Modeling is based on mathematical or software tools to simulate and predict systems. Based on the design of our project, we expect our model to achieve the following aspects.
1. To understand the relationship between ATP concentration in the tumor microenvironment (TME)and our target protein, RTAC.
2. To study the growth curve of engineered yeast as well as the threshold and sensitivity interval of RTAC secretion.
3. Use 3D modeling to understand the effect of protein action in our project.
The creation of these models fills a gap in our wet lab and provides a better understanding of how our projects work or should be implemented.
In our project, we constructed an engineered yeast with Saccharomyces cerevisiae as the chassis bacterium, responding to the work of our engineered yeast by the expression of our RTAC protein. Therefore, we refer to the 2021 BIT-china project while using a series of ODE equations based on the signaling pathway of single cells in Saccharomyces cerevisiae1 and modeling in Matlab platform to obtain the relationship between ATP concentration and RTAC expression in tumor microenvironments to reflect the work of our engineered yeast from the perspective of dry lab.
Figure 1 Signaling Pathway Model pathway
In the signaling pathway model, we made some assumptions about the model to adapt in our project.
1. We hypothesized that P2Y2 receptors have no synergistic effect when bounding to ATP in the tumor microenvironment.
2. We assumed that when binding to the P2Y2 receptor, the amount of bound ligand ATP is the same.
3. We assumed that the binding rate and initial binding concentration of ligand ATP are the same as those of the P2Y2 receptor.
4. We assumed that the knockout gene does not change for some parameters in the signaling pathway simulation.
5. We did not consider the leakage of promoter expression.
6. Cell growth in individual cells has no effect on protein expression.
We used a series of ODE equations based on the signaling pathways of single cells in Saccharomyces cerevisiae1 and modeled in the Matlab platform in the following panels.
The ligand is eATP, which first binds to the P2Y2 receptor of the sensing ligand. During this process, the conformation of the receptor changes. The activated receptor will participate in the next step of the G-protein cycle, and the activation of the G-protein cycle produces Gβγ further activation of the next step of the pathway. The process diagram of the process is shown below,
Figure 2 Receptor activation and G protein cycle activation
Name | value | unit | reference |
k1 | 0.0012 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k2 | 0.6 | min-1 | Kofahl B, Klipp E., 2004 |
k3 | 0.24 | min-1 | Kofahl B, Klipp E., 2004 |
k4 | 0.024 | min-1 | Kofahl B, Klipp E., 2004 |
k5 | 0.0036 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k6 | 0.24 | min-1 | Kofahl B, Klipp E., 2004 |
k7 | 2000 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
Prior to the MAPK pathway, it is required to generate the previous step Gβγ and the ste5 complex (complex C), therefore, the following shows the generation of complex C. The process diagram is as follow.
Figure 3 Formation of ste5 complexes
Name | value | unit | reference |
k8 | 0.1 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k9 | 5 | min-1 | Kofahl B, Klipp E., 2004 |
k10 | 1 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k11 | 3 | min-1 | Kofahl B, Klipp E., 2004 |
k12 | 1 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k13 | 3 | min-1 | Kofahl B, Klipp E., 2004 |
k14 | 3 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k15 | 100 | min-1 | Kofahl B, Klipp E., 2004 |
The MAPK cascade reaction is activated by the first two reactions and is achieved through a series of phosphorylation processes. The final signal output is achieved by the activated Ste12 protein activated by Fus3, and the activated Ste12 protein acts as a signal to regulate the expression of RTAC in the next step. The process diagram is as follow.
