Abstracts

In order to illustrate the implementation of our modeling and meaning better, we will divide the entire modeling of expression group into two parts. The first part is to verify the feasibility of the gene line of the expression group. The second part is to verify the model of the double fluorescence system as soon as the single fluorescence system was modified into a double fluorescence system before the experiment. In the modeling of the first part, we used the principle of Hill equation to construct a mathematical model which described the promoter activity in the gene line while considered the gene lines and combined the processes of inhibition, induction, transcription, translation, degradation and catalysis, and then determined the parameters in the model equation in various ways. Finally, the expression of the fluorescence system is described by the ordinary differential equation to construct the model. In the second part, we tentatively designed a single fluorescence system before the experiment, but because of the weak fluorescence intensity, it is not easy to detect. Therefore, we propose to use the double fluorescence system to detect the fluorescence intensity. We could achieve the effect of amplification signal and improve the detection limits and accuracy by using the ratio of GFP to RFP. We supported the construction of this part of the model through the support of the literature, and managed to play a guiding role in the experiment of the expression group.

Objective

One part of our aim of modeling is to verify the effect of signal molecules on the promoter and to make the biological expression process clearer and more organized. What’s more, the main purpose is to verify the feasibility of the experiments of expression group and guide the progress of the experiment more smooth. However, the expression of the gene line is relatively long, if the theory is wrong, and the mistakes are found after the experiment, there will be a great harm on the experiment schedule, and moreover, the change will be very difficult. Therefore, the feasibility of modeling validation before expression experiments can provide a theoretical basis for expression groups and provide guidance for the success of their subsequent experiments. In addition, the detection of biomolecules is usually difficult to achieve, because the amount of biomolecules in the human body is too small, so we considered using the double fluorescence system to achieve the amplification by mathematical model and detect the amount of material on . Therefore, we use the support of literature , use the model to verify the linear relationship between the GFP and RFP ratio, to verify that the dual fluorescence system can be used for our project detection link, which play a guiding experimental team successfully completed the role of the experiment.

Introduction

In this model, we made the following assumptions:

(1) having constructed lysine-deficient Escherichia coli and obtained accurate experimental data.

(2) the promoter sequence unchanged after the inhibition of protein binding to the promoter.

(3) the terminator can completely terminate the promoter.

(4) When the inhibitory protein is absent, the promoter can stably express red fluorescent protein (RFP).

(5) don’t consider the expression of the leakage of gene lines.

The first part

1.The gene line which produce green fluorescent

First, according to the gene line above, we can get the expression, transcription and degradation of the following genes. Among them, k₁ is the producing rate of mRNA_lacI, k_-1 is the degrading rate of mRNA_lacI, k₂ is the producing rate of protein_lacI , k_-2 is the degrading rate of protein_lacI :

The expression formula of promoter activity was constructed by Hill equation. β₁ is the maximum starting ability of the promoter (generally set to 1), M₁ is the amount of leakage of the promoter, S_luxR is the amount of regulation factor, k_d is the S_luxR value when the model change trend is changed:

Finally, according to the differential equation to express the expression, transcription and degradation process of the whole gene line:

According to our gene line, it can be concluded that the amount of protein_lacI can be approximated as the amount of protein_GFP (green fluorescence).

Among them, according to the database in the official website of igem , we can know the value of some parameters: the maximum capacity of start-up promoterβ₁ = 0.6; the amount of the leakage of promoter M₁ = 0; n₁ = 2. So we put these known parameters into the equation and get the value of kd at equal distances: 50,100,150,200, finally draw a rough image:

From these differential equations, combining the gene line of the whole expression group,we can get the model of green fluorescent protein expression and get the conclusion: the concentration of lysine from the upstream is higher , the rate of survival of lysine-deficient Escherichia coli is higher , the fluorescence intensity of GFP is greater . And this is also consistent with the original intention of the team members who design this line diagram. We proved the feasibility of this gene line.

2.The gene line which produce red fluorescent

Without considering the inhibitory effect of protein lacI on the promoter pLac, according to the gene map of the above chart, imitating the green fluorescence generation process, we can get the expression, transcription and degradation of the following genes. Among them, k₃ is the producing rate of mRNA_RFP, k_-3 is the degrading rate of mRNA_RFP, k₄ is the producing rate of protein_RFP , k_-4 is the degrading rate of protein_RFP:

The expression formula of promoter activity was constructed by Hill equation. β₂ is the maximum starting ability of the promoter (generally set to 1), M₂ is the amount of leakage of the promoter, S is the amount of regulation factor, kd is the S value when the model change trend is changed:

Finally, according to the differential equation to express the expression, transcription and degradation process of the whole gene line:

From these differential equations, theoretically, the RFP expression rate is approximately the same as the expression rate of GFP, regardless of the effect of protein lacI on the expression of the promoter pLac. While taking the inhibition of protein lacI on the promoter pLac into account, from these differential equations, combining the gene line of the whole expression group,we can get the model of green fluorescent protein expression and get the conclusion: the concentration of lysine from the upstream is higher , the rate of survival of lysine-deficient Escherichia coli is higher , compared with GFP ,the fluorescence intensity of GFP is lower. And this is also consistent with the original intention of the team members who design this line diagram. We proved the feasibility of this gene line.

The following was the initial value of each dependent variable in the model.

Through the modeling of the first part, we could verify the feasibility of the gene line of the expression group and verify that the dual fluorescence system can really play the role of mathematical amplification in theoretically.

The second part

Dual fluorescence system

We introduced a gain factor, Fg, which could be used to quantify the change in fluorescence.

GFPs and RFPs represented GFP and RFP fluorescence measurements at the level of expression of the relative fluorescence units, whereas GFP₀ and RFP₀ represented the fluorescence measurements of the leaked expression. From the above conditions,GFP₀/RFP₀=1

Considering the dual fluorescence system in the expression will have a very complex side effects, affected by many factors, beyond our current level, so we decided to assuming that the linear relationship for first, then combined with our search of the literature data, using professional literature data prove that the dual fluorescence system linear relationship.

From the experimental data and the conclusion shown in the literature, it could be seen clearly that there is an obvious mathematical linear relationship between the two fluorescence systems.

It could be proved by the literature data that the dual fluorescence detection system was feasible and had a great amplification effect. During the next experiment, we could construct a feasible dual fluorescence detection system based on the literature.

Conclusion

According to the modeling of two parts, we could guarantee that the feasibility verification of gene line and the theory of dual fluorescence system, and then determine the relationship between output and input by simulating the expression of dual fluorescent system. Based on the modeling of two parts, we can also get this conclusion: The input signal was further linear amplified by the ratio of red and green fluorescent signal. So we succeeded in modeling, providing theoretical basis for the expression group, providing theoretical support for the purpose of our team's final testing, providing the necessary guidance for the success of their subsequent experiments.