Team:ShanghaiTech/Model
Overview
According to previous reports, we found that designed negative feedback loop (NFBL) system is effective to increase the resetting speed of a circuit and result in higher fidelity of the expression system. Therefore, with the help of modeling, we were able to select a suitable NFBL to meet our project goal. Meanwhile, we studied the transcriptional layer and used Hill function as the best description for gene transcription. Initially, our data indicated that orthogonal ribosome was efficient to prevent resource competition. Through modeling, we found that orthogonal ribosome had no negative influence on the fidelity of our expression system before and after adding the o-ribosome. After the proof-of-concept, we decided to add the o-ribosome into our expression system. Furthermore, we designed an method to optimize our NFBL circuit, and made a software. Some optimized parameters in our model still need to be tested by experiments in the future. Looking forward, our initial model could be adapted and applied to other projects that aim to fast response and fidelity control.
Transcription Level
Test idea
Knowing that negative feedback loop (NFBL) could help to maintain hormones in vivo, we compared NFBL with simple two nodes system. We found that NFBL could fulfilling our goal to build a system with High Fidelity.
simple system structure
simple system result
NFBL structure
NFBL result
Build the model
We studied the gene transcription in the loop, and fond that Hill function as the best tool to describe the dynamic reactions in transcription layer.
$ rate(downstream) = T\cdot \frac{upstream^{n_{upstream}}}{K_{downstream}+upstream^{n_{upstream}}}$ (Positive influence)
$ rate(downstream) = T\cdot \frac{1}{K_{downstream}+upstream^{n_{upstream}}}$ (Negative influence)
Choose the best pattern
There are 3 feedback loops available for our system. We compared their properties, and chose system 3-1 to be our circuit template.
system 2 structure
system 2 result
system 3-1 structure
system 3-1 result
system 3-2 structure
system 3-2 result
Computer experiment
As the experiment went on, we found that it would take too much time that we would not have more time to test many other parts. Then, we turned to model. We built a optimization model to simulate the behavior of the system under different parameters and found the best combination of parameters.
Error function $Err = \sum_{i=1}^{n}([SystemOutput]_i-[ExpectOutput]_i)^2$
optimum solution search Method
Translation Level
$$\frac{d[Protein]}{dt} = K_{S16}\cdot[S16]-d_{protein}\cdot[Protein]$$
We decided to use orthogonal ribosome to overcome this problem. Before we added orthogonal ribosome to our $\textit{E. coli}$, we used model to illustrate that the orthogonal ribosome would not have negative influence on the fidelity of our system.