Difference between revisions of "Team:FAFU-CHINA/Modeling"
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+ | </head> | ||
− | + | <body lang=ZH-CN style='tab-interval:21.0pt;text-justify-trim:punctuation'> | |
− | + | ||
− | + | ||
− | + | <div class=WordSection1 style='layout-grid:15.6pt'> | |
− | + | <p class=MsoTitle><a name="OLE_LINK2"></a><a name="OLE_LINK1"><span | |
+ | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:14.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif";font-weight:normal;mso-bidi-font-weight: | ||
+ | bold'>Modeling<o:p></o:p></span></span></a></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>In | |
+ | FAFU’s project, it is difficult to measure the quantitative data and determine | ||
+ | the amount of <span class=SpellE>dsRNAs</span> which is fed to the larvae. So | ||
+ | in the modeling part, we <a name="OLE_LINK6"></a><a name="OLE_LINK5"></a><a | ||
+ | name="OLE_LINK4"><span style='mso-bookmark:OLE_LINK5'><span style='mso-bookmark: | ||
+ | OLE_LINK6'>devote</span></span></a>d 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 <span class=GramE>dsRNA .</span> | ||
+ | Then we can <span class=GramE>control <span | ||
+ | style='mso-spacerun:yes'> </span>the</span> amount of <span class=SpellE>dsRNAs</span> | ||
+ | which if fed to the larvae by controlling the concentration of IPTG easily.<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>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.<o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><b style='mso-bidi-font-weight:normal'><span lang=EN-US | |
− | + | style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></b></span></span></p> | |
− | + | ||
− | + | ||
− | < | + | |
− | + | ||
− | + | ||
− | + | ||
− | + | <p class=MsoListParagraph style='margin-left:18.0pt;text-indent:-18.0pt; | |
+ | mso-char-indent-count:0;mso-list:l0 level1 lfo1'><span style='mso-bookmark: | ||
+ | OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><![if !supportLists]><b | ||
+ | style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><span style='mso-list:Ignore'>1.<span | ||
+ | style='font:7.0pt "Times New Roman"'> </span></span></span></b><![endif]><b | ||
+ | style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'>The Model Simulating the Change of | ||
+ | dsRNA with Time in Different Concentration of IPTG<o:p></o:p></span></b></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>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 <span style='position:relative;top:14.0pt; | |
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− | + | stroked="f"> | |
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+ | <v:f eqn="sum @0 1 0"/> | ||
+ | <v:f eqn="sum 0 0 @1"/> | ||
+ | <v:f eqn="prod @2 1 2"/> | ||
+ | <v:f eqn="prod @3 21600 pixelWidth"/> | ||
+ | <v:f eqn="prod @3 21600 pixelHeight"/> | ||
+ | <v:f eqn="sum @0 0 1"/> | ||
+ | <v:f eqn="prod @6 1 2"/> | ||
+ | <v:f eqn="prod @7 21600 pixelWidth"/> | ||
+ | <v:f eqn="sum @8 21600 0"/> | ||
+ | <v:f eqn="prod @7 21600 pixelHeight"/> | ||
+ | <v:f eqn="sum @10 21600 0"/> | ||
+ | </v:formulas> | ||
+ | <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> | ||
+ | <o:lock v:ext="edit" aspectratio="t"/> | ||
+ | </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:114.75pt; | ||
+ | height:36pt' o:ole=""> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image001.wmz" o:title=""/> | ||
+ | </v:shape></span><!--[if gte mso 9]><xml> | ||
+ | <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" | ||
+ | DrawAspect="Content" ObjectID="_1504112933"> | ||
+ | </o:OLEObject> | ||
+ | </xml><![endif]--><span style='mso-spacerun:yes'> </span>in the following | ||
+ | fitting, where <span class=GramE><b style='mso-bidi-font-weight:normal'>a</b> | ||
+ | is</span> the concentration of dsRNA in the steady state.<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>When | |
− | + | the concentration of IPTG=0.3mmol/L, the result of curve fitting is: <o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | |
− | < | + | |
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>General | ||
+ | model:<o:p></o:p></span></span></span></p> | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | style='position:relative;top:14.0pt;mso-text-raise:-14.0pt'><v:shape id="_x0000_i1026" | ||
+ | type="#_x0000_t75" style='width:153pt;height:48pt' o:ole=""> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image002.wmz" o:title=""/> | ||
+ | </v:shape></span><!--[if gte mso 9]><xml> | ||
+ | <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" | ||
+ | DrawAspect="Content" ObjectID="_1504112934"> | ||
+ | </o:OLEObject> | ||
+ | </xml><![endif]--><o:p></o:p></span></span></span></p> | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Coefficients | ||
