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First: establishment principle of prediction model

Second: modeling assumption

1)  The prediction model is an experimental analysis which based on the experimental principle and the Hill function by drawing up the relevant parameters.
2)  It is assumed that there is less attenuation of the AHL when it is in low concentration.
3)  The molecular weight of AHL-LuxR does not vary with time and remains stable.
4)  The fixed parameters used in the model are based on the experimental principle and related literature hypothesis, for there may be about the predicted trend of curve and the problems which may arise in the process of experiment.
5)  The model does not consider the impact of environmental factors on the change of natural causes.
6)  The threshold can be chosen according to the experimental phenomena, and the threshold in ours prediction model is chosen as [LR]/2.
7)  The model does not consider the impact of background expression on GFP accumulation.

Third: theoretical Basis

• Character definition

• Hill function

• Derivation process of discrete forecasting model

Fourth:model building

1) The effect of different initial AHL concentration：

Figure 1

Fig. 1 represents the variation of AHL-LuxR corresponding to time at different initial AHL concentrations.And it can be seen that the distance between curves from left to right is getting larger and larger, which indicates that the lower the initial AHL concentration, the higher the accuracy of the measurement data.

2)The effect of background expression on AHL accumulation：

1) A small amount of background expression

2) No background expression

Fig.2  As shown, when the other parameters are all the same values, we only transform the value of the background expression, but show completely different results. Due to the background expresses the LuxI rather than the AHL, which can produce AHL constantly. So in the case of not adding the AHL, the background expression on AHL accumulation may also have a greater impact on the system after the switch is switched on with IPTG. It also suggests that we are likely to add AiiA hydrolase to inhibit the effect of background expression. To avoid the effect of initial AHL addition, the expression intensity of AiiA hydrolase is also worthy of attention, and it can not express too strongly.

3)The relationship between time and concentration when the AHL-LuxR is reaching the threshold([LR]=[LR]/2):

Figure 3

Fig.3 is the main basis for the feasibility, which reflects the different initial concentration of AHL corresponding to reach the threshold of time, so as to reflect the initial concentration through time, used to trace detection. According to the forecast curve, it shows that the slope of the curve with the increasing of the concentration gradually decreased. When the initial concentration of AHL molecules is at a low level, the same changes of AHL molecules, and the corresponding time difference vary greatly, which indicates that the positive feedback system is more suitable for the accurate detection of low concentration substances.

4)The change of fluorescence with time under different initial AHL concentration：

Figure 4

Fig.4 Combining with Fig.1 and Fig.3, it’s easy to find out that in Fig.4, also exist such a relationship. This shows that when the initial AHL at low concentrations, by measuring the changes of the fluorescence intensity in real time, finding out a suitable threshold, the relationship can also be found between the initial AHL and time.When the initial concentration of AHL molecules is at a low level, the same changes of AHL molecules, and the corresponding time difference vary greatly. It is also shown that the lower the initial AHL concentration, the higher the accuracy of the measurement results under low background expression.

Fifth:feasibility analysis

      Based on the discrete forecasting model, we can see that the positive feedback system is very suitable for the detection of trace. If the background expression accumulation can be controlled at a low level, then the relationship between fluorescence and time will be more obvious at the same group of initial AHL concentration. The minimum detection limit of the system is that the AHL expressed in the background is completely degraded by the AiiA hydrolase.

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