Difference between revisions of "Team:HokkaidoU Japan/Model"

 
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<span class="nomal2">
 
<span class="nomal2">
  
−
<br>To think about the power of stabilization by  
+
<br>In our project, we tried to stabilize protein structure
−
circularization using SAPs, we used HP (Hydrophobic-Polar) model.  
+
by circularization using SAR. About the detailed concept of
 +
circularization, please read <a href="https://2016.igem.org/Team:HokkaidoU_Japan/Circularization">circularization page</a>. To think about the power  
 +
of stabilization by  
 +
circularization using SAP, we used HP (Hydrophobic-Polar) model.  
 
HP model is a kind of simplified protein folding model and in this model,  
 
HP model is a kind of simplified protein folding model and in this model,  
 
protein chain is given as zig-zag stick on 2D lattice. Each residue has  
 
protein chain is given as zig-zag stick on 2D lattice. Each residue has  
Line 22: Line 25:
 
  interaction. In our model, the decreased energy by each hydrophobic interaction
 
  interaction. In our model, the decreased energy by each hydrophobic interaction
 
  is defined as -E<span class="sitatuki">H</span>. We added another
 
  is defined as -E<span class="sitatuki">H</span>. We added another
−
  characteristic SAP into this model. Through thinking about this model,
+
  characteristic SAR into this model. Through thinking about this model,
−
  we can simply think about the effect of SAPs reflected as the effect to  
+
  we can simply think about the effect of SAR reflected as the effect to  
−
probability to fold as native state. We thought SAPs interaction is so strong,
+
probability to fold as native state. We thought SAR interaction is so strong,
−
  so in the case we add SAPs at N terminus and C terminus, both ends are set  
+
  so in the case we add SAR at N terminus and C terminus, both ends are set  
 
next to each other in the model. So, let's think about the simplest model.
 
next to each other in the model. So, let's think about the simplest model.
  
 
<br>The simplest model is the model with the number of residue is  
 
<br>The simplest model is the model with the number of residue is  
−
4 and the sequence is HPPH. In this case, without SAPs, the number  
+
4 and the sequence is HPPH. In this case, without SAR, the number  
 
of states is 4, excluding enantiomers and rotamers. The possible states
 
of states is 4, excluding enantiomers and rotamers. The possible states
−
  and the energy are listed below.
+
  and the energy are listed below. K<span class="sitatuki">B</span> is Boltzmann constant 1.38064852*10<sup>-23</sup> (J/K), T is temperature (K).
  
  
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       <tr>
 
       <tr>
 
<td style="border-style:none; float:center">
 
<td style="border-style:none; float:center">
−
<img src="図１" width="300px" height="auto" alt="Fig_1"></td>  
+
<img src="https://static.igem.org/mediawiki/2016/d/da/T--HokkaidoU_Japan--Basicpart_Model_fig1.png" width="600px" height="auto" alt="Fig_1"></td>  
 
       </tr>
 
       </tr>
 
       <tr>
 
       <tr>
−
<td style="border-style: none"; align="center"><h2>Fig. 1
+
<td style="border-style: none;" align="center"><span class="small">Fig. 1
  
−
</h2></td>
+
</span></td>
 
       </tr>
 
       </tr>
 
</table>
 
</table>
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<br>Only the first one is stable and its energy is -E<span class="sitatuki">H</span>.  
 
<br>Only the first one is stable and its energy is -E<span class="sitatuki">H</span>.  
 
  Because it's most stable, we thought it's native state.  
 
  Because it's most stable, we thought it's native state.  
−
The probability to fold as native state is below.
+
The probability to fold as native state (P<sup>wild</sup><span class="sitatuki">HPPH</span>) is below.
  
 
<br>
 
<br>
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<br>To calculate this, we used canonical ensemble from statistical mechanics. The probability of causing state <span class="italic">i</span> is calculated through the function below.
 
<br>To calculate this, we used canonical ensemble from statistical mechanics. The probability of causing state <span class="italic">i</span> is calculated through the function below.
 +
E<span class="sitatuki">i</SARn> is the energy of state <span class="italic">i</Span>, E<SARn class="sitatuki">j</span> is the energy of the state <span class="italic">j</span>.
  
  
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−
<br>But with SAPs, the number of states is 1 and the state is the most stable one.
+
<br>But with SAR, the number of states is 1 and the state is the most stable one.
  
  
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       <tr>
 
       <tr>
 
<td style="border-style:none; float:center">
 
<td style="border-style:none; float:center">
−
<img src="図2" width="300px" height="auto" alt="Fig_2"></td>  
+
<img src="https://static.igem.org/mediawiki/2016/3/31/T--HokkaidoU_Japan--Basicpart_Model_fig2.png" width="250px" height="auto" alt="Fig_2"></td>  
 
       </tr>
 
       </tr>
 
       <tr>
 
       <tr>
−
<td style="border-style: none"; align="center"><h2>Fig. 2
+
<td style="border-style: none"; align="center"><span class="small">Fig. 2
  
−
</h2></td>
+
</span></td>
 
       </tr>
 
       </tr>
 
</table>
 
</table>
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−
<br>The possibility to fold native conformation is of course 1.
+
<br>The possibility to fold native conformation (P<span class="sitatuki">HPPH</span> <sup>SAR</sup>) is of course 1.
  
