Team:CIDEB-UANL Mexico/math capture

From 2014hs.igem.org

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<div class="container-text">
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<p>The capture module is based in the use of NhaS gene, but as NhaS is not the only gene expressed in the circuit because we used RFP as a reporter inside it, we needed to consider that factor. The circuit is shown below:</p>
+
<p>The capture module is based in the use of NhaS, but NhaS was not the only gene expressed in the circuit (also RFP was used as a reporter). It was needed to consider this factor. The circuit is shown below:</p>
-
<center><p><img width=334 height=100 src="https://static.igem.org/mediawiki/2014hs/6/60/Nhas_circuit_math.png"
+
<br><center><p><img width=334 height=100 src="https://static.igem.org/mediawiki/2014hs/6/60/Nhas_circuit_math.png"
align=center hspace=12 alt="IMG_0317"></p></center>
align=center hspace=12 alt="IMG_0317"></p></center>
-
<p>As it is shown in the circuit, the transcription rate is affected by Uv light, so we needed to use the stablished parameters with data from NhaS and IrrE. Uv promoters, according to Shuang Li’s team (2006), have less efficiency than constitutive promoters, which is aproximately 60% of the constitutive promoters.</p>
+
<br>
 +
<p>As it is shown in the circuit, the transcription rate is affected by Uv light. Uv promoters, according to Shuang Li’s team (2006), have less efficiency than constitutive promoters, which is approximately 60% of constitutive promoters.</p>
 +
<br>
\begin{equation}
\begin{equation}
\large \frac{d\left [ mRNA \right ]}{dt}=\alpha_{1}\cdot f_{y}-d1\left [ mRNA \right ]
\large \frac{d\left [ mRNA \right ]}{dt}=\alpha_{1}\cdot f_{y}-d1\left [ mRNA \right ]
-
\end{equation}
+
\end{equation}<br>
\begin{equation}
\begin{equation}
Line 357: Line 359:
\end{equation}
\end{equation}
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<p>We assumed that <b><i>“f<sub>y</sub>”</i></b>, the regulatory function that can activate or inhibit the system of x gene, was 0.6 because of the percentage given by Shuang Li’s team. Uv rays activate the promoter, but it is not as efficient as constitutive promoters in the transcription process.</p>
+
<br>
 +
<p>It was  assumed that <b><i>“f<sub>y</sub>”</i></b>, is the regulatory function that can activate or inhibit the system of a given gene; it was assumed 0.6 of the percentage given by Shuang Li’s team. Uv rays activate the promoter, but it is not as efficient as constitutive promoters in the transcription process.</p>
-
<p>We used the parameters from Singapore 2008 iGEM team for the translation and transcription rates as well as the speed at which <i>E. coli</i> carries out transcription and translation, assuming a transcription speed of 70nt/s and a translation speed of 40aa/s. So we used them in the equations below with the NhaS and RFP gene (1019 nt), NhaS with 69 aa and RFP with 235 aa respectively.</p>
+
<br>
 +
<p>The parameters for translation and transcription rates from <a href="https://2008.igem.org/Team:NTU-Singapore">Singapore 2008</a> team were used,  as well as the transcription and translation speeds carried out by <i>E. coli</i>, assuming a transcription speed of <i>70nt/s</i> and a translation speed of <i>40aa/s</i>. They were used in the equations below with the NhaS and RFP gene <i>(1019nt)</i>, NhaS with <i>69aa</i>.It was not needed to model RFP because is not the purpose of the team, so this section is only focused in NhaS.</p>
 +
<br>
\begin{equation}
\begin{equation}
-
\large \alpha_{1} =\frac{transcription speed}{gene length \cdot(nt)}
+
\large \alpha_{1} =\frac{transcription speed}{gene length (nt)}
-
\end{equation}
+
\end{equation}<br>
\begin{equation}
\begin{equation}
-
\large \alpha_{2} =\frac{transcription speed}{protein length \cdot(aa)}
+
\large \alpha_{2} =\frac{trasnlation speed}{protein length (aa)}
-
\end{equation}
+
\end{equation}<br>
\begin{equation}
\begin{equation}
\large \alpha_{1}=\frac{(70)(60)}{1019}=4.12
\large \alpha_{1}=\frac{(70)(60)}{1019}=4.12
-
\end{equation}
+
\end{equation}<br>
\begin{equation}
\begin{equation}
\large \alpha_{2}(NhaS)=\frac{(40)(60)}{69}=34.78
\large \alpha_{2}(NhaS)=\frac{(40)(60)}{69}=34.78
-
\end{equation}
+
\end{equation}<br>
-
 
