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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>We know that T7 promoter is a kind of inducible promoter. Hill equation can be used to simulate the effect of T7 promoter. In T7 strength model, the independent variable is the concentration of IPTG, and the dependent variable is the production of dsRNA.</p></div>
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− | <div id="sub"><div id="headline2">1.The Model Simulating the Change of dsRNA with Time in Different Concentration of IPTG</div></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>By observing the pattern of the data, we figure out that the Logistic equation, which is often used to simulate the growth of population, can model the trend best. Thus, we adapt the formula<img src="https://static.igem.org/mediawiki/2015/6/67/FAFU-CHINA_MD1.png" height="53" width="178" />in the following fitting, where a is the concentration of dsRNA in the steady state.</p></div><br>
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− | <div id="sub"><p>When the concentration of IPTG=0.3mmol/L, the result of curve fitting is: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>General model: <img src="https://static.igem.org/mediawiki/2015/6/67/FAFU-CHINA_MD1.png" height="53" width="178" /></p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Coefficients (with 95% confidence bounds): </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>a = 0.3241 (0.299, 0.3492)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>b = 35.95 (-79.99, 151.9)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>c = 1.829 (0.3231, 3.334)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Goodness of fit: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>SSE: 0.00333</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>R-square: 0.9676</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>Adjusted R-square: 0.9567</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>RMSE: 0.02356</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span><img src="https://static.igem.org/mediawiki/2015/2/2c/FAFU-CHINA_MD2.png" height="393.3" width="608.4"/></p></div>
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− | <div id="sub"><i><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Figure 1: The curve is matched by the formula mentioned above.</i></div>
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− | <div id="sub"><p>When the concentration of IPTG=0.4mmol/L, the result of curve fitting is: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>General model: <img src="https://static.igem.org/mediawiki/2015/6/67/FAFU-CHINA_MD1.png" height="53" width="178" /></p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Coefficients (with 95% confidence bounds): </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>a = 0.3474 (0.3261, 0.3686)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>b = 46.66 (-63.55, 156.9)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>c = 1.828 (0.7647, 2.892)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Goodness of fit: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>SSE: 0.00232</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>R-square: 0.9808</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>Adjusted R-square: 0.9744</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>RMSE: 0.01966</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span><img src="https://static.igem.org/mediawiki/2015/e/ea/FAFU-CHINA_MD3.png" height="393.3" width="608.4"/></p></div>
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− | <div id="sub"><i><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Figure 2: The curve is matched by the formula mentioned above.</i></div>
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− | <div id="sub"><p>When the concentration of IPTG=0.5mmol/L, the result of curve fitting is: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>General model: <img src="https://static.igem.org/mediawiki/2015/6/67/FAFU-CHINA_MD1.png" height="53" width="178" /></p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Coefficients (with 95% confidence bounds): </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>a = 0.3465 (0.3206, 0.3723)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>b = 49.63 (-79.79, 179)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>c = 1.76 (0.6333, 2.886)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Goodness of fit: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>SSE: 0.003338</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>R-square: 0.9732</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>Adjusted R-square: 0.9642</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>RMSE: 0.02359</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span><img src="https://static.igem.org/mediawiki/2015/e/e6/FAFU-CHINA_MD4.png" height="393.3" width="608.4"/></p></div>
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− | <div id="sub"><i><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Figure 3: The curve is matched by the formula mentioned above.</i></div>
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− | <div id="sub"><div id="headline2">2.The Hill Equation</div></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>By the work of first part, it is found that the concentration of dsRNA will become steady after around 4 hours, so we regard the concentration of dsRNA after 4 hours’ culture as that of steady state. Then the Hill equation is applied to model the relationship between the concentration of IPTG and the production of dsRNA, the result of curve fitting is: (where is the maximal data we can get from the data)</p></div><br>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>General model: <img src="https://static.igem.org/mediawiki/2015/f/f2/FAFU-CHINA_MD5.png" height="53" width="178" /></p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Coefficients (with 95% confidence bounds): </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>Xm = 0.1265 (0.08411, 0.1689)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>n = 2.239 (0.8187, 3.658)</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Goodness of fit: </p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>SSE: 0.003107</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>R-square: 0.9062</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>Adjusted R-square: 0.8828</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:50px;"></span>RMSE: 0.02787</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span><img src="https://static.igem.org/mediawiki/2015/7/73/FAFU-CHINA_MD6.png" height="393.3" width="608.4"/></p></div>
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− |
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− | <div id="sub"><i><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Figure 4: The curve is matched by the formula mentioned above.</i></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>We sorted out data and parameters and then beautified the graph.</p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span><img src="https://static.igem.org/mediawiki/2015/d/d6/FAFU-CHINA_MD7.png" width="608"/></p></div>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span><img src="https://static.igem.org/mediawiki/2015/e/ea/FAFU-CHINA_MD8.png" height="393.3" width="608.4"/></p></div>
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− | <div id="sub"><i><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Figure 5: It shows the relationship between the concentration of IPTG and the production of dsRNA.</i></div>
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− | <br>
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− | <div id="sub"><p><span style="display:-moz-inline-box; display:inline-block; width:25px;"></span>Figure 5 shows the relationship between the concentration of IPTG and the production of dsRNA. According to this mathematical model, we can work out the accurate production of dsRNA which is fed to the larvae with the concentration of IPTG which is put into the bacterial system to induce T7 promoter.</p></div>
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