Difference between revisions of "Team:NUDT CHINA/Model"

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<br/><br/><br/>NUDT_CHINA: This page is under construction.<br/><br/><br/>
+
<!--标题-->
 +
<h2>
 +
<span><span style="color:#7f1015">Abstract</span></span><hr />
 +
</h2>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">This model is created to evaluate the effectiveness of initial design, and offers guidelines about how the system can (or must) be improved. (You can go PROJECT page to see more.) The core idea is to simulate the process of producing the signal which can be detected, and draw a conclusion by obtaining the relationship between the signal intensity and the concentration of miRNA. </span>
 +
</p>
 +
</br>
 +
 
 +
<!--标题-->
 +
<h2>
 +
<span><span style="color:#7f1015">Introduction </span></span><hr />
 +
</h2>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">We create mathematical models of two aspects of our project, a RCA model and a signal detection model.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The RCA model is based on the Michaelis-Menten equation. We can obtain the relationship between the concentration of miRNA and the number of stem-loop structures through theoretical calculation, and we use our experimental results to calculate the parameters we introduced previously.</span>  
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">In the signal detection model, we combine a probability model with the kinetic equation of enzymatic reaction, so we can obtain the relationship between the number of stem-loop structures and the signal intensity under the premise of adding a certain amount of the fusion proteins of dCas9 and split-HRP fragments. </span>  
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">By integrating the two models, we can theoretically predict the impacts of the molecule number of proteins on the signal to noise ratio and explained the trend of the signal intensity with the change of the concentration of miRNA in our wet-lab work.
 +
</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--标题-->
 +
<h2>
 +
<span><span style="color:#7f1015"> Assumption and Justification  </span></span><hr />
 +
</h2>
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">  About model    </span></span><hr />
 +
</h3>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">? We assume that miRNA is not degraded throughout the reaction process.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">? We assume that the two fusion proteins of dCas9 and split-HRP fragments have the same ability to combine with the stem-loop structure, and only when two different proteins next to each other, can they have the ability to catalyze substrate and produce signal.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">? We assume that the number of stem-loop structures in each RCA product is equal under a certain reaction time. </span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">? We assume that the enzymatic activity remains unchanged with time under the premise of excessive amount of enzymes or a short-time reaction.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">  About the data  </span></span><hr />
 +
</h3>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">? ? We assume that the data we obtain from wet-lab experiment are reliable.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">? ? We assume that all the results are trustworthy in the process of statistical processing and data calculation.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--标题-->
 +
<h2>
 +
<span><span style="color:#7f1015">Model </span></span><hr />
 +
</h2>
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">Notations </span></span><hr />
 +
</h3>
 +
 