+ | (with 95% confidence bounds):<o:p></o:p></span></span></span></p> | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>a =<span | ||
+ | style='mso-spacerun:yes'> </span><span class=GramE>0.3241<span | ||
+ | style='mso-spacerun:yes'> </span>(</span>0.299, 0.3492)<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>b =<span | ||
+ | style='mso-spacerun:yes'> </span><span class=GramE>35.95<span | ||
+ | style='mso-spacerun:yes'> </span>(</span>-79.99, 151.9)<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | |
− | + | style='mso-spacerun:yes'> </span>c =<span | |
+ | style='mso-spacerun:yes'> </span><span class=GramE>1.829<span | ||
+ | style='mso-spacerun:yes'> </span>(</span>0.3231, 3.334)<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | |
− | + | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Goodness | ||
+ | of fit:<o:p></o:p></span></span></span></p> | ||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>SSE: 0.00333<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | |
− | + | style='mso-spacerun:yes'> </span>R-square: 0.9676<o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | |
− | + | style='mso-spacerun:yes'> </span>Adjusted R-square: 0.9567<o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | |
− | + | style='mso-spacerun:yes'> </span>RMSE: 0.02356<o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"; | |
− | + | mso-no-proof:yes'><v:shape id="图片_x0020_1" o:spid="_x0000_i1034" type="#_x0000_t75" | |
− | + | style='width:415.5pt;height:268.5pt;visibility:visible;mso-wrap-style:square'> | |
− | + | <v:imagedata src="collaboration-FAFU-CHINA.files/image003.png" o:title="IPTG3"/> | |
− | + | </v:shape></span></span></span><span style='mso-bookmark:OLE_LINK1'><span | |
− | + | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:12.0pt; | |
− | + | font-family:"Arial Unicode MS","sans-serif"'><o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
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− | + | ||
− | + | ||
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− | + | ||
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− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | < | + | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
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− | + | ||
− | + | ||
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− | + | ||
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− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
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− | + | ||
− | + | ||
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− | + | ||
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− | + | ||
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− | + | ||
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− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | < | + | |
− | < | + | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
− | < | + | OLE_LINK2'><span class=GramE><span lang=EN-US style='font-size:12.0pt; |
+ | font-family:"Arial Unicode MS","sans-serif"'>Figure 1.</span></span></span></span><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'> | ||
+ | The curve is matched by the formula mentioned above.<o:p></o:p></span></span></span></p> | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
− | < | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>When |
+ | the concentration of IPTG=0. 4mmol/L, the result of curve fitting is:<o:p></o:p></span></span></span></p> | ||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>General | ||
+ | model:<o:p></o:p></span></span></span></p> | ||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | style='position:relative;top:14.0pt;mso-text-raise:-14.0pt'><v:shape id="_x0000_i1027" | ||
+ | type="#_x0000_t75" style='width:179.25pt;height:56.25pt' o:ole=""> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image004.wmz" o:title=""/> | ||
+ | </v:shape></span><!--[if gte mso 9]><xml> | ||
+ | <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" | ||
+ | DrawAspect="Content" ObjectID="_1504112935"> | ||
+ | </o:OLEObject> | ||
+ | </xml><![endif]--><o:p></o:p></span></span></span></p> | ||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Coefficients | ||
+ | (with 95% confidence bounds):<o:p></o:p></span></span></span></p> | ||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>a =<span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>0.3474<span style='mso-spacerun:yes'> </span>(</span>0.3261, | ||
+ | 0.3686)<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>b =<span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>46.66<span style='mso-spacerun:yes'> </span>(</span>-63.55, | ||
+ | 156.9)<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | |
− | + | style='mso-spacerun:yes'> </span>c =<span | |
− | + | style='mso-spacerun:yes'> </span><span | |
