This summer, we firstly used RNA thermometer as the Thermosensitive Regulator. As this was a part constructed by other team, our wet lab members could perform the experiments based on the former teams’ experiences. Consequently, we didn’t construct the model of RNA thermometer.
Except for RNA thermometer, we designed the T7 platform as an alternative for Thermosensitive Regulator. It contains arabinose induced promoter, T7 polymerase inserted by thermosensitive intein, T7 promoter and GFP. Combined with Magnetic Receiver, T7 platform should take charge of controlling reporter proteins’ expression level under the temperature changing.
(If you want to learn more details about the Thermosensitive Regulator, you can click here)
Thus in order to validate the feasibility of the T7 platform, we got two targets in this part to achieve:
1.To analyze platform’s sensitivity on the temperature change according to the intein’s splicing efficiency;
2.Determine the stability of GFP’s expression level to ensure the regulating effect.
Deterministic Model
Schematic Diagram:
Simplified Schematic Diagram:
We translated the schematic diagram into the following ordinary differential equations:
The first equation describes the expression level of T7 polymerase controlled by arabinose. Because the complex bio-process was a induction process, we used Hill function to describe the production rate.
The second equation describes the amount of mRNA of GFP transcribed by T7 polymerase. In this equation we used Michaelis-Menten function to explain its enzyme kinetics.
The third equation describes the translation rate from mRNA to GFP.
Parameter Choice
Degradation Rate of T7 Polymerase β1
Because there be a degradation label “LVA tag” on the T7 polymerase, the degradation rate of it was larger than the common condition. After searching many articles we got the approximate degradation of it.
Intein Splicing Constant α
The most important parameter that we considered was α. GFP’s expression quantity would fluctuate with the change of α. And it influenced the platform’s sensitivity on the temperature change.
After some literature research, we found that the splicing efficiency of the intein we decided to use was between 20% and 70%. So we started from the conditions when the initial α equaled to 0.1% 1% and 10% respectively when the temperature didn’t meet the threshold. Then the α changed into a number between 20% and 70% while the temperature got over the threshold. And the comparing results were shown as follow:
As we can see in the figures above, when the temperature doesn't go over the threshold, the smaller splicing efficiency is, the higher sensitivity platform can reach. So we can conclude that the initial splicing efficiency is reasonable to be taken into great consideration when designing the T7 platform.
Initial Results
With the parameters chosen above and α equals to 70%, we simulated the expression level of the T7 platform when the temperature got over threshold, which was shown as blow:
Sensitivity Analysis
We performed sensitivity analysis to discover ways to control the expression quantity of the final interest proteins and find ways to adjust the accuracy of the platform.
Local sensitivity analysis involves computing the relative change of the steady state with respect to a change in the parameter. We used MATLAB and sensitivities were calculated for 5% changes in the parameters. The sensitivity coefficient was defined as the ratio of the value with changed parameters and the value with unchanged parameters:
And the sensitivity of some important parameters were shown as follow:
From the sensitivity analysis, we drew the conclusion that we could adjust the response level of our platform from followed several ways:
1.Polymerase controls the output of proteins, so we could use different kinds of polymerase in different condition to achieve the best regulation effect;
2.The output was also really sensitive to the vector’s copy number. Thus we could optimize the ideal platform by choosing a better vector;
3.While the degradation rate also played an important role in the process, we’d better take degradation rate into consideration when we were finding the best effect of platform.
Stochastic Model and Noise Analysis
As a thermosensitive platform, noise would affect the stability of the GFP’s expression a lot. So we need to determine whether the GFP’s expression quantity could be stable enough to perform its duty of response to the temperature change.
Firstly, we constructed the stochastic model based on the following schematic diagram:
With the initial condition that the amount of T7 polymerase was a constant and there was no mRNA of GFP and GFP itself, we used MATLAB and Gillespie SSA to establish this model. We did 100000 realizations and showed 10 of them in the following graphs.
According to the stochastic model, we calculated the stationary distribution of GFP and its mRNA, which were shown as follow. From the stationary distributionwe got the noise of GFP and mRNA to be 0.0023 and 0.0224 respectively. It was obvious that the noise was really small. Thus we considered our platform to be a design with good stability.
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