A list of 8 119 protein structures was extracted from the PDB of May 2008 with PISCES software 40 , using the following criteria: data obtained by X-ray diffraction, with a resolution better than 2.5 Å, longer than 30 residues, less than 50% sequence identity between any pair. We restricted this list to the 5 429 structures classified in SCOP 19 . As it is assumed that proteins grouped in the same SCOP superfamily have similar structure and function, this level was chosen for our analysis. For statistical analysis, we further restricted the list to proteins classified into superfamilies with at least two members in the data set, corresponding to 4 911 proteins from 1 493 superfamilies. On average, a superfamily contains 7.90 proteins (±13.78).

To validate the functional role of over-represented structural words, we analyzed their correspondence with functional annotations extracted from the Swiss-Prot database. Swiss-Prot is a curated sequence database providing a high level of annotation (description of protein function, domain structure, post-translational modifications, variants, etc.), a minimal level of redundancy and a high level of integration with other databases 41 . To extract functional annotations from our initial data set, we used the PDB/UniProt Mapping database 42 , which consists of several files mapping the PDB and UniProt codes, and PDB and UniProt sequence numbering. Only 1 487 of the 4 911 protein structures of our initial data set are present in the PDB/UniProt Mapping database. From this set of 1 487 proteins, called annotation data set, we extracted the Swiss-Prot annotations. We focused on the feature table listing post-translational modifications, binding sites, enzyme active sites, local secondary structure or other features. We extracted only the following annotations: "Repeat" (Positions of repeated sequence motifs or repeated domains), calcium, DNA, nucleotide-binding sites, metal-binding sites (cobalt, copper, iron, magnesium, manganese, molybdenum, nickel, sodium), zinc finger, active sites, and binding sites for any chemical group (co-enzyme, prosthetic group, etc).

This data set was used to double-check the correspondence between structural motifs and Swiss-Prot annotations. From PDB/UniProt Mapping database, we extracted a set of 2 640 proteins classified in SCOP. From this protein set, we retained the 2 636 proteins obtained by X-ray diffraction, with a resolution better than 3 Å, longer than 40 residues and presenting less than 95% sequence identity between any pair.

HMM-SA is a structural alphabet of 27 structural prototypes of four residues, called structural letters, established with hidden Markov models. The main steps of HMM-SA construction are the following (see 34 36 for details):

1. the backbone of protein structures of a large data set are split in overlapping fragments of four residues,

2. each four-residue fragment is described by the three distances between the non-successive α-carbons and the projection of the fourth α-carbon on the plan formed by the first three ones,

3. four-residue fragments are classified according to their geometry and their succession in protein structures, using a hidden Markov model where the inputs are the vectors of distance descriptors of each fragment.

4. the optimal structural alphabet model is selected using the parsimony principle to choose the model that better fits the data with the smallest possible complexity. In this goal, structural alphabets of different lengths are compared using the Bayesian Information Criterion, which balances the log-likelihood of the model and a penalty term related to the number of parameters of the model and the sample size.

The optimal HMM-SA resulted in 27 classes of four-residue fragments and the transition matrix between these classes. For each class, labelled by letters (a, A-Z) and named structural letters, a representative four-residue fragment, presented in Figure 2A, is computed. It has been shown that four structural letters (A, a, W, V) are specific to α-helices, five (L, M, N, T, X) are specific to β-strands and the remaining 18 describe loops 36 .

HMM-SA can be used to simplify a protein structure of n residues into a sequence of (n - 3) structural letters. This simplification takes into account the structural similarity of four-residue fragments with the 27 structural letters. It is achieved by a dynamic programming algorithm based on Markovian process to obtain maximum a posteriori encoding using the Viterbi algorithm. The input is the sequence of distance descriptors of the four-residue fragments of the input structure. The output is a sequence of structural letters, where each structural letter describes the geometry of a four-residue fragment.

