Team:CIDEB-UANL Mexico/math union

From 2014hs.igem.org

(Difference between revisions)
 
(32 intermediate revisions not shown)
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<div class="container-text">
<div class="container-text">
-
<p>The union module is based in the use of a fusion protein composed by L2 and AIDA. L2+AIDA is a protein which is not affected by external factors during its transcription as well as its translation, so we needed to use the established parameters but with the data we obtained from it:</p>
+
<p>The union module is based on the use of a fusion protein composed by L2 and AIDA. L2+AIDA is a protein which is not affected by external factors during its transcription or in its translation, so the established parameters were needed to use:</p>
 +
<br>
\begin{equation}
\begin{equation}
\large \frac{d\left [ mRNA \right ]}{dt}= \alpha_{1}-d_{1}\left [ mRNA \right ]
\large \frac{d\left [ mRNA \right ]}{dt}= \alpha_{1}-d_{1}\left [ mRNA \right ]
Line 349: Line 350:
</p><br>
</p><br>
 +
<p>The parameters for translation and transcription rates from Singapore 2008 iGEM team were used, as well as the speeds at which <i>E. coli</i> carried out the transcription and translation, assuming a transcription speed of <i>70nt/s</i> and a translation speed of <i>40aa/s</i>. These data were used in the equations below with the L2+AIDA gene length <i>(2620nt)</i> and protein length
 +
(856aa) respectively:<br>
-
<p>We used the parameters for translation and transcription rate from Singapore 2008 iGEM team as well as the speeds at which <i>E. coli</i> carry out transcription and translation assuming a transcription speed of <i>70nt/s</i> and a translation speed of <i>40aa/s</i>. So we used them in the equations below with the L2+AIDA gene length <i>(2620nt)</i> and protein length (856aa) respectively:<br><br>
+
<br>
-
 
+
\begin{equation}
\begin{equation}
\large    \alpha_{1} =  \frac{transcription speed}{gene length (nt)}
\large    \alpha_{1} =  \frac{transcription speed}{gene length (nt)}
Line 368: Line 370:
\end{equation}<br>
\end{equation}<br>
-
<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 Beijing PKU 2009 iGEM team:</p>
 +
<br>
\begin{equation}
\begin{equation}
-
\large    d_{1} =  \frac{1}{half-life} + \frac{1}{30} min
+
\large    d_{1} =  \frac{1}{half-life(min)} + \frac{1}{30min}
\end{equation}<br>
\end{equation}<br>
\begin{equation}
\begin{equation}
-
\large    d_{2} =  \frac{1}{half-life} + \frac{1}{30} min
+
\large    d_{2} =  \frac{1}{half-life(min)} + \frac{1}{30min}  
\end{equation}<br>
\end{equation}<br>
-
<p>As the protein was the fusion of two we need to search for each half-life. The half-life of membrane proteins range between 2 to 20 hours in <i>E. coli</i> (Hare, 1991), and as AIDA-I is a membrane protein its half-life must be between that range since it is not determined the specific half-life of AIDA. To find the half-life of L2 we assumed it was 7.8 hours (Bergant, 2010). Bergant’s team made test with a homologous protein but found in the minor capsid of the Human Papillomavirus (HPV). Although the function of the L2 strand in HPV is viral, and in <i>E. coli</i> is ribosomal, both share similar structures and sequences. Once we have decided to use the half-life from the homologous L2 we determined to use it as the half-life for the fusion protein because it was between the range of AIDA-I, and also because it was the lower half-life assuming as <i>E. coli</i> start the L2 degradation, it would degrade the whole protein.</p>
+
<p>Since it was a fusion protein, a research was made to find out the half-life of each protein. The half-life of membrane proteins range between 2 to 20 hours in <i>E. coli</i> (Hare, 1991), and as AIDA-I is a membrane protein its half-life must be between that range, but it was not obtained the specific AIDA’s half-life. L2’s half-life was assumed to be 7.8 hours (Bergant, 2010). Bergant’s team made a test with a homologous protein, but found in the minor capsid of the Human Papillomavirus (HPV). Although the function of the L2 strand in HPV is viral and in <i>E. coli</i> is ribosomal, both share similar structures and sequences. Once it was decided to use the half-life from the homologous L2, it was used as the half-life for the fusion protein because it was between the range of AIDA-I and also because it was the lower half-life, assuming when <i>E. coli</i> starts L2 degradation, the whole protein would be degraded.</p>
-
<p>For determining the degradation rate of average mRNA we used the information from Selinger’s team (2003). They carried several experiments for finding average mRNA half-life in <i>E. coli</i>. They used mRNAs about <i>1100nt</i> concluding they have an average half-life of 5min. So with this we found the average mRNA half-life of L2+AIDA was 11.9min.</p><br>
+
<p>Later, 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 they have an average half-life of 5min. Using the previous relation was found mRNA’s half-life from L2+AIDA which was about 11.9min.</p>
 +
<br>
\begin{equation}
\begin{equation}
\large    HL =  \frac{1100(nt)}{5 min}
\large    HL =  \frac{1100(nt)}{5 min}
-
\end{equation}
+
\end{equation}<br>
-
<br><p>With all these information we could find the degradation rates for both transcription and translation of L2+AIDA
 
