Team:CIDEB-UANL Mexico/Math-Parameters
From 2013hs.igem.org
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font-family: 'PT Sans Narrow'; | font-family: 'PT Sans Narrow'; | ||
color: #FFFFFF; | color: #FFFFFF; | ||
+ | padding: 12px; | ||
} | } | ||
- | + | #title {height: 55px; padding-left: 10px; background-color: #B45F04; font-size:50px; color:white; font-weight:bold; text-decoration:none; text-align:left;} | |
- | + | #subtitle {height: 35px; padding-left: 10px; background-color: #FF8000; font-size:30px; color:white; font-weight:bold; text-decoration:none; text-align:left;} | |
p {padding: 14px;} | p {padding: 14px;} | ||
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<body> | <body> | ||
+ | <!-- MathJax (LaTeX for the web) --> | ||
+ | <script type="text/x-mathjax-config"> | ||
+ | MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}}); | ||
+ | MathJax.Hub.Config({ | ||
+ | TeX: { | ||
+ | equationNumbers: { autoNumber: "AMS" } | ||
+ | } | ||
+ | }); | ||
+ | </script> | ||
+ | <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> | ||
+ | <table id="title" width="100%"> | ||
+ | <tr> | ||
+ | <td> | ||
+ | <div class="Estilo6"> | ||
+ | Math Model</div> | ||
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
- | < | + | <table id="subtitle" width="100%"> |
- | + | <tr> | |
- | < | + | <td> |
- | <div> | + | <div class="Estilo6"> |
- | + | Parameters and Variables | |
- | + | ||
- | + | ||
</div> | </div> | ||
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
<div style="background-color: #FFFFFF;"> | <div style="background-color: #FFFFFF;"> | ||
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<td> | <td> | ||
- | <p>Our gene circuit is made of six different variables: the concentrations of three proteins (cI, VIP and GFP) and their respective mRNA inside a cell. In table 1, the symbols for each variable are shown. Proteins are represented by a single letter and their mRNAs are represented by that same letter with a lowercase "m" before it.</p> | + | <p align="justify">Our gene circuit is made of six different variables: the concentrations of three proteins (cI, VIP and GFP) and their respective mRNA inside a cell. In table 1, the symbols for each variable are shown. Proteins are represented by a single letter and their mRNAs are represented by that same letter with a lowercase "m" before it.</p> |
- | + | <center> | |
- | <table border="6" cellpadding="1" cellspacing="1"> | + | <table border="6" cellpadding="1" align="center" cellspacing="1"> |
- | <caption>Variables</caption> | + | <caption><center><b>Variables</b></center></caption> |
<tr> | <tr> | ||
<td>Symbol</td> | <td>Symbol</td> | ||
<td>Definition</td> | <td>Definition</td> | ||
- | <td>Gene size | + | <td>Gene size(bp)</td> |
<td>Source</td> | <td>Source</td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td BGCOLOR="#2E64FE">mC, C</td> | + | <td align="center" BGCOLOR="#2E64FE">mC, C</td> |
<td BGCOLOR="#2E64FE">Transcription factor cI (mRNA and protein)</td> | <td BGCOLOR="#2E64FE">Transcription factor cI (mRNA and protein)</td> | ||
- | <td>775</td> | + | <td align="center">775</td> |
- | <td><a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051">http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051</a></td> | + | <td><a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051";><font color="blue"> http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051 </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td BGCOLOR="#BF00FF">mV, V</td> | + | <td align="center" BGCOLOR="#BF00FF">mV, V</td> |
<td BGCOLOR="#BF00FF">Insecticide protein VIP (mRNA and protein)</td> | <td BGCOLOR="#BF00FF">Insecticide protein VIP (mRNA and protein)</td> | ||
- | <td>2412</td> | + | <td align="center">2412</td> |
- | <td><a href="http://www.ncbi.nlm.nih.gov/nuccore/HQ876489">http://www.ncbi.nlm.nih.gov/nuccore/HQ876489</a></td> | + | <td><a href="http://www.ncbi.nlm.nih.gov/nuccore/HQ876489"><font color="blue"> http://www.ncbi.nlm.nih.gov/nuccore/HQ876489 </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td BGCOLOR="#01DF01">mG, G</td> | + | <td align="center" BGCOLOR="#01DF01">mG, G</td> |
<td BGCOLOR="#01DF01">Reporter protein GFP (mRNA and protein)</td> | <td BGCOLOR="#01DF01">Reporter protein GFP (mRNA and protein)</td> | ||
- | <td>876</td> | + | <td align="center">876</td> |
- | <td><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240">http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240</a></td> | + | <td><a href="http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240"><font color="blue"> http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240 </font></a></td> |
</tr> | </tr> | ||
</table> | </table> | ||
+ | </center> | ||
- | + | <p align="justify">To parameterize our model, we chose to follow the approach of team Beijing 2009; they propose a relationship between the gene length in base pairs and the maximum transcription rate and, similarly, between the protein length in amino acid numbers and maximum translation rate. Assuming that the number of polymerase and ribosomes are the average values determined for <i>E.Coli</i>, the following equations are used:</p> | |
- | <p>To parameterize our model, we chose to follow the approach of team Beijing 2009; they propose a relationship between the gene length in base pairs and the maximum transcription rate and, similarly, between the protein length in amino acid numbers and | + | <center> |
