Team:HZAU-China/Modeling

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         <body>
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         <ul class="menu">
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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling"><span>Overview</span></a></li>
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         <li><a href="https://2013.igem.org/Team:HZAU-China/Modeling"><span style="font-size:19px;color=#fff;">Overview</span></a></li>
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         <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/Gray logistic"><span>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>
          
          
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     <center><span style="font-size:46px;font-family:Cambria;margin-top:10px;line-height:80%">Gray logistic</span></center>
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     <center><span style="font-size:46px;font-family:Cambria;margin-top:10px;line-height:80%">Overview</span></center>
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<h3>Aim:</h3>
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<p style="font-size:16px;font-family:arial, sans-serif;"><b>Abstract</b>: In order to know how many fleas that carry our engineered strain could make the stray dogs in an area immune to the rabies virus, we developed computational models to simulate the process and to demonstrate our ideas. Our model consists of three parts: “immune response”, “gray logistic”, and “cellular automaton”. The “immune response” model is to analyze the kinetic relationship between the antigen and antibody during the immunologic processes. The “gray logistic” model is to simulate the growth curves of the <i>Bacillus subtilis</i> in the blood of dogs. The “cellular automaton” model is used to simulate the spread of our engineered bacteria in dogs.</p>
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<p style="font-size:16px;font-family:arial, sans-serif;">To know the growth curve of Bacillus subtilis in the dog’s blood.</p>
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<h3>Steps:</h3>
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<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>
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<p style="font-size:16px;font-family:arial, sans-serif;">1. Experimentally measure the number of bacteria;  </p>
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<p style="font-size:13px;font-family:arial, sans-serif;text-align:center;"><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Gray logistic">Predicted value and actual value change over time</a></p>
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<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;">3. Determine the parameters through experiments;</p>
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<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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<div id="pic00">
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<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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        <p style="text-align:center;padding-bottom:5px;"><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Immune responce" ><img width="360" src="https://static.igem.org/mediawiki/2013/3/3c/The-antibody-consentration.png" ></a></br></p>
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<h3>Background:</h3>
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        <p style="font-size:13px;font-family:arial, sans-serif;text-align:center;"><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Immune responce" >The concentrations of antibody and antigen during immune response</a></p>
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<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>
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<h3>Establishing the logistic model:</h3>
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        <p  style="text-align:center;"><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Cellular automata"><img width="250" src="https://static.igem.org/mediawiki/2013/b/b8/Cell.png" ></a></br></p>
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<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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        <p style="font-size:13px;font-family:arial, sans-serif;text-align:center;"><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Cellular automata"> The percentage of immune dogs</a></p>
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<center><a><img width="250" src="https://static.igem.org/mediawiki/2013/5/5d/Gongshi1.png"></a></center>
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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/d/d8/G_shi2.png"></a></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 r 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="110" src="https://static.igem.org/mediawiki/2013/7/7d/Gongshi5.png"></a>and <i>r</i> are unknown parameters.<i>N</i> is the logarithm of the colony-forming unit of <i>Bacillus subtilis</i>.</p>
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<h3>Determining the parameters using the gray system theory:</h3>
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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>
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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>,</br><a><img width="200" src="https://static.igem.org/mediawiki/2013/2/26/G_shi7.png"></a>,</br><a><img width="210" src="https://static.igem.org/mediawiki/2013/5/51/G_shi8.png"></a>;</p>
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<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 .<a><img width="150" 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>
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<p  style="text-align:center;"><a><img width="600" src="https://static.igem.org/mediawiki/2013/f/f5/90.png" ></a></br></p>
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<center><a href="https://2013.igem.org/Team:HZAU-China/Modeling/Gray logistic"><img width="550" src="https://static.igem.org/mediawiki/2013/1/1d/Gray.png" ></a></center>
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<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>
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<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>
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<h3>Reference:</h3>
 
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<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>
 
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<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>
 
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Latest revision as of 03:00, 28 September 2013


Overview


Abstract: In order to know how many fleas that carry our engineered strain could make the stray dogs in an area immune to the rabies virus, we developed computational models to simulate the process and to demonstrate our ideas. Our model consists of three parts: “immune response”, “gray logistic”, and “cellular automaton”. The “immune response” model is to analyze the kinetic relationship between the antigen and antibody during the immunologic processes. The “gray logistic” model is to simulate the growth curves of the Bacillus subtilis in the blood of dogs. The “cellular automaton” model is used to simulate the spread of our engineered bacteria in dogs.


Predicted value and actual value change over time


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