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.