Team:HZAU-China/Modeling/Gray logistic

From 2013.igem.org

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<h3>Using the gray system theory to determine the parameters:</h3>
<h3>Using the gray system theory to determine the parameters:</h3>
<p style="font-size:16px;font-family:arial, sans-serif;">To determine the parameters of the equation,we use the gray system theory.The equation can be rewritten:<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/0/09/4.png"></a>;<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/8/82/5.png"></a>;<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/f/f1/6.png"></a>;</p>
<p style="font-size:16px;font-family:arial, sans-serif;">To determine the parameters of the equation,we use the gray system theory.The equation can be rewritten:<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/0/09/4.png"></a>;<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/8/82/5.png"></a>;<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/f/f1/6.png"></a>;</p>
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<p style="font-size:16px;font-family:arial, sans-serif;">段落</p>
 
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<p style="font-size:16px;font-family:arial, sans-serif;">段落</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  and  .<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/9/9e/7.png"></a>,<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/6/60/8.png">,</a><a><img width="250" src="https://static.igem.org/mediawiki/igem.org/7/7a/9.png"></a></p>
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<p style="font-size:16px;font-family:arial, sans-serif;">段落</p>
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<p style="text-align:center;"><a><img width="" src="https://static.igem.org/mediawiki/2013/f/f5/90.png" ></a></br></p>
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<p style="font-size:16px;font-family:arial, sans-serif;">From the result ,we know the value of posterior-variance is 0.1931.The posterior-variance is 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 a conclution,Our engineering bacterium growth curve is in the dog's blood is<a><img width="250" src="https://static.igem.org/mediawiki/igem.org/5/58/10.png"></a>;is the logarithm of the CFU of Bacillus subtilis.</p>
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<a><img width="250" src=""></a>
 
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Revision as of 13:10, 25 September 2013


Gray logistic


Aim:

To know the growth curve in the dog’s blood

Steps:

1.Do experiment to measure the number of bacteria;

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

3.Determine the parameter through the experiment;

4.Test the predicted results.

Results:

The gray logistic model gets the good forecasting result.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.Then we choose dilution-plate method to detect the number of total bacteria. So we coated a large number of plates.The logistic model of population can well predict the increase of population.

Establish the logistic model:

In the environment of the blood,the number of bacteria have a maximum value K.And when the number of bacteria approach K,the growth rate is next to nil.Then the population growth equation is as follows:

The solution of the equation is :

is the number of bacterial population.r is population growth rate.To make it convenient to calculate,we simplify the equation;A,B and r are unknown parameters. is the logarithm of the CFU of Bacillus subtilis.

Using the gray system theory to determine the parameters:

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

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


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

In a conclution,Our engineering bacterium growth curve is in the dog's blood is;is the logarithm of the CFU of Bacillus subtilis.