Difference between revisions of "Team:NYMU-Taipei/Model"
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width:70%; | width:70%; | ||
font-size: 14px; | font-size: 14px; | ||
| − | color:# | + | color:#555555; |
background-color:rgba(246, 255, 178, 0); | background-color:rgba(246, 255, 178, 0); | ||
| + | border: 1px solid #555555; | ||
margin:auto; | margin:auto; | ||
| − | + | margin-top:25px; | |
| − | + | ||
} | } | ||
.igem_2017_content_wrapper th { | .igem_2017_content_wrapper th { | ||
padding:3px; | padding:3px; | ||
| − | border: 1px solid # | + | border: 1px solid #555555; |
} | } | ||
| − | |||
.model_wrapper { | .model_wrapper { | ||
| Line 231: | Line 230: | ||
} | } | ||
| − | + | function toggleHeight13(e, maxHeight) { | |
| + | e = document.getElementById("s13"); // e = the gray div | ||
| + | |||
| + | if(e.style.height != '30px') { | ||
| + | e.style.height = '30px'; // height of one line: 20px | ||
| + | } else { | ||
| + | e.style.height = maxHeight + 'px'; | ||
| + | } | ||
| + | } | ||
| + | |||
| + | function toggleHeight14(e, maxHeight) { | ||
| + | e = document.getElementById("s14"); // e = the gray div | ||
| + | |||
| + | if(e.style.height != '30px') { | ||
| + | e.style.height = '30px'; // height of one line: 20px | ||
| + | } else { | ||
| + | e.style.height = maxHeight + 'px'; | ||
| + | } | ||
| + | } | ||
</script> | </script> | ||
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<center><img src='https://static.igem.org/mediawiki/2017/9/99/T--NYMU-Taipei--model_header.png' | <center><img src='https://static.igem.org/mediawiki/2017/9/99/T--NYMU-Taipei--model_header.png' | ||
style='width:80%;' alt='MODELING'></center> | style='width:80%;' alt='MODELING'></center> | ||
| − | < | + | <h3></h3> |
<!-- Abstract --> | <!-- Abstract --> | ||
<div class='model_wrapper'> | <div class='model_wrapper'> | ||
| − | <p> | + | <p> This year, our modeling focuses on predicting the effect of our modified microbes on productivity. It is an extremely important part to our project because it helps us accurately check and predict information from our experiments that are tested in the wet lab. In our project, there are two essential types of microalgae that play very important roles, <i>Synechococcus PCC7942</i> and <i>Chlorella vulgaris</i>. The following descriptions will show our success in modeling. |
</p> | </p> | ||
</div> | </div> | ||
<!--PCC7942--> | <!--PCC7942--> | ||
| − | + | ||
<h1><i>Synechococcus PCC7942</i></h1> | <h1><i>Synechococcus PCC7942</i></h1> | ||
| − | <p> The modeling from | + | <div class='model_wrapper' > |
| + | <p> The modeling from Figure 1 to Figure 5 belongs to the experiments of <i>Synechococcus PCC7942</i> pigments for better photosynthetic efficiencies. We need to check if another microalgae contains an exogenous pigment that can successfully reach new photosynthesis rate and further increase the proportion of biomass. We already have models about the influence of energy adsorption, but pigments will certainly affect other factors. Therefore, we construct several models that each represents an important factor in the growth and cell composition. Thus, we can determine the best culturing collocation by combining these models. | ||
| + | </p> | ||
</div> | </div> | ||
| Line 259: | Line 278: | ||
<div id="s8" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s8" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight8(this, | + | <a href="#!" onclick="toggleHeight8(this, 1680); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Photosynthesis rate of algae | Photosynthesis rate of algae | ||
</a> | </a> | ||
| − | <p> We want to use pigments to enhance the photosynthesis rate. Different | + | <p> We want to use pigments to enhance the photosynthesis rate. Different pigment absorbs different wavelength of sunlight and bring about different irradiance, body temperature, and photosynthesis rate. These two models show the influence of irradiance and temperature on photosynthesis rate. |
</p> | </p> | ||
<!-- 1-1 --> | <!-- 1-1 --> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | R= | + | R = R<sub>max</sub> * i<sup>n</sup> / [k<sub>i</sub> * exp(i*m) + i<sup>n</sup>] |
</h6> | </h6> | ||
| Line 281: | Line 300: | ||
<tr> | <tr> | ||
<th>R</th> | <th>R</th> | ||
| − | <th> | + | <th>CO<sub>2</sub> productive rate</th> |
<th>mol/g*min </th> | <th>mol/g*min </th> | ||
<th>0.000046</th> | <th>0.000046</th> | ||
| Line 287: | Line 306: | ||
<tr> | <tr> | ||
<th>i</th> | <th>i</th> | ||
| − | + | <th>irradiance</th> | |
| − | <th>uE/m | + | <th>uE/m<sup>2</sup></th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | + | <th>n</th> | |
| − | <th> irradiance exponential constant</th> | + | <th>irradiance exponential constant</th> |
| − | <th></th> | + | <th>-</th> |
<th>1.19</th> | <th>1.19</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | + | <th>k<sub>i</sub></th> | |
<th>productive coefficient</th> | <th>productive coefficient</th> | ||
| − | <th>uE/(m | + | <th>uE/(m<sup>2</sup>)*s</th> |
<th>174</th> | <th>174</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | + | <th>m</th> | |
<th>constant</th> | <th>constant</th> | ||
| − | <th> (m | + | <th>(m<sup>2</sup>)*s /uE</th> |
<th>0.0022</th> | <th>0.0022</th> | ||
</tr> | </tr> | ||
| Line 317: | Line 336: | ||
alt='irradiance-photosynthesis rate plot' | alt='irradiance-photosynthesis rate plot' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.1-1 Influence of irradiance on photosynthesis rate</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
| Line 323: | Line 342: | ||
<!-- 1-2 --> | <!-- 1-2 --> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | R= | + | R = A<sub>1</sub> exp(-E<sub>1</sub>rT) - A<sub>2</sub> exp(-E<sub>2</sub>/rT) |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>R</th> | <th>R</th> | ||
| − | <th> | + | <th>CO<sub>2</sub> productive rate</th> |
| − | <th></th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>A<sub>1</sub></th> |
<th>preexponential factor at i=400</th> | <th>preexponential factor at i=400</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>1147.7</th> | <th>1147.7</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>A<sub>2</sub></th> |
<th>preexponential factor at i=200</th> | <th>preexponential factor at i=200</th> | ||
| − | <th></th> | + | <th>-</th> |
| − | <th>3.818*10 | + | <th>3.818*10<sup>8</sup></th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>E<sub>1</sub></th> |
<th>activation energy at i=400</th> | <th>activation energy at i=400</th> | ||
<th>mol/J </th> | <th>mol/J </th> | ||
| Line 358: | Line 377: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>E<sub>2</sub></th> |
<th>activation energy at i=200</th> | <th>activation energy at i=200</th> | ||
<th>mol/J</th> | <th>mol/J</th> | ||
| Line 367: | Line 386: | ||
<th>temperature</th> | <th>temperature</th> | ||
<th>K</th> | <th>K</th> | ||
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
</table> | </table> | ||
| Line 376: | Line 395: | ||
alt='temperature-photosynthesis rate plot' | alt='temperature-photosynthesis rate plot' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.1-2 Influence of temperature on photosynthesis rate</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight8(this, | + | <a href="#!" onclick="toggleHeight8(this, 1680);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 392: | Line 411: | ||
<div id="s9" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s9" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight9(this, | + | <a href="#!" onclick="toggleHeight9(this, 1040); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Simulation of energy absorption of each pigment | Simulation of energy absorption of each pigment | ||
</a> | </a> | ||
| − | <p> The simplified graph is used to calculate how much energy is absorbed by each pigment | + | <p> The simplified graph from sunshine distribution is used to approximately calculate how much energy is absorbed by each pigment and quantifies the photon adsorption amount after conversion. |
</p> | </p> | ||
| + | |||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | y=0. | + | y = 0.01x - 3.5, 400<=x<=500 |
<br> | <br> | ||
| − | <br>y=1.5, 501<=x<=600 | + | <br>y = 1.5, 501<=x<=600 |
<br> | <br> | ||
