Line 13: | Line 13: | ||
<span class="nomal2"> | <span class="nomal2"> | ||
− | <br>To think about the power of stabilization by circularization, | + | <br>To think about the power of stabilization by |
− | we used HP (Hydrophobic-Polar) model. HP model is a kind of simplified protein | + | circularization using SAPs, we used HP (Hydrophobic-Polar) model. |
− | folding model and in | + | HP model is a kind of simplified protein folding model and in this model, |
− | Each residue has the characteristic H or P (Hydrophobic or Polar). | + | protein chain is given as zig-zag stick on 2D lattice. Each residue has |
− | residue is next to another H residue | + | the characteristic H or P (Hydrophobic or Polar). To calculate the stability |
− | free energy because of hydrophobic interaction. In our model, the decreased energy by each hydrophobic | + | of protein structures, in this model, if an H residue is next to another H |
− | interaction is defined as -E<span class="sitatuki">H</span>. We added another characteristic | + | residue without covalent bond, it decreases free energy because of hydrophobic |
− | Through thinking about this model, we can simply think about the effect of SAPs reflected as the effect to | + | interaction. In our model, the decreased energy by each hydrophobic interaction |
− | to fold | + | is defined as -E<span class="sitatuki">H</span>. We added another |
− | C terminus, both ends are set next to each other in the model. So, let's think about the simplest model. | + | characteristic SAP into this model. Through thinking about this model, |
+ | we can simply think about the effect of SAPs reflected as the effect to | ||
+ | probability to fold as native state. We thought SAPs interaction is so strong, | ||
+ | so in the case we add SAPs 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. | ||
− | <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 of | + | <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 | ||
+ | of states is 4, excluding enantiomers and rotamers. The possible states | ||
+ | and the energy are listed below. | ||
Line 48: | Line 55: | ||
− | <br>Only the first one is stable and its energy is -E<span class="sitatuki">H</span>. Because it's most stable, | + | <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. | |
+ | The probability to fold as native state is below. | ||
<br> | <br> | ||
Line 71: | Line 79: | ||
− | <br>To calculate this, we used canonical ensemble from statistical mechanics. The | + | <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. |
Line 95: | Line 103: | ||
− | <br>But with SAPs, the number of | + | <br>But with SAPs, the number of states is 1 and the state is the most stable one. |
− | + | ||
Line 143: | Line 150: | ||
− | <br>Compared with both models, we can obviously think that thanks to the addition of SAPs, we can increase the | + | <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> | <br> | ||
Line 167: | Line 173: | ||
− | <br>Let's think about more complicated case. The number of residue is 6 and the sequence is HPPHPH. The possible | + | <br>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. |
− | + | ||
Line 192: | Line 197: | ||
− | <br>As we did in the simplest model, we thought the most stable state is the native state; 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 is below. |
Line 217: | Line 222: | ||
− | <br>With SAPs, the possible | + | <br>With SAPs, the possible states are shown below. |
Line 242: | Line 247: | ||
− | <br>The | + | <br>The probability to fold as native structure is below. |
− | + | ||
Line 268: | Line 272: | ||
− | <br>As we have shown in the simplest case, by the addition of SAPs, the | + | <br>As we have shown in the simplest case, by the addition of SAPs, the probability to fold correctly is definitely increased. |
− | + | ||
Line 293: | Line 296: | ||
− | <br>However, we should be careful about SAPs' characteristic; SAPs can limit the structure by circularization, but of course, if the stabilized structure is different from native structure, the addition of SAPs means | + | <br>As we have shown, circularization using SAPs |
− | + | can stabilize protein native structure. However, | |
+ | we should be careful about SAPs' characteristic; | ||
+ | SAPs can limit the structure by circularization, | ||
+ | but of course, if the stabilized structure is different | ||
+ | from native structure, the addition of SAPs means that | ||
+ | it increase the stability of the denatured structure. | ||
+ | This can be shown in the model. If we add SAPs to the ends | ||
+ | of HPHPHHPPPHHH model, the most stable structure is changed. | ||
Line 317: | Line 327: | ||
− | <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 protein | + | <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. |
− | + | ||
</span> | </span> |
Revision as of 13:39, 19 October 2016
Team:HokkaidoU Japan
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To think about the power of stabilization by circularization using SAPs, 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 SAP into this model. Through thinking about this model, we can simply think about the effect of SAPs reflected as the effect to probability to fold as native state. We thought SAPs interaction is so strong, so in the case we add SAPs 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 SAPs, the number of states is 4, excluding enantiomers and rotamers. The possible states and the energy are listed below.
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 is below.
To calculate this, we used canonical ensemble from statistical mechanics. The probability of causing state i is calculated through the function below.
But with SAPs, the number of states is 1 and the state is the most stable one.
The possibility to fold native conformation is of course 1.
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.
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.
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 is below.
With SAPs, the possible states are shown below.
The probability to fold as native structure is below.
As we have shown in the simplest case, by the addition of SAPs, the probability to fold correctly is definitely increased.
As we have shown, circularization using SAPs can stabilize protein native structure. However, we should be careful about SAPs' characteristic; SAPs can limit the structure by circularization, but of course, if the stabilized structure is different from native structure, the addition of SAPs means that it increase the stability of the denatured structure. This can be shown in the model. If we add SAPs to the ends of HPHPHHPPPHHH model, the most stable structure is changed.
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 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.
[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
To think about the power of stabilization by circularization using SAPs, 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 SAP into this model. Through thinking about this model, we can simply think about the effect of SAPs reflected as the effect to probability to fold as native state. We thought SAPs interaction is so strong, so in the case we add SAPs 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 SAPs, the number of states is 4, excluding enantiomers and rotamers. The possible states and the energy are listed below.
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 is below.
To calculate this, we used canonical ensemble from statistical mechanics. The probability of causing state i is calculated through the function below.
But with SAPs, the number of states is 1 and the state is the most stable one.
Fig. 2 |
The possibility to fold native conformation is of course 1.
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.
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 |
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 is below.
With SAPs, the possible states are shown below.
Fig. 4 |
The probability to fold as native structure is below.
As we have shown in the simplest case, by the addition of SAPs, the probability to fold correctly is definitely increased.
As we have shown, circularization using SAPs can stabilize protein native structure. However, we should be careful about SAPs' characteristic; SAPs can limit the structure by circularization, but of course, if the stabilized structure is different from native structure, the addition of SAPs means that it increase the stability of the denatured structure. This can be shown in the model. If we add SAPs to the ends of HPHPHHPPPHHH model, the most stable structure is changed.
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 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.
[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