<br>
<br>
-
 
+
<p>With all these information, the degradation rates for both transcription and translation of L2+AIDA were found:
 +
<br>
 +
<br>
\begin{equation}
\begin{equation}
\large    d_{1} =  \frac{1}{11.9} + \frac{1}{30} = 0.11
\large    d_{1} =  \frac{1}{11.9} + \frac{1}{30} = 0.11
Line 398: Line 403:
</p><br>
</p><br>
-
<p>For the simulation we used Simbiology using the previous data in the equations for finding the amount of proteins <i>E. coli</i> would produce at certain time.  The results obtained are the following:</p>
+
<p>Simbiology® was used for the simulation. The previous data from the equations were used to calculate the amount of proteins <i>E. coli</i> would produce at certain time.  The results obtained are shown in the following graph:</p>
<br><center><p><img width=535 src="https://static.igem.org/mediawiki/2014hs/0/05/Aida_total.png"
<br><center><p><img width=535 src="https://static.igem.org/mediawiki/2014hs/0/05/Aida_total.png"
align=center hspace=12 alt="IMG_0317"></p></center>
align=center hspace=12 alt="IMG_0317"></p></center>
-
<br><p>But for translation there was another factor we had to consider, the <b><i>“f<sub>post</sub>”</i></b> which were the posttranslational variables affecting the production of the functional protein:<br>
+
<br>
 +
<p>For translation there was another factor that was needed to be taken into consideration, the <b><i>“f<sub>post</sub>”</i></b>, which were the post-translational variables affecting the production of the functional protein:<br>
\begin{equation}
\begin{equation}
Line 410: Line 416:
</p><br>
</p><br>
-
<p>As the fusion 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 movement of a protein to the membrane and 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 determined to use 5.5min because L2+AIDA are not too small or too big in length <i>(2620nt)</i>.</p>
+
<p>Since the fusion 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 proteins to its  membrane. The process by which bacteria exports its proteins are divided into three phases: the “breathing” (which happens between translation and the second phase), the second phase (which is protein movement), and translocation (in this phase the protein attaches to the membrane of the bacteria) (Peskin, 1991).With the previous data it was determined <i>E. coli</i> completes these phases in an average of 5 to 6 min, depending on the protein size (Driessen, 1990). The time used was 5.5min because L2+AIDA is not too big <i>(2620nt)</i>.</p>
-
<p>According to Ikeda y Kuroda (2011) L2 carries out an unfolding process to become functional. We found that the 50S ribosomal proteins L2, L3, L14, L23, L24, and L32, as well as the 30S ribosomal proteins S12 and S18 were native premolten globules in their free forms but adopted rigid well-folded conformations during the formation of a functional ribosome. They exhibit some amount of ordered secondary structure; the unfolding of a protein molecule results in an essential increase in its hydrodynamic volume. For instance, there is a well-documented 15–20% increase in the hydrodynamic radius of globular proteins upon their transformation into the molten globule state (Unversky, 2002). Also, we used the equation from Unversky to find the L2 unfolding rate in <i>E. coli</i> which is shown below:
 