| − | <br>y=3-0.0025*x, 601<=x<=800 | + | <br>y = 3 - 0.0025*x, 601<=x<= 800 |
</h6> | </h6> | ||
| + | <table> | ||
| + | <tr> | ||
| + | <th>Symbol</th> | ||
| + | <th scope="col">Definition</th> | ||
| + | <th scope="col"&>Unit</th> | ||
| + | <th scope="col"&>Value</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>x</th> | ||
| + | <th>wavelength</th> | ||
| + | <th>nm</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>y</th> | ||
| + | <th>irradiance</th> | ||
| + | <th>W/m<sup>2</sup></th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | </table> | ||
| + | |||
| + | <!-- | ||
<blockquote> | <blockquote> | ||
<p style='color:#702828;font-size:16px; font-family:"Roboto Mono", monospace;'> | <p style='color:#702828;font-size:16px; font-family:"Roboto Mono", monospace;'> | ||
| Line 413: | Line 455: | ||
<br>y: | <br>y: | ||
</p> | </p> | ||
| − | </blockquote> | + | </blockquote>--> |
<p></p> | <p></p> | ||
| Line 420: | Line 462: | ||
alt='Simulation of energy absorption of each pigment' | alt='Simulation of energy absorption of each pigment' | ||
style='width:55%'> | style='width:55%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.2 Simulation of energy absorption of each pigment</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight9(this, | + | <a href="#!" onclick="toggleHeight9(this, 1040);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 433: | Line 475: | ||
| − | <!-- Microalgae productivity in different | + | <!-- Microalgae productivity in different temperatures --> |
<div class='panel'> | <div class='panel'> | ||
<div id="s10" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s10" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight10(this, | + | <a href="#!" onclick="toggleHeight10(this, 960); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| − | Microalgae productivity in different | + | Microalgae productivity in different temperatures |
</a> | </a> | ||
| − | <p> After we get the influential degree on temperature, we can use our modeling to predict the productivity of microalgae at different temperature without other affecting factors. | + | <p> After we get the influential degree on temperature, we can use our modeling to predict the productivity of microalgae at different temperature without other affecting factors. Modeling is used to ensure that our experiments are under control. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | U = | + | U = U<sub>max</sub> * K<sub>ss</sub> |
<br> | <br> | ||
| − | <br> | + | <br>U<sub>max</sub> = A*exp(-E/RT) |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>U</th> | <th>U</th> | ||
<th>specific growth rate</th> | <th>specific growth rate</th> | ||
| − | <th> day | + | <th>day<sup>-1</sup></th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>U<sub>max</sub></th> |
<th>maximum specific growth rate</th> | <th>maximum specific growth rate</th> | ||
| − | <th> day | + | <th>day<sup>-1</sup></th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>K<sub>ss</sub></th> |
<th>substrate parameter</th> | <th>substrate parameter</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>1</th> | <th>1</th> | ||
</tr> | </tr> | ||
| Line 479: | Line 521: | ||
<th>A</th> | <th>A</th> | ||
<th>constant</th> | <th>constant</th> | ||
| − | <th> day | + | <th>day<sup>-1</sup></th> |
| − | <th>1.0114*10 | + | <th>1.0114*10<sup>10</sup></th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>E</th> | <th>E</th> | ||
<th>activation energy</th> | <th>activation energy</th> | ||
| − | <th> cal/mol</th> | + | <th>cal / mol</th> |
<th>6842</th> | <th>6842</th> | ||
</tr> | </tr> | ||
| Line 491: | Line 533: | ||
<th>R</th> | <th>R</th> | ||
<th>gas constant </th> | <th>gas constant </th> | ||
| − | <th>cal/K*mol </th> | + | <th>cal / K*mol </th> |
<th>8.314</th> | <th>8.314</th> | ||
</tr> | </tr> | ||
| Line 499: | Line 541: | ||
<center> | <center> | ||
<img src='https://static.igem.org/mediawiki/2017/8/8c/T--NYMU-Taipei--model_t-spr.png' | <img src='https://static.igem.org/mediawiki/2017/8/8c/T--NYMU-Taipei--model_t-spr.png' | ||
| − | alt='Microalgae productivity in different | + | alt='Microalgae productivity in different temperatures' |
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.3 Microalgae productivity in different temperatures</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight10(this, | + | <a href="#!" onclick="toggleHeight10(this, 960);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 513: | Line 555: | ||
</div> | </div> | ||
| − | <!-- Microalgae productivity in different pH --> | + | <!-- Microalgae productivity in different pH values--> |
<div class='panel'> | <div class='panel'> | ||
<div id="s11" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s11" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight11(this, | + | <a href="#!" onclick="toggleHeight11(this, 1020); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| − | Microalgae productivity in different pH | + | Microalgae productivity in different pH values |
</a> | </a> | ||
| − | <p> When our <i>Synechococcus PCC7942</i> grows at each phase, the equilibrium of pH value is different. This model can be used to collocate with our device, and also | + | <p> When our <i>Synechococcus PCC7942</i> grows at each phase, the equilibrium of the pH value is different. This model can be used to collocate with our device, and also accomplish the purpose of enhancing productivity. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | R= | + | R = A<sub>1</sub> exp(-B<sub>1</sub>/pH) - A<sub>2</sub> exp(-B<sub>2</sub>/pH) |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>R</th> | <th>R</th> | ||
| − | <th> | + | <th>CO<sub>2</sub> productive rate</th> |
| − | <th></th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>A<sub>1</sub></th> |
| − | + | <th>preexponential factor at i=400</th> | |
| − | <th></th> | + | <th>-</th> |
| − | <th>8.625*10 | + | <th>8.625*10<sup>-5</sup></th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>A<sub>2</sub></th> |
<th>preexponential factor at i=200</th> | <th>preexponential factor at i=200</th> | ||
| − | <th></th> | + | <th>-</th> |
| − | <th>1.83885*10 | + | <th>1.83885*10<sup>-2</sup></th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | + | <th>B<sub>1</sub></th> | |
<th>activation energy at i=400</th> | <th>activation energy at i=400</th> | ||
| − | <th>mol/J </th> | + | <th>mol/J</th> |
<th>6.45</th> | <th>6.45</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | + | <th>B<sub>2</sub></th> | |
<th>activation energy at i=200</th> | <th>activation energy at i=200</th> | ||
<th>mol/J</th> | <th>mol/J</th> | ||
| Line 573: | Line 615: | ||
alt='Microalgae productivity in different pH' | alt='Microalgae productivity in different pH' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.4 Microalgae productivity in different pH</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight11(this, | + | <a href="#!" onclick="toggleHeight11(this, 1020);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 585: | Line 627: | ||
</div> | </div> | ||
| − | <!-- The relation between photosynthetic rate and total | + | <!-- The relation between photosynthetic rate and total absorption --> |
<div class='panel'> | <div class='panel'> | ||
<div id="s12" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s12" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight12(this, | + | <a href="#!" onclick="toggleHeight12(this, 960); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| − | The relation between photosynthetic rate and total | + | The relation between photosynthetic rate and total absorption |
</a> | </a> | ||
| − | <p> The model tells us that theoretically there is no faster photosynthetic rate | + | <p> The model tells us that theoretically, there is no faster photosynthetic rate unless more energy is absorbed. After working with other models, we established the relationship between photosynthetic rate and total absorption for the purpose of best balance. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | R= | + | R = R<sub>max</sub> * e<sup>n</sup> / [k<sub>e</sub> * exp(e*m) + e<sup>n</sup>] |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>R<sub>max</sub></th> |
<th>maximum rate</th> | <th>maximum rate</th> | ||
| − | <th>mol/g*min </th> | + | <th>mol / g*min </th> |