− | + | class=GramE>1.828<span style='mso-spacerun:yes'> </span>(</span>0.7647, | |
− | + | 2.892)<o:p></o:p></span></span></span></p> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | </ | + | |
− | + | ||
− | + | ||
− | < | + | |
− | + | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Goodness | ||
+ | of fit:<o:p></o:p></span></span></span></p> | ||
− | < | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: |
− | < | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span |
− | + | style='mso-spacerun:yes'> </span>SSE: 0.00232<o:p></o:p></span></span></span></p> | |
− | < | + | |
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>R-square: 0.9808<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | |
− | + | style='mso-spacerun:yes'> </span>Adjusted R-square: 0.9744<o:p></o:p></span></span></span></p> | |
− | < | + | |
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>RMSE: 0.01966<o:p></o:p></span></span></span></p> | ||
− | + | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | |
− | < | + | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"; |
− | + | mso-no-proof:yes'><v:shape id="图片_x0020_2" o:spid="_x0000_i1033" type="#_x0000_t75" | |
− | < | + | style='width:415.5pt;height:264pt;visibility:visible;mso-wrap-style:square'> |
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image005.png" o:title="IPTG4"/> | ||
+ | </v:shape></span></span></span><span style='mso-bookmark:OLE_LINK1'><span | ||
+ | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span class=GramE><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'>Figure 2.</span></span></span></span><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'> | ||
+ | The curve is matched by the formula mentioned above.<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>When | ||
+ | the concentration of IPTG=0. 5mmol/L, the result of curve fitting is:<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>General | ||
+ | model:<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | style='position:relative;top:14.0pt;mso-text-raise:-14.0pt'><v:shape id="_x0000_i1028" | ||
+ | type="#_x0000_t75" style='width:181.5pt;height:57pt' o:ole=""> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image006.wmz" o:title=""/> | ||
+ | </v:shape></span><!--[if gte mso 9]><xml> | ||
+ | <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" | ||
+ | DrawAspect="Content" ObjectID="_1504112936"> | ||
+ | </o:OLEObject> | ||
+ | </xml><![endif]--><o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Coefficients | ||
+ | (with 95% confidence bounds):<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>a =<span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>0.3465<span style='mso-spacerun:yes'> </span>(</span>0.3206, | ||
+ | 0.3723)<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>b =<span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>49.63<span style='mso-spacerun:yes'> </span>(</span>-79.79, | ||
+ | 179)<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>c =<span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>1.76<span style='mso-spacerun:yes'> </span>(</span>0.6333, | ||
+ | 2.886)<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Goodness | ||
+ | of fit:<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>SSE: 0.003338<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>R-square: 0.9732<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>Adjusted R-square: 0.9642<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>RMSE: 0.02359<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"; | ||
+ | mso-no-proof:yes'><v:shape id="图片_x0020_3" o:spid="_x0000_i1032" type="#_x0000_t75" | ||
+ | style='width:415.5pt;height:264pt;visibility:visible;mso-wrap-style:square'> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image007.png" o:title="IPTG5"/> | ||
+ | </v:shape></span></span></span><span style='mso-bookmark:OLE_LINK1'><span | ||
+ | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Figure | ||
+ | 3 <span class=GramE>The</span> curve is matched by the formula mentioned above.<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoListParagraph style='margin-left:18.0pt;text-indent:-18.0pt; | ||
+ | mso-char-indent-count:0;mso-list:l0 level1 lfo1'><span style='mso-bookmark: | ||
+ | OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><![if !supportLists]><b | ||
+ | style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><span style='mso-list:Ignore'>2.<span | ||
+ | style='font:7.0pt "Times New Roman"'> </span></span></span></b><![endif]><b | ||
+ | style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'>The Hill Equation<o:p></o:p></span></b></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>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 </span></span></span><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span><!--[if gte msEquation 12]><m:oMath><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span><m:sSub><m:sSubPr><span | ||
