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

Line 333: Line 333:
 
                                   <span style="line-height:46px;" class="line">Development of A Novel</span></span>
 
                                   <span style="line-height:46px;" class="line">Development of A Novel</span></span>
 
                                 <span style="line-height:46px;" class="line-wrap">
 
                                 <span style="line-height:46px;" class="line-wrap">
                                   <span style="line-height:46px;" class="line">Blood-MicroRNA Rapid Detection System with CRISPR</span></span>
+
                                   <span style="line-height:46px;" class="line">Blood-MicroRNA Handy Detection System with CRISPR</span></span>
 
                                 <!--</a>--></h2>
 
                                 <!--</a>--></h2>
 
                             </div>
 
                             </div>
Line 354: Line 354:
 
<a style="color:rgb(10,31,84);" href="/Team:NUDT_CHINA">HomePage</a> &bull;  
 
<a style="color:rgb(10,31,84);" href="/Team:NUDT_CHINA">HomePage</a> &bull;  
 
<!-- 修改这里!! -->AWARDS &bull;  
 
<!-- 修改这里!! -->AWARDS &bull;  
<a style="color:rgb(10,31,84);" href="/Team:NUDT_CHINA/Model"><!-- 修改这里!! -->Model</a>
+
<a style="color:rgb(10,31,84);" href="/Team:NUDT_CHINA/Description"><!-- 修改这里!! -->Model</a>
 
</h5><hr style="width:40%;margin-left:60%;border-top:1px solid rgb(10,31,84);" /></div>
 
</h5><hr style="width:40%;margin-left:60%;border-top:1px solid rgb(10,31,84);" /></div>
  
Line 377: Line 377:
  
  
+
<!--在这里插入内容-->
 
+
<!--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<a
+
 
+
href="/Team:NUDT_CHINA/Design"> PROJECT.page </a>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></su
+
 
+
b
+
 
+
></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>
+
 
+
<!--正文-->
+
<p>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure 1. Schematic diagram</b></span>
+
</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|210px|center]]
+
<html>
+
</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>
+
 
+
 
+
 
+
<!--插入图片-->
+
</br>
+
</html>
+
[[File:T--NUDT_CHINA--model7.jpg|70px|center]]
+
<html>
+
</br>
+
 
+
 
+
 
+
<!--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>
+
</html>
+
[[File:T--NUDT_CHINA--modelfig2.jpg|700px|center]]
+
<html>
+
</br>
+
<p>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure2. Frequency Distribution</b> Plot of frequency
+
 
+
distribution of the molecule number of formed intact HRP proteins through
+
 
+
binding with stem-loop structure. </span>
+
 
+
</br>
+
 
+
 
+
<!--图和图注-->
+
</br>
+
</html>
+
[[File:T--NUDT_CHINA--modelfig3.jpg|700px|center]]
+
<html>
+
</br>
+
<p>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure 3. The result of the probability model</b> 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>
+
</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|70px|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|105px|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|50px|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|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 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|280px|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|105px|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 2.
+
 
+
(D) in the<a href="/Team:NUDT_CHINA/Results"> RESULTS.page. </a>) 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>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure 4. Fitting curve</b>  Fitting curve of fluorescence
+
 
+
intensity of DNA-dye-complex (RFU) against the concentrations of miRNA
+
 
+
(pM).</span>
+
</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>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure
+
5. The signal intensity (OD<sub>450</sub>)</b> Three-dimensional map of signal
+
 
+
intensity (OD<sub>450</sub>)
+
against miRNA concentration(pM) and additional 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;">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>
+
 
+
 
+
 
+
<!--图和图注-->
+
</br>
+
</html>
+
[[File:T--NUDT_CHINA--modelfig6.jpg|700px|center]]
+
<html>
+
</br>
+
<p>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure 6. The result of SNR</b>  Three-dimensional map of signal
+
 
+
to noise ratio against miRNA concentration (pM) and additional 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
+
 
+
signal-to-noise ratio decreases as the value of the molecule number of fusion
+
 
+
proteins increases. </span>
+
</p>
+
</br>
+
 
+
 
+
<!--标题-->
+
<h3>
+
<span><span style="color:#7f1015">Test of model </span></span><hr />
+
</h3>
+
 
+
<!--正文-->
+
<p style="text-indent:22pt;">
+
<span style="line-height:2;font-family:Perpetua;font-size:18px;">Our
+
 
+
model predicts the relationship between the signal intensity and the
+
 
+
concentration of miRNA under the premise of adding a certain amount of the
+
 
+
fusion proteins of dCas9 and split-HRP fragments. So we can test if our model
+
 
+
is reasonable by comparing the curves predicted by the model with those
+
 
+
obtained from the experiment. The results are shown below.</span>
+
</p>
+
</br>
+
 
+
<!--图和图注-->
+
</br>
+
</html>
+
[[File:T--NUDT_CHINA--modelfig7-1.jpg|700px|center]]
+
<html>
+
</br>
+
</br>
+
</html>
+
[[File:T--NUDT_CHINA--modelfig7-2.jpg|700px|center]]
+
<html>
+
</br>
+
<p>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure 7. Test of model</b>  (A) Plot of the signal
+
intensity (OD<sub>450</sub>) against miRNA concentration (pM) predicted by the
+
model with the value of the molecule number of the fusion proteins set to be
+
 
+
4.66e+13.
+
(B)<span> Plot of the signal
+
intensity (OD<sub>450</sub>) against miRNA concentration (pM) obtained from the
+
experiment with the value of the molecule number of the fusion proteins set to
+
be 4.66e+13. (C) Plot of the signal intensity
+
(OD<sub>450</sub>) against miRNA concentration (pM) predicted by the model with
+
the value of the molecule number of the fusion proteins set to be 4.66e+14. (D)
+
Plot of the signal intensity (OD450) against miRNA concentration (pM) obtained
+
from the experiment with the value of the molecule number of the fusion
+
proteins set to be 4.66e+14.</span>
+
</p>
+
</br>
+
 
+
<!--正文-->
+
<p style="text-indent:22pt;">
+
<span style="line-height:2;font-family:Perpetua;font-size:18px;">We can
+
 
+
learn from the figure above that the curves predicted by the model are in good
+
 
+
agreement with the experimental results.</span>
+
</p>
+
</br>
+
 
+
<!--标题-->
+
<h3>
+
<span><span style="color:#7f1015">Model extension </span></span><hr />
+
</h3>
+
 
+
<!--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 value of signal
+
 
+
intensity and SNR 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>
+
<span style="line-height:2;font-family:Perpetua;font-
+
 
+
size:18px;"><b>Figure 8. Ideal region</b>  Region of qualified logarithm of
+
 
+
concentrations of miRNA (pM) and logarithm of the additional 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;">When
+
 
+
the
+
value of <i>N</i> is set to e+13.3, the range of the value of<i> x</i>
+
 
+
contained in the ideal region is<span> maximum, which means when the value of
+
 
+
the
+
molecule number of the fusion proteins is e+13.3, the concentration range of
+
miRNA that can be detected is maximum. </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
+
 
+
curves predicted by the model are in good agreement with the experimental
+
 
+
results, thus indicating that our model is reasonable.</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 the 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
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concentration range of miRNA that can be detected is maximum when we set the
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value of the molecule number of the fusion proteins to be e+13.3, building on
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which, our wet-lab protocol could be optimized in our future work.</span>
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<h2>
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<span><span style="color:#7f1015">Reference  </span></span><hr />
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<p >
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<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>
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Revision as of 03:36, 19 October 2016

NUDT_CHINA 2016

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