<th>0.000046</th> | <th>0.000046</th> | ||
</tr> | </tr> | ||
| Line 617: | Line 659: | ||
<th>e</th> | <th>e</th> | ||
<th>absorbed energy</th> | <th>absorbed energy</th> | ||
| − | <th>w/m | + | <th>w/m<sup>2</sup></th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>n</th> | <th>n</th> | ||
<th>energy exponential constant</th> | <th>energy exponential constant</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>1.252</th> | <th>1.252</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>k<sub>e</sub></th> |
<th>productive coefficient</th> | <th>productive coefficient</th> | ||
| − | <th>uE/(m | + | <th>uE / (m<sup>2</sup>)*s</th> |
<th>157.88</th> | <th>157.88</th> | ||
</tr> | </tr> | ||
| Line 635: | Line 677: | ||
<th>m</th> | <th>m</th> | ||
<th>constant</th> | <th>constant</th> | ||
| − | <th> (m | + | <th>(m<sup>2</sup>)*s / uE</th> |
<th>0.0035</th> | <th>0.0035</th> | ||
</tr> | </tr> | ||
| Line 645: | Line 687: | ||
alt='The relation between photosynthetic rate and total yield' | alt='The relation between photosynthetic rate and total yield' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.5 The relation between photosynthetic rate and total absorption</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight12(this, | + | <a href="#!" onclick="toggleHeight12(this, 960);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 659: | Line 701: | ||
<!--chorella--> | <!--chorella--> | ||
| − | + | ||
<h1><i>Chlorella vulgaris</i></h1> | <h1><i>Chlorella vulgaris</i></h1> | ||
| − | <p> The modeling from | + | <div class='model_wrapper' > |
| + | <p> The modeling from Figure 6 to Figure 13 belongs to the experiments of <i>Chlorella vulgaris</i> for nitrogen starvation. To precisely calculate the timing of starting co-culturing and to ensure there are enough high-affinity E. coli in the bioreactor, we built several models that include the original and new system. They demonstrated the significant improvement of productivity after successfully deprived the microalgae from nitrogen. For instance, one of them provides a variety of information about population when two organisms in the pool start building some relationship. | ||
| + | </p> | ||
</div> | </div> | ||
| Line 667: | Line 711: | ||
<div class='panel'> | <div class='panel'> | ||
<div id="s1" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s1" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight1(this, | + | <a href="#!" onclick="toggleHeight1(this, 1580); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Growth curve of <i>Chlorella vulgaris</i> | Growth curve of <i>Chlorella vulgaris</i> | ||
</a> | </a> | ||
| − | <p> The timing of adding engineered <i>E.coli</i> or purified protein to <i>Chlorella vulgaris</i> culture is critical to our project. By analyzing the initial and final biomass concentration data | + | <p> The timing of adding engineered <i>E.coli</i> or purified protein to <i>Chlorella vulgaris</i> culture is critical to our project. By analyzing the initial and final biomass concentration data the instantaneous rate would be gained. This instantaneous rate is based on reference time and other lab environment data. We have simulated the change in biomass concentration throughout the culture cycle. The intermittent information in the culture medium at each point is ultimately gained through combining other modeling results, which aims to determine the best timing and corresponding state. |
</p> | </p> | ||
| − | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'>ln( | + | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> |
| + | ln(X<sub>t</sub>/X<sub>0</sub>) / t | ||
| + | <br> | ||
| + | <br>= A + B exp[-C(t-M)] | ||
| + | <br> | ||
| + | <br>= μ (specific growth rate)</h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 687: | Line 736: | ||
<th>biomass concentration</th> | <th>biomass concentration</th> | ||
<th>g/l</th> | <th>g/l</th> | ||
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 693: | Line 742: | ||
<th>time</th> | <th>time</th> | ||
<th>hr</th> | <th>hr</th> | ||
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>A</th> | <th>A</th> | ||
| − | <th>the asymptotic of ln | + | <th>the asymptotic of ln X<sub>t</sub>/X<sub>0</sub> as t decrese indefinitely</th> |
| − | <th></th> | + | <th>-</th> |
<th>1.252</th> | <th>1.252</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>B</th> | <th>B</th> | ||
| − | <th>the asymptotic of ln | + | <th>the asymptotic of ln X<sub>t</sub>/X<sub>0</sub> as t increase indefinitely</th> |
| − | <th></th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>C</th> | <th>C</th> | ||
| − | <th>the relative growth rate at time </th> | + | <th>the relative growth rate at time</th> |
| − | <th> M</th> | + | <th>M</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
</table> | </table> | ||
| Line 720: | Line 769: | ||
alt='Growth curve of Chlorella vulgaris' | alt='Growth curve of Chlorella vulgaris' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.6-1 Growth curve of <i>Chlorella vulgaris</i></p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
| Line 728: | Line 777: | ||
alt='Growth rate of Chlorella vulgaris' | alt='Growth rate of Chlorella vulgaris' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.6-2 Growth rate of <i>Chlorella vulgaris</i></p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight1(this, | + | <a href="#!" onclick="toggleHeight1(this, 1580);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 745: | Line 794: | ||
<div id="s2" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s2" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight2(this, | + | <a href="#!" onclick="toggleHeight2(this, 1250); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| − | Oil accumulation & | + | Oil accumulation & Nitrogen source consumption |
</a> | </a> | ||
| − | <p> By simulating common | + | <p> By simulating common systems of oil accumulation and nitrogen source consumption, we cannot only get the reference data before the improvement, but also make it a basic equation after joining some parameters or organisms into the system. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | dP/dt= | + | dP/dt = αdX/dt + βX; |
<br> | <br> | ||
| − | <br>dN/dt=-V*X; | + | <br>dN/dt = -V*X; |
<br> | <br> | ||
| − | <br>V=( | + | <br>V = [(q<sub>M</sub>-Q)/(q<sub>M</sub>-q)] * [(V<sub>m</sub>*N)/(N+V<sub>h</sub>)] |
<br> | <br> | ||
| − | <br>Q=( | + | <br>Q = (X<sub>0</sub>*Q<sub>0</sub> + N<sub>0</sub> - N) / X |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col | + | <th scope="col">Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
| + | <tr> | ||
| + | <th>P</th> | ||
| + | <th>lipid</th> | ||
| + | <th>g/L</th> | ||
| + | <th>-</th> | ||
| + | <tr> | ||
<tr> | <tr> | ||
<th>N</th> | <th>N</th> | ||
| − | <th | + | <th>nitrogen</th> |
| − | <th | + | <th>g/L</th> |
| − | + | <th>-</th> | |
| − | <tr> | + | <tr> |
| + | <tr> | ||
| + | <th>X</th> | ||
| + | <th>biomass</th> | ||
| + | <th>g/L</th> | ||
| + | <th>-</th> | ||
| + | <tr> | ||
<th>α</th> | <th>α</th> | ||
| − | <th | + | <th>the instantaneous yield coefficient of product formation due to cell growth</th> |
| − | <th | + | <th>g/g</th> |
| − | + | <th>0.1973</th> | |
</tr> | </tr> | ||
| + | <tr> | ||
| + | <th>β</th> | ||
| + | <th>the specific formation rate of product</th> | ||
| + | <th>day<sup>-1</sup></th> | ||
| + | <th>0.00037</th> | ||
| + | <tr> | ||
<tr> | <tr> | ||
<th>q</th> | <th>q</th> | ||
| − | <th | + | <th>Minimum N quota</th> |
| − | <th | + | <th>g/g</th> |
| − | <th | + | <th>0.0178</th> |
| + | </tr> | ||
| + | <tr> | ||
| + | <th>q<sub>M</sub></th> | ||
| + | <th>Maximum N quota</th> | ||
| + | <th>g/g</th> | ||
| + | <th>0.0935</th> | ||
| + | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>Q</th> | <th>Q</th> | ||
| − | <th | + | <th>N quota</th> |
| − | <th | + | <th>g/g</th> |
| − | <th | + | <th>-</th> |
| + | </tr> | ||
| + | <tr> | ||
| + | <th>V<sub>m</sub></th> | ||
| + | <th>Maximum uptake rate of nitrogen</th> | ||
| + | <th>g/g*day</th> | ||
| + | <th>0.596</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>V<sub>h</sub></th> |
| − | <th | + | <th>Half-saturation coefficient</th> |
| − | <th | + | <th>g/m<sup>3</sup></th> |
| − | <th | + | <th>0.0000103</th> |
</tr> | </tr> | ||