Figure 4 MAPK cascade reaction
Name | value | unit | reference |
k16 | 5 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k17 | 1 | min-1 | Kofahl B, Klipp E., 2004 |
k18 | 10 | min-1 | Kofahl B, Klipp E., 2004 |
k19 | 47 | min-1 | Kofahl B, Klipp E., 2004 |
k20 | 345 | min-1 | Kofahl B, Klipp E., 2004 |
k21 | 50 | min-1 | Kofahl B, Klipp E., 2004 |
k22 | 140 | min-1 | Kofahl B, Klipp E., 2004 |
k23 | 10 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k24 | 1 | min-1 | Kofahl B, Klipp E., 2004 |
k25 | 250 | min-1 | Kofahl B, Klipp E., 2004 |
k26 | 5 | min-1 | Kofahl B, Klipp E., 2004 |
k27 | 5 | min-1 | Kofahl B, Klipp E., 2004 |
k28 | 5 | min-1 | Kofahl B, Klipp E., 2004 |
k29 | 5 | min-1 | Kofahl B, Klipp E., 2004 |
k30 | 5 | min-1 | Kofahl B, Klipp E., 2004 |
k31 | 50 | min-1 | Kofahl B, Klipp E., 2004 |
k32 | 18 | min-1 nM-1 | Kofahl B, Klipp E., 2004 |
k33 | 10 | min-1 | Kofahl B, Klipp E., 2004 |
The MAPK pathway produces activated Ste12 protein, which acts as a regulator of RTAC protein expression and expresses RTAC protein. The process is as follow.
Figure 5 RTAC protein expression
Name | value | unit | reference |
k34 | 2.44*10-4 | min-1 | calculation |
k35 | 0.6186 | min-1 | calculation |
k36 | 0.0313 | min-1 | calculation |
k37 | 0.0133 | min-1 | calculation |
kp | 120 | nM | simulation |
Figure 6 simulation results of P2Y2 activated and Gβγ
Our modified human-derived antibody to P2Y2 can efficiently accept extracellular ATP from the tumor microenvironment (TME) and transmit the signal to the next level.
Figure 7 simulation result of ste12 active
As can be seen from Figure 7, our cascade pathway can function normally, the knockdown gene has no effect on the whole MAPK cascade pathway, and ste12 active can participate in the next step of messaging normally.
Figure 8 simulation result of RTAC
As shown in Figure 8, RTAC can be expressed normally after undergoing a series of yeast pheromone pathways conducted by eATP, confirming the feasibility of our project from a modeling perspective .
To understand the expression of RTAC at different locations in the human body, we simulated the changes in RTAC protein concentration at eATP=10 nanomole; eATP=500 nanomole respectively. eATP concentration was selected based on normal body and the maximum eATP concentration that can be tolerated in Matlab, and the results are as follows.
Figure 9 simulation results of RTAC under different concentration of eATP
From the comparison in Figure 9, we can clearly see the difference in the amount of RTAC secretion between the two figures, but since the modeling simulations were run with data that did not have a limit on the amount of eATP, our results only indicate at a very superficial level that RTAC gets highly expressed around the tumor, and verification of this specific aspect we hope can be done in future wet lab.
Combining the above analysis, we can conclude that Our yeast system can express RTAC normally and there is a clear difference in the expression around normal and tumor cells.
To understand the effect on the growth of the engineered yeast itself after we knocked out the genes ste2 and sst2, we decided to react by a yeast growth model.
We assume that the in vitro culture conditions are similar to the actual in vivo situation.
We cultured our engineered yeast under suitable conditions in vitro and measured at 4h, 8h, 12h, 24h, 36h, 48h, 60h, and 72h. The following data is as follow.
Time | Mean | SD |
4h | 0.196 | 0.005 |
8h | 0.607 | 0.012 |
12h | 1.236 | 0.17 |
24h | 1.654 | 0.132 |
36h | 1.897 | 0.125 |
48h | 1.997 | 0.238 |
60h | 1.976 | 0.145 |
72h | 1.99 | 0.202 |
After that, we fitting the data by logestic model to confirm the growth of our engineered yeast. The fitting formula is as follow,
Figure 10 Growth curve of engineered yeast
Figure 11 Fitting effect of yeast growth curve
The analysis of the graph and the equation show that the engineered yeast can grow normally.
To understand the threshold of eATP activation pathway and the concentration interval in which the pathway is sensitive to eATP concentration, we combined data from wet lab to construct a model of the fluorescence intensity of target gene activation corresponding to eATP concentration.
