Team:NUDT CHINA/Model
Model
Figure 1. Description of the overall framework of the model.
In this year's project, we intents to optimize the Predator Pro system (PrePro) proposed last year to achieve a light-controlled cell cycle via blue light-initiated targeted degradation of cyclin protein (Cyclin D/Cyclin E, click here for detail)
There are two main changes in this years’ system compared with PrePro (Fig1):
1. The constitutive DocS-Coh2 interaction pair in the PrePro system is replaced with light-induced dimerization pairs (such as CRY2/CIB1).
2. The targeting module (GFP nanobody) in the PrePro system is replaced with a Cyclin-targeting module (such as CyclinD/E-targeting scFv), which enables targeted degradation of Cyclin and therefore regulate the cell cycle.
To characterize blue light-controlled dimerization of CRY2/CIB1, we redesigned a mathematical module to describe the dynamics of the binding between CRY2 and CIB1 in mammalian cells and integrate the module with modules we constructed last year (Protein expression, Natural degradation, protein dimerization module, Ubiquitination module, and Degradation module). To describe how the system regulates cell cycle, a mechanism-based mathematical description of the complete cell cycle process (Cell cycle simulation module) is constructed and integrated with other modules in our model.
2.1 General Assumption
1. Since the biochemical reactions in cells are too complex to be completely simulated, the interactions of intermediates throughout the whole process were ignored.
2. To ensure that the effect of plasmids on the degradation of target proteins can be studied more clearly, the effect of the in vitro antibody proteins expressed by the plasmids on the degradation of target protein was ignored.
2.2 Cell cycle simulation module
This module simulates the complete cell cycle regulated by cyclin proteins in mammalian cells under ideal conditions.
Figure 2. Diagram of the cell cycle.
To understand the specific impact of the targeted protein degradation system on the entire cell cycle, we develop a dynamic mathematical model to describe the whole cell cycle regulated by Cyclin protein and related protein-protein interactions. However, to better highlight the experimental focus of this project, the simulation of Cyclin D in the overall model will be the focus.
It is known that the entry of the cell cycle into the G1 phase is mainly regulated by cyclin D, and at this stage, the generation of cyclin D mainly depends on the regulation of two substances, AP1 and transcription factor E2F, respectively[1]-[2]. These two substances will promote the expression of cyclin D, to give more details, the growth factor called GF can activate the transcription of AP1(equation 1), which indicates that GF indirectly promotes the expression of cyclin D [1].
Because cyclin D activates the cyclin-dependent kinase Cdk4-6, and, in mammalian cells, Cyclin D binds with Cdk4-6 instantaneously to form a complex named Cyclin D/Cdk4-6. It is ideally considered that Cyclin D only exists as a complex form after generation in our model. At the same time, p27, a Cyclin-dependent protein kinase inhibitor, binds to Cyclin D in an inhibitory manner, forming another complex “cyclin D/Cdk4-6/p27”(equation 7 and 8) , which reduce the intracellular level of Cyclin D and block the downstream progression of the cell cycle.
In addition, the regulation of cyclin D on the cell cycle is also affected by the inhibitory factor pRB, which will inhibit the synthesis of cyclin D (equations 2 and 3). Conversely, both Cyclin D complexes promote the phosphorylation process of p27 (equation 11), depleting its intracellular concentration.
With the decrease of intracellular p27 content, the cell cycle gradually entered the S phase. The substances that play a key role in this phase are Cyclin A and Cyclin E.
During the modeling process, the first thing we looked at was Cyclin E, whose formation is inhibited by the suppressor pRB but promoted by the transcription factor E2F(equation 5). Similarly, we reasonably assume that Cyclin E activates CDK-2 and forms a complex with it immediately after production, which can also bind to p27 in an inhibitory manner, forming the complex “cyclin E/Cdk2/p27”(equation 9 and 10), and will promote the phosphorylation of p27 forming p27p(equation 12), which will degrade naturally. Therefore, Cyclin E can consume intracellular p27 content, but it is important to note that this process is reversible(equation 11). The Cyclin E complex will be rapidly degraded by SKP2.