We used HMM-SA to extract structural motifs from protein loops using the protocol established in a previous study 39 and summarized in Figure 2. We first simplified all the 4 911 structures of our initial data set in sequences of structural letters. Since we focused our analysis on protein loops, regular secondary structures were removed, based on the fact that some structural letters are specific to regular secondary structures 36 37 . From the initial data set, we obtain 90 811 protein loops encoded into structural-letter sequences. In these 90 811 protein loops, we chose to study the structural motifs formed by four consecutive structural letters (i.e., seven residues). The choice of the length of four structural letters is motivated by our previous work 39 , where we showed that it allows a compromise between considering long fragments on the one hand, and avoiding data sparsity on the other hand. The 90 811 protein loops are split into 238 158 seven-residue fragments, described by 25 304 different words of four structural letters. As we have previously shown that structural words with low frequencies are linked to structural flexibility and regions with uncertain coordinates 39 , we did not consider structural words seen less than five times in our initial data set. This results in a set of 11 294 different structural words, grouping 224 148 seven-residue fragments. Each word is seen on average 20 times (±32), meaning that it groups on average 20 seven-residue fragments.

We used the SPatt software 38 43 , available from http://stat.genopole.cnrs.fr/spatt/index.html to identify structural motifs over-represented in SCOP superfamilies.

Here, we computed the over-representation of four-structural-letter motifs in sets of protein loops grouped by SCOP superfamilies. The considered sequences are typically short. The SPatt approach allows the calculation of exact statistics in sets of short sequences 44 45 . The over-representation of a word w in a set of sequences is assessed by comparing its observed occurrence (N_obs ) with the theoretical occurrence (N_theo ) expected under a background model. The over-representation score Lp of w is given by

where the p - value is defined by:

where P denotes the probability of the events. For instance, a Lp score of 3 means that a word is over-represented with a p - value of 10^-3. SPatt allows the exact computation of the distribution of the word occurrence N_theo and thus the corresponding p - value. The approach implemented in SPatt is based on the notion of automata. We briefly present it below, see 44 45 for details. Let us consider, for example, the word PZCD. The first step in SPatt consists in building an optimal Markov chain embedding through a Deterministic Finite Automata (DFA) shown in Figure 3A. The second step in SPatt consists in passing the structural-letter sequences in the DFA, resulting in the corresponding state sequence as illustrated in Figure 3B. By definition these state sequences are a heterogeneous first order Markov chain embedding over the alphabet , with a starting distribution m_d (d ∈ [1, r]) and a transition matrix T. The computation of m_d and T are explained in 44 . Then, these corresponding Markov chain embedding parameters allow the computation of the generating function of N_w in each structural-letter sequence. From the generating functions, , of N _theo, all terms of equation 1 are deduced, see 44 :

A simple example of the computation of p - value of word using DFA is presented in details 44 . Note that, contrary to approaches based on the hypergeometric distribution approximation, the exact approach does not require any correction to take into account the size of the data set in which the patterns are searched. This is explicitly taken into account during the exact p - value computation.

In this work, we computed the over-representation scores for four structural-letter words, in the loop regions of proteins classified into SCOP superfamilies. In each of the 1 493 superfamilies, we computed the Lp scores of those words, among the 11 294 that meet the condition of being observed at least five times in the superfamily. In order to take into account multiple testing, we used the Bonferroni correction to set the significance threshold, resulting in a final threshold equal to 5.97.

We further considered two criteria:

• Lp_max : the maximal Lp score of a word among all superfamilies,

• nb_sf* : the number of superfamilies in which a word is significantly over-represented.

These two criteria enabled us to differentiate two types of over-represented structural words, as defined in Table 1: words over-represented in a large number of SCOP superfamily, with Lp_max > 5:97 and nb_sf* >= 5, which we refer to as ubiquitous words and highly over-represented in one superfamily, with Lp_max > 5.97 and nb_sf* < 5, which we refer to as superfamily-specific words.

For comparison, we also calculated these criteria over randomized data sets obtained by randomly reassigning loops to SCOP superfamilies.