 +
 
 +
 
 +
<!--表格-->
 +
<table class="MsoTableGrid" border="1" cellspacing="0" cellpadding="0" style="border:none;">
 +
<tbody>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>Symbol </span>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>Definition </span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>x</span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK7"></a><a name="OLE_LINK6"></a><span>The concentration of</span><span> miRNA (pM)</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>C<sub>1</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The concentration of initiated probe (Abbreviated
 +
  to iprobe)</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>k<sub>1</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK8"></a><span>A constant representing
 +
  the scale factor</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>K<sub>m </sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>One of the characteristic constants of
 +
  phi29 DNA polymerase</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>V<sub>max</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>One of the characteristic constants of phi29
 +
  DNA polymerase</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>k<sub>2</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>A constant representing the scale factor</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>V</span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The initial speed of RCA </span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK9"></a><i><span>n<sub>1</sub></span></i><i><sub><span></span></sub></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The moles of RCA product</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>n<sub>2</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK10"></a><span>The number of
 +
  stem-loop structures in each RCA product</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>n</span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The total amount of <a name="OLE_LINK23"></a><a name="OLE_LINK22"></a>stem-loop structures</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>N</span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK41"></a><a name="OLE_LINK16"></a><span>The molecule number of the
 +
  fusion protein of dCas9 and split-HRP fragments</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>k<sub>3</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>A constant representing the scale factor</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>y<sub>1</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The fluorescence intensity of
 +
  DNA-dye-complex (RFU)</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>N<sub>1</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The molecule number of the fusion protein
 +
  of dCas9 and split-HRP fragments in the solution</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>N<sub>2</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK45"></a><span>The molecule number
 +
  of the fusion protein of dCas9 and split-HRP fragments binding with stem-loop
 +
  structure</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>k<sub>4</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>A constant representing the scale factor</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span>k<sub>5</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>A constant representing the scale factor</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span style="font-family:宋体;">ρ</span><span></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>Signal to noise ratio(Abbreviated to SNR)</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span style="font-family:宋体;">I</span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The molecule number of formed intact HRP
 +
  proteins </span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span style="font-family:宋体;">I<sub>1</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The molecule number of formed intact HRP
 +
  proteins in the solution</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span style="font-family:宋体;">I<sub>2</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<a name="OLE_LINK43"></a><span>The molecule number
 +
  of formed intact HRP proteins through binding with stem-loop structure</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span style="font-family:宋体;">t</span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>Reaction time</span>
 +
</p>
 +
</td>
 +
</tr>
 +
<tr>
 +
<td width="66" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<i><span style="font-family:宋体;">y<sub>2</sub></span></i>
 +
</p>
 +
</td>
 +
<td width="487" valign="top" style="border:solid windowtext 1.0pt;">
 +
<p class="MsoNormal">
 +
<span>The signal intensity (OD<sub>450</sub>)</span>
 +
</p>
 +
</td>
 +
</tr>
 +
</tbody>
 +
</table>
 +
 
 +
 
 +
 
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">  The RCA model    </span></span><hr />
 +
</h3>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Firstly, we assume that there is a linear relationship between the concentration of the initiated probes and miRNA as the combination reaction between miRNA and probe occurs spontaneously<sup>1 </sup> . This can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model1.jpg|70px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Next, RCA is an enzymatic reaction, the reaction equation is written as: iprobe+dNTP→iprobe-dN+PPi, under the premise of excessive amount of enzymes and dNTPs, the relationship between the concentration of iprobe and the initial speed of RCA can be described by the Michaelis-Menten equation. This can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model2.jpg|105px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">It is obvious that there is a linear relationship between the molecule numbers of iprobe-dN (n<sub>1 </sub>
 +
, reflects the molecule numbers of RCA product) and the initial speed of RCA reaction. Notably, under the premise of excessive amount of enzymes, the extending of each RCA production is related to the reaction time, not the concentration of the iprobe. It is a linear relationship when we assume that the enzymatic activity remains unchanged with time, thus, the number of stem-loop structures (n<sub>2 </sub>
 +
) in each RCA product is stable under the premise of a certain reaction time.  </span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--modelfig1.jpg|500px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--图注-->
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure 1. Schematic diagram</span></b>
 +
</p>
 +
 
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">This can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model3.jpg|70px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model4.jpg|70px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">And then, SYBR Green binds to DNA. The
 +
resulting DNA-dye-complex absorbs blue light (<i>λ<sub>max</sub></i> = 497nm) and emits green light (<i>λ<sub>max</sub></i> = 520nm). Thus, there is
 +
a linear relationship between the total amount of stem-loop structures and the fluorescence
 +
intensity of DNA-dye-complex. This can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model5.jpg|70px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">In summary, the relationship between the concentration of miRNA and the fluorescence intensity of DNA-dye-complex can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model6.jpg|280px|center]]
 +
<html>
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</br>
 +
 
