• Data source for reference structures
• Accessibility and secondary structure assignment
• Score of an individual position
• Score of a match
• Benchmark
• Score calibration
• Background score distributions

Data source for reference structures

Before the structural context of ELM matches can be evaluated, it is necessary to define and select the structural unit. Structure files may contain large protein complexes, single proteins, single or multiple chains, single globular domains and many other types of molecule. The dependency of ELM accessibility on globular domain rearrangements implies that multi-domain structures are not a suitable structural unit for structure filtering. The appropriate units therefore appear to be the individual globular domains themselves. Therefore we chose the SCOP protein domain definition as provided by the ASTRAL resource as the reference structure dataset to be used to implement the structure filter.

The user-submitted query sequence is first scanned for ELM matches and then aligned to the database of ASTRAL sequences derived from SCOP domains. The hit with the highest sequence identity and coverage to the query sequence is selected as the reference structure. If more than one hit has the same sequence identity and coverage to the query sequence, the structure with the best experimental resolution is taken as reference and, for the same resolution, one hit is chosen randomly. This approach may result in, for example, the organism source of the reference structure being different from the organism source of the user query sequence. However, since proteins with identical sequences fold into identical structures, the procedure for the selection of the reference structure will only introduce minimal bias in the calculation of solvent accessibility and secondary structure values.

For the structure filter to be applicable, two conditions must hold:

1) it is possible to align the query sequence or a region of it to one or more (non-overlapping) structural domains.
   (≥70% identity to the query sequence)
2) at least one ELM match falls in an aligned region, i.e. can be mapped onto a 3D domain.

Accessibility and secondary structure assignment

The solvent accessibility and secondary structure values are collected from DSSP files. For the solvent exposure of a residue, a relative (normalized) value is calculated as the ratio of the residue's accessibility DSSP value to the residue accessible surface area value as defined by Miller and co-workers (Miller et al., 1987). The latter is calculated for the residue in a Gly-Xaa-Gly tripeptide in extended conformation. The relative accessibility varies between 0 and 1.5.

The DSSP secondary structure types are: H = alpha helix, B = residue in isolated beta-bridge, E = extended strand (participates in beta ladder), G = 3-helix (3/10 helix), I = 5 helix (pi helix), T = hydrogen bonded turn, and S = bend. Unstructured regions are marked as U.
In our study we grouped the SSE types into four categories:
1) helices (H, I)
2) 3/10 helices (G)
3) strand (E)
4) loops (B, T, S, U).
Pi helices are usually attached to larger alpha helices; therefore we grouped them with helices. 3/10 helices are often poorly conserved as part of a larger loop but sometimes they are continuously linked to a larger helix and so it was decided to treat them separately. B, T, S and U are grouped together because they usually belong to 3D flexible loop-like regions.

Score of an individual position

Based on the structural study of true motifs, accessibility (q_acc (i)) and secondary structure (q_sse (i)) score of a position i are assigned as follows:

Accessibility:

             0.0 <= q_acc(i) <= 1.5

             strand: q_sse (i) = 0.35
             helix: q_sse(i) = 0.55
             3/10-helix: q_sse (i) = 1.33
             loop: q_sse (i) = 1.5

Score of a match

Given a motif match that can be modeled onto a structure domain and such that N is the number of non-wildcard positions of a match, Ω is the set of non-wildcard positions and i stands for a non-wildcard position, its Q_acc and Q_sse scores are evaluated as:

             Q_acc (match) = ∑(q_acc (i))/N, where i ∈ Ω
             Q_sse (match) = ∑(q_sse (i))/N, where i ∈ Ω

the total combined score on non-wildcard positions Q_and is simply evaluated as:

             Q_and (match) = Q_acc (match) + Q_sse (match)

Benchmark

The benchmark consists of the whole set of ELM true motifs that can be mapped onto a domain structure (at ≥ 70% sequence similarity). A set of random matches is determined as well. Our benchmark is composed of 158 reliable true motif instances and 22,058 random matches.

Score calibration

An accessibility score (Q_acc), a secondary structure score (Q_sse) and a combined score (Q_and = Q_acc + Q_sse) was assigned to the true motif instances of our dataset by considering non-wildcard positions only and to the random matches of the random dataset by considering non-wildcard positions only. The corresponding percentiles for the accessibility score (Q_acc), secondary structure score (Q_sse) and combined score (Q_and = Q_acc + Q_sse) were plotted as functions of the score (Fig. 1, 2, 3, respectively).
In order to futher assess the discriminative power of our scoring scheme and establish if one score is more discriminative than an other, we plotted ROC curves (Fig.4). The ROC curves show that all score types enable discrimination between true motifs and random matches (where it is assumed that random matches are all false positive matches)

Figure 1 - The cumulative distribution of the Q_acc (accessibility score)

Figure 2 - The cumulative distribution of the Q_sse (secondary structure score)

Figure 3 - The cumulative distribution of Q_and = Q_acc + Q_sse

Figure 4 - ROC curves for Q_acc, Q_sse and Q_and = Q_acc + Q_sse score

Based on the percentile plots, we established two score thresholds aimed at defining three score bins: one, “sparse”, lacking in true motifs and enriched in random matches, one identifying “neutral” matches, and one lacking in random matches and “enriched” in true motifs.
This “three bins” scheme roughly means that a predicted match, which is assigned a score in the “enriched” interval, will be indicated by our procedure as a good true motif candidate (i.e. likely to be a valid functional site), motif matches scoring in the bottom interval (“sparse” interval) as unlikely to be valid functional sites and those ranking in the middle one as “neutral”.
We then chose score thresholds that guarantee that at least the top 30% true motifs are retained in the enriched bin and at least the lower 40% random matches fall in the sparse bin. The “neutral” bin is the middle one, naturally defined by the “sparse” and “enriched” cut-offs and will contain the medium quality matches. The score thresholds implemented are those considering non-wildcard positions only as these displayed the highest ratio value in the “enriched” bin.

Background score distributions

Due to the paucity of true motif data, we cannot build a true motif score distribution for each ELM and compare it to the corresponding random motif score distribution. However, we can build ELM-specific random score distributions and use them as background score contexts, telling us something about the average behavior (in terms of accessibility and secondary structure scores), on a large dataset of structures, of each single ELM. These distributions aim to help users in placing the score of their prediction in the proper score background context.