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+ | background-color:#F7F7F7; | ||
+ | } | ||
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+ | .sk{ | ||
+ | width:1000px; | ||
+ | padding:0px 50px 0px 50px; | ||
+ | margin-left: auto; | ||
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#myBtn { | #myBtn { | ||
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</div> | </div> | ||
<!-- Main --> | <!-- Main --> | ||
− | + | <div class="nb"> | |
− | <div class=" | + | <div class="sk"> |
<!-- Features --> | <!-- Features --> | ||
<section class="box features"> | <section class="box features"> | ||
− | <h2 class="major"><span> | + | <h2 class="major"><span>miniToe</span></h2> |
+ | |||
+ | <br/> | ||
+ | To achieve a better post-transcriptional regulation strategy, we designed a system which is composed of an RNA endoribonuclease (Csy4) and an RNA module named miniToe. We modeled to describe the dynamics of the miniToe system and found a way to achieve different regulation level. | ||
+ | <br/><br/> | ||
+ | |||
+ | |||
+ | |||
<p> | <p> | ||
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<div> | <div> | ||
− | \[\rightarrow [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[\rightarrow [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
\[\rightarrow [𝑚𝑅𝑁𝐴_{Csy4}]\] | \[\rightarrow [𝑚𝑅𝑁𝐴_{Csy4}]\] | ||
\[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow [𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\] | \[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow [𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\] | ||
− | \[[Protein_{𝐶𝑠𝑦4}]+[crRNA-RBS-mRNA_{ | + | \[[Protein_{𝐶𝑠𝑦4}]+[crRNA-RBS-mRNA_{sfGFP}]\leftrightarrow [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{ | + | \[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\rightarrow [𝑚𝑅𝑁𝐴_{sfGFP}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\] |
− | \[[𝑚𝑅𝑁𝐴_{ | + | \[[𝑚𝑅𝑁𝐴_{sfGFP}]\rightarrow [𝑚𝑅𝑁𝐴_{sfGFP}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{sfGFP}]\] |
− | \[[crRNA-RBS-mRNA_{ | + | \[[crRNA-RBS-mRNA_{sfGFP}]\rightarrow \emptyset\] |
\[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow \emptyset\] | \[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow \emptyset\] | ||
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\rightarrow \emptyset\] | \[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\rightarrow \emptyset\] | ||
− | \[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{ | + | \[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\rightarrow \emptyset\] |
− | \[[𝑚𝑅𝑁𝐴_{ | + | \[[𝑚𝑅𝑁𝐴_{sfGFP}]\rightarrow \emptyset\] |
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\rightarrow \emptyset\] | \[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\rightarrow \emptyset\] | ||
− | \[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{ | + | \[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{sfGFP}]\rightarrow \emptyset\] |
</div> | </div> | ||
− | <br />Two equations, describing the functional binding and cleavage of Csy4 protein in biology, and three parameters | + | <br />Two equations, describing the functional binding and cleavage of Csy4 protein in biology, and three parameters: |
+ | k<sub>on</sub>, k<sub>off</sub>, k<sub>obs</sub>, describing the same things in mathematics, are the core of our model. | ||
</p> | </p> | ||
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<h3>ODEs</h3> | <h3>ODEs</h3> | ||
− | <br />To simulate the dynamics of | + | <br />To simulate the dynamics of sfGFP, we use ordinary differential equations to model the reactions above. And ODEs are given as follows: |
<div> | <div> | ||
− | \[\frac{d[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[\frac{d[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]}{dt}=𝑘_{1}-𝑘_{d1}[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
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\[\frac{d[Protein_{𝐶𝑠𝑦4}]}{dt}=𝑘_{p2}[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]-𝑘_{dp2}[Protein_{𝐶𝑠𝑦4}]\] | \[\frac{d[Protein_{𝐶𝑠𝑦4}]}{dt}=𝑘_{p2}[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]-𝑘_{dp2}[Protein_{𝐶𝑠𝑦4}]\] | ||
− | \[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{ | + | \[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]}{dt}=\] |
