advertisement: compare things at compare-stuff.com!

Alignment quality for $\alpha \beta$ doubly wound folds

It was noted that the mean alignment shift for the 56 non-self comparisons between the 8 $\alpha \beta$ doubly wound (3.40.330) folds in the dataset, using mapped hydrophobicity, were particularly good (data not shown). Could these folds be more suitable for the mapping approach? 50 replicates of each of the 56 alignments were performed in order to discover if the improved alignment quality was consistent. Figure 5.13 shows the results. The solid line shows the alignment shift for the unmapped alignments, whilst each of the points marks the shift for a replicate of the mapped alignment. The points have a fairly clumpy distribution in many cases. In some cases the clumps are below the line, indicating better alignments from the mapping, and in other cases they are above, indicating worse alignments. The improved average alignment quality we initially observed suggests that there are more improvements than deteriorations.

Figure 5.13: Alignment quality for 50 mapping replicates (mapped hydrophobicity) of $\alpha \beta$ doubly wound (3.40.330) folds compared to alignments using unmapped hydrophobicity. For the eight doubly wound queries there are a total of 56 alignments with other doubly wound folds. These are distributed along the horizontal axis, with a numeric identifier. The alignment shifts are plotted on the vertical axis (see key). Pairs of domains which are aligned consistently better using mapped information (see text) are marked with a filled rectangle along the x-axis: (2=5p2100:1hurA0, 12=1ntr00:4fxn00, 38=5p2100:1pnrA3, 41=1pnrA3:2ohxA2, 47=4fxn00:1pnrA3, 53=1gdhA2:1pnrA3). One which is worse by the same criteria is marked with an open rectangle: (13=1raaA1:2ohxA2).

In order to test the significance of the results, consider a pair of domains A and B. Suppose we know accurately the mean, $\mu$, of the alignment shifts for A vs. B using unmapped sequences. We could then ask if the observed mean shift, $\overline{x}$, for the sample of 50 alignments of A vs. B was significantly different from $\mu$ using standard tests which assume a normal distribution. However, as discussed above, we do not have an accurate estimate for $\mu$ because we cannot repeat the results with unmapped data. Hence the test cannot be performed. Instead, we can only ask if the single observation of the alignment shift for unmapped sequences A and B is likely to be part of the distribution of alignment shifts for the mapping replicates. Assuming a normal distribution of mapped results for each pair of domains (Figure 5.13 shows that this assumption is wrong in many cases), we calculate for the unmapped result its deviation from the sampled mean in multiples of standard deviations. We find that 6 unmapped alignments are 2 or more standard deviations worse than the mapped alignments, whilst only 1 alignment is conversely better (these are marked in Figure 5.13). Thus the mapping improves more alignments than it degrades, but the number is small compared to the total (56).

Extrapolating from this result, we suggest that only a handful of alignments of other fold topologies will also be improved. The increase in alignment accuracy shown in Figure 5.12(a) is the result of the balance between a small number of successful mappings and an even smaller number of unsuccessful mappings.