+
-
\begin{equation}
+
-
\large \alpha_{2}(RFP)=\frac{(40)(60)}{235}=10.21
+
-
\end{equation}
+
-
<p>Then, we used the parameters for degradation rates for proteins and mRNAs from Beijing PKU 2009 iGEM team:</p>
+
<br>
 +
<p>After, it was needed to use the parameters for degradation rates of proteins and mRNAs obtained from <a href="https://2009.igem.org/Team:PKU_Beijing">PKU Beijing 2009</a> team:</p>
 +
<br>
\begin{equation}
\begin{equation}
-
\large D_{i}= \frac{1}{half-life} + \frac{1}{30} \cdot(min)
+
\large D_{i}= \frac{1}{half-life(min)} + \frac{1}{30min}  
-
\end{equation}
+
\end{equation}<br>
\begin{equation}
\begin{equation}
-
\large D_{p} = \frac{1}{half-life} + \frac{1}{30} \cdot(min)
+
\large D_{p} = \frac{1}{half-life(min)} + \frac{1}{30min}  
\end{equation}
\end{equation}
-
<p>However, since NhaS half-life has not been determined yet, we decided to search about homologous proteins with the same function as NhaS. First, we found that the half-life of membrane proteins produced in E. coli range between 2 to 20 hours (Hare, 1991), so since NhaS is a membrane protein, it should be between those values, but we decided to use 2 hours as NhaS half-life because of its size (69aa), which is relatively small. To obtain the half-life of RFP, we based the time on the GFP protein due to the similarity of their functions (fluorescence). Therefore, the half-life of RFP on which we are based is of 8 hours (Longo, 2006).</p>
+
<br>
 +
<p>However, since NhaS half-life has not been determined yet, it was decided to search for homologous proteins with the same function as NhaS. The team found that the half-life of membrane proteins produced in <i>E. coli</i> range between 2 to 20 hours (Hare, 1991) and as NhaS is a membrane protein, its half life should be between those values. At the end was decided to use 2 hours as NhaS half-life because of its relatively small size (<i>69aa</i>).
-
<p>To determine the degradation rate of average mRNA, we used the information from Selinger’s team (2003). They carried out several experiments to find the average mRNA half-life in <i>E. coli</i>. They used mRNAs about 1100 nt concluding they have an average half-life of 5min. So with this we found that the average mRNA half-life of NhaS with RFP was 4.63 min.</p>
+
<p>Later, it was used the information from Selinger’s team (2003) to determine the mRNA degradation. They performed several experiments for finding the average mRNA half-life in <i>E. coli</i>. They used mRNAs about <i>1100nt</i>  concluding that they have an average half-life of 5min. Using the previous relation was found mRNA's half-life from NhaS and RFP gene was about 4.63min.</p>
 +
<br>
\begin{equation}
\begin{equation}
-
\large HL=\frac{1100\cdot(bp)}{5min}
+
\large HL=\frac{1100(nt)}{5min}
\end{equation}
\end{equation}
-
<p>With all these information, we were able to find the degradation rates for both, the transcription and translation of NhaS and RFP, respectively.</p>
+
<br>
-
 
+
<p>With the previous information the degradation rates for both transcription and translation of NhaS were found.
 +
<br>
\begin{equation}
\begin{equation}
\large d_{1}= \frac{1}{4.63} + \frac{1}{30}=0.25  
\large d_{1}= \frac{1}{4.63} + \frac{1}{30}=0.25  
-
\end{equation}
+
\end{equation}<br>
\begin{equation}
\begin{equation}
\large d_{2}(NhaS)= \frac{1}{120} + \frac{1}{30}=0.041
\large d_{2}(NhaS)= \frac{1}{120} + \frac{1}{30}=0.041
-
\end{equation}
+
\end{equation}<br>
-
 