In the G2 phase, we focused on Cyclin A, whose expression will be promoted by E2F and inhibited by pRBp(equation 6 and 3). Because the binding of the substance to the phosphate group is a relatively weak process, the concentration of intracellular pRBp was so low that its effect on Cyclin A was ignored in our model. At the same time, Cyclin A can be degraded by Cdc20(A) so that the final intracellular concentration of Cyclin A approaches zero.
As we know, Cyclin A can promote the phosphorylation of transcription factor E2F to form E2Fp and eventually degrade naturally, making original E2F lose the function of promoting cyclin protein generation, thus slowing down the generation rate of other cyclins (equation 14 and 15). In addition, Cyclin A can transform the complex Cdh1(A) formed by the combination of APC and Cdh1 into Cdh(I) for natural degradation (Notice that this is a reversible reaction.)(equation 18 and 19). It’s worth noting that Cdh1(A) can target the degradation of SKP2 and Cyclin B complex(equation 13).
After that, the cell cycle will gradually enter phase M. During this stage, cyclin B is produced naturally, and in the model, we think this is a uniform process. The cyclin B complex at this stage promotes Cdc20(a) production(equation 20 and 21), which in turn promotes cyclin A degradation(equation 16 and 17).
At this point, a complete cell cycle model of mammalian cells has been basically constructed, and all the equations for building cell cycle modules are listed below:
1) Growth factor GF stimulates cell division
Equations 1
2) Inhibition factor pRB and activation factor E2F
Equations 2
3) Cyclin D: G1 phase
Equations 3
4) Cyclin E: G1/s phase
Equations 4
5) Dependent kinase inhibit protein p27
Equations 5
6) Cyclin A: S phase and S/G2 phase
Equations 6
7) Cyclin B: M phase
Equations 7
8) Two activators of promoting complex APC in later stage
Equations 8
2.3 Blue light regulation module
In this module, the plasmids obtained in the experiment for cell cycle regulation are simulated, and the different results of blue light conditions on their effect on the cell cycle are simulated. In last year's design, we proposed the “Predator Pro” system, in order to upgrade the protein degradation system to better achieve the desired effect and to enhance the control of the system, in this year, we designed the light-inducible dimerization pairs in this module, including two switches. The one is “Blue_Light On” switch, combining when blue light hits it(equation 25); and the other is called “Blue_Light Off” switch, when blue light is illuminated, dissociation occurs. In our module, we will focus more on the “Blue_Light On” system setup and verification (equation 22,23 and 24).
Figure 3. Graphical representation of ”Blue_Light On” switch.
We use the following differential equation to simulate the blue light conditions of the experiment:
Equations 9
The biological process corresponding to the model is shown in the figure below:
Figure 4. Schematic diagram of blue light control module.
As the plasmid is introduced to cells, mRNA1 and mRNA2 can be produced via DNA transcription, at the rate v1. Synthesized mRNAs are then translocated to the cytoplasm at the rate v2 and subsequently translated into A dimeric complex formed by CRY2 and Rb αHelix. This complex will bind Cyclin D at rate v3 in subsequent reactions, The product will further react with the complex formed by Trim21 and CIB1 at rate v4 to form a new complex, which will eventually lead to the degradation of Cyclin D via ubiquitination-proteasome system as described in our 2020 iGEM model (Ubiquitination module and Degradation module, Fig 1).
3.1 Integrated analysis of Simulation-experimental data
Figure 5. Comparison diagram of experimental data and model results.
To validate the accuracy of our model, we used the model to predict the results of experiments with blue light and dark light respectively. As is shown in the figures above, the simulation showed that multiple sets of model predictions match well with the corresponding wet-lab data, indicating that our model might have correctly reflected the whole processes of blue light-mediated control of cell cycle in our case.
3.2 Experimental data analysis in the whole model
The binding rate kf of the blue light interaction module and cyclin D was analyzed in the whole model using the parameter stepwise screening method. As shown in Fig 6, When kf was set to 0, meaning there was no blue light interaction. The simulation results were shown in Figure 6.
