Team:HUST-China/Modeling on Cellular Level
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Modeling on Cellular Level
With the benefit of synthetic biology, we built up our kit, Euk.Cement, with some characterized parts to carry out the mission of sand solidification. However, whether our kit will be able to achieve its goal depends on the answers to the following questions.
- Will the darkness induction system be able to switch efficiently to control the expression of target proteins?
- How much Si-tag and Mcfp-3 our strains produce in the end?
- What strategy should we take in practice to make full use of our product?
The answer to these questions will be shown in our modeling as well as the guidance for future wet-lab experiments.
To ensure that Euk.Cement is capable, we built a DDEs (Delay Differential Equations) model based on Michaelis-Menten equation[1] and Chemical reaction rate equation[2], which includes three parts, to get the insight of how each part works cooperatively.
The code of our DDEs model can be downloaded here.Parameters
The description of parameters, their values[5] and the references involved in this model are listed in a table.
Brief Parameter Table of DDEs Model
| Parameter | Description |
|---|---|
| copynumpRMH120 | copy number of plasmid pRMH120 |
| copynumpZS3 | copy number of plasmid pZS3 |
| trc1 | rate of mCRY2_BD transcription |
| trc2 | rate of mCIB1_AD transcription |
| trc3 | rate of mRox1 transcription |
| trc4 | rate of mRox1 basic transcription |
| trl1 | rate of CRY2_BD translation |
| trl2 | rate of CIB1_AD translation |
| trl3 | rate of Rox1 translation |
| trl4 | rate of Si_Tag translation |
| trl5 | rate of Mcfp-3 translation |
| trf1 | rate of photoactivation of CRY2_BD |
| trf-1 | rate of photoinactivation of CRY2_BD |
| trf2 | rate of photoactivation of CIB1_AD |
| trf-2 | rate of photoinactivation of CIB1_AD |
| trlc1 | translocation rate of Si_Tag to membrane |
| trlc2 | translocation rate of Mcfp-3 to extracellular |
| deg1 | rate of mCRY2_BD degradation |
| deg2 | rate of CRY2_BD degradation |
| deg3 | rate of mCIB1_AD degradation |
| deg4 | rate of CIB1_AD degradation |
| deg5 | rate of mRox1 degradation |
| deg6 | rate of Rox1 degradation |
| deg7 | rate of mSi_Tag degradation |
| deg8 | rate of Si_Tag degradation |
| deg9 | rate of mMcfp-3 degradation |
| deg10 | rate of Mcfp-3 degradation |
| Km1 | apparent association constant for CRY2_BD binding with UAS |
| Km2 | apparent association constant for CIB1_AD binding with CRY2_BD |
| Km3 | apparent association constant for Rxo1 binding with promoter panb1 |
| Vmax | maximum transcription rate of promoter pAnb1 without the repression of protein Rox1 |
| τ1 | time for AD activating promoter pGal1 |
| τ2 | time for Rox1 binding with promoter panb1 |
Part one: The Darkness Induction System
First of all, we intended to simulate the whole pathway to approximate the final expression rate of target proteins as well as the property of the darkness induction system. To achieve this, we need to translate our biological processes to chemical reactions and finally represent it with mathematical equations.
The Darkness Induction System pathway contains the following reactions:
Formulary
1. Generation of active CIB1_AD
2. Generation of active CRY2_BD
3. Activation of promoter Anb1
The corresponding DDEs of darkness induction system are listed below:
1. Generation of CIB1_AD
(1.4)
(1.5)
(1.6)
2. Generation of CRY2_BD
(1.7)
(1.8)
(1.9)
3. Activation of promoter Anb1
(1.10)
If exposed to light
(1.11)
Elseif in darkness
(1.12)
Results
Before the circuit was determined, there were two kinds of darkness induction system for choice: the CRY2-CIB1 system and the PhyA-FHL system. To find out the system that suits our circuit better, we simulated both of them with the DDEs model.
We can safely derive the following conclusions from the figures above.
- The photoactive subjects are of low concentration but they remain at a certain level.
- Compared to the PhyA-FHL system, the CRY2-CIB1 system is more sensitive to light exposure (The peak of CRY2-CIB1 system appears earlier than the one of PhyA-FHL system) and the PhyA-FHL system has a time-lag for photoactivation.