 +
<p>According to Ikeda  and Kuroda (2011), L2 carries out an unfolding process to become functional . It was found  that 50S ribosomal proteins L2, L3, L14, L23, L24, and L32, as well as the 30S ribosomal proteins, S12 and S18 are native premolten globules in their free forms, but adopted rigid well-folded conformations during the formation of a functional ribosome. They exhibit several amounts of ordered secondary structures; the unfolding of a protein molecule results in an essential increase in its hydrodynamic volume. For instance, there is a well-documented 15–20% increase in the hydrodynamic radius of globular proteins upon their transformation into the molten globule state (Unversky, 2002). Also, Unversky developed an equation used to determine unfolding rates shown next:</p>
 +
 +
<br>
<br>\begin{equation}
<br>\begin{equation}
\large  [H]boundary = \frac{[R]+1.51}{2.785}
\large  [H]boundary = \frac{[R]+1.51}{2.785}
Line 419: Line 427:
</p><br>
</p><br>
-
<p>This equation gives the estimation of the "boundary" mean hydrophobicity value, <b><i>“[H]boundary”</i></b>, below which a polypeptide chain with a given net charge <b><i>“[R]”</i></b> will most probably be unfolded. Thus, sequences of natively unfolded proteins may be characterized by a low sequence complexity and/or high net charge coupled with low mean hydrophobicity (the values are specified for globular proteins). According to Ikeda and Kuroda (2011) the net charge <b><i>“[R]”</i></b> of L2 is 10.9, so we substituted it in the equation below:</p>
+
<p>This equation gives the estimation of the "boundary" mean hydrophobicity value, <b><i>“[H]boundary”</i></b>, below which a polypeptide chain with a given net charge <b><i>“[R]”</i></b> will most probably be unfolded. Thus, sequences of natively unfolded proteins may be characterized by a low sequence complexity and/or high net charge coupled with low mean hydrophobicity (the values are specified for globular proteins). According to Ikeda and Kuroda (2011) the net charge <b><i>“[R]”</i></b> of L2 is 10.9, so it was substituted in the equation below:</p>
 +
<br>
\begin{equation}
\begin{equation}
\large  [H]boundary = \frac{10.9 + 1.51}{2.785} = 4.45
\large  [H]boundary = \frac{10.9 + 1.51}{2.785} = 4.45
Line 426: Line 435:
</p><br>
</p><br>
-
<p>With the unfolding value and the rate of membrane transport in <i>E. coli</i> we could use it in Simbiology for modelling the functional L2+AIDA production. The results obtained were the following:</p>
+
<p>With the unfolding value and the rate of membrane transport in <i>E. coli</i> Simbiology® was used to model the functional L2+AIDA production. The results obtained were the following:</p>
<center><p><img width=490  src="https://static.igem.org/mediawiki/2014hs/9/99/Aida_y_l2.png"
<center><p><img width=490  src="https://static.igem.org/mediawiki/2014hs/9/99/Aida_y_l2.png"
align=center hspace=12 alt="IMG_0317"></p></center>
align=center hspace=12 alt="IMG_0317"></p></center>
-
<center><p><img width=540 src="https://static.igem.org/mediawiki/2014hs/1/16/Nonfunctional_irre.png"
+
<center><p><img width=540 src="https://static.igem.org/mediawiki/2014hs/5/53/Aida_y_l2_functional.png"
-
align=center hspace=12 alt="IMG_0317"></p></center><br>
+
align=center hspace=12 alt="IMG_0317"></p></center>
 +
<center><p><strong>Graph 2</strong>. Amount of functional and nonfunctional L2+AIDA protein</p></center><br>
-
<p>Comparing both graphs (<b>Graph 1</b> and <b>Graph 2</b>) we realize that although <i>E. coli</i> needs to transport the L2+AIDA proteins to its membrane, the rate at which <i>E. coli</i> does it is slower than the production of the fusion protein, but one thing we noticed and was great is that according to Simbiology, almost all the proteins once they are inserted in the membrane unfold correctly leaving less than 25 nonfunctional proteins.</p>
+
<p> When both graphs were compared (Graph 1 and Graph 2) it was concluded that although <i>E. coli</i> needs to transport L2+AIDA proteins to its membrane, the rate at which <i>E. coli</i> does it is slower than the fusion protein production, but something that was noticed (and was great) is that according to Simbiology®, almost all the proteins, once they are inserted in the membrane, unfold correctly leaving less than 25 nonfunctional proteins which are later degraded.</p>
-
<br>
+
<br><p><b><h2>Bibliography/References</h2></b></p>
-
<p><b>Bibliography</b></p>
+
 