+
-
\begin{equation}
+
-
\large d_{2}(RFP)= \frac{1}{480} + \frac{1}{30}=0.035
+
-
\end{equation}
+
-
<p>For the simulation we used Simbiology, using the previous data in the equations to find the amount of proteins <i>E. coli</i> would produce at certain time. The simulation ended up with the next graph as a result (assuming <i>E. coli</i> is under UV rays which actives its promoter):</p>
+
<br>
 +
<p>For the simulation, the team used Simbiology® by plugging in the previously calculated data from the equations to find the amount of proteins <i>E. coli</i> would produce at certain time. The next graph shows the results of the simulation (assuming <i>E. coli</i> is under UV rays which actives its promoter):</p>
 +
<br>
-
<center><p><img width=500 height=400 src="https://static.igem.org/mediawiki/2014hs/c/c7/Nhas_graph_1.png"
+
<center><p><img width=400 height=300 src="https://static.igem.org/mediawiki/2014hs/9/9d/NhaS_only.png"
align=center hspace=12 alt="IMG_0317"></p></center>
align=center hspace=12 alt="IMG_0317"></p></center>
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<p>For translation, there was another factor we had to consider, the<b><i>“f<sub>post</sub>” </i></b>                      which were the post-translational variables affecting the production of the functional protein:</p>
+
<br>
 +
<p>But for translation, there was another factor taken in consideration, the <b><i>“f<sub>post</sub>”</i></b>                      which were the post-translational variables affecting the production of the functional protein:</p>
 +
<br>
\begin{equation}
\begin{equation}
Line 425: Line 431:
\end{equation}
\end{equation}
-
<p>As NhaS’s protein needs to be expressed in the membrane of <i>E. coli</i>, we needed to find the average velocity at which <i>E. coli</i> exports its proteins. The process by which bacteria exports its proteins are divided into three phases, the “breathing” between translation and the second phase, which is the movement of a protein to the membrane and the translocation; in this phase the protein attaches to the membrane of bacteria (Peskin, 1991). Using this information, we found <i>E. coli</i> completes these phases in an average of 5 to 6 min, depending on the protein size (Driessen, 1990). We used 5min because of the fact that NhaS is relatively small and we assumed RFP had no posttranslational variables to consider as well as it was not the protein we wanted to measure.
+
<br>
 +
<p>Since NhaS protein needs to be expressed in <i>E. coli's</i> membrane, it was needed to find the average velocity at which <i>E. coli</i> exports its proteins. The process by which bacteria exports its proteins is divided into three phases, the “breathing” (which happens between translation and the second phase), the second phase (which is the protein movement to the membrane) and finally, the translocation (in this phase the protein attaches to the membrane of bacteria) (Peskin, 1991). With the previous data it was determined <i>E. coli</i> completes these phases in an average time of 5 to 6 min, depending on the protein size (Driessen, 1990). 5min were plugged into the data because NhaS protein is relatively small (69aa).
-
<p>With the rate of protein transport we could use Simbiology to model the functional NhaS production. The results are shown in next diagrams (assuming <i>E. coli</i> is under UV rays which actives its promoter):</p>
+
<p>With the rate of protein transport, Simbiology® was used to model the functional NhaS production. The results are shown in the next diagrams (assuming <i>E. coli</i> is under UV rays which actives its promoter):</p><br>
<center><p><img width=400 height=300 src="https://static.igem.org/mediawiki/2014hs/e/e1/Nhas_diagram.png"
<center><p><img width=400 height=300 src="https://static.igem.org/mediawiki/2014hs/e/e1/Nhas_diagram.png"
align=center hspace=12 alt="IMG_0317"></p></center>
align=center hspace=12 alt="IMG_0317"></p></center>
-
<center><p><img width=500 height=400 src="https://static.igem.org/mediawiki/2014hs/1/1f/Nhas_graph_2.png"
+
<center><p><img width=500 height=350 src="https://static.igem.org/mediawiki/2014hs/f/fb/Nhas_not_alone.png"
align=center hspace=12 alt="IMG_0317"></p></center>
align=center hspace=12 alt="IMG_0317"></p></center>
-
<p>When we compared both graphs (<b>Graph 1</b> and <b>Graph 2</b>) we realized that not all the NhaS production was functional and that the production of NhaS was really big. We assumed this happens because NhaS is only 69aa in length. Also we concluded NhaS once they are in the membrane they are functional meaning they have the potential to capture Na<SUB>+</SUB> ions and be able to give resistance to saline environments in <i>E. coli</i>. As is shown in Graph 2 the amount is of proteins produced are about 6500; we assumed those proteins are ready to bind Na<SUB>+</SUB> ions.</p>
+
<br>
 +
<p>When both graphs were compared  (Graph 1 and Graph 2) it was concluded that the amount of functional NhaS is really big. It was assumed that this happened because NhaS is only <i>69aa</i> in length. Also, it was concluded that NhaS is functional  when it is located in the membrane (by functional is meant that it has the potential to capture Na<SUP>+</SUP> ions and be able to give resistance to saline environments) of <i>E. coli</i>. As is shown in Graph 2 the amount is of proteins ready to bind Na<SUP>+</SUP> produced are about 6500.
 +
 
