Team:HZAU-China/Modeling/Gray logistic

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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling"><span>Overview</span></a></li>
         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling"><span>Overview</span></a></li>
         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Gray logistic"><span style="font-size:19px;color=#fff;">Gray logistic</span></a></li>  
         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Gray logistic"><span style="font-size:19px;color=#fff;">Gray logistic</span></a></li>  
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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Immune responce"><span>Immune responce</span></a></li>
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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Immune responce"><span>Immune response</span></a></li>
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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Cellular automata"><span>Cellular automata</span></a></li>
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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Cellular automata"><span>Cellular automaton</span></a></li>
          
          
       </body>
       </body>
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     <p><br></p>
     <p><br></p>
      
      
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<h3>Aim:</h3>
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<h3><b>Aim:</b></h3>
<p style="font-size:16px;font-family:arial, sans-serif;">To know the growth curve of Bacillus subtilis in the dog’s blood.</p>
<p style="font-size:16px;font-family:arial, sans-serif;">To know the growth curve of Bacillus subtilis in the dog’s blood.</p>
-
<h3>Steps:</h3>
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<h3><b>Steps:</b></h3>
<p style="font-size:16px;font-family:arial, sans-serif;">1. Experimentally measure the number of bacteria;  </p>
<p style="font-size:16px;font-family:arial, sans-serif;">1. Experimentally measure the number of bacteria;  </p>
<p style="font-size:16px;font-family:arial, sans-serif;">2. Establish the gray logistic model to simulate the growth of bacteria;</p>
<p style="font-size:16px;font-family:arial, sans-serif;">2. Establish the gray logistic model to simulate the growth of bacteria;</p>
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<p style="font-size:16px;font-family:arial, sans-serif;">4. Test the predicted results.</p>
<p style="font-size:16px;font-family:arial, sans-serif;">4. Test the predicted results.</p>
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<h3>Results:</h3>
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<h3><b>Results:</b></h3>
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<p style="font-size:16px;font-family:arial, sans-serif;">The gray logistic model gets the good forecasting result.And the model precision is excellent.</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">The gray logistic model gives good prediction and the model precision is excellent.</p>
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<h3>Background:</h3>
+
<h3><b>Background:</b></h3>
-
<p style="font-size:16px;font-family:arial, sans-serif;">The color of blood is so deep that it is not fit to measure the OD value to determine the growth of bacteria in the blood. So we chose  dilution-plate method to detect the number of total bacteria. We coated a large number of plates. If you want to know the details of the experiment,please click <a href="https://static.igem.org/mediawiki/2013/5/50/The_procedure_of_dilution_plating_%28edited%29.pdf">here</a>. The logistic model of population can well predict the increase of population.</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">The color of blood is so deep that it is not fit to measure the OD value to determine the growth of bacteria in the blood. So we chose  dilution-plate method to detect the number of total bacteria. We coated a large number of plates. If you want to know the details of the experiment, please click <a href="https://static.igem.org/mediawiki/2013/5/50/The_procedure_of_dilution_plating_%28edited%29.pdf"><font color=#00ff00><u>here</u></font></a>. The logistic model of population can well predict the increase of population.</p>
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<h3>Establishing the logistic model:</h3>
+
<h3><b>Establishing the logistic model:</b></h3>
<p style="font-size:16px;font-family:arial, sans-serif;">In the blood environment, the number of bacteria has a maximum value <i>K</i>. When the bacteria number approaches <i>K</i>, the growth rate approaches zero. Then the population growth equation is as follows: </p>
<p style="font-size:16px;font-family:arial, sans-serif;">In the blood environment, the number of bacteria has a maximum value <i>K</i>. When the bacteria number approaches <i>K</i>, the growth rate approaches zero. Then the population growth equation is as follows: </p>
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<center><a><img width="250" src="https://static.igem.org/mediawiki/2013/9/9d/10000000.png"></a></center>
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<center><a><img width="250" src="https://static.igem.org/mediawiki/2013/9/9d/10000000.png"></a>.</center></p>
 +
 