  
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−
<br>Compared with both models, we can obviously think that thanks to the addition of SAPs, we can increase the probability to fold correctly; the stability of native state is definitely increased.
+
<br>Compared with both models, we can obviously think that thanks to the addition of SAR, we can increase the probability to fold correctly; the stability of native state is definitely increased.
  
 
<br>
 
<br>
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       <tr>
 
       <tr>
 
<td style="border-style:none; float:center">
 
<td style="border-style:none; float:center">
−
<img src="図3" width="300px" height="auto" alt="Fig_3"></td>  
+
<img src="https://static.igem.org/mediawiki/2016/9/9e/T--HokkaidoU_Japan--Model_fig3.png" width="900px" height="auto" alt="Fig_3"></td>  
 
       </tr>
 
       </tr>
 
       <tr>
 
       <tr>
−
<td style="border-style: none"; align="center"><h2>Fig. 3
+
<td style="border-style: none"; align="center"><span class="small">Fig. 3
  
−
</h2></td>
+
</span></td>
 
       </tr>
 
       </tr>
 
</table>
 
</table>
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−
<br>As we did in the simplest model, we thought the most stable state is the native state; the native state has -2E<span class="sitatuki">H</span> as its energy. In this case, the possibility to fold as native structure is below.
+
<br>As we did in the simplest model, we  
 +
thought the most stable state is the native state;  
 +
the native state has -2E<span class="sitatuki">H</span>
 +
as its energy. In this case, the possibility to fold as  
 +
native structure (P<span class="sitatuki">HPPHPH</span><sup>wild</sup>) is below.
  
  
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−
<br>With SAPs, the possible states are shown below.
+
<br>With SAR, the possible states are shown below.
  
  
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       <tr>
 
       <tr>
 
<td style="border-style:none; float:center">
 
<td style="border-style:none; float:center">
−
<img src="図4" width="300px" height="auto" alt="Fig_4"></td>  
+
<img src="https://static.igem.org/mediawiki/2016/1/10/T--HokkaidoU_Japan--Model_fig4.png" width="550px" height="auto" alt="Fig_4"></td>  
 
       </tr>
 
       </tr>
 
       <tr>
 
       <tr>
−
<td style="border-style: none"; align="center"><h2>Fig. 4
+
<td style="border-style: none"; align="center"><span class="small">Fig. 4
  
−
</h2></td>
+
</span></td>
 
       </tr>
 
       </tr>
 
</table>
 
</table>
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−
<br>The probability to fold as native structure is below.
+
<br>The probability to fold as native structure (P<span class="sitatuki">HPPHPH</span><sup>SAR</sup>) is below.
  
  
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−
<br>As we have shown in the simplest case, by the addition of SAPs, the probability to fold correctly is definitely increased.
+
<br>As we have shown in the simplest case, by the addition of SAR, the probability to fold correctly is definitely increased.
  
  
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−
<br>As we have shown, circularization using SAPs
+
<br>As we have shown, circularization using SAR
 
can stabilize protein native structure. However,  
 
can stabilize protein native structure. However,  
−
we should be careful about SAPs' characteristic;  
+
we should be careful about SAR' characteristic;  
−
SAPs can limit the structure by circularization,  
+
SAR can limit the structure by circularization,  
 
but of course, if the stabilized structure is different  
 
but of course, if the stabilized structure is different  
−
from native structure, the addition of SAPs means that  
+
from native structure, the addition of SAR means that  
 
it increase the stability of the denatured structure.  
 
it increase the stability of the denatured structure.  
−
This can be shown in the model. If we add SAPs to the ends  
+
This can be shown in the model. If we add SAR to the ends  
 
of HPHPHHPPPHHH model, the most stable structure is changed.
 
of HPHPHHPPPHHH model, the most stable structure is changed.
  
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       <tr>
 
       <tr>
 
<td style="border-style:none; float:center">
 
<td style="border-style:none; float:center">
−
<img src="図5" width="300px" height="auto" alt="Fig_5"></td>  
+
<img src="https://static.igem.org/mediawiki/2016/f/fb/T--HokkaidoU_Japan--Model_fig5.png" width="550px" height="auto" alt="Fig_5"></td>  
 
       </tr>
 
       </tr>
 
       <tr>
 
       <tr>
−
<td style="border-style: none"; align="center"><h2>Fig. 5
+
<td style="border-style: none"; align="center"><span class="small">Fig. 5
  
−
</h2></td>
+
</span></td>
 
       </tr>
 
       </tr>
 
</table>
 
</table>
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−
<br>As shown above, native state's free energy is -5E<span class="sitatuki">H</span>, but stabilized structure's lowest energy is only -3E<span class="sitatuki">H</span>. This means that if we want to stabilize a protein with circularization using SAPs, we have to be careful about the difference between its native structure and stabilized structure. If they have huge difference, we have to add linkers not to break its native structure by circularization using SAPs.
+
<br>As shown above, native state's free energy is -5E<span class="sitatuki">H</span>, but stabilized structure's lowest energy is only -3E<span class="sitatuki">H</span>. This means that if we want to stabilize a protein with circularization using SAR, we have to be careful about the difference between its native structure and stabilized structure. If they have huge difference, we have to add linkers not to break its native structure by circularization using SAR.
  