Ubiquitous words were compared with well-characterized 3D motifs: β-turns, niche and nest motifs. β-turns are detected in protein structures with ExtractTurn software 46 . Turns are defined as tetrapeptides with an distance lower than 7 Å, with the two central residues i + 1 and i + 2 in a non helical state 47 . Nest and niche motifs are identified using the Motivated Proteins database 48 . Nest motifs are fragments of three consecutive residues, in which the main-chain NH of residue i and the main-chain NH of residue i + 2 have the potential to interact weakly with an anionic group 49 . Niche motifs are formed by three or four consecutive residues in which the main-chain CO of residue i and the main-chain CO of the last residue i + 2 or i + 3 have the potential to interact weakly with a cationic group 50 . The Motivated Protein database stores the nest and niche motifs detected in a data set of 400 representative proteins. Only 249 of these 400 proteins are also included in our initial data set. The comparison of structural words with nest and niche motifs is thus restricted to these 249 proteins. The Motivated Protein database was also used to detect ends of β-turns. For a pair formed by a structural word and a known structural motif, we computed a precision measure given by the proportion of fragments encoded by the structural word that contain the known structural motif.

The functional implication of superfamily-specific structural words was explored using the biological annotations from the Swiss-Prot database extracted from the annotation data set. The comparison of structural words with Swiss-Prot annotations extracted from annotation data set is limited to the 1 487 proteins. In an effort to limit this gap, we built a second data set, named validation data set composed of 2 636 proteins and favoring the selection of annotated proteins.

In order to quantify the correspondence between structural word and biological annotations, we computed precision and sensitivity measures of the detection of annotations using words. We considered two levels of annotation: the first level, named annotation, corresponds to the "Feature key" and the second level, named second-level annotation, corresponds to the "Description" that provides a description of the annotation. For example, when the annotation is "binding", the second-level annotation indicates the ligand type.

The precision is defined as the proportion of fragments encoded by a structural word that are annotated by a given annotation considering the two levels of annotation. A structural word with high precision is said to be functional. In order to take into account the sparsity of Swiss-Prot annotations, we set a permissive threshold of 40% precision. The sensitivity (also called recall) is defined by the proportion of a given annotation that is covered by a structural word. To compute the sensitivity, we retained only annotations extracted from protein loops, annotations seen in regular secondary structures regions are discarded.

In complement to Swiss-Prot annotations, which are of high quality but far from complete, we used various external tools to identify putative functional motifs.

• The Catalytic Site Atlas (CSA) database 51 documents enzyme active sites and catalytic residues in enzymes of known 3D structure. It identifies the residues directly involved in the enzymatic reaction.

• The Ligplot software 52 allows the identification of interactions between proteins and ligands, by providing schematic diagrams of protein-ligand interactions from a given PDB file.

• The REP software 53 is used to predict repeat regions from protein sequences. This software uses an iterative homology-based repeat finding method.

• The SitePredict software 24  http://sitepredict.org/ is used to predict nucleotide and calcium-binding sites. SitePredict is a machine learning method based on diverse residue properties, including the spatial clustering of residue types and conservation during evolution. Only residues with a score above 0.5 are considered to be involved in the binding site.

We compared extreme ubiquitous words and standard β-turns 54 55 . As β-turns are four-residue long and we consider seven-residue motifs, the question is to know whether β-turns are included in, or overlap with extreme ubiquitous words. As shown in Table 4, eleven structural words (PZCD, HBDS, ZCDS, UFQK, GYUQ, YBDS, FQLG, YZDS, GUDO, FFFI, FQKG) are clearly associated with β-turns, and two words (SLGI, QLGI) contain the three last residues of a turn motif. To evaluate the structural diversity of this set of eleven extreme ubiquitous words, we computed the α-carbon Root-Mean-Square Deviation (RMSD) between all word-pairs. The RMSD between two words is measured by the average RMSD between 30 fragment pairs randomly selected within pairs of seven-residue fragments encoded by the two words. The set of eleven words clearly associated with β-turns comprises structural words with very different conformations, with a mean RMSD of 2.12 Å (± 1.05). This reflects the diversity of β-turns motifs. For example, word PZCD contains two type I turns, whereas word UFQK contains one type II turn.