 +
<p style="font-size:16px;font-family:arial, sans-serif;">The solution of the equation is :<a><img width="250" src="https://static.igem.org/mediawiki/2013/4/4c/2000000000.png"></a>,</center></p>
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<p style="font-size:16px;font-family:arial, sans-serif;">The solution of the equation is :<a><img width="250" src="https://static.igem.org/mediawiki/2013/4/4c/2000000000.png"></a></p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">where <i>N<sub>0</sub></i> is the size of bacterial population and <i>r</i> is population growth rate. For convenience, we rewrite the above equation as<a><img width="150" src="https://static.igem.org/mediawiki/2013/0/0d/G_shi3.png"></a>  where <i>A=K</i>,  <a><img width="100" src="https://static.igem.org/mediawiki/2013/7/7d/Gongshi5.png"></a>and <i>r</i> is unknown parameter. <i>N</i> is the logarithm of the colony-forming unit (CFU) of <i>Bacillus subtilis</i>.</p>
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<p style="font-size:16px;font-family:arial, sans-serif;">where <i>N0</i> is the size of bacterial population and <i>r</i>, we rewrite the above equation as<a><img width="250" src="https://static.igem.org/mediawiki/2013/0/0d/G_shi3.png"></a>where <i>A=K</i>,<a><img width="250" src="https://static.igem.org/mediawiki/2013/7/7d/Gongshi5.png"></a>and <i>r</i> are unknown parameters. is the logarithm of the colony-forming unit of <i>Bacillus subtilis</i>.</p>
+
<h3><b>Determining the parameters using the gray system theory:</b></h3>
 +
<p style="font-size:16px;font-family:arial, sans-serif;">To determine the parameters of the equation,we used the gray system theory. The equation can be rewritten as: </p>
-
<h3>Determining the parameters using the gray system theory:</h3>
+
<p style="font-size:16px;font-family:arial, sans-serif;"><center><a><img width="240" src="https://static.igem.org/mediawiki/2013/5/5e/G_shi6.png"></a>,</center></p>
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<p style="font-size:16px;font-family:arial, sans-serif;">To determine the parameters of the equation,we used the gray system theory. The equation can be rewritten as:</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;"><center><a><img width="200" src="https://static.igem.org/mediawiki/2013/2/26/G_shi7.png"></a>,</center></p>
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<p style="font-size:16px;font-family:arial, sans-serif;"><a><img width="240" src="https://static.igem.org/mediawiki/2013/5/5e/G_shi6.png"></a>,</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;"><center><a><img width="240" src="https://static.igem.org/mediawiki/2013/5/51/G_shi8.png"></a>;</center></p>
-
<p style="font-size:16px;font-family:arial, sans-serif;"><a><img width="240" src="https://static.igem.org/mediawiki/2013/2/26/G_shi7.png"></a>,</p>
+
-
<p style="font-size:16px;font-family:arial, sans-serif;"><a><img width="240" src="https://static.igem.org/mediawiki/2013/5/51/G_shi8.png"></a>;</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">Using the matrix equation in linear algebra we could determine the parameters α and β .</p>
<p style="font-size:16px;font-family:arial, sans-serif;">Using the matrix equation in linear algebra we could determine the parameters α and β .</p>
-
<p style="font-size:16px;font-family:arial, sans-serif;"><a><img width="200" src="https://static.igem.org/mediawiki/2013/6/6c/G_shi9.png"></a>,<a><img width="250" src="https://static.igem.org/mediawiki/2013/a/a1/G_shi10.png">,</a><a><img width="250" src="https://static.igem.org/mediawiki/2013/d/dc/Gongshi_12.png"></a></p>
+
<p style="font-size:16px;font-family:arial, sans-serif;"><a><img width="160" src="https://static.igem.org/mediawiki/2013/6/6c/G_shi9.png"></a>,<a><img width="250" src="https://static.igem.org/mediawiki/2013/a/a1/G_shi10.png"></a>,<a><img width="250" src="https://static.igem.org/mediawiki/2013/d/dc/Gongshi_12.png"></a></p>
-
<p  style="text-align:center;"><a><img width="600" src="https://static.igem.org/mediawiki/2013/f/f5/90.png" ></a></br></p>
+
<p  style="text-align:center;"><a><img width="600" src="https://static.igem.org/mediawiki/2013/3/37/Pic.png" ></a></br></p>
 +
<p  style="text-align:center;"><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Gray logistic"><img width="500" src="https://static.igem.org/mediawiki/2013/1/1d/Gray.png" ></a></br></p>
<p style="font-size:16px;font-family:arial, sans-serif;">From the results, we know the value of posterior-variance is 0.1931, lower than 0.35, so that the model precision is excellent.</p>
<p style="font-size:16px;font-family:arial, sans-serif;">From the results, we know the value of posterior-variance is 0.1931, lower than 0.35, so that the model precision is excellent.</p>
-
<p style="font-size:16px;font-family:arial, sans-serif;">In conclution, the growth curve of our engineered bacterium in dog's blood is given by<a><img width="300" src="https://static.igem.org/mediawiki/2013/c/ce/G_shi12.png"></a>;where <i>N(t)</i> is the logarithm of the CFU of <i>Bacillus subtilis</i>.</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">In conclution, the growth curve of our engineered bacterium in dog's blood is given by<a><img width="300" src="https://static.igem.org/mediawiki/2013/c/ce/G_shi12.png"></a> where <i>N(t)</i> is the logarithm of the CFU of <i>Bacillus subtilis</i>.</p>
-
<h3>Reference:</h3>
+
<h3><b>Reference:</b></h3>
-
<p style="font-size:16px;font-family:arial, sans-serif;">1.Shiqiang Zhang, China's Population Growth Model Based on Grey System Theory and Logisitic Model[C]. 2010:4.</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">1.Shiqiang Zhang, China's Population Growth Model Based on Grey System Theory and Logisitic Model[C]. 2010:4. (In Chinese)</p>
-
<p style="font-size:16px;font-family:arial, sans-serif;">2.Xiaoyin Wang, Baoping Zhou 2010. Mathematical modeling and mathematical experiment. Beijing : Science press.</p>
+
<p style="font-size:16px;font-family:arial, sans-serif;">2.Xiaoyin Wang, Baoping Zhou 2010. Mathematical modeling and mathematical experiment. Beijing : Science press. (In Chinese)</p>
     </div>
     </div>