</table> | </table> | ||
| Line 805: | Line 885: | ||
alt='Oil accumulation and nirogen source consumption at normal situation' | alt='Oil accumulation and nirogen source consumption at normal situation' | ||
style='width:90%'> | style='width:90%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.7 Oil accumulation and nirogen source consumption at normal situation(lipid:green;nitrogen:blue)</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight2(this, | + | <a href="#!" onclick="toggleHeight2(this, 1250);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 818: | Line 898: | ||
</div> | </div> | ||
| − | <!-- Biomass in different nitrogen | + | <!-- Biomass in different nitrogen concentrations--> |
<div class='panel'> | <div class='panel'> | ||
<div id="s3" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s3" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight3(this, | + | <a href="#!" onclick="toggleHeight3(this, 1250); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| − | Biomass in different nitrogen | + | Biomass in different nitrogen concentrations |
</a> | </a> | ||
| − | <p> To find out the best quantity of nitrogen removal, we | + | <p> To find out the best quantity of nitrogen removal, we modeled several situations of decreasing the biomass in different environments with different concentration of nitrogen. We then find the best productivity by comparing these two situations. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | + | n<sub>2</sub> = exp{[A + C*exp(-exp(-B(t-M)))] * (t<sub>2</sub>-t<sub>1</sub>)} * n<sub>1</sub>; | |
<br> | <br> | ||
| − | <br> | + | <br>x<sub>2</sub> = x<sub>1</sub> + (n<sub>2</sub>-n<sub>1</sub>) * {[k[ln(b(n<sub>s</sub>+a))<sup>-1</sup>]]-e}; |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col | + | <th scope="col">Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
| − | + | </tr> | |
<tr> | <tr> | ||
| − | <th> | + | <th>n<sub>1</sub></th> |
| − | <th | + | <th>biomass at frist state</th> |
| − | <th | + | <th>g/l</th> |
| − | + | <th>-</th> | |
| − | <tr> | + | </tr> |
| + | <tr> | ||
| + | <th>n<sub>2</sub></th> | ||
| + | <th>biomass at secind state</th> | ||
| + | <th>g/l</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
<th>x</th> | <th>x</th> | ||
| − | <th | + | <th>biomass concentration</th> |
| − | <th | + | <th>g/l</th> |
| − | <th | + | <th>-</th> |
| + | </tr> | ||
| + | <tr> | ||
| + | <th>t</th> | ||
| + | <th>time</th> | ||
| + | <th>hr</th> | ||
| + | <th>-</th> | ||
</tr> | </tr> | ||
</table> | </table> | ||
| Line 858: | Line 951: | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col">Unit</th> |
| + | <th scope="col"&>Value</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>A</th> | <th>A</th> | ||
| − | <th>the asymptotic of ln | + | <th>the asymptotic of ln X<sub>t</sub>/X<sub>0</sub> as t decrese indefinitely</th> |
| + | <th>-</th> | ||
<th>-39.9532</th> | <th>-39.9532</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>B</th> | <th>B</th> | ||
| − | <th>the asymptotic of ln | + | <th>the asymptotic of ln X<sub>t</sub>/X<sub>0</sub> as t increase indefinitely </th> |
| + | <th>-</th> | ||
<th>-0.0222</th> | <th>-0.0222</th> | ||
</tr> | </tr> | ||
| Line 875: | Line 971: | ||
<th>C</th> | <th>C</th> | ||
<th>the relative growth rate at time M hr</th> | <th>the relative growth rate at time M hr</th> | ||
| + | <th>-</th> | ||
<th>45.6931</th> | <th>45.6931</th> | ||
</tr> | </tr> | ||
| Line 880: | Line 977: | ||
<th>k</th> | <th>k</th> | ||
<th>constant</th> | <th>constant</th> | ||
| + | <th>-</th> | ||
<th>8.15229</th> | <th>8.15229</th> | ||
</tr> | </tr> | ||
| Line 885: | Line 983: | ||
<th>b</th> | <th>b</th> | ||
<th>yield coefficient</th> | <th>yield coefficient</th> | ||
| + | <th>-</th> | ||
<th>1207.569</th> | <th>1207.569</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>n<sub>s</sub></th> |
<th>initial nitrogen concentration</th> | <th>initial nitrogen concentration</th> | ||
| − | <th></th> | + | <th>-</th> |
| + | <th>-</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>a</th> | <th>a</th> | ||
<th>regression constant</th> | <th>regression constant</th> | ||
| + | <th>-</th> | ||
<th>0.01</th> | <th>0.01</th> | ||
</tr> | </tr> | ||
| Line 900: | Line 1,001: | ||
<th>e</th> | <th>e</th> | ||
<th>a perturbation</th> | <th>a perturbation</th> | ||
| + | <th>-</th> | ||
<th>0.50678</th> | <th>0.50678</th> | ||
</tr> | </tr> | ||
| Line 909: | Line 1,011: | ||
alt='Biomass in different nitrogen concentration' | alt='Biomass in different nitrogen concentration' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.8 Biomass in different nitrogen concentration(concentration after nitrogen deletion,black:0.1;red:0.03;green:0.02;blue:0.01;yellow:0.005 g/l)</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight3(this, | + | <a href="#!" onclick="toggleHeight3(this, 1250);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 925: | Line 1,027: | ||
<div id="s4" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s4" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight4(this, | + | <a href="#!" onclick="toggleHeight4(this, 900); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Nitrogen concentration in nitrogen starvation | Nitrogen concentration in nitrogen starvation | ||
</a> | </a> | ||
| − | <p> We put normal and modified nitrogen source systems together to see their demonstration | + | <p> We put normal and modified nitrogen source systems together to see their demonstration like speed and occasion. By constructing this model, we can find out the declining rate of each state and then adjust our experiments. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | dn/dt= | + | dn/dt = Y<sub>xn</sub> * dx/dt + m*x |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>n</th> | <th>n</th> | ||
<th>nitrogen concentration</th> | <th>nitrogen concentration</th> | ||
| − | <th> </th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>Y<sub>xn</sub></th> |
<th>nitrate coefficient</th> | <th>nitrate coefficient</th> | ||
<th>g/g</th> | <th>g/g</th> | ||
| − | <th> 0.21016</th> | + | <th>0.21016</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>m</th> | <th>m</th> | ||
<th>maintenance parameter</th> | <th>maintenance parameter</th> | ||
| − | <th>hr | + | <th>hr<sup>-1</sup></th> |
<th>0.0014393</th> | <th>0.0014393</th> | ||
</tr> | </tr> | ||
| Line 964: | Line 1,066: | ||
<th>x</th> | <th>x</th> | ||
<th>biomass concentration</th> | <th>biomass concentration</th> | ||
| − | <th></th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
</table> | </table> | ||
| Line 974: | Line 1,076: | ||
alt='Nitrogen source in nitrogen starvation' | alt='Nitrogen source in nitrogen starvation' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.9 Nitrogen source in nitrogen starvation(normal:blue;starvation:red)</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight4(this, | + | <a href="#!" onclick="toggleHeight4(this, 900);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
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<div id="s5" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s5" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight5(this, | + | <a href="#!" onclick="toggleHeight5(this, 960); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Oil accumulation in nitrogen starvation | Oil accumulation in nitrogen starvation | ||
| Line 999: | Line 1,101: | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | dp/dt= | + | dp/dt = k<sub>1</sub>(dx/dt)<sup>2</sup> + k<sub>2</sub>(dx/dt)(x) + e |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>p</th> | <th>p</th> | ||
<th>lipid concentrtion</th> | <th>lipid concentrtion</th> | ||
| − | <th> </th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>K<sub>1</sub></th> |
<th>growth correlation coefficient</th> | <th>growth correlation coefficient</th> | ||
| − | <th>g | + | <th>g<sup>2</sup>/g<sup>2</sup></th> |
<th>122.40085</th> | <th>122.40085</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>K<sub>2</sub></th> |
| − | <th> non-growth correlation coefficient</th> | + | <th>non-growth correlation coefficient</th> |
| − | <th> g | + | <th>g<sup>-1</sup></th> |
<th>0.28736</th> | <th>0.28736</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>e</th> | <th>e</th> | ||