-
<p>● Arnold Driessen, W. W. (1990). Proton transfer rate-limiting for translocation of precursor proteins by the Escherichia coli translocase. <i></i>Biochemistry, 2471-2475.</p>
+
<font size="2">
-
<p>● Charles Peskin, S. S. (1991). What drives the translocation of proteins. <i>Biophysics</i>, 3770-3774.</p>
+
<p>● BERGANT, Martina  N. M. (2010). Modification of Human Papillomavirus Minor Capsid Protein L2 by Sumoylation. <i>Journal of Virology</i>, 11585-11589.</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>
+
<p>● DRIESSEN, Arnold  W. W. (1990). Proton transfer rate-limiting for translocation of precursor proteins by the Escherichia coli translocase. <i></i>Biochemistry, 2471-2475.</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>● 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>● Martina Bergant, N. M. (2010). Modification of Human Papillomavirus Minor Capsid Protein L2 by Sumoylation. <i>Journal of Virology</i>, 11585-11589.</p>
+
<p>● IKEDA, Takeshi A. K. (2011). Why does the silica-binding protein "Si-tag" bind strongly to silica surfaces? Implications of conformational adaptation of the intrinsically disordered polypeptide to soli surfaces. <i>Colloids and Surfaces</i>, 359-363.</p>
-
<p>● Takeshi Ikeda, A. K. (2011). Why does the silica-binding protein "Si-tag" bind strongly to silica surfaces? Implications of conformational adaptation of the intrinsically disordered polypeptide to soli surfaces. <i>Colloids and Surfaces</i>, 359-363.</p>
+
<p>● PESKIN, Charles  S. S. (1991). What drives the translocation of proteins. <i>Biophysics</i>, 3770-3774.</p>
-
<p>● Uversky, V. (2002). Natively unfolded proteins: A point where biology waits for physics. <i>Protein Science</i>, 739-756.</p><br>
+
<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>● UVERSKY, V. (2002). Natively unfolded proteins: A point where biology waits for physics. <i>Protein Science</i>, 739-756.</p><br>
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Latest revision as of 01:59, 21 June 2014

iGEM CIDEB 2014 - Project

Union Module

The union module is based on the use of a fusion protein composed by L2 and AIDA. L2+AIDA is a protein which is not affected by external factors during its transcription or in its translation, so the established parameters were needed to use:


\begin{equation} \large \frac{d\left [ mRNA \right ]}{dt}= \alpha_{1}-d_{1}\left [ mRNA \right ] \end{equation}


The parameters for translation and transcription rates from Singapore 2008 iGEM team were used, as well as the speeds at which E. coli carried out the transcription and translation, assuming a transcription speed of 70nt/s and a translation speed of 40aa/s. These data were used in the equations below with the L2+AIDA gene length (2620nt) and protein length (856aa) respectively:

\begin{equation} \large \alpha_{1} = \frac{transcription speed}{gene length (nt)} \end{equation}
\begin{equation} \large \alpha_{2} = \frac{translation speed}{protein length (aa)} \end{equation}
\begin{equation} \large \alpha_{1} = \frac{(70)(60)}{2620} = 1.6 \end{equation}
\begin{equation} \large \alpha_{2} = \frac{(40)(60)}{856} = 2.8 \end{equation}

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


\begin{equation} \large d_{1} = \frac{1}{half-life(min)} + \frac{1}{30min} \end{equation}
\begin{equation} \large d_{2} = \frac{1}{half-life(min)} + \frac{1}{30min} \end{equation}

Since it was a fusion protein, a research was made to find out the half-life of each protein. The half-life of membrane proteins range between 2 to 20 hours in E. coli (Hare, 1991), and as AIDA-I is a membrane protein its half-life must be between that range, but it was not obtained the specific AIDA’s half-life. L2’s half-life was assumed to be 7.8 hours (Bergant, 2010). Bergant’s team made a test with a homologous protein, but found in the minor capsid of the Human Papillomavirus (HPV). Although the function of the L2 strand in HPV is viral and in E. coli is ribosomal, both share similar structures and sequences. Once it was decided to use the half-life from the homologous L2, it was used as the half-life for the fusion protein because it was between the range of AIDA-I and also because it was the lower half-life, assuming when E. coli starts L2 degradation, the whole protein would be degraded.