− | \[-𝑘_{of}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{ | + | \[𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[-𝑘_{d1}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{ | + | \[-𝑘_{of}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\] |
− | \[-𝑘_{obs}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{ | + | \[-𝑘_{d1}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\] |
+ | \[-𝑘_{obs}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\] | ||
− | \[\frac{d[𝑚𝑅𝑁𝐴_{ | + | \[\frac{d[𝑚𝑅𝑁𝐴_{sfGFP}]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]-𝑘_{d3}[𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{ | + | \[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]\] |
− | \[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[-𝑘_{dc2}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\] |
− | \[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{ | + | \[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] |
+ | \[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\] | ||
− | \[\frac{d[Protein_{ | + | \[\frac{d[Protein_{sfGFP}]}{dt}=𝑘_{p1}[𝑚𝑅𝑁𝐴_{sfGFP}]-𝑘_{dp1}[Protein_{sfGFP}]\] |
</div> | </div> | ||
<br />For the readability, the complex symbol is simplified as: | <br />For the readability, the complex symbol is simplified as: | ||
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<h3>Data Processing</h3> | <h3>Data Processing</h3> | ||
− | <br /> The leak in the experiment is | + | <br /> The leak in the experiment is a big problem in estimating parameters in our ODEs model, so we processing the data by following formula; |
\[Data(without leak)=Data(+IPTG)-Data(-IPTG)\] | \[Data(without leak)=Data(+IPTG)-Data(-IPTG)\] | ||
− | <br /> By doing this, we can reduce some factor which may be | + | <br /> By doing this, we can reduce some factor which may be influenced estimation, not just the leak, but also some background noise. So we can get more precise parameters of the Csy4. |
</p> | </p> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
− | <th scope="row"> | + | <th scope="row"> [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴<sub>sfGFP</sub>]</th> |
− | <td>A</td> | + | <td align="center">A</td> |
− | <td>15</td> | + | <td align="center">15</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <th scope="row"> | + | <th scope="row">[𝑚𝑅𝑁𝐴<sub>Csy4</sub>]</th> |
− | <td>B</td> | + | <td align="center">B</td> |
− | <td>0</td> | + | <td align="center">0</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">[Protein<sub>𝐶𝑠𝑦4</sub>]</th> | |
− | <td>C</td> | + | <td align="center">C</td> |
− | <td>0</td> | + | <td align="center">0</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">[Protein<sub>𝐶𝑠𝑦4</sub>-crRNA-RBS-mRNA<sub>sfGFP</sub>]</th> | |
− | <td>D</td> | + | <td align="center">D</td> |
− | <td>0</td> | + | <td align="center">0</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">[𝑚𝑅𝑁𝐴<sub>sfGFP</sub>]</th> | |
− | <td>E</td> | + | <td align="center">E</td> |
− | <td>0</td> | + | <td align="center">0</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">[Protein<sub>𝐶𝑠𝑦4</sub>-𝑐𝑟𝑅𝑁𝐴]</th> | |
− | <td>F</td> | + | <td align="center">F</td> |
− | <td>0</td> | + | <td align="center">0</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <th scope="row"> | + | <th scope="row">[Protein<sub>sfGFP</sub>]</th> |
− | <td>G</td> | + | <td align="center">G</td> |
− | <td>0</td> | + | <td align="center">0</td> |
− | <td> | + | <td align="center">mol/L</td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
</table> | </table> | ||
− | <br /> Because the [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴<sub> | + | <br /> Because the [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴<sub>sfGFP</sub>] is under controlled by a constitutive promoter, so we set the initial concentration to 15mol/L . |
− | <br /> The | + | <br /> <br /> The parament we used in the ODEs is listed in the following table: <table width="200" border="1"> |
<tbody> | <tbody> | ||
<tr> | <tr> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>1</sub></th> | |
− | <td> | + | <td align="center">The transcription rate of [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴<sub>sfGFP</sub>]</td> |
− | + | <td align="center">h<sup>-1</sup></td> | |
− | <td>1.955</td> | + | <td align="center">1.955</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>d1</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴<sub>sfGFP</sub>]</td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.002</td> | + | <td align="center">0.002</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>2</sub></th> | |