| − | <th> a perturbation</th> | + | <th>a perturbation</th> |
<th>g/l*hr</th> | <th>g/l*hr</th> | ||
<th>-0.078</th> | <th>-0.078</th> | ||
| Line 1,040: | Line 1,142: | ||
alt='Oil accumulation in nitrogen starvation' | alt='Oil accumulation in nitrogen starvation' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.10 Oil accumulation in nitrogen starvation</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight5(this, | + | <a href="#!" onclick="toggleHeight5(this, 960);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 1,056: | Line 1,158: | ||
<div id="s6" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s6" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight6(this, | + | <a href="#!" onclick="toggleHeight6(this, 2050); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Population of Co-cultured <i>Chlorella vulgaris</i> and Modified <i>E.coli</i> | Population of Co-cultured <i>Chlorella vulgaris</i> and Modified <i>E.coli</i> | ||
</a> | </a> | ||
| − | <p> According to our reference of | + | <p> According to our reference of experimental data, we find that <i>E.coli</i> can build a relationship, which is like symbiosis, with <i>Chlorella vulgaris</i>. Therefore, we build a model and use three kinds of values from different situations to simulate their change when they are co-cultured. According to this, we get the proper experimental proportion of them at each need. |
</p> | </p> | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | + | x<sub>2</sub> = [ax-x<sup>2</sup>/(1+b*x*z)] / R<sub>x</sub> + x / Y<sub>x</sub> | |
<br> | <br> | ||
| − | <br> | + | <br>z<sub>2</sub> = [cz-z<sup>2</sup>/(1+g*z*x)] / R<sub>z</sub> + z / Y<sub>z</sub> |
</h6> | </h6> | ||
| − | + | <table> | |
| − | + | <tr> | |
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
| − | + | <tr> | |
<th>Z</th> | <th>Z</th> | ||
<th>e.coil</th> | <th>e.coil</th> | ||
| − | <th> </th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>X</th> |
| − | + | <th>chlorella vulgaris</th> | |
| + | <th>-</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | |||
| + | <tr> | ||
| + | <th>R<sub>x</sub></th> | ||
| + | <th>symbiosis coefficient</th> | ||
<th>g/hr</th> | <th>g/hr</th> | ||
<th>1.0000023</th> | <th>1.0000023</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>R<sub>z</sub></th> |
<th>symbiosis coefficient</th> | <th>symbiosis coefficient</th> | ||
<th>g/hr</th> | <th>g/hr</th> | ||
| Line 1,096: | Line 1,205: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>Y<sub>x</sub></th> |
| − | <th> correlation coefficient</th> | + | <th>correlation coefficient</th> |
| − | <th></th> | + | <th>-</th> |
<th>12.576</th> | <th>12.576</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>Y<sub>z</sub></th> |
| − | <th> correlation coefficient</th> | + | <th>correlation coefficient</th> |
| − | <th></th> | + | <th>-</th> |
<th>2.276</th> | <th>2.276</th> | ||
</tr> | </tr> | ||
| Line 1,110: | Line 1,219: | ||
<th>a</th> | <th>a</th> | ||
<th>population constant</th> | <th>population constant</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>0.80467</th> | <th>0.80467</th> | ||
</tr> | </tr> | ||
| Line 1,116: | Line 1,225: | ||
<th>c</th> | <th>c</th> | ||
<th>population constant</th> | <th>population constant</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>0.61198</th> | <th>0.61198</th> | ||
</tr> | </tr> | ||
| Line 1,122: | Line 1,231: | ||
<th>b</th> | <th>b</th> | ||
<th>relative parameter</th> | <th>relative parameter</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>0.00027</th> | <th>0.00027</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | + | <th>g</th> | |
<th>relative parameter</th> | <th>relative parameter</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>0.0013</th> | <th>0.0013</th> | ||
</tr> | </tr> | ||
| Line 1,138: | Line 1,247: | ||
alt='Population of co-cultured Chlorella and modified E.coli' | alt='Population of co-cultured Chlorella and modified E.coli' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.11-1 Population of co-cultured Chlorella and modified E.coli(initial concentration 0.1g/l) (chlorella vulgaris:green;e.coli:orange) </p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
| Line 1,146: | Line 1,255: | ||
alt='Population of co-cultured Chlorella and modified E.coli' | alt='Population of co-cultured Chlorella and modified E.coli' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.11-2 Population of co-cultured Chlorella and modified E.coli(initial concentration 0.012g/l)(chlorella vulgaris:green;e.coli:orange)</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
| Line 1,154: | Line 1,263: | ||
alt='Population of co-cultured Chlorella and modified E.coli' | alt='Population of co-cultured Chlorella and modified E.coli' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.11-3 Population of co-cultured Chlorella and modified E.coli(initial concentration 0.3g/l)</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight6(this, | + | <a href="#!" onclick="toggleHeight6(this, 2050);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
| Line 1,171: | Line 1,280: | ||
<div id="s7" class="expandable" style='height: 30px;padding-top:15px;'> | <div id="s7" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| − | <a href="#!" onclick="toggleHeight7(this, | + | <a href="#!" onclick="toggleHeight7(this, 1000); return false" |
style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
Nitrogen-lipid plot | Nitrogen-lipid plot | ||
| Line 1,180: | Line 1,289: | ||
<h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| − | l=k | + | l = k[ln(b(n<sub>s</sub>+a))<sup>-1</sup>] - e |
</h6> | </h6> | ||
<table> | <table> | ||
<tr> | <tr> | ||
| − | <th></th> | + | <th>Symbol</th> |
| − | <th scope="col"></th> | + | <th scope="col">Definition</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Unit</th> |
| − | <th scope="col"&></th> | + | <th scope="col"&>Value</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>l</th> | <th>l</th> | ||
<th>lipid proportion in cell</th> | <th>lipid proportion in cell</th> | ||
| − | <th> </th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>k</th> | <th>k</th> | ||
<th>constant</th> | <th>constant</th> | ||
| − | <th> g/100g</th> | + | <th>g/100g</th> |
<th>1.13372</th> | <th>1.13372</th> | ||
</tr> | </tr> | ||
| Line 1,205: | Line 1,314: | ||
<th>b</th> | <th>b</th> | ||
<th>yield coefficient</th> | <th>yield coefficient</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>1.57172</th> | <th>1.57172</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>n<sub>s</sub></th> |
<th>initial nitrogen concentration</th> | <th>initial nitrogen concentration</th> | ||
| − | <th></th> | + | <th>-</th> |
| − | <th></th> | + | <th>-</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>a</th> | <th>a</th> | ||
| − | <th> correlation coefficient</th> | + | <th>correlation coefficient</th> |
| − | <th></th> | + | <th>-</th> |
<th>2.276</th> | <th>2.276</th> | ||
</tr> | </tr> | ||
| Line 1,223: | Line 1,332: | ||
<th>a</th> | <th>a</th> | ||
<th>regression constant</th> | <th>regression constant</th> | ||
| − | <th></th> | + | <th>-</th> |
<th>0.51653</th> | <th>0.51653</th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th>e</th> | <th>e</th> | ||
| − | <th> a perturbation</th> | + | <th>a perturbation</th> |
| − | <th> g/100g</th> | + | <th>g/100g</th> |
<th>-55.2776</th> | <th>-55.2776</th> | ||
</tr> | </tr> | ||
| Line 1,240: | Line 1,349: | ||
alt='Nitrogen-lipid plot' | alt='Nitrogen-lipid plot' | ||
style='width:65%'> | style='width:65%'> | ||
| − | <p style='font-size:20px'> | + | <p style='font-size:20px'>Fig.12 Nitrogen-lipid plot</p> |
</center> | </center> | ||
<p></p> | <p></p> | ||
<center> | <center> | ||
| − | <a href="#!" onclick="toggleHeight7(this, | + | <a href="#!" onclick="toggleHeight7(this, 1000);" style='font-size:20px;color:#2c498c'> |
click to close | click to close | ||
</a> | </a> | ||
</center> | </center> | ||
| + | |||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <!-- Out --> | ||
| + | <div class='panel'> | ||
| + | <div id="s13" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| + | |||
| + | <a href="#!" onclick="toggleHeight13(this, 1900); return false" | ||
| + | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| + | NrtA exocrine secretion | ||
