Team:BIT-China/Model
Our system can work if we can prove the "in-promoter" will have different activities under different concentrations of inhibitor and the inhibitor can be used as a signal to sense the plasmid numbers. So we need to do two things to prove that our system could work. Our modeling part is aim at solving the two main problems to model the situation in the experiment and application.
·EXPERIMENT part·
Aim
To model the different concentrations of the intracellular inhibitor and the relationship between the inhibitor and "in-promoter".
Find out the threshold of inhibitors’ concentration which can decide whether the "in-promoter" expresses or not.
FIRST step: The relationship between the "in-promoter" activity and inhibitor.
In this part, in order to model the situations with different concentrations of the intracellular inhibitor, we use the PBAD promoter induced by different concentrations of the arabinose in this circuit (Fig. 1).
Fig.1 The circuit constructed to model the situations with different concentrations of the intracellular inhibitor.
So "in-promoter" will be repressed on different levels under the different concentration of the inhibitor.
We can separate this circuit into two parts. For the first part (Fig. 2), after adding the different concentration of arabinose, the AraC protein will combine with the arabinose and form a complex. Then the complex will combine with the PBAD promoter sequence to positively control the expression of the downstream inhibitor. The reaction direction is along the direction of the DNA → mRNA → inhibitor protein (Fig. 2).
Fig.2 AraC protein will combine with the arabinose and form a complex. Then the complex will combine with the PBAD promoter sequence to positively control the expression of the downstream inhibitor.
For the second part (Fig. 3), the inhibitor protein will combine with the "in-promoter" sequence to negatively control the expression of the RFP protein.
Fig.4 The inhibitor protein will combine with the "in-promoter" sequence to negatively control the expression of the RFP protein.
According to this mechanism, we modeled this circuits to build the relationship between the RFP intensity and the arabinose. Main considerations in this model are the process of repression, induction, transcription, translation, degradation and catalysis.
The assumptions we made are:
(1) AraC protein is enough to combine with the arabinose
(2) The concentration of repressor protein will not change while a part of them are combined with the promoter sequence
(3) When the arabinose doesn’t exist, PBAD promoter can be completely silent
(4) The effect of PBAD promoter’s will be fully terminated by the terminator B0015
(5)The "in-promoter" will constitutively express the RFP protein when the inhibitor protein doesn’t exist
(2) The concentration of repressor protein will not change while a part of them are combined with the promoter sequence
(3) When the arabinose doesn’t exist, PBAD promoter can be completely silent
(4) The effect of PBAD promoter’s will be fully terminated by the terminator B0015
(5)The "in-promoter" will constitutively express the RFP protein when the inhibitor protein doesn’t exist
The reaction processes of circuit are described as below:
PBAD promoter activity:
"In-promoter" activity:
And groups of differential equations are:
We chose the cI-PR circuit to apply this model. There are some parameters for promoter activity equations:
The initial values and description of variables are:
So we can get the curve describing the relationship between the RFP intensity and time under the different concentrations of arabinose (Fig. 4).
Fig.4 PBAD promoter induced by different concentration of the arabinose from 0.0000％ to 0.0050％ and the PR promoter respond to different concentration of inhibitor to express the corresponding RFP intensity. More arabinose added, less RFP expressed.
From this curve (Fig. 4), we can clearly see the RFP intensity changes with time going on. The concentration of the arabinose will affect the expression of RFP negatively.
After this, in order to get the relationship between the RFP intensity and the concentration of arabinose more intuitive, we also got this curve about the relationship between RFP intensity and arabinose when the RFP intensity was stable (Fig. 5).
Fig.5 this curve is about the corresponding RFP intensity under the different concentration of the arabinose.
From this picture, we can know the "in-promoter" activity have a relationship with the different concentrations of the arabinose. That means when we add different concentrations of arabinose, the concentration of inhibitor will also be different. We regarded the concentration of arabinose 0.003% as a threshold, the corresponding expression of RFP (stands for killer) is about 12.05 units. At this point the expression of killer is regarded as just be repressed. Once the concentration of inhibitor decreases further, the killer gene can start to work. Conversely, more inhibitor remains, the killer will be repressed harder. Thus we can say the "in-promoter" can have different responses to the inhibitor.
SECOND step: The relationship between the inhibitor and arabinose.
Meanwhile, the concentration of the inhibitor is the most important factor connecting with the "in-promoter". So under different concentrations of the arabinose, how can we know the concentration of intracellular inhibitor? In order to make the model simulate the real condition better, we use another circuit to model and combine it with the experimental results to improve it.
We use the same inducible promoter PBAD to express the inhibitor protein and replace the gene locus of inhibitor protein with RFP.
Fig.6 The circuit constructed to find out the relationship of the concentrations of inhibitor and arabinose.
The main reaction is similar with the first part, after adding different concentrations of the arabinose, the AraC protein will combine with the inducer. Then the complex will combine with the PBAD promoter sequence to positively control the expression of the inhibitor. The reaction direction is from the DNA → mRNA → inhibitor protein.
Fig.7 Then the complex of arabinose and AraC protein will combine with the PBAD promoter sequence to positively control the expression of the inhibitor.
According this mechanism, we modeled this circuits to build the relationship between the inhibitor protein and the arabinose. Main considerations in this model are the process of repression, induction, transcription, translation, degradation and catalysis.
