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model

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{% extends "layout.html" %}
{% block title %}Model{% endblock %}
{% block title %}Modeling{% endblock %}
{% block page_content %}
......@@ -9,11 +9,180 @@
<div class="page">
<div class="container">
<div class="article">
<h1 class="content-header2">Model</h1>
<h1 class="content-header2">Modeling</h1>
<section>
<h2></h2>
<p></p>
<p>
In this section, numerical model was applied to investigate the rapamycin production ability of two types of
<i>Streptomyces rapamycin</i>, including wild-type and double-knockout <i>Streptomyces rapamycin</i>. Table 1
presents the
experimental data of the rapamycin producing ability of these two <i>Streptomyces rapamycin</i> species over
time.
</p>
<div class="table-container m-t-2">
<span class="figure rw-75">
Table 1. Rapamycin producing ability of the wild-type (NRRL 5491) and double-knockout
(ΔM271_14685/M271_14690) <i>Streptomyces rapamycin</i>.
</span>
<table class="rw-50 mx-auto text-center">
<tbody>
<tr>
<th>Time (day)</th>
<th>NRRL 5491</th>
<th>ΔM271_14685/M271_14690</th>
</tr>
<tr>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>5</td>
<td>45.5965146</td>
<td>82.57416684</td>
</tr>
<tr>
<td>7</td>
<td>54.28979251</td>
<td>116.8113409</td>
</tr>
<tr>
<td>9</td>
<td>49.71953386</td>
<td>121.6081859</td>
</tr>
<tr>
<td>11</td>
<td>20.71710012</td>
<td>58.60825695</td>
</tr>
</tbody>
</table>
</div>
<br>
<p>
Considering the changing trend of the experimental data and the fact that the simulation results must be
positive in the definition domain (0&lt;time≤11), we choose the following model for simulation:
</p>
<p class="text-center rw-75 mx-auto m-t-2 m-b-2">
<span class="fs-5">
<i>f</i> (<i>x</i>) = <i>p<sub>1</sub></i> ∙ <i>x<sup>4</sup></i> + <i>p<sub>2</sub></i>
∙<i>x<sup>3</sup></i> + <i>p<sub>3</sub></i> ∙ <i>x<sup>2</sup></i> + <i>p<sub>4</sub></i> ∙ <i>x</i> + <i>p<sub>5</sub></i>
</span>
<span style="float: right">(1)</span>
</p>
<p>
Where <i>p<sub>1</sub></i>, <i>p<sub>2</sub></i>, <i>p<sub>3</sub></i>, <i>p<sub>4</sub></i> and
<i>p<sub>5</sub></i> are the parameters need to be fitted.
</p>
</section>
<section>
<br>
<h2 class="hs-4"><b>Coding</b></h2>
<p>The Matlab program code is shown below:</p>
<pre class="m-t-1" style="font-size: .95rem">
clear;clc;
% exp. data
Data=importdata('data.txt')
time=Data(:,1);
NRRL=Data(:,2);
M=Data(:,3);
% model simulation
p1=[-0.01129 -0.0346];
p2=[0.1287 0.3082];
p3=[-0.9952 0.16];
p4=[12.29 12.34];
p5=[3.035e-14 2.083e-14];
x=0:0.1:12;x=x';
y1=p1(1)*x.^4 + p2(1)*x.^3 + p3(1)*x.^2 + p4(1)*x+ p5(1);
y2=p1(2)*x.^4 + p2(2)*x.^3 + p3(2)*x.^2 + p4(2)*x+ p5(2);
% figures
figure, plot(time,NRRL,'o')
hold on, plot(x,y1,'-')
%
figure, plot(time,M,'s')
hold on, plot(x,y2,'-')
</pre>
</section>
<section>
<h2 class="hs-4"><b>Model Results:</b></h2>
<section>
<h3 class="hs-5 upper">1. NRRL 5491</h3>
<div class="imager">
<img class="rw-50" src="https://static.igem.wiki/teams/4281/wiki/modeling/t-ecnuas-modeling-01.jpg" alt="">
<span class="figure rw-65">
Figure 1. Comparison between simulation results and experimental data of wild-type <i>Streptomyces
rapamycin</i>.
</span>
</div>
<p>Coefficients:</p>
<p class="rw-85 mx-auto m-t-2 m-b-2">
p1 = -0.01129 <br>
p2 = 0.1287 <br>
p3 = -0.9952 <br>
p4 = 12.29 <br>
p5 = 3.035e-14
</p>
<p>Goodness of fit:</p>
<p class="rw-85 mx-auto m-t-2 m-b-2">
SSE: 2.89e-27 <br>
R-square: 1 <br>
Adjusted R-square: NaN <br>
RMSE: NaN
</p>
</section>
<section>
<h3 class="hs-5">2. M271_14685/M271_14690</h3>
<div class="imager">
<img class="rw-50" src="https://static.igem.wiki/teams/4281/wiki/modeling/t-ecnuas-modeling-02.jpg" alt="">
<span class="figure rw-65">
Figure 2. Comparison between simulation results and experimental data of double-knockout <i>Streptomyces
rapamycin</i>.
</span>
</div>
<p>Coefficients:</p>
<p class="rw-85 mx-auto m-t-2 m-b-2">
p1 = -0.0346 <br>
p2 = 0.3082 <br>
p3 = 0.16 <br>
p4 = 12.34 <br>
p5 = 2.083e-14
</p>
<p>Goodness of fit:</p>
<p class="rw-85 mx-auto m-t-2 m-b-2">
SSE: 4.725e-27 <br>
R-square: 1 <br>
Adjusted R-square: NaN <br>
RMSE: NaN
</p>
</section>
</section>
<section>
<h2 class="hs-4"><b>Conclusion</b></h2>
<p>
The model (1) can accurately simulate the variation of the experimental data with high R-square. According to
the model simulation results, we predicted the maximum value and corresponding time of rapamycin production
ability by these two Streptomyces. As shown in Figure 1 and 2, the wild-type <i>Streptomyces rapamycin</i>
will reach
peak on yield rapamycin of 7.5 day; In contrast, the double-knockout <i>Streptomyces rapamycin</i> will reach
peak on
yield rapamycin of 8.3 day.
</p>
</section>
</div>
......
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