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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<tr>
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<div class="Estilo6">
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Math Model</div>
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<table id="subtitle" width="100%">
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<h1>Project</h1></div>
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<div class="Estilo6">
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<h3>Abstract</h3>
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Parameters and Variables
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<h4></h4>
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<p><b>Thermonator III: The crop guardian</b></p>
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<p align="justify">Our project is about a genetic engineered machine in E. coli with the ability to produce Vip3ca3 which acts as a pesticide protein. Vip3ca3 production will be regulated by specific temperatures in order to avoid overproduction and it will show activity against target organisms Coleoptera and Lepidoptera, which are related to a local problem concerning potato crops. The Vip3ca3 production is regulated with a constitutive promoter and a riboswitch that initiate translation around 32°C. Since we want to produce the Vip3ca3 below the 32°C, we use a set of promoter-repressors in order to invert the activation of the protein production. This model may be used as a regulator in future transgenic plant generations for the production of substances against plagues, avoiding pesticide overproduction, thus reducing the effect in Non-Target Organisms and bioaccumulation and can be used with different temperature ranges and/or different proteins to attack other target organisms.</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" align="center" cellspacing="1">
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<img src="https://static.igem.org/mediawiki/2013hs/d/d3/D9b5b18226b32476e3e16622aae4da9e.jpg" height="300px" />
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<caption><center><b>Variables</b></center></caption>
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<tr>
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<td>Symbol</td>
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<td>Definition</td>
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<td>Gene size(bp)</td>
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<td>Source</td>
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</tr>
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<tr>
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<td  align="center" BGCOLOR="#2E64FE">mC, C</td>
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<td BGCOLOR="#2E64FE">Transcription factor cI (mRNA and protein)</td>
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<td align="center">775</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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</tr>
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<tr>
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<td align="center" BGCOLOR="#BF00FF">mV, V</td>
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<td BGCOLOR="#BF00FF">Insecticide protein VIP (mRNA and protein)</td>
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<td align="center">2412</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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</tr>
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<tr>
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<td align="center" BGCOLOR="#01DF01">mG, G</td>
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<td BGCOLOR="#01DF01">Reporter protein GFP (mRNA and protein)</td>
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<td align="center">876</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>
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</tr>
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</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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<center>
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<table border="6" cellpadding="2" cellspacing="2">
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<caption><center><b>Parameters</b></center></caption>
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<tr>
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<th>Symbol</th>
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<th>Definition</th>
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<th>Values</th>
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<th>Formula</th>
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<th>Source</th>
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</tr>
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<tr>
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<td align="center">α1</td>
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<td>Transcription rate of cI</td>
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<td>5.6</td>
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<td>4200/Gene Length (nM/min)</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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</tr>
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<tr>
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<td align="center">α2</td>
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<td>Translation rate of cI</td>
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<td>9.6</td>
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<td>2400RBS/Protein Length</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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</tr>
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<tr>
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<td align="center">α3</td>
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<td>Transcription rate of VIP</td>
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<td>1.74129353</td>
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<td>4200/Gene Length (nM/min)</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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</tr>
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<tr>
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<td align="center">α4</td>
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<td>Translation rate of VIP</td>
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<td>2.985075</td>
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<td>2400RBS/Protein Length</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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</tr>
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<tr>
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<td align="center">α5</td>
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<td>Transcription rate of GFP</td>
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<td>5.53359684</td>
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<td>4200/Gene Length (nM/min)</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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</tr>
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<tr>
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<td align="center">α6</td>
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<td>Translation rate of GFP</td>
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<td>9.486166</td>
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<td>2400RBS/Protein Length</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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</tr>
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</table>
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</center>
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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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<center>
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<table border="6" cellpadding="2" cellspacing="2">
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<caption><center><b>Degradation</b></center></caption>
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<tr>
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<th>Symbol</th>
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<th>Definition</th>
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<th>Values</th>
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<th>Formula</th>
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<th>Source</th>
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</tr>
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<tr>
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<td>μ1μ3,μ5,</td>
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<td>Degradation rate of cI (mRNA</td>
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<td>0.18063836</td>
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<td>Half life = 6.8 min, Division time = 30 min</td>
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<td>(Selinger, GW, et al., 2003)</td>
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</tr>
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<tr>
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<td>μ2,μ4,μ6</td>
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<td>Degradation rate of cI (protein)</td>
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<td>0.03885825</td>
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<td>Half life > 10 h; division time = 30 min</td>
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<td>(Varshavsky, (1997) and Tobias et al., 1991)</td>
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</tr>
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</table>
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</center>
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<br>
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<br>
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</td>
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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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