 
</span>
 
</span>
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<span class="nomal2">
 
<span class="nomal2">
−
<br>[1] Dill K.A. (1985). "Theory for the folding and stability of globular proteins". Biochemistry. 24(6): 1501?9. doi:10.1021/bi00327a032. PMID 3986190.
+
<br>[1] Dill K.A. (1985). "Theory for the folding and stability of globular proteins". Biochemistry. 24(6): 1501-9. doi:10.1021/bi00327a032. PMID 3986190.
  
 
<br>[2] Rob Philips. (2008) "Physical Biology Of the Cell". Garland Science
 
<br>[2] Rob Philips. (2008) "Physical Biology Of the Cell". Garland Science

Latest revision as of 23:44, 19 October 2016

Team:HokkaidoU Japan - 2016.igem.org

 

Team:HokkaidoU Japan

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Modeling

In our project, we tried to stabilize protein structure by circularization using SAR. About the detailed concept of circularization, please read circularization page. To think about the power of stabilization by circularization using SAP, we used HP (Hydrophobic-Polar) model. HP model is a kind of simplified protein folding model and in this model, protein chain is given as zig-zag stick on 2D lattice. Each residue has the characteristic H or P (Hydrophobic or Polar). To calculate the stability of protein structures, in this model, if an H residue is next to another H residue without covalent bond, it decreases free energy because of hydrophobic interaction. In our model, the decreased energy by each hydrophobic interaction is defined as -EH. We added another characteristic SAR into this model. Through thinking about this model, we can simply think about the effect of SAR reflected as the effect to probability to fold as native state. We thought SAR interaction is so strong, so in the case we add SAR at N terminus and C terminus, both ends are set next to each other in the model. So, let's think about the simplest model.
The simplest model is the model with the number of residue is 4 and the sequence is HPPH. In this case, without SAR, the number of states is 4, excluding enantiomers and rotamers. The possible states and the energy are listed below. KB is Boltzmann constant 1.38064852*10-23 (J/K), T is temperature (K).
Fig_1
Fig. 1


Only the first one is stable and its energy is -EH. Because it's most stable, we thought it's native state. The probability to fold as native state (PwildHPPH) is below.
Formula_1



To calculate this, we used canonical ensemble from statistical mechanics. The probability of causing state i is calculated through the function below. Ei is the energy of state i, Ej is the energy of the state j.
Formula_2



But with SAR, the number of states is 1 and the state is the most stable one.
Fig_2
Fig. 2


The possibility to fold native conformation (PHPPH SAR) is of course 1.
Formula_3



Compared with both models, we can obviously think that thanks to the addition of SAR, we can increase the probability to fold correctly; the stability of native state is definitely increased.
Formula_4



Let's think about more complicated case. The number of residue is 6 and the sequence is HPPHPH. The possible states are shown below. Also, we excluded enantiomers and rotamers.
Fig_3
Fig. 3


As we did in the simplest model, we thought the most stable state is the native state; the native state has -2EH as its energy. In this case, the possibility to fold as native structure (PHPPHPHwild) is below.
Formula_5



With SAR, the possible states are shown below.
Fig_4
Fig. 4


The probability to fold as native structure (PHPPHPHSAR) is below.
Formula_6



As we have shown in the simplest case, by the addition of SAR, the probability to fold correctly is definitely increased.
Formula_7



As we have shown, circularization using SAR can stabilize protein native structure. However, we should be careful about SAR' characteristic; SAR can limit the structure by circularization, but of course, if the stabilized structure is different from native structure, the addition of SAR means that it increase the stability of the denatured structure. This can be shown in the model. If we add SAR to the ends of HPHPHHPPPHHH model, the most stable structure is changed.
Fig_5
Fig. 5


As shown above, native state's free energy is -5EH, but stabilized structure's lowest energy is only -3EH. This means that if we want to stabilize a protein with circularization using SAR, we have to be careful about the difference between its native structure and stabilized structure. If they have huge difference, we have to add linkers not to break its native structure by circularization using SAR.

reference

[1] Dill K.A. (1985). "Theory for the folding and stability of globular proteins". Biochemistry. 24(6): 1501-9. doi:10.1021/bi00327a032. PMID 3986190.
[2] Rob Philips. (2008) "Physical Biology Of the Cell". Garland Science