+ | style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt; | ||
+ | font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math"; | ||
+ | mso-fareast-font-family:"Arial Unicode MS";mso-hansi-font-family:"Arial Unicode MS"; | ||
+ | mso-bidi-font-family:"Arial Unicode MS"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><m:r><i | ||
+ | style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Cambria Math","serif";mso-fareast-font-family:"Arial Unicode MS"; | ||
+ | mso-bidi-font-family:"Arial Unicode MS"'>P</span></i></m:r></span></span><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span></m:e><m:sub><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><m:r><i | ||
+ | style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Cambria Math","serif";mso-fareast-font-family:"Arial Unicode MS"; | ||
+ | mso-bidi-font-family:"Arial Unicode MS"'>max</span></i></m:r></span></span><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span></m:sub></m:sSub><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><m:r><i | ||
+ | style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Cambria Math","serif";mso-fareast-font-family:"Arial Unicode MS"; | ||
+ | mso-hansi-font-family:"Arial Unicode MS";mso-bidi-font-family:"Arial Unicode MS"'>=0.3375</span></i></m:r></span></span></m:oMath><![endif]--><![if !msEquation]><span | ||
+ | lang=EN-US style='font-size:10.5pt;mso-bidi-font-size:11.0pt;font-family:"Calibri","sans-serif"; | ||
+ | mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font: | ||
+ | minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman"; | ||
+ | mso-bidi-theme-font:minor-bidi;position:relative;top:3.0pt;mso-text-raise:-3.0pt; | ||
+ | mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:AR-SA'><v:shape | ||
+ | id="_x0000_i1025" type="#_x0000_t75" style='width:75.75pt;height:15.75pt'> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image008.png" o:title="" | ||
+ | chromakey="white"/> | ||
+ | </v:shape></span><![endif]><span style='mso-bookmark:OLE_LINK1'><span | ||
+ | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>is the maximal data we can get from the | ||
+ | data)<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>General | ||
+ | model:<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | style='position:relative;top:15.0pt;mso-text-raise:-15.0pt'><v:shape id="_x0000_i1029" | ||
+ | type="#_x0000_t75" style='width:174.75pt;height:57pt' o:ole=""> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image009.wmz" o:title=""/> | ||
+ | </v:shape></span><!--[if gte mso 9]><xml> | ||
+ | <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" | ||
+ | DrawAspect="Content" ObjectID="_1504112938"> | ||
+ | </o:OLEObject> | ||
+ | </xml><![endif]--><o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Coefficients | ||
+ | (with 95% confidence bounds):<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>X<sub>M</sub> | ||
+ | =<span style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>0.1265<span style='mso-spacerun:yes'> </span>(</span>0.08411, | ||
+ | 0.1689)<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>n =<span | ||
+ | style='mso-spacerun:yes'> </span><span | ||
+ | class=GramE>2.239<span style='mso-spacerun:yes'> </span>(</span>0.8187, | ||
+ | 3.658)<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Goodness | ||
+ | of fit:<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>SSE: 0.003107<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>R-square: 0.9062<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>Adjusted R-square: 0.8828<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><span | ||
+ | style='mso-spacerun:yes'> </span>RMSE: 0.02787<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"; | ||
+ | mso-no-proof:yes'><v:shape id="图片_x0020_4" o:spid="_x0000_i1031" type="#_x0000_t75" | ||
+ | style='width:415.5pt;height:264pt;visibility:visible;mso-wrap-style:square'> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image010.png" o:title="Hill"/> | ||
+ | </v:shape></span></span></span><span style='mso-bookmark:OLE_LINK1'><span | ||
+ | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Figure | ||
+ | 4 <span class=GramE>The</span> curve is matched by the formula mentioned above.<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>We | ||
+ | sorted out data and parameters and then beautified the graph.<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 | ||
+ | style='border-collapse:collapse;border:none;mso-border-alt:solid windowtext .5pt; | ||
+ | mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> | ||