The assumptions we made are:
(1) AraC protein is enough to combine with the arabinose.
(2) The concentration of repressor protein will not change while some are combined with the promoter sequence
(3) When the arabinose doesn’t exist, PBAD promoter can be completely silent
(2) The concentration of repressor protein will not change while some are combined with the promoter sequence
(3) When the arabinose doesn’t exist, PBAD promoter can be completely silent
The reaction processes of circuit are described as below:
PBAD promoter activity:
And groups of differential equations are:
The initial values and description of variables are:
So we can get the curve describing the relationship between the inhibitor and time under the different concentration of arabinose.
Fig.8 The concentration of inhibitor protein expressed by PBAD promoter changes with time, induced by different concentrations of inducer.
After this, in order to get the relationship between the protein intensity and the concentration of arabinose more intuitive, we also got this curve about the relationship between protein intensity and arabinose when the protein intensity was stable
Fig.9 The concentration of inhibitor expressed by PBAD changes with different concentrations of inducer.
From this curve, we can clearly see the concentration of arabinose have positive relationship with protein intensity in a proper range.
The point of inducer’s concentration (0.003%) can cast on the protein intensity coordinate axis, and the corresponding intensity is about 24.42 units.
From all these, we can get the conclusion：Since the concentration of arabinose can affect the expression of inhibitor positively, and the concentration of inhibitor can decide the "in-promoter's" activity, we can say that by adding different concentrations of inducer could model the environments with different concentrations of inhibitor. Also the different concentration of the inhibitor will change the condition of "in-promoter" in the end.
·APPLICATION part·
Aim
To model the application situation of plasmid numbers losing on different levels and the relationship between the plasmids and "in-promoter".
Find out the threshold of plasmids number which can decide whether the killer gene expresses or not.
In the plasmids sensing system, in order to model the situation of plasmid losing on different levels, we need to simulate the change of substances under different conditions of plasmid numbers. In this system, a constitutive promoter is used to express the inhibitor under different plasmid numbers. Then the "in-promoter" will also be repressed by the inhibitor protein. The killer gene has been replaced by RFP (Fig. 1).
Fig.1 The circuit constructed to model the situation of plasmid numbers losing on different levels.
The concentration of inhibitors is positively correlated to the plasmid numbers since the constitutive promoter has a stable strength. Main considerations includes the processes of transcription, translation, repression, the effects of products and the number of plasmids. We also considered reversible reactions as well as the production and degradation of substances.
Fig.2 The inhibitor protein will repressor the expression of "in-promoter" and RFP.
The assumptions we made are:
(1) The constitutive promoter can constitutively express the inhibitor
(2) The expression of DNA sequence is directly proportional to the plasmid numbers in a specific range
(3) In a single cell, when the concentration of killer protein reaches a threshold, the cell will be eliminated
(4) Too many plasmids will cause the RNA polymerase and the ribosome overloaded.
(5) Because the rate of transcription is much faster than the rate of the translation, we think the rate-limiting step is the translation.
(2) The expression of DNA sequence is directly proportional to the plasmid numbers in a specific range
(3) In a single cell, when the concentration of killer protein reaches a threshold, the cell will be eliminated
(4) Too many plasmids will cause the RNA polymerase and the ribosome overloaded.
(5) Because the rate of transcription is much faster than the rate of the translation, we think the rate-limiting step is the translation.
The reaction processes of circuits are described as below:
"In-promoter" activity:
And groups of differential equations are:
The initial values and description of variables are:
From all these we can finally get two the diagrams, the first one is about the relationship between the concentration of inhibitor protein and number of plasmids, the second one about the relationship between RFP intensity and number of plasmids
Fig. 3 The intensity of inhibitor expressed by constitutive promoter changes with different plasmid numbers.
From this curves, we can know the inhibitor protein have a positive correlation with number of plasmids. At before, we think when the concentration of inhibitor is above 24.42 units, the in-promoter will be repressed fully. And then from this curve, we can see that when the concentration of inhibitor is 23.95 units are so similar with 24.42 units, the threshold of the plasmids number we calculate is 210 copies.
Fig.3 The intensity of RFP expressed by PR promoter changes with different plasmid numbers.
From this curve, we can see that corresponding to the threshold of RFP intensity (12.05 units), we can calculate out the threshold of plasmid number 210 copies.
Here goes our conclusion: The number of the plasmids will determine the intensity of RFP. When the plasmids number is above the threshold 210 copies, rfp (stands for killer gene) will be just repressed, and the cells with enough plasmids number will be saved.
·Summary·
With these three models, we successfully prove that：
① The number of plasmids will have a positive influence on the corresponding inhibitor’s concentration.
② Since "in-promoter" will respond to the inhibitor with different concentrations differently, we can decide whether the killer gene express or not by changing the concentration of inhibitor.
② Since "in-promoter" will respond to the inhibitor with different concentrations differently, we can decide whether the killer gene express or not by changing the concentration of inhibitor.
To make a long story short, we successfully prove that the number of plasmids will affect the "in-promoter's" activity. By rudimentary calculation, we can say when the number of plasmid is above the threshold (210 copies), the inhibitor can just repress the expression of killer gene and the cell can survive. Once the plasmid number gets smaller, the inhibitor won’t work anymore, our P-SLACKiller time starts!
