Difference between revisions of "Team:Nankai/Modeling"

 
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<p id="place">Your place:&nbsp;<a href="https://2015.igem.org/Team:Nankai">Home</a>&nbsp;&gt;&nbsp;<a href="https://2015.igem.org/Team:Nankai/Modeling">Modeling</a></p>
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<section class="headsection">
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      <h2>3 facts you should know about Project 84</h2>
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<h3>3 models are used to measure our project.</h3>
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      <div class="box_1"> <img src="https://static.igem.org/mediawiki/2015/5/52/Nankai_Model_1_img.png" class="img_1" alt=""  />
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</section>
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<section class="normalsection">
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          <h6>Quick insertion</h6>
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      <div class="box_1">
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          <h5>It just takes 1 hour to improve your life</h5>
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         <img src="https://static.igem.org/mediawiki/2015/5/52/Nankai_Model_1_img.png" class="img0">
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          <p>Come down to our clinic today and we will insert your new favourite toy into your brain and eye within just 1 hour and guaranteed life-long happiness will be yours.</p>
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       <div class="title">
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          <a href="#"></a> </div>
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          <h3>Bacteria scale</h3>
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         <img src="https://static.igem.org/mediawiki/2015/d/db/Nankai_Model_Box_1.png" alt="" class="main_img_1" /> </div>
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          <h5>We use logistic equation to fit the mono-restrict factor growth of bacteria, and the bacteria scale itself is the factor.<a href="https://2015.igem.org/Team:Nankai/Modeling/Bacteria" target="_blank"><img src="https://static.igem.org/mediawiki/2015/c/cd/Nankai_Model_More_info.png"></a></h5>
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       <div class="box_2"> <img src="https://static.igem.org/mediawiki/2015/9/94/Nankai_Model_Box_2.png" alt="" class="main_img_2" /> <img src="https://static.igem.org/mediawiki/2015/a/a7/Nankai_Model_2_img.png" alt="" class="img_2" />
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           <h4>dX/dt=Vmax*(1-X/Xmax)*X</h4>
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        <div class="text_2">
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          <h6>Just think it</h6>
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          <h5>Whatever you want to happen, happens</h5>
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           <p>Want to tweet that you were standing in line for ice cream and  then accidentally farted in the boy's face behind you? All you have to do is think it! Our tech's so fast sometimes it posts before you even think it!</p>
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       </div>
 
