Difference between revisions of "Team:FAFU-CHINA/Modeling"
| (9 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | <html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns="http://www.w3.org/TR/REC-html40"> | + | <html xmlns:o="urn:schemas-microsoft-com:office:office" |
| + | |||
| + | xmlns:w="urn:schemas-microsoft-com:office:word" | ||
| + | |||
| + | xmlns="http://www.w3.org/TR/REC-html40"> | ||
<head> | <head> | ||
| − | <meta http-equiv=Content-Type content="text/html; charset=gb2312" > | + | <meta http-equiv=Content-Type content="text/html; charset=gb2312" |
| + | |||
| + | > | ||
<title>Modeling</title> | <title>Modeling</title> | ||
<style type="text/css"> | <style type="text/css"> | ||
| Line 54: | Line 60: | ||
div#sub > p{ | div#sub > p{ | ||
left:5%; | left:5%; | ||
| + | right:5%; | ||
width:90%; | width:90%; | ||
position:relative; | position:relative; | ||
| Line 62: | Line 69: | ||
div#sub > i{ | div#sub > i{ | ||
left:5%; | left:5%; | ||
| + | right:5%; | ||
width:90%; | width:90%; | ||
position:relative; | position:relative; | ||
| Line 67: | Line 75: | ||
font-weight: bold; | font-weight: bold; | ||
font-size: 2vmin; | font-size: 2vmin; | ||
| + | display:block | ||
} | } | ||
| Line 72: | Line 81: | ||
</head> | </head> | ||
<body> | <body> | ||
| − | <div id="div1"><img src="https://static.igem.org/mediawiki/2015/ | + | <div id="div1"><img |
| + | |||
| + | src="https://static.igem.org/mediawiki/2015/f/f9/Fafu_bg22.jpg"/></div> | ||
<div id="div1"><div id="cbg"> | <div id="div1"><div id="cbg"> | ||
<br> | <br> | ||
| Line 82: | Line 93: | ||
<br> | <br> | ||
| − | <div id="sub"><p><span style="display:-moz-inline-box; | + | <div id="sub"><p><span style="display:-moz-inline-box; |
| − | <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> | + | display:inline-block; width:25px;"></span>Remark: Team SCUT help us with some of our modeling work. |
| + | </p></div><br> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>In FAFU’s project, it | ||
| + | |||
| + | is difficult to measure the quantitative data and determine the | ||
| + | |||
| + | amount of dsRNAs which is fed to the larvae. So in the modeling | ||
| + | |||
| + | part, we devoted to establishing an accurate mathematical model to | ||
| + | |||
| + | simulate the dsRNA expression according to the mechanism of T7 | ||
| + | |||
| + | promoter. After the model is built, we can determine the | ||
| + | |||
| + | relationship between the concentration of IPTG and the production | ||
| + | |||
| + | of dsRNA . Then we can control the amount of dsRNAs which if fed | ||
| + | |||
| + | to the larvae by controlling the concentration of IPTG | ||
| + | |||
| + | easily.</p></div><br> | ||
| + | |||
| + | <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> | ||
<br> | <br> | ||
| − | <div id="sub"><div id="headline2">1.The Model Simulating the Change of dsRNA with Time in Different Concentration of IPTG</div></div> | + | <div id="sub"><div id="headline2">1.The Model Simulating the |
| + | |||
| + | Change of dsRNA with Time in Different Concentration of | ||
| + | |||
| + | IPTG</div></div> | ||
<br> | <br> | ||
| − | <div id="sub"><p><span style="display:-moz-inline-box; | + | <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> | |
| − | <div id="sub"><p> | + | <div id="sub"><p>When the concentration of IPTG=0.3mmol/L, the |
| − | + | result of curve fitting is: </p></div> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | <div id="sub"><p><span style="display:-moz-inline-box; | + | <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> | |
| − | <div id="sub"><p><span style="display:-moz-inline-box; | + | <div id="sub"><p><span style="display:-moz-inline-box; |
| − | + | display:inline-block; width:25px;"></span>Coefficients (with 95% | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | confidence bounds): </p></div> | |
| − | <div id="sub"><p><span style="display:-moz-inline-box; | + | <div id="sub"><p><span style="display:-moz-inline-box; |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | display:inline-block; width:50px;"></span>a = 0.3241 (0.299, | |
| − | <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> | + | 0.3492)</p></div> |
| + | <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> | ||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Goodness of fit: | ||
| + | |||
| + | </p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>SSE: 0.00333</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>R-square: | ||
| + | |||
| + | 0.9676</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>Adjusted R-square: | ||
| + | |||
| + | 0.9567</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>RMSE: 0.02356</p></div> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p>When the concentration of IPTG=0.4mmol/L, the | ||
| + | |||
| + | result of curve fitting is: </p></div> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Coefficients (with 95% | ||
| + | |||
| + | confidence bounds): </p></div> | ||
| + | <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> | ||
| + | <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> | ||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Goodness of fit: | ||
| + | |||
| + | </p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>SSE: 0.00232</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>R-square: | ||
