With a general view on our projects, modeling aims to connect the DSF sensor design and phage release system to visualize the molecular interaction between our DSF and RpfC, RpfG, etc. and its effect on downstream Acr production as well as on the major tail protein and endolysin protein viability of bacteriophage xoo-sp2 in general.
Due to lack of experimental data in the COVID-19 pandemic, modeling plays an even more vital role than usual. We designed three models: DSF sensor model to test the sensibility of DSF sensor, dCas inhibitory model to depict the inhibitory mechanisms of SgRNA and dCpf1 on transcription, Acr anti-inhibitory model to combine the preceding models and reveal the reactivation mechanism of DSF on downstream protein production.
DSF sensor model I. Aim
- This model aims to test the sensibility of DSF sensor according to the pathway we designed using Michaelis-Menten equation
- We expect the model to predict downstream protein production (EYFP) that we use to symbolize the expression of Acr.
II. General Assumption
1. We apply the level of molecules rather than binding sites or residue as reaction units.
2. There are only some of the substances that have an initial value (DSF, RpfC, RpfG, c-di-GMP), other substances are initially absent and are the intermediate products of the reactions.
3. Because of the similarities between RpfC and RpfG, it is assumed that the binding rate of RpfC to the phosphate is the same to the binding rate of RpfC to the phosphate.
4. For simplicity, we ignored the impact of RpfC in the repression of DSF biosynthesis, we just considered it as a reverse reaction of DSF.RpfC.
5. For simplicity, we ignored some minor regulatory relationship, it is assumed that only the substances in the reactions regulate each other through reactions.
III. Pathway and Reactions
The binding of DSF molecules to sensory input domain of RpfC will trigger its autophosphorylation, phosphorelay via the receiver and histidine phosphotransfer domains, and phosphotransfer to the receiver domain of the response regulator RpfG. The HD-GYP domain on RpfG is a cyclic di-GMP (c-di-GMP) phosphodiesterase. The reception of DSF molecules will therefore break the connection between vc2-riboswitch and c-di-GMP and lead to degradation of c-di-GMP (Ryan, 2015). The vc2-riboswitch without the attachment of c-di-GMP will enter its activation phase and promote expression of downstream protein.

The equilibrium equations of pathways are shown below:
IV. Modeling
According to the law of mass action, the rate of a reaction is proportional to the product of the concentration of the reactants, based on the pre-set parameters and initial values, we can write down the functions:

1. The concentration rate of DSF:

2. The concentration rate of RpfC:

3. The concentration rate of DSF·RpfC:

4. The concentration rate of DSF·RpfC(P):

5. The concentration of RpfG:

6. The concentration of RpfG(P):

7. The concentration of c-di-GMP:

8. The concentration of C-di-GMP·vc2-riboswitch:

9. The concentration of vc2-riboswitch:

Consequently, we can obtain the changing pattern of each substance in the DSF sensor pathway. Later, in order to find out the correlation between vc2-riboswitch content (which directly affects EYFP con.) and DSF input, we created a loop to import different DSF initial values and collect the vc2-riboswitch concentration in equilibrium.
V. Visualization and Analysis using Matlab Figure 1: DSF sensor model: concentration change of all components in the reaction with time Figure 2: the effect of different DSF input on vc2-riboswitch (on) concentration
Here vc2-riboswitch concentration directly determines the production of EYPF (or Acr). As shown from Figure 1, while the concentration of DSF, RpfG, C-di-GMP.vc2-riboswitch goes low, vc2-riboswitch, RpfG(P), and DSF·RpfC(P) increases. For Figure 2, with the increase of DSF input, the vc2-riboswitch concentration increases slowly at first and rises rapidly after the DSF content reaches around 1μM.
dCas inhibitory model I. Aim
This model aims to reveal the inhibitory mechanisms of dCpf1·SgRNA complex on transcription of DNA region.
II. Pathways and Reactions
Elaborated on the design page, when no DSF activates the expression of the downdream protein (Acr), SgRNA and dCpf1 (dCas12a) protein bind and form complex to inhibit the transcription of specific region of DNA, thus repressing the expression level of GFP (major tail protein and endolysin). This part of model aims to explore the inhibitory effect with the increase in SgRNA·dCpf1 level. We apply Michaelis-Menten equation to model the reactions.

Transcription only occurs in the absence of the inhibitor SgRNA·dCpf1.
III. Modeling procedures
We used ODE to model the reactions. Following equations represent the rate of reactions of different components.