       </div>
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<p>In this equation, ‘X’ means the bacteria scale, it’s the function of‘t’, time. 'Vmax' represents the possible max relative growth speed of the bacteria . 'Xmax' is the upper limit of the growth. In this function, we can find out that the instantaneous growth speed is determined by the relative growth speed, upper limit of the growth, and the instantaneous scale. With time passing by, the scale grows larger, while the speed turns down.
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          <h6>Fewer &amp; fewer incidents</h6>
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</p>
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          <h5>We take all the necessary precautions</h5>
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<div class="firstpic">
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          <p>We are hard at work to bring safer methods of implementing chips into the brains of users. Over the past 4 months we have decreased the amount of incidents so you have almost nothing to fear!</p>
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         <img src="https://static.igem.org/mediawiki/2015/c/c6/Nankai_modchar1.png">
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          <a href="#"></a> </div>
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         <img src="https://static.igem.org/mediawiki/2015/1/1f/Nankai_Model_Box_3.png" alt="" class="main_img_3" /> </div>
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<div class="secondpic">
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        <img src="https://static.igem.org/mediawiki/2015/b/b2/Nankai_modpic1.jpg">
 +
<h6>Fig.1 The fitting curve of the growth of bacteria cells.</h6>
 +
<p>1. Fit Results:</br>
 +
(1)General model:</br>
 +
f(x) = X/(exp(-X*(C3 + V*x)) + 1)</br>
 +
(2)Coefficients (with 95% confidence bounds):</br>
 +
C3 = -1.248 (-1.962, -0.5334)</br>
 +
V = 0.07547 (0.02994, 0.121)</br>
 +
X = 3.055 (2.717, 3.393)</p>
 +
 +
<p class="gap">2. Goodness of fit:</br>
 +
SSE: 1.99</br>
 +
R-square: 0.9164</br>
 +
Adjusted R-square: 0.9045</br>
 +
RMSE: 0.3771</p>
 +
</div>
 +
<p class="downtext">As the foundation of our modeling, the logistic model fits quite well with our data. It takes about 30 hours for the bacteria to reach the upper limit. According to the growth law, we can say that the highest growth speed is around 15h, when the scale is half of the maximum.</p>
 +
      </div>
 +
 +
</div>
 +
 +
<div class="box_2">
 +
        <img src="https://static.igem.org/mediawiki/2015/a/a7/Nankai_Model_2_img.png" class="img0">
 +
      <div class="title">
 +
          <h3>Product scale</h3>
 +
          <h5>We assume that our product comes from two parts, one is during the growth, and the other is through their livelihood.<a href="https://2015.igem.org/Team:Nankai/Modeling/Product" target="_blank"><img src="https://static.igem.org/mediawiki/2015/c/cd/Nankai_Model_More_info.png"></a></h5>
 +
          <h4>dP/dt=α*dX/dt+β*X</h4>
 +
      </div>
 +
      <div class="text">
 +
<p>In this equation, ‘X’ and ‘t’ are the bacteria scale and time. ‘P’ means the product. We can see the familiar ‘X’ and ‘t’, that is how we base the production on the bacteria growth. 'α' and 'β' indicates the proportion of the two processes. With these parameters, we can find out when is the most important part of time in the whole fermentation process. This is quite useful, because we can decide the length of fermentation and decide the timing to do some changes.
 +
</p>
 +
<div class="firstpic">
 +
        <img src="https://static.igem.org/mediawiki/2015/f/fc/Nankai_modpic2.jpg">
 +
<h6>Fig.2 The original fitting curve of product formation</h6>
 +
<p>1. Fit Results:</br>
 +
(1)General model:</br>
 +
f(x) = C+(A*0.0255*3.055*exp(0.0754*x))/(3.055-0.0255+0.0255*exp(0.0754*x))+B*3.055/0.0754*log((3.055-0.0255+0.0255*exp(0.0754*x))/3.055)</br>
 +
(2)Coefficients (with 95% confidence bounds):</br>
 +
      A = 8392 (4254, 1.253e+04)</br>
 +
      B = -588.1 (-885.2, -291)</br>
 +
      C = -201.6 (-312.1, -91.16)</p>
 +
 +
<p class="gap">2. Goodness of fit:</br>
 +
  SSE: 344.8</br>
 +
  R-square: 0.9165</br>
 +
  Adjusted R-square: 0.898</br>
 +
  RMSE: 6.19</p>
 +
</div>
 +
<div class="secondpic">
 +
        <img src="https://static.igem.org/mediawiki/2015/9/97/Nankai_modchar2.png">
 +
</div>
 +
<p class="downtext">Although this can reach a better R-square, our parameter β meet a negative number which should not happen. However, it can show that the product is mainly synthesized from the first part. Then we fit the data again with only the first part of our equation.</p>
 +
      </div>
 +
</div>
 +
 +
<div class="box_1">
 +
        <img src="https://static.igem.org/mediawiki/2015/9/99/Nankai_Model_3_img.png" class="img0">
 +
      <div class="title">
 +
          <h3>Substrate scale</h3>
 +
          <h5>Bacteria use the provided carbon source to propagate, maintain their livelihood and synthesize the product.<a href="https://2015.igem.org/Team:Nankai/Modeling/Substrate" target="_blank"><img src="https://static.igem.org/mediawiki/2015/c/cd/Nankai_Model_More_info.png"></a></h5>
 +
          <h4>dS/dt=-γ*dX/dt-δ*X-ε*dP/dt</h4>
 +
      </div>
 +
      <div class="text">
 +
<p>
 +
In this equation, 'S' is the substrate, 'γ', 'δ',and  'ε' are the ratio of the three outlets. Our genetic operation is aimed to make the bacteria put more energy into the product. In a way, these parameters can show whether our strategies are effective or not.
 +
</p>
 +
<div class="firstpic">
 +
<img src="https://static.igem.org/mediawiki/2015/3/33/Nankai_modchar3.png">
 +
</div>
 +
<div class="secondpic">
 +
<img src="https://static.igem.org/mediawiki/2015/2/25/Nankai_modpic3.jpg">
 +
<h6>Fig.3 The altered fitting curve of product formation</h6>
 +
<p>1. Fit Results:</br>
 +
(1)General model:</br>
 +
f(x) = C+(A*0.0255*3.055*exp(0.0754*x))/(3.055-0.0255+0.0255*exp(0.0754*x))</br>
 +
(2)Coefficients (with 95% confidence bounds):</br>
 +
A = 204 (115.1, 292.9)</br>
 +
C = 16.45 (4.215, 28.68)</p>
 +
<p class="gap">
 +
2. Goodness of fit:</br>
 +
SSE: 344.8</br>
 +
R-square: 0.9165</br>
 +
Adjusted R-square: 0.898</br>
 +
RMSE: 6.19</p>
 +
</div>
 +
<p class="downtext">This one loses some goodness of fit, but the data is reasonable. Anyway, it shows that our product mainly comes from the growth process.</p>
 +
      </div>
 +
</div>
 +
</section>
 
