DSF on the formation of mRNA complex

To further analyse the effect of concentration of DSF on the formation of mRNA complex, graphs of 0uM, 0.01uM, 0.1uM, 1uM, 10uM, 100uM and 1000uM DSF was generated.

Figure 8 & 9: Concentration of components under 0uM DSF and 0.01uM DSF.

Figure 10 & 11: Concentration of components under 0.1uM DSF and 1uM DSF.

Figure 12 & 13: Concentration of components under 10uM DSF and 100uM DSF.

Figure 14: Concentration of components under 1000uM DSF.

From the graphs we generated, though the difference of parameters is minute, we concluded that (1)from 0 uM to 1 uM DSF added, the mRNA transcript level is low as there are background transcripts, (2) from 10uM to 1000uM DSF, the mRNA transcript level slightly increases. Thus, it is concluded that with the increase of DSF from 10uM to 1000uM DSF, the system would generate mRNA transcript of eforRed.

(C) The detection limit of the phosphorelay system

As our wet lab results subsequently revealed that under the control of T7 promoter and IPTG induction, red signal was generated in our engineered system in 4 hours. To add on, our system works omitting the effect of Sigma54 and polymerase. Thus, the time for reaction is set at 4 hours to see how much DSF in the system would trigger the phosphorelay system for its operation.

Figure 15 & 16: Concentration of components under 67.42uM DSF and 223.53uM DSF.

From the graphs and data, we modeled the range of detection of DSF. We found that our system works fine at the range of 67.42uM to 223.53uM, but not over the range. Possible reasons are (1) the system is saturated as all RpfC is occupied with DSF, and cannot phosphorylate RpfG to be RpfG[P], or (2) all RpfG in the system is turned into RpfG[P], such that RpfG in the system is not regenerated to support the phospho-relay system.

Based on the wet-lab dat we obtained from the DSF assay, there is no visible red signal even the DSF used to fall within this range, With reference to the positive data in rt-qPCR, it indicates the system is functional under the DSF stimulation. We proposed that this may due to the low translation rate due to the expressing stress. It is due to the fact that our cell is over-expressing four of our protein candidates within our system under the T7 promoter, and cause excess stress to the translation mechanism. There will need a more sophisticated dry-lab model for further design modification, mostly to optimize (lower) the expression of some of the other proteins to maintain an optimum translation environment for our reporter.

Reference:

1. (n.d.). Retrieved from https://2014.igem.org/Team:Dundee.

2. Chin, K. H., Lee, Y. C., Tu, Z. L., Chen, C. H., Tseng, Y. H., Yang, J. M., ... & Chou, S. H. (2010). The cAMP receptor-like protein CLP is a novel c-di-GMP receptor linking cell–cell signaling to virulence gene expression in Xanthomononas campestris. Journal of molecular biology, 396(3), 646-662.

3. Leake, M. C., Greene, N. P., Godun, R. M., Granjon, T., Buchanan, G., Chen, S., ... & Berks, B. C. (2008). Variable stoichiometry of the TatA component of the twin-arginine protein transport system observed by in vivo single-molecule imaging. Proceedings of the National Academy of Sciences, 105(40), 15376-15381.

4. Twigg, A. J., & Sherratt, D. (1980). Trans-complementable copy-number mutants of plasmid ColE1. Nature, 283(5743), 216.

Team:Hong Kong-CUHK/Testification

Modeling

Overview