− | <td> | + | <td align="center">The transcription rate of [𝑚𝑅𝑁𝐴<sub>Csy4</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>1.116</td> | + | <td align="center">1.116</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>d2</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [𝑚𝑅𝑁𝐴<sub>Csy4</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.241</td> | + | <td align="center">0.241</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>p2</sub></th> | |
− | <td> | + | <td align="center">The translation rate of [Protein<sub>𝐶𝑠𝑦4</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>1.134</td> | + | <td align="center">1.134</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>dp2</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [Protein<sub>𝐶𝑠𝑦4</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>6.547</td> | + | <td align="center">6.547</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>on</sub></th> | |
− | <td> | + | <td align="center">The binding constant of [Protein<sub>𝐶𝑠𝑦4</sub>] and [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴<sub>sfGFP</sub>]</td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>23995.469</td> | + | <td align="center">23995.469</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>off</sub></th> | |
− | <td> | + | <td align="center">The dissociation constant of [Protein<sub>𝐶𝑠𝑦4</sub>] and [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴<sub>sfGFP</sub>]</td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>2.703</td> | + | <td align="center">2.703</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>dc1</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [Protein<sub>𝐶𝑠𝑦4</sub>-crRNA-RBS-mRNA<sub>sfGFP</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.024</td> | + | <td align="center">0.024</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>obs</sub></th> | |
− | <td> | + | <td align="center">The cleavage rate of [Protein<sub>𝐶𝑠𝑦4</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.327</td> | + | <td align="center">0.327</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>d3</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [𝑚𝑅𝑁𝐴<sub>sfGFP</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.472</td> | + | <td align="center">0.472</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>dc2</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [Protein<sub>𝐶𝑠𝑦4</sub>-𝑐𝑟𝑅𝑁𝐴] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.024</td> | + | <td align="center">0.024</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">𝑘<sub>p1</sub></th> | |
− | <td> | + | <td align="center">The translation rate of [Protein<sub>sfGFP</sub>]</td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>1.711</td> | + | <td align="center">1.711</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | + | <th scope="row">k<sub>dp1</sub></th> | |
− | <td> | + | <td align="center">The degradation rate of [Protein<sub>sfGFP</sub>] </td> |
− | <td> | + | <td align="center">h<sup>-1</sup></td> |
− | <td>0.479</td> | + | <td align="center">0.479</td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
Line 381: | Line 404: | ||
<br /> | <br /> | ||
− | <div align="center"><img src=" | + | <div align="center"><img src="https://static.igem.org/mediawiki/2018/2/24/T--OUC-China--min1.png" width="600" > |
</div> | </div> | ||
<br /> | <br /> | ||
− | <div align="center"><p >Fig.1 The dynamics of | + | <div align="center"><p >Fig.1 The dynamics of sfGFP by model prediction</p></div> |
We compare the experimental data to the simulation: | We compare the experimental data to the simulation: | ||
− | <div align="center"><img src=" | + | <div align="center"><img src="https://static.igem.org/mediawiki/2018/8/89/T--OUC-China--min2.png" width="600" > |
</div> | </div> | ||
<br /> | <br /> | ||
Line 392: | Line 415: | ||
<h3>Discussion</h3> | <h3>Discussion</h3> | ||
− | <br />Combining the biology and math, we now discuss why the dynamics of | + | <br />Combining the biology and math, we now discuss why the dynamics of sfGFP is like the curve in the Fig.1. In order to explain in detail, we plot the dynamics of all species in the miniToe system in Fig.3. |
− | <div align="center"><img src=" | + | <div align="center"><img src="https://static.igem.org/mediawiki/2018/2/2e/T--OUC-China--res6.png" width="600" > |