Latest revision as of 03:51, 28 September 2013


Gray logistic


Aim:

To know the growth curve of Bacillus subtilis in the dog’s blood.

Steps:

1. Experimentally measure the number of bacteria;

2. Establish the gray logistic model to simulate the growth of bacteria;

3. Determine the parameters through experiments;

4. Test the predicted results.

Results:

The gray logistic model gives good prediction and the model precision is excellent.

Background:

The color of blood is so deep that it is not fit to measure the OD value to determine the growth of bacteria in the blood. So we chose dilution-plate method to detect the number of total bacteria. We coated a large number of plates. If you want to know the details of the experiment, please click here. The logistic model of population can well predict the increase of population.

Establishing the logistic model:

In the blood environment, the number of bacteria has a maximum value K. When the bacteria number approaches K, the growth rate approaches zero. Then the population growth equation is as follows:

.

The solution of the equation is :,

where N0 is the size of bacterial population and r is population growth rate. For convenience, we rewrite the above equation as where A=K, and r is unknown parameter. N is the logarithm of the colony-forming unit (CFU) of Bacillus subtilis.

Determining the parameters using the gray system theory:

To determine the parameters of the equation,we used the gray system theory. The equation can be rewritten as:

,

,

;

Using the matrix equation in linear algebra we could determine the parameters α and β .

,,



From the results, we know the value of posterior-variance is 0.1931, lower than 0.35, so that the model precision is excellent.

In conclution, the growth curve of our engineered bacterium in dog's blood is given by where N(t) is the logarithm of the CFU of Bacillus subtilis.

Reference:

1.Shiqiang Zhang, China's Population Growth Model Based on Grey System Theory and Logisitic Model[C]. 2010:4. (In Chinese)

2.Xiaoyin Wang, Baoping Zhou 2010. Mathematical modeling and mathematical experiment. Beijing : Science press. (In Chinese)