Difference between revisions of "Team:Nankai/Modeling"

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          <h3>bacteria scale</h3>
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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="#"><img src="https://static.igem.org/mediawiki/2015/c/cd/Nankai_Model_More_info.png"></a></h5>
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          <h4>dX/dt=Vmax*(1-X/Xmax)*X</h4>
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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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          <h3>Product scale</h3>
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          <h5>We assume that our product comes from two parts, one is during the growth, and the other is through their livelihood.<a href="#"><img src="https://static.igem.org/mediawiki/2015/c/cd/Nankai_Model_More_info.png"></a></h5>
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          <h4>dP/dt=α*dX/dt+β*X</h4>
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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.
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       <div class="box_2"> <img src="https://static.igem.org/mediawiki/2015/1/1f/Nankai_Model_Box_3.png" alt=""  class="main_img0" /> <img src="https://static.igem.org/mediawiki/2015/a/a7/Nankai_Model_2_img.png" alt="" class="img0" />
 
       <div class="box_2"> <img src="https://static.igem.org/mediawiki/2015/1/1f/Nankai_Model_Box_3.png" alt=""  class="main_img0" /> <img src="https://static.igem.org/mediawiki/2015/a/a7/Nankai_Model_2_img.png" alt="" class="img0" />
 
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           <h6>Product scale</h6>
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           <p>We assume that our product comes from two parts, one is during the growth, and the other is through their livelihood.</p>
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           <h5>dP/dt=α*dX/dt+β*X</h5>
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Revision as of 04:43, 8 September 2015

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Power House

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.

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.

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.

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
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