</div> | </div> | ||
<br /> | <br /> | ||
Line 400: | Line 423: | ||
− | As we can see in the Fig.3, the red line refers to the dynamics of | + | As we can see in the Fig.3, the red line refers to the dynamics of sfGFP, which is increasing in the beginning and then drop down to a stable level. The reason for this is that the cleavage rate of Csy4 is faster than the production rate of [crRNA-RBS-mRNA<sub>sfGFP</sub>] , which cause that the [mRNA<sub>sfGFP</sub>] is decreasing after 10 hours. Before we add IPTG into our system to induce the Tac promoter, the [crRNA-RBS-mRNA<sub>sfGFP</sub>] is accumulated because it is under control by a constitutive promoter. After we add IPTG, the initial concentration of [crRNA-RBS-mRNA<sub>sfGFP</sub>] plays an important role in the production of sfGFP during the early 10 hours: even the Csy4 cleavage rate is faster than the production rate of [crRNA-RBS-mRNA<sub>sfGFP</sub>] , the [crRNA-RBS-mRNA<sub>sfGFP</sub>] which is accumulated before make the keep increasing. But after the initial amount of [crRNA-RBS-mRNA<sub>sfGFP</sub>] is used out, the [mRNA<sub>sfGFP</sub>] then drop down into a stable level with the balance of the production rate and decay rate, which result in the drop down of sfGFP curve. |
− | + | <br /><br /> | |
− | + | <h3 id="MM">Sensitivities Analysis</h3> | |
− | + | <br />After building the ODE model, we try to do something more deeply to our miniToe system by analyzing the sensitivity of parameters. Fig.4 shows the numerical integration of sensitivities of parameters in 30 hours. | |
+ | <div align="center"><img src="https://static.igem.org/mediawiki/2018/c/c4/T--OUC-China--design3-2.png" width="950" > | ||
+ | </div> | ||
+ | <br /> | ||
+ | <div align="center"><p >Fig.4 The numerical integration of sensitivities of parameters in 30h</p></div> | ||
+ | According to the sensitivity analysis, we can find that three core parameters, k<sub>on</sub> ,k<sub>off</sub> , k<sub>obs</sub> , which is related to the protein Csy4, has different effect in the expression of sfGFP. The two binding parameters, k<sub>on</sub> ,k<sub>off</sub> , will not influence sfGFP while the cleavage parameter, , will influence the expression in sfGFP, which indicated if we change the wild-type Csy4 to some mutation then we can achieve the different expression of sfGFP. | ||
+ | <br /><br />Enlighten by the sensitivity analysis, we give a prediction curve that shows what will happen in the sfGFP expression curve if we change the Csy4, and it can be seen in the Fig.5. | ||
− | + | <div align="center"><img src="https://static.igem.org/mediawiki/2018/c/ca/T--OUC-China--res23.png" width="600" > | |
+ | </div> | ||
+ | <br /> | ||
+ | <div align="center"><p >Fig.5 The curve of sfGFP with the changing cleavage rate</p></div> | ||
+ | And the Fig.6 shows that the relationship between the stable expression level of sfGFP and the claevage rate,k<sub>obs</sub> . | ||
+ | <div align="center"><img src="https://static.igem.org/mediawiki/2018/5/55/T--OUC-China--min6.png" width="600" > | ||
+ | </div> | ||
+ | <br /> | ||
+ | <div align="center"><p >Fig.6 The relationship between the stable expression level of sfGFP and the claevage rate</p></div> | ||
</p> | </p> | ||
− | + | <br /><br /><br /><br /> | |
</section> | </section> | ||
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− | + | <div class="copyright1">Contact Us : oucigem@163.com | ©2018 OUC IGEM.All Rights Reserved. <br /> | |
+ | <img src="https://static.igem.org/mediawiki/2017/b/b4/T--OUC-China--foot1.jpeg"alt="banner"width="80px"> | ||
+ | <img src="https://static.igem.org/mediawiki/2017/6/62/T--OUC-China--foot2.jpeg"alt="banner"width="80px"> | ||
+ | <img src="https://static.igem.org/mediawiki/2018/f/f3/T--OUC-China--lalala.png"alt="banner"width="80px"> | ||
+ | <img src="https://static.igem.org/mediawiki/2017/5/51/T--OUC-China--NSG.png"alt="banner"height="65px"> | ||
+ | <img src="https://static.igem.org/mediawiki/2017/2/2a/T--OUC-China--ML.png"alt="banner"height="65px">  | ||
+ | </div> | ||
Latest revision as of 17:25, 5 December 2018
miniToe
To achieve a better post-transcriptional regulation strategy, we designed a system which is composed of an RNA endoribonuclease (Csy4) and an RNA module named miniToe. We modeled to describe the dynamics of the miniToe system and found a way to achieve different regulation level.