| + | </a> | ||
| + | |||
| + | <p> NrtA is an endocrine secretion protein and this characteristic is a bound to reach our goal because it does not have enough efficiency to make microalgae to produce a significant amount of biofuel. We have tried to turn NrtA into exocrine secretion protein but unfortunately, we didn’t make it in time. If we have successfully transform it into a exocrine secretion protein, and with the help of the connected constitutive promoter, we might have a better result than before theoretically. And this model provide the predictive quantity of change and productivity of new method. | ||
| + | </p> | ||
| + | |||
| + | <h6 style='color:#bc0101; font-family:"Roboto Mono", monospace;'> | ||
| + | dr<sub>1</sub>/dt = [1/(1+p<sub>1</sub>/a<sub>1</sub>)]c1p1 - [1/(1+p<sub>2</sub>/b<sub>1</sub>)]v<sub>1</sub>r<sub>1</sub> | ||
| + | <br> | ||
| + | <br>dr<sub>2</sub>/dt = [1/(1+p<sub>2</sub>/a<sub>2</sub>)]c<sub>2</sub>p<sub>1</sub> - [1/(1+p<sub>2</sub>/b<sub>2</sub>)]v<sub>2</sub>r<sub>2</sub> | ||
| + | <br> | ||
| + | <br>dr<sub>3</sub>/dt = [1/(1+p<sub>3</sub>/a<sub>3</sub>)]c<sub>3</sub>p<sub>1</sub> - [1/(1+p<sub>2</sub>/b<sub>3</sub>)]v<sub>3</sub>r<sub>3</sub> | ||
| + | <br> | ||
| + | <br>dp<sub>1</sub>/dt = [1/(1+p<sub>1</sub>/d<sub>1</sub>)]l<sub>1</sub>r<sub>1</sub> - u<sub>1</sub>p<sub>1</sub> | ||
| + | <br> | ||
| + | <br>dp<sub>2</sub>/dt = [1/(1+p<sub>2</sub>/d<sub>2</sub>)]l<sub>2</sub>r<sub>2</sub> - u<sub>2</sub>p<sub>2</sub> | ||
| + | <br> | ||
| + | <br>dp<sub>3</sub>/dt = [1/(1+p<sub>3</sub>/d<sub>3</sub>)]l<sub>3</sub>r<sub>3</sub> - u<sub>3</sub>p<sub>3</sub> | ||
| + | </h6> | ||
| + | |||
| + | <table> | ||
| + | <tr> | ||
| + | <th>Symbol</th> | ||
| + | <th scope="col">Definition</th> | ||
| + | <th scope="col"&>Unit</th> | ||
| + | <th scope="col"&>Value</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>Type 1</th> | ||
| + | <th>protein initialize others</th> | ||
| + | <th>-</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>Type 2</th> | ||
| + | <th>protein stabilize others</th> | ||
| + | <th>-</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>Type 3</th> | ||
| + | <th>functional protein</th> | ||
| + | <th>-</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>t</th> | ||
| + | <th>time</th> | ||
| + | <th>min</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>r</th> | ||
| + | <th>mRNA</th> | ||
| + | <th>nMolar</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>p</th> | ||
| + | <th>protein</th> | ||
| + | <th>nMolar</th> | ||
| + | <th>-</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>c</th> | ||
| + | <th>relative transcription rate</th> | ||
| + | <th>mRNA/(protein·min)</th> | ||
| + | <th> 0.03/0.03/0.12</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>l</th> | ||
| + | <th>relative translation rate</th> | ||
| + | <th>protein/(mRNA·min)</th> | ||
| + | <th>2/2/2</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>v</th> | ||
| + | <th>relative degradation rates of mRNA</th> | ||
| + | <th>min<sup>-1</sup></th> | ||
| + | <th>0.03/0.03/0.023</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>u</th> | ||
| + | <th>relative degradation rates of proteins</th> | ||
| + | <th>min<sup>-1</sup></th> | ||
| + | <th>0.15/0.015/0.009</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>an, bn, and dn</th> | ||
| + | <th>the effectiveness factors of the respective feedback loops for type n</th> | ||
| + | <th>-</th> | ||
| + | <th>a1:60 | ||
| + | b1:120 | ||
| + | d1:120 a2:140 b2:140 d2:150 a3:200 b3:140 d3:310</th> | ||
| + | </tr> | ||
| + | |||
| + | |||
| + | </table> | ||
| + | |||
| + | <p></p> | ||
| + | <center> | ||
| + | <img src='https://static.igem.org/mediawiki/2017/f/fe/T--NYMU-Taipei--model_out.gif' | ||
| + | alt='NrtA exocrine secretion' | ||
| + | style='width:65%'> | ||
| + | <p style='font-size:20px'>Fig.13 NrtA exocrine secretion | ||
| + | (normal quantity in cell:green;exocrine quantity in cell:yellow;normal productive speed:purple;exocrine productive speed:pink)</p> | ||
| + | </center> | ||
| + | <p></p> | ||
| + | |||
| + | <center> | ||
| + | <a href="#!" onclick="toggleHeight13(this, 1900);" style='font-size:20px;color:#2c498c'> | ||
| + | click to close | ||
| + | </a> | ||
| + | </center> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | |||
| + | <h3></h3> | ||
| + | <h3></h3> | ||
| + | <!--reference--> | ||
| + | <div class='panel'> | ||
| + | <div id="s14" class="expandable" style='height: 30px;padding-top:15px;'> | ||
| + | |||
| + | <a href="#!" onclick="toggleHeight14(this, 900); return false" | ||
| + | style="font-family:'Acme', sans-serif;font-size:34px;color:#393a1f;height: 30px;"> | ||
| + | Reference | ||
| + | </a> | ||
| + | |||
| + | <div style="font-size:16px;"> | ||
| + | <p style="padding-top:5px;"></p> | ||
| + | <ol style="font-size:16px;"> | ||
| + | <li>Lars Brammer Nejrup. (2013). Temperature- and light-dependent growth and metabolism of the invasive red algae Gracilaria vermiculophylla – a comparison with two native macroalgae. <i>European journal of phycology</i> (2013), 48(3): 295–308. | ||
| + | <li>Joel C. Goldman, Edward J. Carpenter. (1974). A kinetic approach to the effect of temperature on algal growth. <i>Limnology and Oceanography</i> Volume 19, Issue 5 September 1974 Pages 756–766. DOI: 10.4319/lo.1974.19.5.0756 | ||
| + | <li>P. Duarte. (1995). A mechanistic model of the effects of light and temperature on algal primary productivity. <i>Ecological Modelling</i> 82 (1995) 151-160 | ||
| + | <li>Ignatius J. Menzies. (2016). Leaf colour polymorphisms: a balance between plant defence and photosynthesis. <i>Journal of Ecology</i> 2016, 104, 104–113 | ||
| + | <li>T. A. Costache. (2013). Comprehensive model of microalgae photosynthesis rate as a function of culture conditions in photobioreactors. <i>Applied Microbiology and Biotechnology</i> (2013) 97:7627–7637 | ||
| + | <li>Bo Kong. (2014). Simulation of photosynthetically active radiation distribution in algal photobioreactors using a multidimensional spectral radiation model. <i>Bioresource Technology</i> 158 (2014) 141–148 | ||
| + | <li>M. A. Mohammad Mirzaie. (2016). Kinetic modeling of mixotrophic growth of Chlorella vulgaris as a new feedstock for biolubricant. <i>Journal of Applied Phycology</i>. DOI 10.1007/s10811-016-0841-4 | ||
| + | <li>Junhai Ma. (2012). Stability of a three-species symbiosis model with delays. <i>Nonlinear Dynamics</i> (2012) 67:567–572. DOI:10.1007/s11071-011-0009-3 | ||
| + | <li>M. Bekirogullari. (2017). Production of lipid-based fuels and chemicals from microalgae: An integrated experimental and model-based optimization study. <i>Algal Research</i> 23 (2017) 78–87. | ||
| + | <li>JinShui Yang. (2011). Mathematical model of Chlorella minutissima UTEX2341 growth and lipid production under photoheterotrophic fermentation conditions. <i>Bioresource Technology</i> 102 (2011) 3077–3082 | ||
| + | <li>Steven A. Morris. (2003). Analysis of the Lotka–Volterra competition equations as a technological substitution model. <i>Technological Forecasting & Social Change</i> 70 (2003) 103–133 | ||
| + | <li>Xian-Ming Shia. (2000). Heterotrophic production of biomass and lutein by Chlorella protothecoides on various nitrogen sources. <i>Enzyme and Microbial Technology</i> 27 (2000) 312–318 | ||
| + | <li>Aaron Packer. (2011). Growth and neutral lipid synthesis in green microalgae: A mathematical model. <i>Bioresource Technology</i> 102 (2011) 111–117 | ||
| + | <li>Joseph Hunt, California State Polytechnic University, Pomona and Loyola Marymount (2005). A Continuous Model of Gene Expression. <i>University Department of Mathematics Technical Report</i> August 2005 | ||
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Latest revision as of 19:22, 1 November 2017
This year, our modeling focuses on predicting the effect of our modified microbes on productivity. It is an extremely important part to our project because it helps us accurately check and predict information from our experiments that are tested in the wet lab. In our project, there are two essential types of microalgae that play very important roles, Synechococcus PCC7942 and Chlorella vulgaris. The following descriptions will show our success in modeling.