Figure 6. Simulation results(kf=0).
The following figure shows the cell cycle alteration after being illuminated by blue light. Figure 7 shows the kf=10, figure 8 shows the kf=20.
Figure 7. Simulation results(kf=10).
Figure 8. Simulation results(kf=20).
The figure showed that, as the binding rate kf in Blue light-inducible interaction module and cyclin D increases, the binding capacity of the two pairs is significantly enhanced, and as well as the blue light interaction module's ability to regulate the degradation of targeted proteins (Fig 8), which increases the amount of Cyclin D bound and therefore prolonging the cell cycle.
3.3 Sensitivity analysis of parameters in the whole model
To find out which parameter has the most direct and significant effect on the promotion of Cyclin D expression, we used the built-in sensitivity analysis program to calculate the time dependence of cyclin D production rate with respect to each parameter and its sensitivity (i.e., derivative). By examining the computational sensitivity over time, we observed that k3f, a rate parameter characterizing the recognition and binding of CIB1-CRY2 and Rb αHelix targeting modules and Cyclin D concentrations in cells (k45), showed the highest sensitivity, suggesting that the level of Cyclin D content was most sensitive to k3f (Figure 9).
In contrast, k45 (the rate parameter of the binding of CIB1-CRY2 with C-targeting bodies and Cyclin D content in cells) also showed high sensitivity, but it did not directly and significantly affect the final expression of Cyclin D, while other sensitivities were significantly lower.
Figure 9. Sensitivity analysis of the model.
A similar trend can be observed in Figure 10. Compared with k3f, the curve of other parameters, even k45, maintains or basically maintains a relatively flat trend. All these results indicate that k3f is the most important parameter in determining the rate of cyclin D expression.
Figure 10. Parametric curve diagram.
In order to further verify the influence of k3f(K) on Cyclin D concentration, the initial value of k3f was scanned in a range, and the simulation showed that when the initial value of k3f was 0, Cyclin D showed regular fluctuations, which is in accordance with normal cell cycle. The result is shown below:
Figure 11. Level of cyclin D under different circumstances.
With the increase of the initial value of k3f, the fluctuation part of the curve of Cyclin D content began to be significantly delayed and the protein D concentrations and the cycle of their alteration also decreased accordingly, indicating that the normal division of cells began to be affected by the delay.
The results suggest that we can regulate the process of cell division by appropriately increasing the duration and intensity of blue light illumination time.
In conclusion, we constructed the mathematical model of Blue light-inducible interaction module and complete cell cycle module and integrate them with controllable targeted protein degradation model we constructed last year, enabling a mathematical description of blue light-mediated control of cell cycle via targeting protein degradation of cyclin protein.
(1) Integrated analysis using simulation combined with experimental data showed that our model (the periodical change of Cyclin protein, or the final prediction of cell number) and experimental data were matched very well, showing the way we built mathematical model of complete cell cycle is heuristic and effective, which might be beneficial to other iGEM teams and cell cycle-related research project.
(2) After construction of model. sensitivity analysis showed that targeting affinity kf between targeting module and targets (in our case, the interaction between Cyclin and Rb αHelix/CDK4 αHelix) are the most sensible parameters. These helped experiments group to figure out how to improve the effectiveness of our CycleBlue system , which showed that the model we built can provide a new outlet for further optimization of targeted protein degradation system in the future.
Table 1. Parameter Description of Cell Cycle Model
- Luo Haitao, Tao Chuming, Long Xiaoyan & Huang Kai(2021). Early 2 factor (E2F) transcription factors contribute to malignant progression and have clinical prognostic value in lower-grade glioma. Bioengineered, 12(1), 7765-7779.
- Xie Dan, Pei Qin, Li Jingyuan & Ye Ting(2021). Emerging Role of E2F Family in Cancer Stem Cells. Frontiers in Oncology, 11, 723137-723137.
- Golubev, A. . (2010). Random discrete competing events vs. dynamic bistable switches in cell proliferation in differentiation. Journal of Theoretical Biology, 267(3), 341-354.