Reactions
We can describe our miniToe system to be followings:
\[\rightarrow [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[\rightarrow [𝑚𝑅𝑁𝐴_{Csy4}]\]
\[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow [𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\]
\[[Protein_{𝐶𝑠𝑦4}]+[crRNA-RBS-mRNA_{sfGFP}]\leftrightarrow [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\rightarrow [𝑚𝑅𝑁𝐴_{sfGFP}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\]
\[[𝑚𝑅𝑁𝐴_{sfGFP}]\rightarrow [𝑚𝑅𝑁𝐴_{sfGFP}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{sfGFP}]\]
\[[crRNA-RBS-mRNA_{sfGFP}]\rightarrow \emptyset\]
\[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow \emptyset\]
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\rightarrow \emptyset\]
\[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\rightarrow \emptyset\]
\[[𝑚𝑅𝑁𝐴_{sfGFP}]\rightarrow \emptyset\]
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\rightarrow \emptyset\]
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{sfGFP}]\rightarrow \emptyset\]
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 sfGFP, we use ordinary differential equations to model the reactions above. And ODEs are given as follows:
\[\frac{d[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]}{dt}=𝑘_{1}-𝑘_{d1}[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[\frac{d[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]}{dt}=𝑘_{2}-𝑘_{d2}[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\]
\[\frac{d[Protein_{𝐶𝑠𝑦4}]}{dt}=𝑘_{p2}[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]-𝑘_{dp2}[Protein_{𝐶𝑠𝑦4}]\]
\[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]}{dt}=\]
\[𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[-𝑘_{of}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\]
\[-𝑘_{d1}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\]
\[-𝑘_{obs}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{sfGFP}]\]
\[\frac{d[𝑚𝑅𝑁𝐴_{sfGFP}]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]-𝑘_{d3}[𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[-𝑘_{dc2}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\]
\[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{sfGFP}]\]
\[\frac{d[Protein_{sfGFP}]}{dt}=𝑘_{p1}[𝑚𝑅𝑁𝐴_{sfGFP}]-𝑘_{dp1}[Protein_{sfGFP}]\]
For the readability, the complex symbol is simplified as:
\[\frac{d[A]}{dt}=𝑘_{1}-𝑘_{d1}[A]-𝑘_{on}[C][A]+𝑘_{off}[D]\]
\[\frac{d[B]}{dt}=𝑘_{2}-𝑘_{d2}[B]\]
\[\frac{d[C]}{dt}=𝑘_{p2}[B]-𝑘_{dp2}[C]-𝑘_{on}[C][A]+𝑘_{off}[D]\]
\[\frac{d[D]}{dt}=𝑘_{on}[C][A]-𝑘_{dp2}[C]-𝑘_{off}[D]-𝑘_{dc1}[D]-𝑘_{obs}[D]\]
\[\frac{d[E]}{dt}=𝑘_{obs}[D]-𝑘_{d3}[E]\]
\[\frac{d[F]}{dt}=𝑘_{obs}[D]-𝑘_{d3}[F]\]
\[\frac{d[G]}{dt}=𝑘_{p1}[E]-𝑘_{dp1}[G]\]
Data Processing
The leak in the experiment is a big problem in estimating parameters in our ODEs model, so we processing the data by following formula; \[Data(without leak)=Data(+IPTG)-Data(-IPTG)\]
By doing this, we can reduce some factor which may be influenced 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 |
---|---|---|---|
[𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴sfGFP] | A | 15 | mol/L |
[𝑚𝑅𝑁𝐴Csy4] | B | 0 | mol/L |
[Protein𝐶𝑠𝑦4] | C | 0 | mol/L |
[Protein𝐶𝑠𝑦4-crRNA-RBS-mRNAsfGFP] | D | 0 | mol/L |
[𝑚𝑅𝑁𝐴sfGFP] | E | 0 | mol/L |
[Protein𝐶𝑠𝑦4-𝑐𝑟𝑅𝑁𝐴] | F | 0 | mol/L |
[ProteinsfGFP] | G | 0 | mol/L |
Because the [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴sfGFP] is under controlled by a constitutive promoter, so we set the initial concentration to 15mol/L .
