Team:CIDEB-UANL Mexico/Math-Parameters

From 2013hs.igem.org

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<!-- MathJax (LaTeX for the web) -->
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    <script type="text/x-mathjax-config">
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        MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
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        MathJax.Hub.Config({
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            TeX: {
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                equationNumbers: {  autoNumber: "AMS"  }
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            }
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        });
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    </script>
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    <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<table id="title" width="100%">
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<div class="Estilo6">
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Math Model</div>
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<div style="background-color: #0B3B24;" class="Estilo6">
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<table id="subtitle" width="100%">
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<h1>MathModel</h1></div>
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<div class="Estilo6">
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<h3>Parameters and variables</h3>
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Parameters and Variables
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<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>
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<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>
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<table border="6" cellpadding="1" cellspacing="1">
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<table border="6" cellpadding="1" align="center" cellspacing="1">
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<caption>Variables</caption>
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<caption><center><b>Variables</b></center></caption>
<tr>
<tr>
<td>Symbol</td>
<td>Symbol</td>
<td>Definition</td>
<td>Definition</td>
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<td>Gene size in bp</td>
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<td>Gene size(bp)</td>
<td>Source</td>
<td>Source</td>
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<td BGCOLOR="#2E64FE">Transcription factor cI (mRNA and protein)</td>
<td BGCOLOR="#2E64FE">Transcription factor cI (mRNA and protein)</td>
<td align="center">775</td>
<td align="center">775</td>
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<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>
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<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>
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<td BGCOLOR="#BF00FF">Insecticide protein VIP (mRNA and protein)</td>
<td BGCOLOR="#BF00FF">Insecticide protein VIP (mRNA and protein)</td>
<td align="center">2412</td>
<td align="center">2412</td>
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<td><a href="http://www.ncbi.nlm.nih.gov/nuccore/HQ876489">http://www.ncbi.nlm.nih.gov/nuccore/HQ876489</a></td>
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<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>
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<td BGCOLOR="#01DF01">Reporter protein GFP (mRNA and protein)</td>
<td BGCOLOR="#01DF01">Reporter protein GFP (mRNA and protein)</td>
<td align="center">876</td>
<td align="center">876</td>
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<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>
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<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>
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</table>
</table>
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</center>
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<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>
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<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 the maximum translation rate. Assuming that the number of polymerases and ribosomes are the average values determined for E. coli, the following equations are used:</p>
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<center>
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<table border="6" cellpadding="2" cellspacing="2">
<table border="6" cellpadding="2" cellspacing="2">
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<caption>Parameters</caption>
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<caption><center><b>Parameters</b></center></caption>
<tr>
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<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>
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<td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td>
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<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>
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<td>9.6</td>
<td>9.6</td>
<td>2400RBS/Protein Length</td>
<td>2400RBS/Protein Length</td>
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<td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td>
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<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>
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<td>1.74129353</td>
<td>1.74129353</td>
<td>4200/Gene Length (nM/min)</td>
<td>4200/Gene Length (nM/min)</td>
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<td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td>
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<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>
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<td>2.985075</td>
<td>2.985075</td>
<td>2400RBS/Protein Length</td>
<td>2400RBS/Protein Length</td>
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<td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td>
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<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>
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<td>5.53359684</td>
<td>5.53359684</td>
<td>4200/Gene Length (nM/min)</td>
<td>4200/Gene Length (nM/min)</td>
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<td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td>
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<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>
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<td>9.486166</td>
<td>9.486166</td>
<td>2400RBS/Protein Length</td>
<td>2400RBS/Protein Length</td>
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<td><a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a></td>
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<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>
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</table>
</table>
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</center>
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<p>For all the variables the degradation rate is expressed by the formula (ln(2)/half life)+(ln(2)/division time), with the same division time of e. coli (30 min), because all the process occurs within it. The only thing that change is the half time; for cI, VIP and GFP (mRNA) 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>
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<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>
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<table border="6" cellpadding="2" cellspacing="2">
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<caption>Degradation</caption>
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<caption><center><b>Degradation</b></center></caption>
<tr>
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<th>Symbol</th>
<th>Symbol</th>
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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.

Variables
Symbol Definition Gene size(bp) Source
mC, C Transcription factor cI (mRNA and protein) 775 http://partsregistry.org/wiki/index.php?title=Part:BBa_C0051
mV, V Insecticide protein VIP (mRNA and protein) 2412 http://www.ncbi.nlm.nih.gov/nuccore/HQ876489
mG, G Reporter protein GFP (mRNA and protein) 876 http://parts.igem.org/wiki/index.php?title=Part:BBa_E0240

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:

Parameters
Symbol Definition Values Formula Source
α1 Transcription rate of cI 5.6 4200/Gene Length (nM/min) https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
α2 Translation rate of cI 9.6 2400RBS/Protein Length https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
α3 Transcription rate of VIP 1.74129353 4200/Gene Length (nM/min) https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
α4 Translation rate of VIP 2.985075 2400RBS/Protein Length https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
α5 Transcription rate of GFP 5.53359684 4200/Gene Length (nM/min) https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
α6 Translation rate of GFP 9.486166 2400RBS/Protein Length https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters

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).

Degradation
Symbol Definition Values Formula Source
μ1μ3,μ5, Degradation rate of cI (mRNA 0.18063836 Half life = 6.8 min, Division time = 30 min (Selinger, GW, et al., 2003)
μ2,μ4,μ6 Degradation rate of cI (protein) 0.03885825 Half life > 10 h; division time = 30 min (Varshavsky, (1997) and Tobias et al., 1991)


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