 +
 
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">  The signal detection model    </span></span><hr />
 +
</h3>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Firstly, it is obvious that there is a linear relationship between the molecule number of formed intact HRP proteins in the solution (consider as NOISE) and the molecule number of the fusion proteins in the solution. This can be written as:</span>
 +
</p>
 +
</br>
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 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model7.jpg|70px|center]]
 +
<html>
 +
</br>
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 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Next, we build a probability model to find the expression of the molecule number of formed intact HRP proteins (fused with dCas9) through binding with stem-loop structure (consider as SIGNAL). It is related to the total amount of stem-loop structures and the molecule number of DNA-bound fusion proteins. We obtain the result by Monte Carlo method.  </span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
 
 +
 
 +
<!--图和图注-->
 +
</br>
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</html>
 +
[[File:T--NUDT_CHINA--modelfig2.jpg|700px|center]]
 +
<html>
 +
</br>
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure2. Frequency Distribution Plot of frequency distribution of the molecule number of formed intact HRP proteins through binding with stem-loop structure. </span></b>
 +
 
 +
</br>
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 +
 
 +
<!--图和图注-->
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</br>
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</html>
 +
[[File:T--NUDT_CHINA--modelfig3.jpg|700px|center]]
 +
<html>
 +
</br>
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure 3. The result of the probability model Plot of the expect value of the molecule number of formed intact proteins against the total amount of stem-loop structures, carried out at 0.1, 0.3, 0.5, 0.7, 0.9 of N<sub>2</sub> to n ratio.</span></b>
 +
</p>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The result can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model8.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">As for <i>N<sub>2</sub></i>,
 +
which refers to the molecule number of the fusion proteins binding with
 +
stem-loop structure. The equation is formulated based on the limiting case. The
 +
equation can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model9.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">And then, we can obtain the expressions for <i>ρ</i></span> <span>and<i> I</i> separately.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model10.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model11.jpg|70px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Notably, under the premise of excessive substrates,
 +
it is a linear relationship between the reaction rate and the concentration of
 +
enzymes when we assume that the enzymatic activity remain unchanged with time,
 +
thus, we can obtain the expression of the signal intensity at <i>t<sub>th</sub> </i>time-step. This is
 +
written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model12.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">In summary, the relationship between the number of stem-loop structures and SNR under the premise of adding a certain amount of the fusion proteins can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model13.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The relationship between the number of Stem-loop structures and the signal intensity under the premise of adding a certain amount of the fusion proteins can be written as:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model14.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">  The calculation of the constants    </span></span><hr />
 +
</h3>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">To simplify the equation (1), the constants
 +
can be integrated. As can be seen from the above table, <i>k<sub>1</sub></i>, <i>k<sub>2</sub></i>, <i>k<sub>3</sub></i><sub> </sub>are
 +
constants representing the scale factor, <i>K<sub>m</sub></i> and <i>V<sub>max</sub></i> are
 +
characteristic constants of phi 29 DNA polymerase, and <i>n<sub>2</sub></i>, which refers to the number of stem-loop structures
 +
in each RCA product, is stable under the premise of a certain reaction time.
 +
Thus, define two constants, mark as <i>a</i> and <i>b</i>, and then the equation can be
 +
simplified as:</span>
 +
</p>
 +
</br>
 +
 
 +
<!--插入图片-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--model15.jpg|140px|center]]
 +
<html>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">We use this equation to fit the data points obtained through experiments. (Figure …in the ….page) The fitting curve is shown below.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--图和图注-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--modelfig4.jpg|700px|center]]
 +
<html>
 +
</br>
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure 4. Fitting curve Fitting curve of fluorescence intensity of DNA-dye-complex (RFU) against the concentrations of miRNA (pM).</span></b>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">With regard to the equation (2), we set the parameters based on the experiments as follows:
 +
<i>k<sub>3</sub> </i>=8.35*10<sup>-16 </sup>(<i>n</i>=<i>y<sub>1</sub></i>/<i>k<sub>3</sub></i>); <i>k<sub>4</sub></i> =0.038;<i> k<sub>5</sub>t</i>=5.9*10<sup>-12</sup>.
 +
</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--标题-->
 +
<h3>
 +
<span><span style="color:#7f1015">  Results and Analysis    </span></span><hr />
 +
</h3>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">By integrating the two models, we can obtain the relationships between SNR, the signal intensity respectively and the concentration of miRNA under different addition amount of fusion proteins.
 +
</span>
 +
</p>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The results are shown below.</span>  
 +
</p>
 +
</br>
 +
 