The parament we used in the ODEs is listed in the following table:
Parameters | Definition | Units | Value |
---|---|---|---|
𝑘1 | The transcription rate of [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴sfGFP] | h-1 | 1.955 |
𝑘d1 | The degradation rate of [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴sfGFP] | h-1 | 0.002 |
𝑘2 | The transcription rate of [𝑚𝑅𝑁𝐴Csy4] | h-1 | 1.116 |
𝑘d2 | The degradation rate of [𝑚𝑅𝑁𝐴Csy4] | h-1 | 0.241 |
𝑘p2 | The translation rate of [Protein𝐶𝑠𝑦4] | h-1 | 1.134 |
𝑘dp2 | The degradation rate of [Protein𝐶𝑠𝑦4] | h-1 | 6.547 |
𝑘on | The binding constant of [Protein𝐶𝑠𝑦4] and [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴sfGFP] | h-1 | 23995.469 |
𝑘off | The dissociation constant of [Protein𝐶𝑠𝑦4] and [𝑐𝑟𝑅𝑁𝐴−𝑅𝐵𝑆−𝑚𝑅𝑁𝐴sfGFP] | h-1 | 2.703 |
𝑘dc1 | The degradation rate of [Protein𝐶𝑠𝑦4-crRNA-RBS-mRNAsfGFP] | h-1 | 0.024 |
𝑘obs | The cleavage rate of [Protein𝐶𝑠𝑦4] | h-1 | 0.327 |
𝑘d3 | The degradation rate of [𝑚𝑅𝑁𝐴sfGFP] | h-1 | 0.472 |
𝑘dc2 | The degradation rate of [Protein𝐶𝑠𝑦4-𝑐𝑟𝑅𝑁𝐴] | h-1 | 0.024 |
𝑘p1 | The translation rate of [ProteinsfGFP] | h-1 | 1.711 |
kdp1 | The degradation rate of [ProteinsfGFP] | h-1 | 0.479 |
Simulation
With the help of Simbiology toolbox in Matlab,we simulate our miniToe system for 30h, the result can be seen in the Fig.1.
Fig.1 The dynamics of sfGFP by model prediction
Fig.2 The comparison between experimental data and simulation data
Discussion
Combining the biology and math, we now discuss why the dynamics of sfGFP is like the curve in the Fig.1. In order to explain in detail, we plot the dynamics of all species in the miniToe system in Fig.3.
Fig.3 The dynamics of all species in the miniToe system
Sensitivities Analysis
After building the ODE model, we try to do something more deeply to our miniToe system by analyzing the sensitivity of parameters. Fig.4 shows the numerical integration of sensitivities of parameters in 30 hours.
Fig.4 The numerical integration of sensitivities of parameters in 30h
Enlighten by the sensitivity analysis, we give a prediction curve that shows what will happen in the sfGFP expression curve if we change the Csy4, and it can be seen in the Fig.5.
Fig.5 The curve of sfGFP with the changing cleavage rate
Fig.6 The relationship between the stable expression level of sfGFP and the claevage rate
Contact Us : oucigem@163.com | ©2018 OUC IGEM.All Rights Reserved.