Team:HokkaidoU Japan - 2016.igem.org

Team:HokkaidoU Japan

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To think about the power of stabilization by circularization, we used HP (Hydrophobic-Polar) model. HP model is a kind of simplified protein folding model and in the model, protein chain is given as zig-zag stick on 2D lattice. Each residue has the characteristic H or P (Hydrophobic or Polar). In this model, if an H residue is next to another H residue except the case it is due to the covalent bond, it decrease free energy because of hydrophobic interaction. In our model, the decreased energy by each hydrophobic interaction is defined as -EH. We added another characteristic SAPs into this model. Through thinking about this model, we can simply think about the effect of SAPs reflected as the effect to possibility to fold into native conformation. 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 folding 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, so we thought it's native state. The possibility to fold as native state is below.

To calculate this, we used canonical ensemble from statistical mechanics. The possibility of causing state i is calculated through the function below.

But with SAPs, the number of folding is 1 and the structure is the stablest 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 possibility to fold correctly; the stability of native structure is definitely increased.

Let's think about more complicated case. The number of residue is 6 and the sequence is HPPHPH. The possible foldings are shown below.

Fig. 3

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

With SAPs, the possible structures are shown below.

Fig. 4

The possibility to fold as native structure is below.

As we have shown in the simplest case, by the addition of SAPs, the possibility to fold correctly is definitely increased.

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 the increase of the stability of the denatured structure. This fact 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 protein of interest with circularization using SAPs, we have to add linkers carefully to make their ends closed without breaking their native structure.