 +
<br><p><b>
 +
<h2>Bibliography/References</h2>
 +
</b></p>
-
<p><b>Bibliography</b></p>
+
<font size="2">
 +
<p>● DRIESSEN, Arnold  W. W. (1990). Proton transfer rate-limiting for translocation of precursor proteins by the Escherichia coli translocase. <i>Biochemistry</i>, 2471-2475.</p>
 +
<p>● HARE, James  K. T. (1991). Mechanisms of plasma membrane protein degradation: Recycling proteins are degraded more rapidly than those confined to the cell surface. <i>PNAS</i>, 5902-5906.</p>
 +
<p>● LI, Shuang  L. X. (2007). A set of UV-inducible autolytic vectors for high throughput screening. <i>Journal of biotechnology</i>, 647-652.</p>
 +
<p>● LONNGO, Diane  J. H. (2006). Dynamics of single-cell gene expression. <i>Molecular Systems Biology</i>, 1-10.</p>
 +
<p>● PESKIN, Charles S. S. (1991). What drives the translocation of proteins. <i>Biophysics</i>, 3770-3774.</p>
 +
<p>● SELINGER, Douglas  R. M. (2003). Global RNA Half-Life Analysis in Escherichia coli Reveals Positional Patterns of Transcript Degradation. <i>Genome Research</i>, 216-223. </p>
-
<p>● Arnold Driessen, W. W. (1990). Proton transfer rate-limiting for translocation of precursor proteins by the Escherichia coli translocase. <i>Biochemistry</i>, 2471-2475.</p>
 
-
<p>● Charles Peskin, S. S. (1991). What drives the translocation of proteins. <i>Biophysics</i>, 3770-3774.</p>
 
-
<p>● Diane Lonngo, J. H. (2006). Dynamics of single-cell gene expression. <i>Molecular Systems Biology</i>, 1-10.</p>
 
-
<p>● James Hare, K. T. (1991). Mechanisms of plasma membrane protein degradation: Recycling proteins are degraded more rapidly than those confined to the cell surface. <i>PNAS</i>, 5902-5906.</p>
 
-
<p>● Shuang Li, L. X. (2007). A set of UV-inducible autolytic vectors for high throughput screening. <i>Journal of biotechnology</i>, 647-652.</p>
 
-
<p>● Douglas Selinger, R. M. (2003). Global RNA Half-Life Analysis in Escherichia coli Reveals Positional Patterns of Transcript Degradation. <i>Genome Research</i>, 216-223. </p>
 
 +
<div style="text-align: right;"><a href="https://2014hs.igem.org/Team:CIDEB-UANL_Mexico/math_capture#"><font color="blue">Return to the Top</font></a></p></div>
</div>
</div>

Latest revision as of 01:52, 21 June 2014

iGEM CIDEB 2014 - Project

Capture Module

The capture module is based in the use of NhaS, but NhaS was not the only gene expressed in the circuit (also RFP was used as a reporter). It was needed to consider this factor. The circuit is shown below:


IMG_0317


As it is shown in the circuit, the transcription rate is affected by Uv light. Uv promoters, according to Shuang Li’s team (2006), have less efficiency than constitutive promoters, which is approximately 60% of constitutive promoters.


\begin{equation} \large \frac{d\left [ mRNA \right ]}{dt}=\alpha_{1}\cdot f_{y}-d1\left [ mRNA \right ] \end{equation}
\begin{equation} \large f_{y}=0.6 \end{equation}

It was assumed that “fy, is the regulatory function that can activate or inhibit the system of a given gene; it was assumed 0.6 of the percentage given by Shuang Li’s team. Uv rays activate the promoter, but it is not as efficient as constitutive promoters in the transcription process.


