All-Atom Peptide Cluster Analysis

As exemplars, in Figure 3.10 we show the centroid structure for each of the top four peptide clusters for RGD, obtained using the TIPS3P water model. To give an idea of the typical RMSD between the peptide clusters obtained using the same water model, in Table 3.3 we summarise these data for RGD and SPT, obtained using both water models for the top four clusters. Since RMSD values were all greater than the 0.1 nm cutoff, this was confirmation that none of the representatives would have been assigned to the same cluster. However, RMSD values were small and ranged from 0.12 to 0.26 nm. This demonstrated that the conformational similarity between clusters and indicated

that a significant number of members of the most popular clusters would have small enough RMSD values to be considered part of the clusters of lesser population had they not already been assigned.

Figure 3.10: Centroid (as defined in section 2.1.3) cluster structures for the top four peptide clusters of RGD obtained using the TIPS3P model.

Table 3.3: RMSD values (nm) between all unique pairs among top four peptide clusters obtained with the same water model, for both TIPS3P and SPC/Fw.

Cluster ID #1 Cluster ID #2 TIPS3P RMSD SPC/Fw RMSD

RGD 1 2 0.24 0.19 1 3 0.25 0.17 1 4 0.23 0.24 2 3 0.16 0.14 2 4 0.18 0.21 3 4 0.13 0.23 SPT 1 2 0.20 0.21 1 3 0.12 0.12 1 4 0.26 0.26 2 3 0.23 0.23 2 4 0.24 0.26 3 4 0.20 0.24

Figure 3.7(b),(d) shows the growth of the number of peptide clusters with simu- lation time steps for the TIPS3P and SPC/Fw systems, for both RGD and SPT, respec- tively. We note that, in the case of RGD, unlike in the case of the corresponding back- bone clustering analysis, neither the TIPS3P or SPC/Fw plots had a plateau, although the ’cut’ data did approach plateau behaviour. The ’cut’ data represented significant clusters, which were defined as clusters that had more than 10 members over the 50 ns trajectory. In this instance, both the ’cut’ and ’all’ data-sets had a greater growth rate in the TIPS3P system. This was in contrast to the backbone clustering analysis, where the number of clusters increased at approximately the same rate for both the TIPS3P and SPC/Fw systems. This suggested that the behaviour of the side chains was affected by the water model. To test this, we calculated the distribution of dihedral angles for each of the side chains in both RGD and SPT for both the water models (see Figure B.3, Appendix A). We found for each dihedral that the angle distribution for TIPS3P and SPC/Fw showed only small differences. Indeed, the distributions had the same general shape and peak positions were the same for both water models. The only dif- ferences concerned the magnitude of some of the peaks, particularly for side chains of the R residue, as shown in Figure B.3(b)-(d). The peak that occurred between 50 and

100◦ was greater in magnitude in the TIPS3P case compared to SPC/Fw for two of the three highlighted cases, while the reverse was true for the corresponding negative part of the distribution. We propose that the cut-off used in our clustering analysis over the whole peptide may have been sufficiently small such that these small differences in dihedral angles translated into different clusters. This effect appeared more profound for RGD where there was considerably more conformational flexibility, compared with SPT. However, the difference in peptide cluster growth between the two water models may also have been due to the different viscosities of the water models. At 300.2 K and constant volume, SPC/Fw had a viscosity of 0.75 cp, while TIPS3P had a viscosity of

0.31 cp (at 293 K).126As the majority of experiments have demonstrated an inverse rela-

tionship between folding rate and visocity,221it followed that the peptide solvated by the

more viscous SPC/Fw might have taken longer to explore conformational phase space. The observation that there were a greater number of transitions between regions of the Ramachandran plot for the RGD peptide solvated by TIPS3P compared to SPC/Fw, as discussed in a previous subsection, added further support to this hypothesis. Conforma- tional rearrangements that enabled the transition from one region of the Ramachandran plot to another were less likely in the SPC/Fw case. Figure 3.8 (b) shows, in order of descending population for the two systems, the percentage populations of the clusters defined from the independent clustering analyses over the entire peptide for the TIPS3P and SPC/Fw systems. As opposed to our like-for-like cluster comparison (see Figure 3.9 (b)), in Figure 3.8 (b), clusters labelled with the same ID did not neccessarily have the same cluster representative and so should not be automatically considered as being the same cluster. The general trend in population distribution was the same between the two systems.

For both RGD and SPT, the four most populated peptide clusters for each water model were further analysed to see how similar the regions of conformational phase space represented by them were. All of the top four clusters could be matched up within the 0.1 nm cutoff (see Table 3.4). This showed that the most popular regions of phase space sampled by the peptide were similar for both water models for both peptides. As with the backbone cluster analysis, all-atom peptide cluster analysis for the two systems has also been conducted using a common set of reference cluster structures. Figure 3.9(b),(d) shows a direct comparison of the most popular regions of conformational phase space as defined by the representative structures from the top four TIPS3P peptide

clusters (T1-T4). As seen for the backbone cluster populations, the distributions were within statistical uncertainty for the SPT peptide. Again, as found with the backbone clustering analysis, there was relatively less agreement for the RGD peptide between the water models, although for both water models, the absolute populations were low and

the population distributions were quite flat. Overall, thetrendsbetween the two models

were not too dissimilar. It should be emphasised that as with the backbone cluster analysis, the small cut-off (0.1 nm) again meant that this conformational analysis is highly resolved. Although the top four cluster populations were not within error, there were only slight differences in the side-chain dihedral angle distributions between the TIPS3P and SPC/Fw cases. Again, this suggested that the differences in population are perhaps not as significant as the percentage values suggest.

Table 3.4: RMSD values (nm) for matchings of the representative structures from the top four TIPS3P and SPC/Fw peptide clusters.

TIPS3P Cluster ID SPC/Fw Cluster ID RMSD

RGD 1 2 0.05 2 4 0.02 3 3 0.06 4 1 0.05 SPT 1 1 0.04 2 2 0.04 3 3 0.11 4 4 0.05