Results and Discussion
Angiotensin was simulated using ProtTorter(Jung, 2013). While other simulation programs are invisible and untouchable, this can check each structure in every step. This can directly manipulate. Energetically stable local minima structure which is still smaller than the reference structure was observed.
The structure of 1n9v from the simulation with ProtTorter is shown in figure 5. Loop structure was found in most of the 8 residues except the first aspartate residue in the angiotensin peptide. The dihedral angles(ϕ, ψ) were usually around the range of (25º-30º, 0º-5º). We can see the vivid difference between this and other simulations (Figure 3). Experimental structure regularly oscillated above and below the 0º, while simulated angles were positive in the N-terminal region. These deviated far from the C-terminal region.
After simulating, we obtained angles and local energy minima. And all of these were arranged into table 1 for clarity. The initial and six iterations were arrayed in the row of the table and seven bonds in the column. In the end, 49 arguments were placed in the table. The ψ angle is written on the top of the cell and the φ in the bottom. In each cell, angles and the number of local minima are written.
The structure was simulated from very large search space. As table 1 shows, initial structure of cotranslational folding was from about 52 conformations. For this peptide composed with 8 residues, the most stable structure was from usually about 70-90 structures. It is very efficient to compare with typical molecular dynamics.
logPr value(Table 2) signifies the difference of the two compared structures with more weight on the more closer similarity. There are eight dihedral angles each for residue from 1 to 8 in both reference and simulated structures. When the two angles of the same residue is very similar, those values were made to be equivalent. On the contrary, they were made to be different.
The logPr values of simulated structures increased toward the later iterations implying the convergence in optimizations. The lowest logPr value of -15.18 was observed from the pair of 5th and 6th optimization. The fact that lower logPr values in the pairs of nearer iterations than the farther ones was found. The highest logPr value among the pairs of adjacent passes was -4.62 in init. and opt. 1(Table 2). There were difference between the cotranslational path and the torsional one.
RamRMSD(Table 2) is the RMS(root mean square) deviation between the positions of residues on the Ramachandran plot(Ramakrishinan and Ramachandan, 1965). RamRMSD is similar to logPr. This includes the growing similarity among later iterations. Pairs in closer passes had lower RamRMSD values than farther passes. The highest RamRMSD among the pairs of adjacent passes was 47.17. This was calculated from the pair between the initial and the first optimization pass.
In figure 4, the change of energy in the folding of initial structure and in the optimization were illustrated. The potential energy drastically fluctuated in the simulation of initial structure in cotranslational folding. This partly indicates that addition of amino acid is either favorable or unfavorable in each different circumstance. This fluctuation is different from following iterations. This reflects the strong effect of the change of configurations. During the six passes of optimizations, the potential energy decreased saltatorily. This shows that there are a few critical bonds which strongly influence the potential energy of the whole molecule. Demonstrating the fast convergence of the algorithm to the global energy minima, the potential energy remained as being conserved after three passes of optimizations.
Comparing this simulation and others’ experimental structure of 1n9v with RamRMSD and logPr, this is more stable than others by global minimum of –1.704(kcal/mol). The most correlation between each generated structure from its initial structure with adjacent passes have displayed. This increased for the later rounds of iterations. During the folding simulation, the energy dropped saltatorily(Figure 4).
The structure from NMR spectroscopy was very different from this simulation. The average of all logPr values ranged from -0.80 to -1.01. RamRMSD varied from 116.68 to 136.28. Although the simulated structure is somewhat different from the reference experiment, it is quite appreciable regarding the low and negative potential energy of -1.704(kcal/mol). This negative potential energy remark that this structure is stable in the vacuum environment. This structure is not only a low and stable energy structure but also a possible actual energy minimum because it is an energy minimum along the torsional propensity path. The torsional propensity path must be the path from Levinthal paradox.
Results suggest five parts to be discussed as follows. First, the difference of structure was due to the electrostatic interaction of atoms and the torsional barrier of rotatable bonds. Given motive force, a stronger turn is induced. This shortens the length of the loop structure. The structure of α-helix was observed from lattice model without the consideration of any detailed electrostatic or torsional potential energy(Leach, 2001). Thus, additional restraints of non-electrostatic interaction would induce the current loop structure into well-known helices.
Second, another reason for the difference is the utilized force field. There was difference between NMR spectroscopy and this simulation. It is because that was conducted within an aqueous solution and this was performed under the vacuum environment. The difference between the simulated and the NMR structures was brought by the neglect of the interaction of solvents with the protein molecule. And hydrophobic effect and free energy from solvent accessible surface area could be obtained from experiments. This could be applied to structure simulation.
Third, it is very interesting for its fast convergence of the iterations. Although there is a false convergence, It is quite fast finding converging structure in 6 passes. Converging energy minima were quickly obtained following this method.
Fourth, simplified representation of the three dimensional structure of a protein in torsional system was applied. This regenerates the movements of atoms of polypeptide chain in the cellular environment. The fundamental characters of ribosome bound cotranslational folding could be generated. Three dimensional information can be transformed into one dimension by computing easily. This could be operated with sequence alignment algorithms in personal computer fast and correctly as BLAST(Altshul, 1990).
Fifth, ProtTorter adopted torsional representation of atomic movements(Jung, 2013). The results showed fast convergence to the stable form and which was negative and big in the potential energy. However, this path should be solidly validated referring longer polypeptide chains and larger numbers of test proteins. The structure from this program is different from that of the representative NMR in torsion angle. This occurred in folding pathway or force field.