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| | <div id="wrapper"><!--Top Wrapper End Here--> | | <div id="wrapper"><!--Top Wrapper End Here--> |
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| | + | <p id="place">Your place: <a href="https://2015.igem.org/Team:Nankai">Home</a> > <a href="https://2015.igem.org/Team:Nankai/Modeling">Modeling</a></p> |
| | <section class="headsection"> | | <section class="headsection"> |
| − | <h2>3 models are used to measure our project.</h2> | + | <h3>3 models are used to measure our project.</h3> |
| | </section> | | </section> |
| | <section class="normalsection"> | | <section class="normalsection"> |
| | <div class="box_1"> | | <div class="box_1"> |
| − | <img src="https://static.igem.org/mediawiki/2015/5/52/Nankai_Model_1_img.png" class="img0" alt=""/> | + | <img src="https://static.igem.org/mediawiki/2015/5/52/Nankai_Model_1_img.png" class="img0"> |
| | <div class="title"> | | <div class="title"> |
| − | <h3>bacteria scale</h3> | + | <h3>Bacteria scale</h3> |
| − | <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> | + | <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> |
| | <h4>dX/dt=Vmax*(1-X/Xmax)*X</h4> | | <h4>dX/dt=Vmax*(1-X/Xmax)*X</h4> |
| | </div> | | </div> |
| | <div class="text"> | | <div class="text"> |
| − | <p>Although the production is the most important, we base all of our modeling on the bacteria scale equation, since we think the production we get is a result of the whole flora. We assume that all the bacteria are the same, so that our modeling can be much easier.
| |
| − | Actually there are several equations to fit the bacteria growth. Since our target is to increase the production in an industrial process, our fermentation takes 48h, a rather long time, with relatively abundant sources, and happens in the big fermentation cylinder. This environment means with the growth of bacteria, the scale itself is the only restrictive factor. Thus we use logistic model, the best choice to illustrate the growth with mono-restrictive factor.</p>
| |
| − | <img src="https://static.igem.org/mediawiki/2015/1/1f/Nankai_Model_Box_3.png" alt="" class="main_img0" />
| |
| | <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. | | <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. |
| | </p> | | </p> |
| | + | <div class="firstpic"> |
| | + | <img src="https://static.igem.org/mediawiki/2015/c/c6/Nankai_modchar1.png"> |
| | + | </div> |
| | + | <div class="secondpic"> |
| | + | <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> | | </div> |
| − | <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"> |
| − | <h6>Product scale</h6> | + | <img src="https://static.igem.org/mediawiki/2015/a/a7/Nankai_Model_2_img.png" class="img0"> |
| − | <p>We assume that our product comes from two parts, one is during the growth, and the other is through their livelihood.</p> | + | |
| − | <h5>dP/dt=α*dX/dt+β*X</h5> | + | <h3>Product scale</h3> |
| − | <a href="#"></a> </div>
| + | <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> |
| − | <div class=" box_1"> <img src="https://static.igem.org/mediawiki/2015/ 9/ 99/ Nankai_Model_3_img. png" class="img0" alt="" /> | + | <div class="text"> |
| − | <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. |
| − | <h6>Substrate scale</h6>
| + | </p> |
| − | <p> Bacteria use the provided carbon source to propagate, maintain their livelihood and synthesize the product.</ p> | + | <div class="firstpic"> |
| − | <h5>dS/dt=-γ*dX/dt-δ*X-ε*dP/dt</h5>
| + | <img src="https://static.igem.org/mediawiki/2015/ f/ fc/ Nankai_modpic2. jpg"> |
| − | <a href="#"></a> </div>
| + | <h6>Fig.2 The original fitting curve of product formation</h6> |
| − | <img src="https://static.igem.org/mediawiki/2015/1/1f/Nankai_Model_Box_3.png" alt="" class="main_img0" /> </div>
| + | <p>1. Fit Results:</br> |
| − | </div>
| + | (1)General model:</br> |
| − | </section>
| + | 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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