- The rate of Rox1 degradation in CRY2-CIB1 system is higher than the one in PhyA-FHL system, which means the darkness induction could shut down quickly so that the downstream systems could be activated.
Hence, we considered CRY2-CIB1 system more advantageous and applied it to our project.
Part two: The Surface Display System of Si-tag
With the simulation of Darkness Induction System above, we are able to determine when the Surface Display System of Si-tag would be activated. However, to predict whether Si-tag would be sufficient in the end and to provide essential parameters for the next model, we need to simulate the Surface Display System of Si-tag.
Formulary
(1.13)
The corresponding DDEs of Surface Display System of Si-tag are listed below:
(1.14)
(1.15)
(1.16)
(1.17)
(1.18)
Results
With the DDEs model we built, we could run the simulation of the expression of Si-tag and determine its amount at any time. To test the function of our darkness induction system, the timeline would be set as darkness-light-darkness.
From figure 2, we can see that the Si-tag remains at a low concentration and the Displayed Si-tag accumulates very efficiently when Euk.Cement is in darkness for the first time (0-200min). However, when exposed to light (200-500min), the expression of Si-tag is blocked and the rate of Displayed Si-tag accumulation decreases greatly. After light exposure (500-1500min), the expression of Si-tag and the rate of Displayed Si-tag accumulation gradually recover. Generally speaking, the darkness induction system is capable of controlling the downstream system and the expression of Si-tag is sufficient.
Part three: The Expression of Mcfp-3
Besides Si-tag, Mcfp-3 is another important product that we must quantify its amount. It’s promoter is the same with the promoter of Si-tag and therefore, we could easily simulate it with the DDEs model and MATLAB.
Formulary
(1.19)
The corresponding DDEs of the expression of Mcfp-3 are listed below
(1.20)
(1.21)
(1.22)
Results
To test the darkness induction system again as well as to quantify the amount of Mcfp-3, we set the same timeline with that of Si-tag and run the simulation with MATLAB.
As we can see in figure 3, the amount of Mcfp-3 was approximately twice as Si-tag. Besides, the darkness induction system took effect again. At 200 minutes when the light is turned off, the slope of Si-tag and Mcfp-3 decrease significantly. After 500 minutes when the light is turned on, the slope of these two substances gradually increase again.
Conclusions
With our DDEs model, we can safely conclude that:
- Our darkness induction system could switch efficiently from darkness to light to shut down the downstream systems. However, it takes some time to switch back from light to darkness.
- Our strains could produce sufficient Si-tag as well as Mcfp-3 to do the job.
- We can quantify the amount of Si-tag and Mcfp-3 at any time so that we can move on to the next model with these data.
Robustness and Parameter Sensitivity Analysis
Considering there are some parameters whose value is uncertain and may have effect on our model, we used numerical solutions to analyze the robustness and parameter sensitivity of our DDEs model.
τ1 &τ2
Since τ1 and τ2 are variables that we could not determine their accurate values (0.1-3min), we run the DDEs model with different values ofτ1 and τ2 to find out what effect they have on our DDEs model.
| Parameters | Values of each figure | |||
|---|---|---|---|---|
| τ1 | 0.1 | 3 | 0.1 | 3 |
| τ2 | 0.1 | 0.1 | 3 | 3 |
Results
Apparently, even the max value of τ1 and τ2 couldn’t produce noticeable time-lag for the whole system, because the time-lag produced byτ1 and τ2 is approximately 5 minutes while the whole simulation process has the timeline of 1.5 thousands minutes. Therefore, we can conclude that our DDEs model has the robustness of τ1 and τ2 .
Rate of Basic Transcription for pAnb1:
Since promoter Anb1 has basic transcription rate, Rox1, Si-tag and Mcfp-3 would be expressed even in darkness. Hence, to figure out how it takes effect on our model, we run the simulation with different rate of pAnb1 basic transcription (0.1*Vmax to 0.2*Vmax with step of 0.005*Vmax).
Results
Our DDEs model is sensitive to the amount of basic transcription of pAnb1. If the rate of pAnb1 basic transcription increases from 0.100*Vmax to 0.200*Vmax, the amount of Rox1 would become 125 percent. Therefore, with less basic transcription of pAnb1, less Rox1 would be expressed and the repressed expression of Si-tag and Mcfp-3 would recover more quickly. We can conclude that our circuit could be improved by reducing the basic transcription of pAnb1.