Later, 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 they have an average half-life of 5min. Using the previous relation was found mRNA’s half-life from L2+AIDA which was about 11.9min.


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

With all these information, the degradation rates for both transcription and translation of L2+AIDA were found:

\begin{equation} \large d_{1} = \frac{1}{11.9} + \frac{1}{30} = 0.11 \end{equation}
\begin{equation} \large d_{2} = \frac{1}{468} + \frac{1}{30} = 0.035 \end{equation}


Simbiology® was used for the simulation. The previous data from the equations were used to calculate the amount of proteins E. coli would produce at certain time. The results obtained are shown in the following graph:


IMG_0317


For translation there was another factor that was needed to be taken into 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 the fusion protein needs to be expressed in E. coli’s membrane, it was needed to find the average velocity at which E. coli exports proteins to its membrane. The process by which bacteria exports its proteins are divided into three phases: the “breathing” (which happens between translation and the second phase), the second phase (which is protein movement), and translocation (in this phase the protein attaches to the membrane of the bacteria) (Peskin, 1991).With the previous data it was determined E. coli completes these phases in an average of 5 to 6 min, depending on the protein size (Driessen, 1990). The time used was 5.5min because L2+AIDA is not too big (2620nt).

According to Ikeda and Kuroda (2011), L2 carries out an unfolding process to become functional . It was found that 50S ribosomal proteins L2, L3, L14, L23, L24, and L32, as well as the 30S ribosomal proteins, S12 and S18 are native premolten globules in their free forms, but adopted rigid well-folded conformations during the formation of a functional ribosome. They exhibit several amounts of ordered secondary structures; the unfolding of a protein molecule results in an essential increase in its hydrodynamic volume. For instance, there is a well-documented 15–20% increase in the hydrodynamic radius of globular proteins upon their transformation into the molten globule state (Unversky, 2002). Also, Unversky developed an equation used to determine unfolding rates shown next:



\begin{equation} \large [H]boundary = \frac{[R]+1.51}{2.785} \end{equation}


This equation gives the estimation of the "boundary" mean hydrophobicity value, “[H]boundary”, below which a polypeptide chain with a given net charge “[R]” will most probably be unfolded. Thus, sequences of natively unfolded proteins may be characterized by a low sequence complexity and/or high net charge coupled with low mean hydrophobicity (the values are specified for globular proteins). According to Ikeda and Kuroda (2011) the net charge “[R]” of L2 is 10.9, so it was substituted in the equation below:


\begin{equation} \large [H]boundary = \frac{10.9 + 1.51}{2.785} = 4.45 \end{equation}


With the unfolding value and the rate of membrane transport in E. coli Simbiology® was used to model the functional L2+AIDA production. The results obtained were the following:

IMG_0317

IMG_0317

Graph 2. Amount of functional and nonfunctional L2+AIDA protein


When both graphs were compared (Graph 1 and Graph 2) it was concluded that although E. coli needs to transport L2+AIDA proteins to its membrane, the rate at which E. coli does it is slower than the fusion protein production, but something that was noticed (and was great) is that according to Simbiology®, almost all the proteins, once they are inserted in the membrane, unfold correctly leaving less than 25 nonfunctional proteins which are later degraded.


Bibliography/References

● BERGANT, Martina N. M. (2010). Modification of Human Papillomavirus Minor Capsid Protein L2 by Sumoylation. Journal of Virology, 11585-11589.

● 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.

● IKEDA, Takeshi A. K. (2011). Why does the silica-binding protein "Si-tag" bind strongly to silica surfaces? Implications of conformational adaptation of the intrinsically disordered polypeptide to soli surfaces. Colloids and Surfaces, 359-363.

● 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.

● UVERSKY, V. (2002). Natively unfolded proteins: A point where biology waits for physics. Protein Science, 739-756.


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