Synechococcus PCC7942
The modeling from Figure 1 to Figure 5 belongs to the experiments of Synechococcus PCC7942 pigments for better photosynthetic efficiencies. We need to check if another microalgae contains an exogenous pigment that can successfully reach new photosynthesis rate and further increase the proportion of biomass. We already have models about the influence of energy adsorption, but pigments will certainly affect other factors. Therefore, we construct several models that each represents an important factor in the growth and cell composition. Thus, we can determine the best culturing collocation by combining these models.
Photosynthesis rate of algae
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We want to use pigments to enhance the photosynthesis rate. Different pigment absorbs different wavelength of sunlight and bring about different irradiance, body temperature, and photosynthesis rate. These two models show the influence of irradiance and temperature on photosynthesis rate.
R = Rmax * in / [ki * exp(i*m) + in]
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| R | CO2 productive rate | mol/g*min | 0.000046 |
| i | irradiance | uE/m2 | - |
| n | irradiance exponential constant | - | 1.19 |
| ki | productive coefficient | uE/(m2)*s | 174 |
| m | constant | (m2)*s /uE | 0.0022 |
Fig.1-1 Influence of irradiance on photosynthesis rate
R = A1 exp(-E1rT) - A2 exp(-E2/rT)
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| R | CO2 productive rate | - | - |
| A1 | preexponential factor at i=400 | - | 1147.7 |
| A2 | preexponential factor at i=200 | - | 3.818*108 |
| E1 | activation energy at i=400 | mol/J | 42700 |
| E2 | activation energy at i=200 | mol/J | 77100 |
| T | temperature | K | - |
Fig.1-2 Influence of temperature on photosynthesis rate
Simulation of energy absorption of each pigment
y = 0.01x - 3.5, 400<=x<=500
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The simplified graph from sunshine distribution is used to approximately calculate how much energy is absorbed by each pigment and quantifies the photon adsorption amount after conversion.
y = 0.01x - 3.5, 400<=x<=500
y = 1.5, 501<=x<=600
y = 3 - 0.0025*x, 601<=x<= 800
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| x | wavelength | nm | - |
| y | irradiance | W/m2 | - |
Fig.2 Simulation of energy absorption of each pigment
Microalgae productivity in different temperatures
U = Umax * Kss
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After we get the influential degree on temperature, we can use our modeling to predict the productivity of microalgae at different temperature without other affecting factors. Modeling is used to ensure that our experiments are under control.
U = Umax * Kss
Umax = A*exp(-E/RT)
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| U | specific growth rate | day-1 | - |
| Umax | maximum specific growth rate | day-1 | - |
| Kss | substrate parameter | - | 1 |
| A | constant | day-1 | 1.0114*1010 |
| E | activation energy | cal / mol | 6842 |
| R | gas constant | cal / K*mol | 8.314 |
Fig.3 Microalgae productivity in different temperatures
Microalgae productivity in different pH values
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When our Synechococcus PCC7942 grows at each phase, the equilibrium of the pH value is different. This model can be used to collocate with our device, and also accomplish the purpose of enhancing productivity.
R = A1 exp(-B1/pH) - A2 exp(-B2/pH)
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| R | CO2 productive rate | - | - |
| A1 | preexponential factor at i=400 | - | 8.625*10-5 |
| A2 | preexponential factor at i=200 | - | 1.83885*10-2 |
| B1 | activation energy at i=400 | mol/J | 6.45 |
| B2 | activation energy at i=200 | mol/J | 69.2 |
Fig.4 Microalgae productivity in different pH
The relation between photosynthetic rate and total absorption
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The model tells us that theoretically, there is no faster photosynthetic rate unless more energy is absorbed. After working with other models, we established the relationship between photosynthetic rate and total absorption for the purpose of best balance.
R = Rmax * en / [ke * exp(e*m) + en]
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| Rmax | maximum rate | mol / g*min | 0.000046 |
| e | absorbed energy | w/m2 | - |
| n | energy exponential constant | - | 1.252 |
| ke | productive coefficient | uE / (m2)*s | 157.88 |
| m | constant | (m2)*s / uE | 0.0035 |
Fig.5 The relation between photosynthetic rate and total absorption
Chlorella vulgaris
The modeling from Figure 6 to Figure 13 belongs to the experiments of Chlorella vulgaris for nitrogen starvation. To precisely calculate the timing of starting co-culturing and to ensure there are enough high-affinity E. coli in the bioreactor, we built several models that include the original and new system. They demonstrated the significant improvement of productivity after successfully deprived the microalgae from nitrogen. For instance, one of them provides a variety of information about population when two organisms in the pool start building some relationship.
