4.2 Consensus Partial Folding Pathway Across Trajectories
Based on the generalized trajectory summarization of BBA5, we identify a consensus partial folding pathway of length 71. In other words, 71 pairs of conformations, one from each trajectory, are considered similar to each other. Figure 3 displays four such pairs along this consensus folding pathway. For instance, the two conformations shown in Figure 3(c), corresponding to the 182th frame in the T23 trajectory and the 116th frame in the T24 trajectory of BBA5 respectively, are considered structurally similar, since both conformations exhibit an α-helix in the left half of the backbone, and a β-turn in the right half.
Figure 11 illustrate 5 pairs of conformations along the consensus folding pathway of the 1st and 3rd trajectories of GSGS. And Figure 12 illustrates 5 conformation-pairs along consensus pathway of the 1st and 5th trajectories of GSGS. We are currently in the process of identifying consensus pathways across more than 2 trajectories of GSGS. Note that by using bit-patterns, we naturally realize a rotation-invariant comparison. To illustrate this, let us again examine the afore-discussed conformation pair of BBA5. One notices that although the β-turn in the two conformations orients differently, the two conformations are still identified as being structurally similar by our approach.
Figure 11  Selected conformation-pairs along the consensus partial folding pathway across the 1st and 3rd trajectories of the GSGS peptide. The figure illustrates five pairs of conformations, one from each trajectory, along the consensus partial folding pathway identified in the 1st and 3rd trajectories.
Figure 12  Selected conformation-pairs along the consensus partial folding pathway across the 1st and 5th trajectories of the GSGS peptide. The figure illustrates five pairs of conformations, one from each trajectory, along the consensus partial folding pathway identified in the 1st and 5th trajectories. Currently, we rely on visual tools to justify these consensus pathways. We did attempt to use several measurements that have been used previously to quantify the similarity between 3D protein conformations, but to no avail. These measurements include RMSD, contact order, and native contacts. If we identify the pathway based on the best match given by any of the above measurements, we often ended up with a very short consensus pathway (as short as 10 frames). Two conformations are said to be a best match if they have the lowest RMSD or have the smallest difference in contact order or native contacts. Moreover, different best-matched measurements rendered very different consensus pathways. Finally, we notice that the best-matched conformations based on any of such measurements can often exhibit very different structural characteristics. We are investigating alternative methods for quantitative validation of our results.