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First principles structures and circular dichroism spectra for the close-packed and the 7/2 motif of collagen

The recently proposed close-packed motif for collagen is investigated using first principles semi-empirical wave function theory and Kohn-Sham density functional theory. Under these refinements the close-packed motif is shown to be stable. For the case of the 7/2 motif a similar stability exists. The electronic circular dichroism of the close-packed model has a significant negative bias and a large signal. An interesting feature of the close-packed structure is the existence of a central channel. Simulations show that, if hydrogen atoms are placed in the cavity, a chain of molecular hydrogens is formed suggesting a possible biological function for molecular hydrogen.

In this Letter, we consider the close-packed (CP) structure for collagen [1] and subject this motif to first principles calculations and compare with calculations for the 7/2 motif.
The motivation behind the CP structural motif is the remarkable coincidence that it is optimally packed while at the same time having a vanishing coupling between strain and twist [2]. While the 7/2 and 10/3 structural motifs are supercoiled triple helix structures, the CP structure is akin to that of a rope where the three polypeptide strands are intertwined.
The CP geometry is the non-periodic triple helix which optimizes the volume fraction, it has a helical pitch of 20Å.
Hitherto, the 10/3 structure suggested by Ramachandran, and Rich and Crick [3][4][5][6] and the 7/2 structure suggested by Okuyama et al. [7,8] have been the most studied motifs for collagen [9] and collagen-like peptides [10,11]. These two motifs belong to the same symmetry class: three left-handed helical polypeptide chains are supercoiled in a righthanded arrangement. For long helical structures the relatively short range of the strand and inter-strand interactions does not favor commensuration, i.e. that an integer number of residues on the polypeptide strands corresponds to a 2π supercoiling. Hence, in general the structure will not be periodic. For the periodic 10/3 structure it takes ten residues to make three full 2π rotations to complete the ∼ 85Å unit cell while for the periodic 7/2 structure it takes seven residues of one polypeptide chain to complete two full 2π rotations which complete a unit cell length of about 60Å. A contributing factor to the original suggestion to change focus from the 10/3 structure to the 7/2 structure was diffraction spots in x-ray patterns corresponding to a longitudinal period of 20Å which were unaccounted for by the 10/3 structure [12].
In high resolution crystallographic studies of peptide-like structures the question of whether the 7/2 or the 10/3 structure describe the data, or not, is not always resolved.
Therefore atoms have been assigned differently to the three strands and hence the assignment of the atoms to the individual strands remains uncertain. And, perhaps a third structure such as the CP structure would be a better overall description which could account for some of the experimental data not yet accounted for by either the 7/2 or the 10/3 structures.
Density functional theory (DFT) studies of various collagen-like peptides is an active research area [17,18] including the interesting issue of studying biomineralization [19]. For the initial configurations of the first principles calculations we used the approximate coordinates for the CP structure obtained by simple geometrical methods [1] and for the 7/2 structure the coordinates obtained from the PDB depository (entry: 1K6F 3[Pro-Pro-Gly] 10 ) [13].
These structures were then truncated to various lengths (3[PPG] 6 , 3[PPG] 3 and 3[PPG] 1 ) and hydrogens were added with the InsightII program from Biosym Technologies, Inc. To treat the effects of an aqueous environment, we have utilized the polarized continuum model (PCM) as implemented in the Gaussian 09 program [20][21][22].
The semi-empirical wave function theory (WFT) PM6 model of Stewart [23] and two Kohn-Sham density functional theory (KS-DFT) exchange correlation functionals, the CAM-B3LYP [24,25] and the LC-wPBE [26] have been used in this work. For the larger model, 3(PPG) 6 , only the PM6 model was used for geometry optimization.  Tables I and II we present the backbone and side chain torsional angles for all of the residues for the three chains for the CP structures 3(PGG) 3 and 3(PGG) 6 . In the Supplementary Material we present the backbone and side chain angles for the complete 3(PGG) 6 CP structure as well as its corresponding xyz file.
In our analysis, the CP and 7/2 structures have nearly the same energy. The PM6 energy difference between the 7/2 structure and CP structure for collagen is E(7/2) − E(CP ) = −1.739 eV, or −0.065 eV per residue for 3(PGG) 3 , and E(7/2) − E(CP ) = −29.58 eV, or −0.37 eV per residue for 3(PGG) 6 . This higher energy difference for the longer structures reflects the difficulties that the applied methods have in properly optimizing long helical structures.
Collagen has also been studied by measurements of circular dichroism (CD) spectra [27- 19 22 29]. Figure 2 shows the calculated ECD spectra of the CP and 7/2 motifs along with experimental data. The experimental ECD spectra is reproduced from Ref. [29]. The data  Torsion angles chain 1 chain 2 chain 3 at predicting the positive peak around 220 nm. We have observed that the detailed shape of the calculated spectra is sensitive to the exact values of the refined coordinates and hence we must assume some level of uncertainty simply due to the accuracy of the methods. The integrated intensities of the spectra (Ref. [29]), of the CP, and of the 7/2 are −8.4 × 10 −2 , −9.2 × 10 −2 , and −2.9 × 10 −2 degrees·cm 3 ·dmol −1 , respectively. Hence, the CP calculation is more in agreement with regards to the negative bias. The reason for this is that the CP structure does not have the right-handed super coil geometry that reduces the overall left-handed chirality of the 7/2 structure.
Surprisingly, the central channel of the CP structure seen in Fig. 1(a) opens the possibility for collagen to hold, intercalate, and transport small molecules. In Ref.
[1], the diameter of the channel was estimated to be about 2Å. In Fig. 3  It is shown that within the method applied both structures behave as stable structures, and both have roughly the same energy. Explicit solvent molecules can not only change the relative energy of various conformations peptides, but they can even stabilize conformers and species that are not stable either in the gas phase or using the simple continuum solvent models like PCM [30]. Complete features of the ECD spectra could not be described by neither of the two calculations while the negative bias is well described by the CP structure.
Atomic hydrogens placed in the channel combine to form molecular hydrogen, and may perhaps contribute to enhance the stabilization of the close-packed structure. The CP structure with its central cavity appears to be a possible hydrogen molecule channel protein as atomic hydrogen can form stable molecular hydrogen in this channel. It is an intriguing possibility that such H 2 molecules will have a biological significance and function.