Line 155: | Line 155: | ||
\[[๐๐๐๐ก๐๐๐_{gfp}]\rightarrow \emptyset\] | \[[๐๐๐๐ก๐๐๐_{gfp}]\rightarrow \emptyset\] | ||
</div> | </div> | ||
โ | <br /><br />Two equations, describing the functional binding and cleavage of Csy4 protein in biology, and three parameters, | + | <br /><br />Two equations, describing the functional binding and cleavage of Csy4 protein in biology, and three parameters,๐_{on} ,\[๐_{off}\] ,\[๐_{obs}\] , describing the same things in mathematics, are the core of our model. |
<div align="center"><img src="https://static.igem.org/mediawiki/2018/9/90/T--OUC-China--design1-1.png" height="450"> | <div align="center"><img src="https://static.igem.org/mediawiki/2018/9/90/T--OUC-China--design1-1.png" height="450"> | ||
<img src="https://static.igem.org/mediawiki/2018/1/16/T--OUC-China--design1-2.png" height="450"> | <img src="https://static.igem.org/mediawiki/2018/1/16/T--OUC-China--design1-2.png" height="450"> | ||
Line 170: | Line 170: | ||
<p> | <p> | ||
โ | <h3> | + | <h3>ODEs</h3> |
โ | <br /> | + | <br />To simulate the dynamics of GFP, we use ordinary differential equations to model the reactions above. And ODEs are given as follows: |
<div> | <div> | ||
โ | + | \[\frac{d[๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]}{dt}=๐_{1}-๐_{d1}[๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | |
โ | + | \[-๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | |
โ | + | \[+๐_{off}[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | |
โ | + | ||
โ | + | ||
โ | + | ||
โ | + | \[\frac{d[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]}{dt}=๐_{2}-๐_{d2}[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]\] | |
โ | + | ||
โ | + | ||
โ | + | \[\frac{d[Protein_{๐ถ๐ ๐ฆ4}]}{dt}=๐_{p2}[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]-๐_{dp2}[Protein_{๐ถ๐ ๐ฆ4}]\] | |
โ | + | \[-๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | |
โ | + | \[+๐_{off}[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | |
โ | + | ||
+ | |||
+ | \[\frac{d[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]}{dt}=๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | ||
+ | \[-๐_{of}[Protein_{๐ถ๐ ๐ฆ4}][Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\] | ||
+ | \[-๐_{d1}[Protein_{๐ถ๐ ๐ฆ4}][Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\] | ||
+ | \[-๐_{obs}[Protein_{๐ถ๐ ๐ฆ4}][Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\] | ||
+ | |||
+ | |||
+ | \[\frac{d[๐๐
๐๐ด_{๐๐๐}]}{dt}=๐_{obs}[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]-๐_{d3}[๐๐
๐๐ด_{gfp}]\] | ||
+ | |||
+ | |||
+ | \[\frac{d[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA]}{dt}=๐_{obs}[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]-๐_{dc2}[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด]\] | ||
+ | \[-๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | ||
+ | \[+๐_{off}[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\] | ||
+ | |||
+ | |||
+ | \[\frac{d[Protein_{gfp}]}{dt}=๐_{p1}[๐๐
๐๐ด_{๐๐๐}]-๐_{dp1}[Protein_{gfp}]\] | ||
</div> | </div> | ||
โ | <br /><br /> | + | <br /><br />For the readability, the complex symbol is simplified as: |
+ | |||
+ | |||
+ | <div> \[\frac{d[A]}{dt}=๐_{1}-๐_{d1}[A]-๐_{on}[C][A]+๐_{off}[D]\] | ||
+ | |||
+ | \[\frac{d[B]}{dt}=๐_{2}-๐_{d2}[B]\] | ||
+ | |||
+ | \[\frac{d[C]}{dt}=๐_{p2}[B]-๐_{dp2}[C]-๐_{on}[C][A]+๐_{off}[D]\] | ||
+ | |||
+ | \[\frac{d[D]}{dt}=๐_{on}[C][A]-๐_{dp2}[C]-๐_{off}[D]-๐_{dc1}[D]-๐_{obs}[D]\] | ||
+ | |||
+ | \[\frac{d[E]}{dt}=๐_{obs}[D]-๐_{d3}[E]\] | ||
+ | |||
+ | \[\frac{d[F]}{dt}=๐_{obs}[D]-๐_{d3}[F]\] | ||
+ | |||
+ | \[\frac{d[G]}{dt}=๐_{p1}[E]-๐_{dp1}[G]\]</div> | ||
<div align="center"><img src="https://static.igem.org/mediawiki/2018/9/90/T--OUC-China--design1-1.png" height="450"> | <div align="center"><img src="https://static.igem.org/mediawiki/2018/9/90/T--OUC-China--design1-1.png" height="450"> | ||