 +
<!--图和图注-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--modelfig5.jpg|700px|center]]
 +
<html>
 +
</br>
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure
 +
5. The signal intensity (OD<sub>450</sub>) Three-dimensional map of signal intensity (OD<sub>450</sub>)
 +
against miRNA concentration(pM) and additional amount of fusion proteins.</span></b>
 +
</p>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">There exists a monotonous relation between the concentration of miRNA and the signal intensity when the value of the molecule number of the fusion proteins is relatively large. While the relationship does not hold when the value of the molecule number of the fusion proteins is relatively small. And the signal intensity increases as the value of the molecule number of the fusion proteins increases.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The trend of the signal intensity with the change of the concentration of miRNA is consistent with that we obtained in our wet-lab work.(…….. in the result page)</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--图和图注-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--modelfig6.jpg|700px|center]]
 +
<html>
 +
</br>
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure 6. The result of signal to noise ratio Three-dimensional map of signal to noise ratio against miRNA concentration (pM) and additional amount of fusion proteins.</span></b>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The signal-to-noise ratio decreases as the value of the molecule number of fusion proteins increases. </span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Furthermore, we consider that it is conducive to signal detection when the values of signal intensity and signal to noise ratio are both greater than two. We obtain the ideal region through calculation, which is shown as below.  </span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
 +
<!--图和图注-->
 +
</br>
 +
</html>
 +
[[File:T--NUDT_CHINA--modelfig7.jpg|700px|center]]
 +
<html>
 +
</br>
 +
<p>
 +
<b><span style="line-height:2;font-family:Perpetua;font-size:18px;">Figure 7. Ideal region  Region of qualified logarithm of concentrations of miRNA (pM) and logarithm of the additional amount of fusion proteins.</span></b>
 +
</p>
 +
 
 +
</br>
 +
 
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">When the value of N is set to 1013.3, the range of the value of x contained in the ideal region is the largest, which means when the value of the molecule number of fusion proteins is 1013.3, the concentration range of miRNA contained in the ideal region is the largest.  </span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--标题-->
 +
<h2>
 +
<span><span style="color:#7f1015">Conclusion </span></span><hr />
 +
</h2>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Based on our simulation, we came to the conclusion that:</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The calculated trend of the signal intensity with the change of the concentration of miRNA from our model is consistent with the trend we obtained in our laboratory work.</span>
 +
</p>
 +
</br>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The value of the molecule number of fusion protein of dCas9 and split-HRP fragments not only affects the signal-to-noise ratio, but also the signal intensity. So we need to weigh its impact on both to select the optimal solution.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">The concentration range of miRNA contained in the ideal region is the largest when we set the value of the molecule number of fusion proteins to be 1013.3, we optimize the value of the addition amount of fusion proteins in our wet-lab work based on it.</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
<!--标题-->
 +
<h2>
 +
<span><span style="color:#7f1015">Reference  </span></span><hr />
 +
</h2>
 +
 
 +
<!--正文-->
 +
<p style="text-indent:22pt;">
 +
<span style="line-height:2;font-family:Perpetua;font-size:18px;">1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Deng, R. <i>et al</i>. Toehold-initiated rolling circle
 +
amplification for visualizing individual microRNAs in situ in single cells. <i>Angew Chem Int Ed Engl </i>53, 2389-2393,
 +
doi:10.1002/anie.201309388 (2014).</span>
 +
</p>
 +
</br>
 +
 
 +
 
 +
 
  
  

Revision as of 01:18, 17 October 2016

NUDT_CHINA 2016