The parameters for translation and transcription rates from Singapore 2008 team were used, as well as the transcription and translation speeds carried out by E. coli, assuming a transcription speed of 70nt/s and a translation speed of 40aa/s. They were used in the equations below with the NhaS and RFP gene (1019nt), NhaS with 69aa.It was not needed to model RFP because is not the purpose of the team, so this section is only focused in NhaS.


\begin{equation} \large \alpha_{1} =\frac{transcription speed}{gene length (nt)} \end{equation}
\begin{equation} \large \alpha_{2} =\frac{trasnlation speed}{protein length (aa)} \end{equation}
\begin{equation} \large \alpha_{1}=\frac{(70)(60)}{1019}=4.12 \end{equation}
\begin{equation} \large \alpha_{2}(NhaS)=\frac{(40)(60)}{69}=34.78 \end{equation}

After, it was needed to use the parameters for degradation rates of proteins and mRNAs obtained from PKU Beijing 2009 team:


\begin{equation} \large D_{i}= \frac{1}{half-life(min)} + \frac{1}{30min} \end{equation}
\begin{equation} \large D_{p} = \frac{1}{half-life(min)} + \frac{1}{30min} \end{equation}

However, since NhaS half-life has not been determined yet, it was decided to search for homologous proteins with the same function as NhaS. The team found that the half-life of membrane proteins produced in E. coli range between 2 to 20 hours (Hare, 1991) and as NhaS is a membrane protein, its half life should be between those values. At the end was decided to use 2 hours as NhaS half-life because of its relatively small size (69aa).

Later, it was used the information from Selinger’s team (2003) to determine the mRNA degradation. They performed several experiments for finding the average mRNA half-life in E. coli. They used mRNAs about 1100nt concluding that they have an average half-life of 5min. Using the previous relation was found mRNA's half-life from NhaS and RFP gene was about 4.63min.


\begin{equation} \large HL=\frac{1100(nt)}{5min} \end{equation}

With the previous information the degradation rates for both transcription and translation of NhaS were found.
\begin{equation} \large d_{1}= \frac{1}{4.63} + \frac{1}{30}=0.25 \end{equation}
\begin{equation} \large d_{2}(NhaS)= \frac{1}{120} + \frac{1}{30}=0.041 \end{equation}

For the simulation, the team used Simbiology® by plugging in the previously calculated data from the equations to find the amount of proteins E. coli would produce at certain time. The next graph shows the results of the simulation (assuming E. coli is under UV rays which actives its promoter):


IMG_0317


But for translation, there was another factor taken in consideration, the “fpost which were the post-translational variables affecting the production of the functional protein:


\begin{equation} \large \frac{d[P]}{dt} = \alpha_{2} \cdot[mRNA] - d_{2}[P] - f_{post} \end{equation}

Since NhaS protein needs to be expressed in E. coli's membrane, it was needed to find the average velocity at which E. coli exports its proteins. The process by which bacteria exports its proteins is divided into three phases, the “breathing” (which happens between translation and the second phase), the second phase (which is the protein movement to the membrane) and finally, the translocation (in this phase the protein attaches to the membrane of bacteria) (Peskin, 1991). With the previous data it was determined E. coli completes these phases in an average time of 5 to 6 min, depending on the protein size (Driessen, 1990). 5min were plugged into the data because NhaS protein is relatively small (69aa).

With the rate of protein transport, Simbiology® was used to model the functional NhaS production. The results are shown in the next diagrams (assuming E. coli is under UV rays which actives its promoter):


IMG_0317

IMG_0317


When both graphs were compared (Graph 1 and Graph 2) it was concluded that the amount of functional NhaS is really big. It was assumed that this happened because NhaS is only 69aa in length. Also, it was concluded that NhaS is functional when it is located in the membrane (by functional is meant that it has the potential to capture Na+ ions and be able to give resistance to saline environments) of E. coli. As is shown in Graph 2 the amount is of proteins ready to bind Na+ produced are about 6500.

Bibliography/References

● DRIESSEN, Arnold W. W. (1990). Proton transfer rate-limiting for translocation of precursor proteins by the Escherichia coli translocase. Biochemistry, 2471-2475.

● HARE, James K. T. (1991). Mechanisms of plasma membrane protein degradation: Recycling proteins are degraded more rapidly than those confined to the cell surface. PNAS, 5902-5906.

● LI, Shuang L. X. (2007). A set of UV-inducible autolytic vectors for high throughput screening. Journal of biotechnology, 647-652.

● LONNGO, Diane J. H. (2006). Dynamics of single-cell gene expression. Molecular Systems Biology, 1-10.

● PESKIN, Charles S. S. (1991). What drives the translocation of proteins. Biophysics, 3770-3774.

● SELINGER, Douglas R. M. (2003). Global RNA Half-Life Analysis in Escherichia coli Reveals Positional Patterns of Transcript Degradation. Genome Research, 216-223.

iGEM CIDEB 2014 - Footer