1. Overview
The cell-free expression systems are a rapidly growing field of research, which has become a handy experimental platform for education and discovery in synthetic biology. The preparation of lysates, the core of cell-free expression systems that provide the molecular machineries of transcription and translation, has been demystified, rendering it more accessible to practices.
The concept of cell-free expression systems is based on the idea of carrying out translation reactions in a test tube using the translation machinery extracted from living cells. E. coli is attractive hosts for cell-free expression systems because it is easily fermentable. The prokaryotic E. coli crude extract system is one of the most widely adopted platforms for protein synthesis. E. coli crude extract has been widely adopted for two main reasons: its high batch yields and the fast, scalable, and cost-effective extract preparation process.
Cell-free expression systems reactions were prepared by mixing E. coli crude extract with other components such as ATP, PEP, amino acid, etc. (see expermiment section for details), and adding its corresponding trigger miRNA.
In order to obtain sensitive and fast detection effects, the reaction conditions for producing reporter protein yield of cell-free expression systems were optimized under different temperature, rotation rate, reaction time and miRNA concentration. These factors also influence each other.
2. Fitting function between reaction conditions and reporter yield
Fitting function is a data processing method that approximately describes or compares the functional relationship between the coordinates represented by the discrete point group on the plane with the continuous curve. In our experiments, the sets of data pairs (xi, yi) (i = 1, 2,... m) of quantities x and y are obtained through experiments, in which each xi is from reaction temperature, reaction time, rotation rate and miRNA concentration, and yi represents the different yield of reporter. Usually, the kind of analytical expression, y = f (x, c), is suitable for the law of experimental data to reflect the dependence between quantity x and y, that is, to "best" fit the known data in a certain sense for reporter yield.
The fitting function of reaction temperature, reaction time, rotation rate and miRNA concentration with reporter yield were shown as follows (Fig.1), which their R2 values are 0.986, 0.979, 0,991 and 0.989, respectively, indicating regression models are accurate. Furthermore, since their P value are less than 0.05, these equations are also valid.
Fig.1 The Fitting function between reaction temperature and reporter yield.
Fig.2 The Fitting function between reaction time and reporter yield.
Fig.3 The Fitting function between rotation rate and reporter yield.
Fig.4 The Fitting function between miRNA concentration and reporter yield.
3. General assumption and parameter
Assumption
First, the CFES reaction happened in an ideal environment with a suitable ECE, ATP and amino acids etc. Second, since there is no formula for explaining the relationship between the reaction temperature, reaction time and miRNA concentration and reporter yield, we assume that they are in a polynomial relation.
Parameter
In order to analyze the relationship between the reaction temperature, reaction time and miRNA concentration and reporter yield, we used MATLAB software to analyze and set relevant parameters as follows (Fig.5).
Fig.5 Parameter setting
4. Mathematic analysis
We assume that the reaction temperature is very important for the reporter yield on the paper strip sensor, and assume that the relationships of reaction temperature and reporter yield are polynomic. According to the setting of parameters, and through the analysis of our experimental data with MATLAB software, we make sure that they are polynomials relationship, and R2=1, indicating that they are highly consistent. The diagram also shows that the reaction temperature is crucial to the test results (Fig.6). The test results change with the temperature, which is the best at 30 ºС.
F (x, y) = -0.2874+0.0338*y-0.0038*x^2-0.0008*y^2+0.0028*x*y
Fig.6 The Fitting function between reaction temperature and reporter yield
The reaction time is very important for the reporter yield on the paper strip sensor, and we assume that they are polynomic relationship. According to the setting of parameters, and through the analysis of our experimental data with MATLAB software, we make sure that they are polynomials relationship, and R2= 0.973, indicating that they are highly consistent. The diagram also shows that the reaction time is crucial to the test results (Fig.7). The test results change with the time, which is ample time at 1h.
F (x, y) = 0.0528+0.0515*x -0.0082*x^2
Fig.7 The Fitting function between reaction time and reporter yield
The target miRNA concentration is very important for the reporter yield on the paper strip sensor, especially in susceptibility, and we assume that the relationship of miRNA concentration and reporter yield are polynomic. According to the setting of parameters, and through the analysis of our experimental data with MATLAB software, we make sure that they are polynomials relationship, and R2= 0.985, indicating that they are highly consistent. The diagram also shows that the miRNA concentration is crucial to the test results (Fig.8). The test results change with the time, which is detectable at 500fM.
F (x, y) = 0.1196+0.0274*x^2-0.0289*y^2
Fig.8 The Fitting function between miRNA concentration and reporter yield
As is shown in the diagram, most of trend of each set of data has one peak-point, thus we obtain that quadric expression can represent the relation of them.
5. Conclusion
In the experiment of our project, reaction temperature (30°C), reaction time (1h), detectable miRNA concentration (500fM) are the best results, because they are effective in all. There is also disadvantage of the model. The assumption that the relation of them can be represented as a polynomial is a little cursory.