Difference between revisions of "Team:OUC-China/miniToe"
| Line 294: | Line 294: | ||
<th scope="row">\[๐_{1}\]</th> | <th scope="row">\[๐_{1}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>1.955</td> | <td>1.955</td> | ||
</tr> | </tr> | ||
| Line 300: | Line 300: | ||
<th scope="row">\[๐_{d1}\]</th> | <th scope="row">\[๐_{d1}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>0.002</td> | <td>0.002</td> | ||
</tr> | </tr> | ||
| Line 306: | Line 306: | ||
<th scope="row">\[๐_{2}\]</th> | <th scope="row">\[๐_{2}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>1.116</td> | <td>1.116</td> | ||
</tr> | </tr> | ||
| Line 312: | Line 312: | ||
<th scope="row">\[๐_{d2}\]</th> | <th scope="row">\[๐_{d2}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>0.241</td> | <td>0.241</td> | ||
</tr> | </tr> | ||
| Line 318: | Line 318: | ||
<th scope="row">\[๐_{p2}\]</th> | <th scope="row">\[๐_{p2}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>1.134</td> | <td>1.134</td> | ||
</tr> | </tr> | ||
| Line 324: | Line 324: | ||
<th scope="row">\[๐_{dp2}\]</th> | <th scope="row">\[๐_{dp2}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>6.547</td> | <td>6.547</td> | ||
</tr> | </tr> | ||
| Line 330: | Line 330: | ||
<th scope="row">\[๐_{on}\]</th> | <th scope="row">\[๐_{on}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>23995.469</td> | <td>23995.469</td> | ||
</tr> | </tr> | ||
| Line 336: | Line 336: | ||
<th scope="row">\[๐_{off}\]</th> | <th scope="row">\[๐_{off}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>2.703</td> | <td>2.703</td> | ||
</tr> | </tr> | ||
| Line 342: | Line 342: | ||
<th scope="row">\[๐_{dc1}\]</th> | <th scope="row">\[๐_{dc1}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>0.024</td> | <td>0.024</td> | ||
</tr> | </tr> | ||
| Line 348: | Line 348: | ||
<th scope="row">\[๐_{obs}\]</th> | <th scope="row">\[๐_{obs}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>0.327</td> | <td>0.327</td> | ||
</tr> | </tr> | ||
| Line 354: | Line 354: | ||
<th scope="row">\[๐_{d3}\]</th> | <th scope="row">\[๐_{d3}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>0.472</td> | <td>0.472</td> | ||
</tr> | </tr> | ||
| Line 360: | Line 360: | ||
<th scope="row">\[๐_{dc2}\]</th> | <th scope="row">\[๐_{dc2}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>0.024</td> | <td>0.024</td> | ||
</tr> | </tr> | ||
| Line 366: | Line 366: | ||
<th scope="row">\[๐_{p1}\]</th> | <th scope="row">\[๐_{p1}\]</th> | ||
<td> </td> | <td> </td> | ||
| โ | <td> | + | <td>\[h^{-1}\]</td> |
<td>1.711</td> | <td>1.711</td> | ||
</tr> | </tr> | ||
Revision as of 03:49, 11 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 kon koff kobs describing the same things in mathematics, are the core of our model.
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:
\[\frac{d[A]}{dt}=๐_{1}-๐_{d1}[A]-๐_{on}[C][A]+๐_{off}[D]\]
\[\frac{d[B]}{dt}=๐_{2}-๐_{d2}[B]\]
\[\frac{d[C]}{dt}=๐_{p2}[B]-๐_{dp2}[C]-๐_{on}[C][A]+๐_{off}[D]\]
\[\frac{d[D]}{dt}=๐_{on}[C][A]-๐_{dp2}[C]-๐_{off}[D]-๐_{dc1}[D]-๐_{obs}[D]\]
\[\frac{d[E]}{dt}=๐_{obs}[D]-๐_{d3}[E]\]
\[\frac{d[F]}{dt}=๐_{obs}[D]-๐_{d3}[F]\]
\[\frac{d[G]}{dt}=๐_{p1}[E]-๐_{dp1}[G]\]
Data Processing
The leak in the experiment is an big problem in estimating parameters in our ODEs model, so we processing the data by following formula๏ผ \[Data(without leak)=Data(+IPTG)-Data(-IPTG)\]
By doing this, we can reduce some factor which may be influence estimation not just the leak, but also some background noise. So we can get more precise parameters of the Csy4.
Species, symbols and parameters
| Species | Symbol | Initial value | Units |
|---|---|---|---|
| \[๐๐๐ ๐๐ด โ ๐ ๐ต๐ โ ๐๐ ๐๐ด_{๐๐๐}\] | A | 15 | \[mol/L\] |
| \[๐๐ ๐๐ด_{Csy4}\] | B | 0 | \[mol/L\] |
| \[Protein_{๐ถ๐ ๐ฆ4}\] | C | 0 | \[mol/L\] |
| \[Protein_{๐ถ๐ ๐ฆ4}-crRNA-RBS-mRNA_{๐๐๐}\] | D | 0 | \[mol/L\] |
| \[๐๐ ๐๐ด_{gfp}\] | E | 0 | \[mol/L\] |
| \[Protein_{๐ถ๐ ๐ฆ4}-๐๐๐ ๐๐ด\] | F | 0 | \[mol/L\] |
| \[Protein_{gfp}\] | G | 0 | \[mol/L\] |
Because the [๐๐๐ ๐๐ด โ ๐ ๐ต๐ โ ๐๐ ๐๐ด๐๐๐] is under controlled by a constitutive promoter, so we set the initial concentration to 15mol/L .
The other parament we used in the ODEs is listed in the following table:
| Parameters | Definition | Units | Value |
|---|---|---|---|
| \[๐_{1}\] | \[h^{-1}\] | 1.955 | |
| \[๐_{d1}\] | \[h^{-1}\] | 0.002 | |
| \[๐_{2}\] | \[h^{-1}\] | 1.116 | |
| \[๐_{d2}\] | \[h^{-1}\] | 0.241 | |
| \[๐_{p2}\] | \[h^{-1}\] | 1.134 | |
| \[๐_{dp2}\] | \[h^{-1}\] | 6.547 | |
| \[๐_{on}\] | \[h^{-1}\] | 23995.469 | |
| \[๐_{off}\] | \[h^{-1}\] | 2.703 | |
| \[๐_{dc1}\] | \[h^{-1}\] | 0.024 | |
| \[๐_{obs}\] | \[h^{-1}\] | 0.327 | |
| \[๐_{d3}\] | \[h^{-1}\] | 0.472 | |
| \[๐_{dc2}\] | \[h^{-1}\] | 0.024 | |
| \[๐_{p1}\] | \[h^{-1}\] | 1.711 | |
| \[๐_{dp1}\] | \[h^{-1}\] | 0.479 |
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