Growth curve of Chlorella vulgaris
ln(Xt/X0) / t
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The timing of adding engineered E.coli or purified protein to Chlorella vulgaris culture is critical to our project. By analyzing the initial and final biomass concentration data the instantaneous rate would be gained. This instantaneous rate is based on reference time and other lab environment data. We have simulated the change in biomass concentration throughout the culture cycle. The intermittent information in the culture medium at each point is ultimately gained through combining other modeling results, which aims to determine the best timing and corresponding state.
ln(Xt/X0) / t
= A + B exp[-C(t-M)]
= μ (specific growth rate)
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| X | biomass concentration | g/l | - |
| t | time | hr | - |
| A | the asymptotic of ln Xt/X0 as t decrese indefinitely | - | 1.252 |
| B | the asymptotic of ln Xt/X0 as t increase indefinitely | - | - |
| C | the relative growth rate at time | M | - |
Fig.6-1 Growth curve of Chlorella vulgaris
Fig.6-2 Growth rate of Chlorella vulgaris
Oil accumulation & Nitrogen source consumption
dP/dt = αdX/dt + βX;
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By simulating common systems of oil accumulation and nitrogen source consumption, we cannot only get the reference data before the improvement, but also make it a basic equation after joining some parameters or organisms into the system.
dP/dt = αdX/dt + βX;
dN/dt = -V*X;
V = [(qM-Q)/(qM-q)] * [(Vm*N)/(N+Vh)]
Q = (X0*Q0 + N0 - N) / X
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| P | lipid | g/L | - |
| N | nitrogen | g/L | - |
| X | biomass | g/L | - |
| α | the instantaneous yield coefficient of product formation due to cell growth | g/g | 0.1973 |
| β | the specific formation rate of product | day-1 | 0.00037 |
| q | Minimum N quota | g/g | 0.0178 |
| qM | Maximum N quota | g/g | 0.0935 |
| Q | N quota | g/g | - |
| Vm | Maximum uptake rate of nitrogen | g/g*day | 0.596 |
| Vh | Half-saturation coefficient | g/m3 | 0.0000103 |
Fig.7 Oil accumulation and nirogen source consumption at normal situation(lipid:green;nitrogen:blue)
Biomass in different nitrogen concentrations
n2 = exp{[A + C*exp(-exp(-B(t-M)))] * (t2-t1)} * n1;
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To find out the best quantity of nitrogen removal, we modeled several situations of decreasing the biomass in different environments with different concentration of nitrogen. We then find the best productivity by comparing these two situations.
n2 = exp{[A + C*exp(-exp(-B(t-M)))] * (t2-t1)} * n1;
x2 = x1 + (n2-n1) * {[k[ln(b(ns+a))-1]]-e};
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| n1 | biomass at frist state | g/l | - |
| n2 | biomass at secind state | g/l | - |
| x | biomass concentration | g/l | - |
| t | time | hr | - |
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| A | the asymptotic of ln Xt/X0 as t decrese indefinitely | - | -39.9532 |
| B | the asymptotic of ln Xt/X0 as t increase indefinitely | - | -0.0222 |
| C | the relative growth rate at time M hr | - | 45.6931 |
| k | constant | - | 8.15229 |
| b | yield coefficient | - | 1207.569 |
| ns | initial nitrogen concentration | - | - |
| a | regression constant | - | 0.01 |
| e | a perturbation | - | 0.50678 |
Fig.8 Biomass in different nitrogen concentration(concentration after nitrogen deletion,black:0.1;red:0.03;green:0.02;blue:0.01;yellow:0.005 g/l)
Nitrogen concentration in nitrogen starvation
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We put normal and modified nitrogen source systems together to see their demonstration like speed and occasion. By constructing this model, we can find out the declining rate of each state and then adjust our experiments.
dn/dt = Yxn * dx/dt + m*x
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| n | nitrogen concentration | - | - |
| Yxn | nitrate coefficient | g/g | 0.21016 |
| m | maintenance parameter | hr-1 | 0.0014393 |
| x | biomass concentration | - | - |
Fig.9 Nitrogen source in nitrogen starvation(normal:blue;starvation:red)
Oil accumulation in nitrogen starvation
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We predict that total lipid will increase under nitrogen starvation. The modeling provides the theoretical information of the maximum of productivity. This graph shows that if we use symbiotic microbe to make nitrogen source isolated from the system temporarily and successfully, the productivity will be enhanced.
dp/dt = k1(dx/dt)2 + k2(dx/dt)(x) + e
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| p | lipid concentrtion | - | - |
| K1 | growth correlation coefficient | g2/g2 | 122.40085 |
| K2 | non-growth correlation coefficient | g-1 | 0.28736 |
| e | a perturbation | g/l*hr | -0.078 |
Fig.10 Oil accumulation in nitrogen starvation
Population of Co-cultured Chlorella vulgaris and Modified E.coli
x2 = [ax-x2/(1+b*x*z)] / Rx + x / Yx
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According to our reference of experimental data, we find that E.coli can build a relationship, which is like symbiosis, with Chlorella vulgaris. Therefore, we build a model and use three kinds of values from different situations to simulate their change when they are co-cultured. According to this, we get the proper experimental proportion of them at each need.
x2 = [ax-x2/(1+b*x*z)] / Rx + x / Yx
z2 = [cz-z2/(1+g*z*x)] / Rz + z / Yz
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| Z | e.coil | - | - |
| X | chlorella vulgaris | - | - |
| Rx | symbiosis coefficient | g/hr | 1.0000023 |
| Rz | symbiosis coefficient | g/hr | 1.178 |
| Yx | correlation coefficient | - | 12.576 |
| Yz | correlation coefficient | - | 2.276 |
| a | population constant | - | 0.80467 |
| c | population constant | - | 0.61198 |
| b | relative parameter | - | 0.00027 |
| g | relative parameter | - | 0.0013 |
Fig.11-1 Population of co-cultured Chlorella and modified E.coli(initial concentration 0.1g/l) (chlorella vulgaris:green;e.coli:orange)
Fig.11-2 Population of co-cultured Chlorella and modified E.coli(initial concentration 0.012g/l)(chlorella vulgaris:green;e.coli:orange)
Fig.11-3 Population of co-cultured Chlorella and modified E.coli(initial concentration 0.3g/l)
Nitrogen-lipid plot
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This chart demonstrates the connection between initial nitrogen concentration and final lipid proportion in algae cell, and it tell us the approximate trend.
l = k[ln(b(ns+a))-1] - e
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| l | lipid proportion in cell | - | - |
| k | constant | g/100g | 1.13372 |
| b | yield coefficient | - | 1.57172 |
| ns | initial nitrogen concentration | - | - |
| a | correlation coefficient | - | 2.276 |
| a | regression constant | - | 0.51653 |
| e | a perturbation | g/100g | -55.2776 |
Fig.12 Nitrogen-lipid plot
NrtA exocrine secretion
dr1/dt = [1/(1+p1/a1)]c1p1 - [1/(1+p2/b1)]v1r1
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NrtA is an endocrine secretion protein and this characteristic is a bound to reach our goal because it does not have enough efficiency to make microalgae to produce a significant amount of biofuel. We have tried to turn NrtA into exocrine secretion protein but unfortunately, we didn’t make it in time. If we have successfully transform it into a exocrine secretion protein, and with the help of the connected constitutive promoter, we might have a better result than before theoretically. And this model provide the predictive quantity of change and productivity of new method.
dr1/dt = [1/(1+p1/a1)]c1p1 - [1/(1+p2/b1)]v1r1
dr2/dt = [1/(1+p2/a2)]c2p1 - [1/(1+p2/b2)]v2r2
dr3/dt = [1/(1+p3/a3)]c3p1 - [1/(1+p2/b3)]v3r3
dp1/dt = [1/(1+p1/d1)]l1r1 - u1p1
dp2/dt = [1/(1+p2/d2)]l2r2 - u2p2
dp3/dt = [1/(1+p3/d3)]l3r3 - u3p3
| Symbol | Definition | Unit | Value |
|---|---|---|---|
| Type 1 | protein initialize others | - | - |
| Type 2 | protein stabilize others | - | - |
| Type 3 | functional protein | - | - |
| t | time | min | - |
| r | mRNA | nMolar | - |
| p | protein | nMolar | - |
| c | relative transcription rate | mRNA/(protein·min) | 0.03/0.03/0.12 |
| l | relative translation rate | protein/(mRNA·min) | 2/2/2 |
| v | relative degradation rates of mRNA | min-1 | 0.03/0.03/0.023 |
| u | relative degradation rates of proteins | min-1 | 0.15/0.015/0.009 |
| an, bn, and dn | the effectiveness factors of the respective feedback loops for type n | - | a1:60 b1:120 d1:120 a2:140 b2:140 d2:150 a3:200 b3:140 d3:310 |
Fig.13 NrtA exocrine secretion (normal quantity in cell:green;exocrine quantity in cell:yellow;normal productive speed:purple;exocrine productive speed:pink)
