Overview
The cell-free expression systems (CFES) carry out translation reactions in a test tube using the translation machinery extracted from living cells. E. coli is attractive hosts for CFES 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.
As key base for the hydrogel biosensor, CFES is 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 CFES that provide the molecular machineries of transcription and translation, has been demystified, rendering it more accessible to practices.
CFES reactions were prepared by mixing E. coli crude extract with other components such as ATP, PEP, amino acid, etc. (Please refer to Experiment section for details), and adding its corresponding substrates. In order to obtain sensitive and fast detection effects, the reaction conditions for producing reporter protein yield of CFES were optimized under different temperature, reaction time, concentration of X-gal, and concentration of complementary fragment. These factors also influence each other.
1. Fitting function between reaction conditions and lacZ catalytic reaction results.
Fitting function used to analyze model is 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, Concentration of X-gal and concentration of complementary fragment, 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, Concentration of X-gal and concentration of complementary fragment with reporter yield were shown as follows (Fig.1-4), which their R2 values are 0.998, 0.997, 0.999 and 0.999, respectively, indicating regression models are accurate. Furthermore, since their P value are less than 0.05, repectively, and these equations are also valid.
Fig.1 The Fitting function between reaction temperature and lacZ catalytic reaction results.
Fig.2 The Fitting function between reaction time and lacZ catalytic reaction results.
Fig.3 The Fitting function between X-gal concentration and lacZ catalytic reaction results.
Fig.4 The Fitting function between concentration of complementary fragment and lacZ catalytic reaction results.
Return to index
2.General assumption and parameter for analysis
Assumption
First, CFES reaction happened in an ideal environment with a suitable cell lysate extract (CLE), ATP and amino acids etc.
Second, since there is no formula for explaining the relationship between the reaction temperature, reaction time, concentration of X-gal, concentration of complementary fragment, 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, concentration of X-gal, concentration of complementary fragment and reporter yield, we used MATLAB software to analyze and set relevant parameters as follows (Fig.5).
Fig.5 Parameter setting for model analysis.
Return to index
3.Mathematic analysis
Assumed that the reaction temperature is very important for the reporter yield on the hydrogel biosensor, 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 =0.998, 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 the best conditions for reaction are 20 ºС.
F (x, y) = 0.454-0.4264*x+0.0711*y-0.0049*y^2+0.0292*x*y
Fig.6 The Fitting function between reaction temperature and lacZ catalytic reaction results.
The reaction time is very important for the reporter yield on the hydrogel biosensor, 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 =0.997, 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 the best conditions for reaction are at 1 h.
F (x, y) = 0.0687+0.077*x-0.0037*x^2-0.0416*y^2+0.0424*x*y
Fig.7 The Fitting function between reaction time and lacZ catalytic reaction results.
The concentration of X-gal is very important for the reporter yield on the hydrogel biosensor, especially in susceptibility, and we assume that the relationship of X-gal 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 =0.999, indicating that they are highly consistent. The diagram also shows that the X-gal is crucial to the test results (Fig. 8). The test results change with the concentration of X-gal, which the best conditions for reaction are at 100 ug/mL.
F (x, y) = 0.454-0.4264*x+0.0711*y-0.0049*y^2+0.0292*x*y
Fig.8 The Fitting function between concentration of X-gal and lacZ catalytic reaction results.
The concentration of complementary fragment is very important for the reporter yield on the hydrogel biosensor, especially in susceptibility, and we assume that the relationship of concentration of complementary fragment 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 =0.999, indicating that they are highly consistent. The diagram also shows that the concentration of complementary fragment is crucial to the test results (Fig. 9). The test results change with the concentration of complementary fragment, which the best conditions for reaction are at 0.5 µM.
F (x, y) = 0.3763+0.3696*x-0.1158*y+0.0405*x^2+0.0436*y^2-0.1066*x*y
Fig.9 The Fitting function between concentration of complementary fragmen and lacZ catalytic reaction results.
Return to index
4.Conclusion
In the experiment of our project, reaction temperature (20°C), reaction time (1 h), concentration of aptamer complementary sequence (0.5 uM) and X-gal (100 ug/mL) 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.
Return to index