| + | |||
| + | 0.9808</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>Adjusted R-square: | ||
| + | |||
| + | 0.9744</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>RMSE: 0.01966</p></div> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p>When the concentration of IPTG=0.5mmol/L, the | ||
| + | |||
| + | result of curve fitting is: </p></div> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Coefficients (with 95% | ||
| + | |||
| + | confidence bounds): </p></div> | ||
| + | <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> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>b = 49.63 (-79.79, 179) | ||
| + | |||
| + | </p></div> | ||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Goodness of fit: | ||
| + | |||
| + | </p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>SSE: 0.003338</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>R-square: | ||
| + | |||
| + | 0.9732</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>Adjusted R-square: | ||
| + | |||
| + | 0.9642</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>RMSE: 0.02359</p></div> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
<br> | <br> | ||
| Line 153: | Line 366: | ||
<br> | <br> | ||
| − | <div id="sub"><p><span style="display:-moz-inline-box; | + | <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> |
| − | <div id="sub">< | + | <div id="sub"><p><span style="display:-moz-inline-box; |
| − | <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 | + | 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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Coefficients (with 95% | ||
| + | |||
| + | confidence bounds): </p></div> | ||
| + | <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> | ||
| + | <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> | ||
| + | |||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:25px;"></span>Goodness of fit: | ||
| + | |||
| + | </p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>SSE: 0.003107</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>R-square: | ||
| + | |||
| + | 0.9062</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>Adjusted R-square: | ||
| + | |||
| + | 0.8828</p></div> | ||
| + | <div id="sub"><p><span style="display:-moz-inline-box; | ||
| + | |||
| + | display:inline-block; width:50px;"></span>RMSE: 0.02787</p></div> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <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> | ||
<br> | <br> | ||
| + | |||
| + | <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> | ||
| + | |||
<br> | <br> | ||
| − | <br> | + | <br> |
| + | |||
<div id="div1"> | <div id="div1"> | ||
<div style="height:100%; width:100%;"></div> | <div style="height:100%; width:100%;"></div> | ||
Latest revision as of 03:28, 19 September 2015
Modeling
Remark: Team SCUT help us with some of our modeling work.
In FAFU’s project, it is difficult to measure the quantitative data and determine the amount of dsRNAs which is fed to the larvae. So in the modeling part, we devoted to establishing an accurate mathematical model to simulate the dsRNA expression according to the mechanism of T7 promoter. After the model is built, we can determine the relationship between the concentration of IPTG and the production of dsRNA . Then we can control the amount of dsRNAs which if fed to the larvae by controlling the concentration of IPTG easily.
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.
1.The Model Simulating the
Change of dsRNA with Time in Different Concentration of
IPTG
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
in the following fitting, where a is the
concentration of dsRNA in the steady state.
When the concentration of IPTG=0.3mmol/L, the result of curve fitting is:
General model:
Coefficients (with 95% confidence bounds):
a = 0.3241 (0.299, 0.3492)
b = 35.95 (-79.99, 151.9)
c = 1.829 (0.3231, 3.334)
Goodness of fit:
SSE: 0.00333
R-square: 0.9676
Adjusted R-square: 0.9567
RMSE: 0.02356
Figure 1: The curve is
matched by the formula mentioned above.
When the concentration of IPTG=0.4mmol/L, the result of curve fitting is:
General model:
Coefficients (with 95% confidence bounds):
a = 0.3474 (0.3261, 0.3686)
b = 46.66 (-63.55, 156.9)
c = 1.828 (0.7647, 2.892)
Goodness of fit:
SSE: 0.00232
R-square: 0.9808
Adjusted R-square: 0.9744
RMSE: 0.01966
Figure 2: The curve is
matched by the formula mentioned above.
When the concentration of IPTG=0.5mmol/L, the result of curve fitting is:
General model:
Coefficients (with 95% confidence bounds):
a = 0.3465 (0.3206, 0.3723)
b = 49.63 (-79.79, 179)
c = 1.76 (0.6333, 2.886)
Goodness of fit:
SSE: 0.003338
R-square: 0.9732
Adjusted R-square: 0.9642
RMSE: 0.02359
Figure 3: The curve is
matched by the formula mentioned above.
2.The Hill Equation
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)
General model: 
Coefficients (with 95% confidence bounds):
Xm = 0.1265 (0.08411, 0.1689)
n = 2.239 (0.8187, 3.658)
Goodness of fit:
SSE: 0.003107
R-square: 0.9062
Adjusted R-square: 0.8828
RMSE: 0.02787
Figure 4: The curve is
matched by the formula mentioned above.
We sorted out data and parameters and then beautified the graph.
Figure 5: It shows the
relationship between the concentration of IPTG and the production
of dsRNA.
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.