<img src="https://static.igem.org/mediawiki/2018/1/16/T--OUC-China--design1-2.png" height="450"> | <img src="https://static.igem.org/mediawiki/2018/1/16/T--OUC-China--design1-2.png" height="450"> |
Revision as of 23:30, 10 October 2018
Design
Reactions
We can describe our miniToe system to be followings:
\[\rightarrow [๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[\rightarrow [๐๐
๐๐ด_{Csy4}]\]
\[[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]\rightarrow [๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}] + [๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}]\]
\[[Protein_{๐ถ๐ ๐ฆ4}]+[crRNA-RBS-mRNA_{gfp}]\leftrightarrow [๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]\]
\[[Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\rightarrow [๐๐
๐๐ด_{gfp}] + [๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด]\]
\[[๐๐
๐๐ด_{gfp}]\rightarrow [๐๐
๐๐ด_{gfp}] + [๐๐๐๐ก๐๐๐_{gfp}]\]
\[[crRNA-RBS-mRNA_{gfp}]\rightarrow \emptyset\]
\[[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]\rightarrow \emptyset\]
\[[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}]\rightarrow \emptyset\]
\[[Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\rightarrow \emptyset\]
\[[๐๐
๐๐ด_{gfp}]\rightarrow \emptyset\]
\[[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด]\rightarrow \emptyset\]
\[[๐๐๐๐ก๐๐๐_{gfp}]\rightarrow \emptyset\]
Two equations, describing the functional binding and cleavage of Csy4 protein in biology, and three parameters,๐_{on} ,\[๐_{off}\] ,\[๐_{obs}\] , describing the same things in mathematics, are the core of our model.
Fig.1-1 The structure of Csy4 Fig.1-2 The structure 22nt hairpin which can be recognized by Csy4. Fig.1-3 The Csy4/RNA complex.
ODEs
To simulate the dynamics of GFP, we use ordinary differential equations to model the reactions above. And ODEs are given as follows:
\[\frac{d[๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]}{dt}=๐_{1}-๐_{d1}[๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[-๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[+๐_{off}[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[\frac{d[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]}{dt}=๐_{2}-๐_{d2}[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]\]
\[\frac{d[Protein_{๐ถ๐ ๐ฆ4}]}{dt}=๐_{p2}[๐๐
๐๐ด_{๐ถ๐ ๐ฆ4}]-๐_{dp2}[Protein_{๐ถ๐ ๐ฆ4}]\]
\[-๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[+๐_{off}[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[\frac{d[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]}{dt}=๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[-๐_{of}[Protein_{๐ถ๐ ๐ฆ4}][Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\]
\[-๐_{d1}[Protein_{๐ถ๐ ๐ฆ4}][Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\]
\[-๐_{obs}[Protein_{๐ถ๐ ๐ฆ4}][Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{gfp}]\]
\[\frac{d[๐๐
๐๐ด_{๐๐๐}]}{dt}=๐_{obs}[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]-๐_{d3}[๐๐
๐๐ด_{gfp}]\]
\[\frac{d[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA]}{dt}=๐_{obs}[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-crRNA-RBS-๐๐
๐๐ด_{๐๐๐}]-๐_{dc2}[๐๐๐๐ก๐๐๐_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด]\]
\[-๐_{on}[Protein_{๐ถ๐ ๐ฆ4}][๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[+๐_{off}[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐
๐๐ด โ ๐
๐ต๐ โ ๐๐
๐๐ด_{๐๐๐}]\]
\[\frac{d[Protein_{gfp}]}{dt}=๐_{p1}[๐๐
๐๐ด_{๐๐๐}]-๐_{dp1}[Protein_{gfp}]\]
For the readability, the complex symbol is simplified as:
\[\frac{d[A]}{dt}=๐_{1}-๐_{d1}[A]-๐_{on}[C][A]+๐_{off}[D]\]
\[\frac{d[B]}{dt}=๐_{2}-๐_{d2}[B]\]
\[\frac{d[C]}{dt}=๐_{p2}[B]-๐_{dp2}[C]-๐_{on}[C][A]+๐_{off}[D]\]
\[\frac{d[D]}{dt}=๐_{on}[C][A]-๐_{dp2}[C]-๐_{off}[D]-๐_{dc1}[D]-๐_{obs}[D]\]
\[\frac{d[E]}{dt}=๐_{obs}[D]-๐_{d3}[E]\]
\[\frac{d[F]}{dt}=๐_{obs}[D]-๐_{d3}[F]\]
\[\frac{d[G]}{dt}=๐_{p1}[E]-๐_{dp1}[G]\]
Fig.1-1 The structure of Csy4 Fig.1-2 The structure 22nt hairpin which can be recognized by Csy4. Fig.1-3 The Csy4/RNA complex.
Contact Us : oucigem@163.com | ©2018 OUC IGEM.All Rights Reserved. | โฆโฆโฆโฆ