We performed induction at different gradients of ATP concentration for 24 hours, followed by coating the plates, photographing them using a fluorescence microscope, and quantifying the fluorescence intensity using Image J software.
We measured three sets of data for each concentration, after which their average and standard deviations were calculated and plotted.
The data is as follow.
Concentration | Average | SD |
0 | 0.02 | 0.005 |
10 | 0.1 | 0.05 |
25 | 0.8 | 0.02 |
50 | 1.2 | 0.01 |
100 | 2 | 0.05 |
150 | 2.5 | 0.1 |
200 | 4.5 | 0.5 |
300 | 7.5 | 0.8 |
400 | 13 | 1 |
500 | 14.5 | 2 |
Figure 12 Fluorescence intensity-eATP change curve
1. The activation threshold of the modified pathway for eATP is roughly around 5 micromolar.
2. The sensitivity range of the pathway to eATP concentration is roughly 150-400 micromolar.
Based on the results of the model, it is known that the activation of the pathway is weak at around 100 micromolar and increases significantly with eATP concentrations above 150 micromolar. Through literature review, we learned that the eATP concentration in the tumor microenvironment of colorectal cancer is usually between 200-500 micromolar. Thus, eATP, a characteristic molecule of the tumor microenvironment, has a strong ability to activate the pathway and keep it at a high expression level so as to secrete enough RTAC proteins to act on RSPOs proteins.
When designing the characterization of RTAC proteins, we performed several iterations to determine the final structure, and in order to better visualize the relationship of our constructed proteins to the RSPO family of proteins, we used a 3D modeling approach for characterization.
Our RTAC proteins can act against all four RSPOs family proteins, and we used RSPO1 as an example for our modeling.
From the description, it is clear that our RTAC protein ends up with ZNRF3 and LGR4 as the main structure, so we want to understand the form and comparative analysis of RTAC, ZNRF3, LGR4 with RSPO protein in 3D protein structure.
We predicted the structures of four proteins, LGR4, ZNRF3, RTAC, and RSPO1, respectively, by Swiss model. After that, the obtained protein structures were visualized and analyzed by chimera software.
After obtaining the 3D structures of each of the four proteins, we used chimera software to superimpose and compare the structures based on the three complexes published in the literature2-4.
After obtaining our three complex structures LGR4-RSPO1, ZNRF3-RSPO1, and RTAC-RSP1, we performed protein interaction analysis using chimera software.
RTAC(Cornflower blue and Light green) with RSPO1(Orchid).
1. We used visual analysis of the protein structure to better understand the structure of our designed protein and the interaction with RSPO proteins.
2. Through our interaction force analysis, it is evident that the RTAC protein has an enhanced number of hydrogen bonds as well as an enhanced force compared to LGR4 or ZNRF3 alone, and the increased effect of our iteration is also demonstrated by modeling, mirroring the wet lab.
We hope that we can further simulate the survival time of our yeast in the human body by coupling the signal pathway model and yeast growth model to provide data for our drug dosage design. However, due to time constraints, we were unable to complete the model. After the competition, we will also make this model to provide data for our next drug design.
1 Kofahl, B. & Klipp, E. Modelling the dynamics of the yeast pheromone pathway. Yeast (Chichester, England) 21, 831-850, doi:10.1002/yea.1122 (2004).
2 Wang, D. et al. Structural basis for R-spondin recognition by LGR4/5/6 receptors. Genes & development 27, 1339-1344, doi:10.1101/gad.219360.113 (2013).
3 Peng, W. C. et al. Structures of Wnt-antagonist ZNRF3 and its complex with R-spondin 1 and implications for signaling. PLoS One 8, e83110 (2013).
4 Zebisch, M. & Jones, E. Y. Crystal structure of R-spondin 2 in complex with the ectodomains of its receptors LGR5 and ZNRF3. Journal of structural biology 191, 149-155, doi:10.1016/j.jsb.2015.05.008 (2015).