- | + | ||
<table border="6" cellpadding="2" cellspacing="2"> | <table border="6" cellpadding="2" cellspacing="2"> | ||
- | <caption>Parameters</caption> | + | <caption><center><b>Parameters</b></center></caption> |
<tr> | <tr> | ||
<th>Symbol</th> | <th>Symbol</th> | ||
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<td>5.6</td> | <td>5.6</td> | ||
<td>4200/Gene Length (nM/min)</td> | <td>4200/Gene Length (nM/min)</td> | ||
- | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td> | + | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters"><font color="blue"> https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td>α2</td> | + | <td align="center">α2</td> |
<td>Translation rate of cI</td> | <td>Translation rate of cI</td> | ||
<td>9.6</td> | <td>9.6</td> | ||
<td>2400RBS/Protein Length</td> | <td>2400RBS/Protein Length</td> | ||
- | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td> | + | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters"><font color="blue"> https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td>α3</td> | + | <td align="center">α3</td> |
<td>Transcription rate of VIP</td> | <td>Transcription rate of VIP</td> | ||
<td>1.74129353</td> | <td>1.74129353</td> | ||
<td>4200/Gene Length (nM/min)</td> | <td>4200/Gene Length (nM/min)</td> | ||
- | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td> | + | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters"><font color="blue"> https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td>α4</td> | + | <td align="center">α4</td> |
<td>Translation rate of VIP</td> | <td>Translation rate of VIP</td> | ||
<td>2.985075</td> | <td>2.985075</td> | ||
<td>2400RBS/Protein Length</td> | <td>2400RBS/Protein Length</td> | ||
- | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td> | + | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters"><font color="blue"> https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td>α5</td> | + | <td align="center">α5</td> |
<td>Transcription rate of GFP</td> | <td>Transcription rate of GFP</td> | ||
<td>5.53359684</td> | <td>5.53359684</td> | ||
<td>4200/Gene Length (nM/min)</td> | <td>4200/Gene Length (nM/min)</td> | ||
- | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td> | + | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters"><font color="blue"> https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters </font></a></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
- | <td>α6</td> | + | <td align="center">α6</td> |
<td>Translation rate of GFP</td> | <td>Translation rate of GFP</td> | ||
<td>9.486166</td> | <td>9.486166</td> | ||
<td>2400RBS/Protein Length</td> | <td>2400RBS/Protein Length</td> | ||
- | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td> | + | <td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters"><font color="blue"> https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters </font></a></td> |
</tr> | </tr> | ||
</table> | </table> | ||
+ | </center> | ||
- | <p>For all the variables the degradation rate is expressed | + | <p align="justify">For all the variables the degradation rate is expressed with the formula (ln(2)/half life)+(ln(2)/division time), with the same division time of <i>E.Coli</i> (30 min), because the whole process occurs within it. The only thing that changes is the half time; for cI, VIP and GFP (mRNA, which is 6.8 minutes and for cI (Selinger, GW, et al., 2003), VIP and GFP protein is more than 10 hours (Varshavsky, (1997) and Tobias et al., 1991).</p> |
- | + | <center> | |
<table border="6" cellpadding="2" cellspacing="2"> | <table border="6" cellpadding="2" cellspacing="2"> | ||
- | <caption>Degradation</caption> | + | <caption><center><b>Degradation</b></center></caption> |
<tr> | <tr> | ||
<th>Symbol</th> | <th>Symbol</th> | ||
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</tr> | </tr> | ||
</table> | </table> | ||
+ | </center> | ||
+ | <br> | ||
+ | <br> | ||
- | |||
- | |||
- | |||
</td> | </td> | ||
</tr> | </tr> |
Latest revision as of 00:43, 22 June 2013
Math Model
|
Parameters and Variables
|
Our gene circuit is made of six different variables: the concentrations of three proteins (cI, VIP and GFP) and their respective mRNA inside a cell. In table 1, the symbols for each variable are shown. Proteins are represented by a single letter and their mRNAs are represented by that same letter with a lowercase "m" before it.
To parameterize our model, we chose to follow the approach of team Beijing 2009; they propose a relationship between the gene length in base pairs and the maximum transcription rate and, similarly, between the protein length in amino acid numbers and maximum translation rate. Assuming that the number of polymerase and ribosomes are the average values determined for E.Coli, the following equations are used:
For all the variables the degradation rate is expressed with the formula (ln(2)/half life)+(ln(2)/division time), with the same division time of E.Coli (30 min), because the whole process occurs within it. The only thing that changes is the half time; for cI, VIP and GFP (mRNA, which is 6.8 minutes and for cI (Selinger, GW, et al., 2003), VIP and GFP protein is more than 10 hours (Varshavsky, (1997) and Tobias et al., 1991).
|
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