1. The concentration rate of SgRNA:

2. The concentration rate of dCpf1:

3. The concentration rate of SgRNA·dCpf1:

4. The concentration rate of DNA:

5. The concentration of DNA·SgRNA·dCpf1:

6. The concentration of GFP:

After we attain the concentration~time data, we then model the effect of change in SgRNA (=dCpf1) concentration initial rate on downstream protein expression (represented by GFP).
IV. Visualization and Analysis Using R Figure 3: dCas Inhibitory System Figure 4: GFP concentration when equilibrium with the change of SgRNR/dCpf1 input
As shown in Figure 3, barring the initial period of quick concentration growth of GFP, the concentration of SgRNA, dCpf1, DNA, and GFP show a decrease with time, while SgRNA∙dCpf1 and DNA∙SgRNA∙dCpf1 have concentrations that increase with time. In Figure 4, different inputs of SgRNA and dCpf1 (in this model, we assume that the initial concentrations of these two always stay the same) produce largely different concentrations of GFP (representing the protein expression rate), from approximately 400 μM at 0 SgRNA/dCpf1 input to 0 GFP at approx. 100 μM. This model has demonstrated the dCas inhibitory system's effectiveness in inhibiting the expression of proteins.
Acr Anti-inhibitory model I. Aim
Introducing DSF-Acr expression to the dCAs inhibitory system, we aim to model the anti-inhibitory function of Acr and how Acr will reactivate expression of GFP.
II. Pathways and reactions
Acr is expressed, it deactivates the binds to SgRNA·dCpf1 complex to prevent the conformational change required to form complex with DNA. This process leads to the disinhibition of DNA transcription, which allows GFP production level to increase. The pathways are described by the following expressions:
III. Modeling procedures
Adding Acr and applying similar methods as above, we first model to attain correlation between GFP and Acr input. Then, obtaining the vc2-riboswitch~DSF data in Model 1, we are allowed to finalize our pathways that are shown above: with the increase in DSF input, the concentration of vc2-riboswitch(on) elevates according to figure 2. As Acr production is connected with vc2-riboswitch by transcription, we can make connections between DSF sensor and dCas system, and reach overall correlation between DSF input and expression level of downstream proteins - major tail protein and endolysin - that regulate the vitality of bacteriophage xoo-sp2.
IV. Visualization and Analysis Using R
According to the figure of the dCas-inhibitory system, we set the concentration of SgRNA and dCpf1 at 100μM (completely inhibiting).
Figure 5: Effect of Acr input on downstream protein expression (GFP) Figure 6: Effect of DSF input on downstream protein expression According to Figure 5, GFP concentration quickly elevates when Acr is in range 0-200 μM, then verges towards equilibrium. In figure 6, we see that the increase of GFP can be divided into two phase: from DSF concentration 10^-3to 1 μM and from 1 to 10^4μM. Therefore, we offer advice for future experiments to consider the input thoroughly to save the cost of materials. *All our code and files are uploaded to iGEM2021 Github References
[1]Cai Z, Yuan Z-H, Zhang H, Pan Y, Wu Y, Tian X-Q, et al. (2017) Fatty acid DSF binds and allosterically activates histidine kinase RpfC of phytopathogenic bacterium Xanthomonas campestris pv. campestris to regulate quorum-sensing and virulence. PLoS Pathog 13(4): e1006304.
[2]Ionescu M, Baccari C, Da Silva AM, Garcia A, Yokota K, Lindow SE. Diffusible signal factor (DSF) synthase RpfF of Xylella fastidiosa is a multifunction protein also required for response to DSF. J Bacteriol. 2013 Dec;195(23):5273-84. doi: 10.1128/JB.00713-13. Epub 2013 Sep 20. PMID: 24056101; PMCID: PMC3837960.
[3]Ko-Hsin Chin, Yen-Chung Lee, Zhi-Le Tu, Chih-Hua Chen, Yi-Hsiung Tseng, Jinn-Moon Yang, Robert P. Ryan, Yvonne McCarthy, J. Maxwell Dow, Andrew H.-J. Wang, Shan-Ho Chou, The cAMP Receptor-Like Protein CLP Is a Novel c-di-GMP Receptor Linking Cell–Cell Signaling to Virulence Gene Expression in Xanthomonas campestris, Journal of Molecular Biology, Volume 396, Issue 3, 2010, Pages 646-662, ISSN 0022-2836,
[4]2019 iGEM Team:Wageningen_UR/Model
[5]2019 iGEM Team:Hong_Kong-CUHK/model
[6]2014 iGEM Team:Dundee/Modeling/dsf
[8]MCB111: Mathematics in Biology (Fall 2021). MCB111 Mathematics in Biology. (n.d.). Retrieved October 20, 2021, from
[9]Dow, M. (2008). Diversification of the Function of Cell-to-Cell Signaling in Regulation of Virulence Within Plant Pathogenic Xanthomonads. Science Signaling, 1(21), pe23–pe23. doi:10.1126/stke.121pe23
[10]Ryan, R. P., An, S., Allan, J. H., McCarthy, Y., & Dow, J. M. (2015). The DSF Family of Cell–Cell Signals: An Expanding Class of Bacterial Virulence Regulators. PLOS Pathogens, 11(7), e1004986. doi:10.1371/journal.ppat.1004986