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{{Nankai}}
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{{Nankaifoot}}

Latest revision as of 23:09, 18 September 2015

Medigo Blue, free responsive template

Modeling

Your place: Home > Modeling

3 models are used to measure our project.

Bacteria scale

We use logistic equation to fit the mono-restrict factor growth of bacteria, and the bacteria scale itself is the factor.

dX/dt=Vmax*(1-X/Xmax)*X

In this equation, ‘X’ means the bacteria scale, it’s the function of‘t’, time. 'Vmax' represents the possible max relative growth speed of the bacteria . 'Xmax' is the upper limit of the growth. In this function, we can find out that the instantaneous growth speed is determined by the relative growth speed, upper limit of the growth, and the instantaneous scale. With time passing by, the scale grows larger, while the speed turns down.

Fig.1 The fitting curve of the growth of bacteria cells.

1. Fit Results:
(1)General model:
f(x) = X/(exp(-X*(C3 + V*x)) + 1)
(2)Coefficients (with 95% confidence bounds):
C3 = -1.248 (-1.962, -0.5334)
V = 0.07547 (0.02994, 0.121)
X = 3.055 (2.717, 3.393)

2. Goodness of fit:
SSE: 1.99
R-square: 0.9164
Adjusted R-square: 0.9045
RMSE: 0.3771

As the foundation of our modeling, the logistic model fits quite well with our data. It takes about 30 hours for the bacteria to reach the upper limit. According to the growth law, we can say that the highest growth speed is around 15h, when the scale is half of the maximum.

Product scale

We assume that our product comes from two parts, one is during the growth, and the other is through their livelihood.

dP/dt=α*dX/dt+β*X

In this equation, ‘X’ and ‘t’ are the bacteria scale and time. ‘P’ means the product. We can see the familiar ‘X’ and ‘t’, that is how we base the production on the bacteria growth. 'α' and 'β' indicates the proportion of the two processes. With these parameters, we can find out when is the most important part of time in the whole fermentation process. This is quite useful, because we can decide the length of fermentation and decide the timing to do some changes.

Fig.2 The original fitting curve of product formation

1. Fit Results:
(1)General model:
f(x) = C+(A*0.0255*3.055*exp(0.0754*x))/(3.055-0.0255+0.0255*exp(0.0754*x))+B*3.055/0.0754*log((3.055-0.0255+0.0255*exp(0.0754*x))/3.055)
(2)Coefficients (with 95% confidence bounds):
A = 8392 (4254, 1.253e+04)
B = -588.1 (-885.2, -291)
C = -201.6 (-312.1, -91.16)

2. Goodness of fit:
SSE: 344.8
R-square: 0.9165
Adjusted R-square: 0.898
RMSE: 6.19

Although this can reach a better R-square, our parameter β meet a negative number which should not happen. However, it can show that the product is mainly synthesized from the first part. Then we fit the data again with only the first part of our equation.

Substrate scale

Bacteria use the provided carbon source to propagate, maintain their livelihood and synthesize the product.

dS/dt=-γ*dX/dt-δ*X-ε*dP/dt

In this equation, 'S' is the substrate, 'γ', 'δ',and 'ε' are the ratio of the three outlets. Our genetic operation is aimed to make the bacteria put more energy into the product. In a way, these parameters can show whether our strategies are effective or not.

Fig.3 The altered fitting curve of product formation

1. Fit Results:
(1)General model:
f(x) = C+(A*0.0255*3.055*exp(0.0754*x))/(3.055-0.0255+0.0255*exp(0.0754*x))
(2)Coefficients (with 95% confidence bounds):
A = 204 (115.1, 292.9)
C = 16.45 (4.215, 28.68)

2. Goodness of fit:
SSE: 344.8
R-square: 0.9165
Adjusted R-square: 0.898
RMSE: 6.19

This one loses some goodness of fit, but the data is reasonable. Anyway, it shows that our product mainly comes from the growth process.

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