+ | <td width=189 valign=top style='width:142.0pt;border:solid windowtext 1.0pt; | ||
+ | mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>Parameter<o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <td width=189 valign=top style='width:142.05pt;border:solid windowtext 1.0pt; | ||
+ | border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: | ||
+ | solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>value<o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <td width=189 valign=top style='width:142.05pt;border:solid windowtext 1.0pt; | ||
+ | border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: | ||
+ | solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>unit<o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | </tr> | ||
+ | <tr style='mso-yfti-irow:1'> | ||
+ | <td width=189 valign=top style='width:142.0pt;border:solid windowtext 1.0pt; | ||
+ | border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt; | ||
+ | padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>n<o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <td width=189 valign=top style='width:142.05pt;border-top:none;border-left: | ||
+ | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; | ||
+ | mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; | ||
+ | mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>2.239<o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <td width=189 valign=top style='width:142.05pt;border-top:none;border-left: | ||
+ | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; | ||
+ | mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; | ||
+ | mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p> </o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | </tr> | ||
+ | <tr style='mso-yfti-irow:2;mso-yfti-lastrow:yes'> | ||
+ | <td width=189 valign=top style='width:142.0pt;border:solid windowtext 1.0pt; | ||
+ | border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt; | ||
+ | padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>X<sub>M</sub><o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <td width=189 valign=top style='width:142.05pt;border-top:none;border-left: | ||
+ | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; | ||
+ | mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; | ||
+ | mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>0.1265<o:p></o:p></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | <td width=189 valign=top style='width:142.05pt;border-top:none;border-left: | ||
+ | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; | ||
+ | mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; | ||
+ | mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> | ||
+ | <p class=MsoNormal align=center style='text-align:center'><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>μ<span | ||
+ | lang=EN-US>g/</span>μ<span lang=EN-US>L<o:p></o:p></span></span></span></span></p> | ||
+ | </td> | ||
+ | <span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'></span></span> | ||
+ | </tr> | ||
+ | </table> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"; | ||
+ | mso-no-proof:yes'><v:shape id="图片_x0020_5" o:spid="_x0000_i1030" type="#_x0000_t75" | ||
+ | style='width:358.5pt;height:268.5pt;visibility:visible;mso-wrap-style:square'> | ||
+ | <v:imagedata src="collaboration-FAFU-CHINA.files/image011.jpg" o:title=""/> | ||
+ | </v:shape></span></span></span><span style='mso-bookmark:OLE_LINK1'><span | ||
+ | style='mso-bookmark:OLE_LINK2'><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'><o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span class=GramE><span lang=EN-US style='font-size:12.0pt; | ||
+ | font-family:"Arial Unicode MS","sans-serif"'>Figure 5.</span></span></span></span><span | ||
+ | style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark:OLE_LINK2'><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'> | ||
+ | It shows the relationship between the concentration of IPTG and the production | ||
+ | of dsRNA<o:p></o:p></span></span></span></p> | ||
+ | |||
+ | <p class=MsoNormal><span style='mso-bookmark:OLE_LINK1'><span style='mso-bookmark: | ||
+ | OLE_LINK2'><span lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'>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.</span></span></span><span | ||
+ | lang=EN-US style='font-size:12.0pt;font-family:"Arial Unicode MS","sans-serif"'><o:p></o:p></span></p> | ||
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Revision as of 12:24, 18 September 2015
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
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
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.
Parameter |
value |
unit |
n |
2.239 |
|
XM |
0.1265 |
μg/μL |
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.
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