An example of an extreme ubiquitous structural word corresponding to β-turn motifs, word PZCD, is illustrated in Figure 6 (upper panel). The superimposition of PZCD-fragments and the amino-acid logo 62 associated to the PZCD-fragments, presented in Figure 6A and 6B, shows that PZCD-fragments are very similar in terms of structure and present some amino-acid specificities at positions 2, 5 and 6. As shown in Figure 6C, this word is very frequent (seen 560 times in the initial data set), and over-represented in 25 superfamilies with an Lp_max equal to 34.82. The representation of two proteins containing PZCD-fragments shows that this ubiquitous word is present in superfamilies with different folds. As reported in Table 4, 99.8% of PZCD-fragments contain β-turns. Specifically, they contain two β-turns, at positions 2:5 and 3:6.

However, some of the fragments encoded by the eleven words strongly associated with β-turns, given in Table 4, do not contain turns as assigned by the ExtractTurn software. This represents a small fraction of the fragments: only 342 fragments out of 8 369, i.e. 4%. Out of these 342 fragments, 79 fail the turn assignment because they have a distance greater than 7 Å and 263 because they have an internal residue in the helical state. For example, only one of YZDS-fragments is not identified as a turn because the distance is equal to 7.08 Å (2ahu_A: 259-262). Our structural words therefore group together fragments including fragments identified as turns and some that narrowly fail the turn assignment. This suggests that structural motifs could be used to assign "relaxed" turns and supports the notion of turn-like conformations, introduced by Fuchs et al, corresponding to four-residue fragments with a distance around 7 Å 63 .

We also compare extreme ubiquitous words with the 12 small hydrogen-bonded 3D motifs extracted from the Motivated Protein database 48 . Results of this analysis are reported in Table 4. As stated in the Methods section, there is very little overlap between our initial data set and the proteins stored in the Motivated Protein database. Even on such a small number of fragments, the comparison reveals that seven extreme ubiquitous words (DRPI, DSPI, DSGI, DSKG, DSKH, DOIP and OIPI) correspond to nest motifs, with precision greater than 93% and two words (BQGI and HBBQ) correspond to niche motifs with precision greater than 95% precision. The set of words corresponding to nest motifs includes structural words with similar conformations, such as DRPI, DSPI and DSGI or DSKG and DSKH. We also note that some structural words overlap: in 81% of cases, structural word DOIP is immediately followed by letter I, forming the five-structural letter word DOIPI.

Figure 6 (lower panel) provides an example of a structural word, DRPI, containing a nest motif. We observe that DRPI-fragments are very similar in terms of structure and present some weak amino-acid specificities in positions 3: 5 and 7. This word is recurrent (seen 232 times in the initial data set and in 94 superfamilies) and over-represented in 15 superfamilies with a Lp_max equal to 14.9. The representation of two proteins containing the DRPI word shows it is present in superfamilies with different folds.

Like turn motifs, nest and niche motifs are detected by applying geometrical thresholds. In this case also, the fact that a very small proportion of our fragments fail the assignment suggest that structural words could be used to assign nest- and niche-like motifs.

Two ubiquitous words, DGPI and SKGI, are extracted from proteins not listed in the Motivated Protein database. It is therefore not possible to compare them with niche and nest motifs. Let us note, however, that DGPI is structurally close to the structural word DRPI (RMSD equal to 0.74 ± 0.24 Å), which contains nest motifs. In the same way, SKGI is similar to SLGI (RMSD equal to 0.76 ± 0.24 Å), a word containing the end of a β-turn.

Two overlapping extreme superfamily-specific words, RNHB and URNH, are strongly over-represented in the immunoglobulin superfamily (SCOP id = 48726). They correspond to regions covalently linked by disulfide bridges and identified by the "Disulfide bond" Swiss-Prot annotation with a precision of 50 and 45%. This annotation provides no functional information per se, but might indicate that these structural motifs result from structural constraints induced by the disulfide bridge. However, the very low sensitivity observed (4 and 6%) shows that a only small fraction of the disulfide annotations are encoded by these words.

Four overlapping extreme superfamily-specific words SUQH, UQHS, QHSG, HSGI are strongly over-represented in the "L domain-like" superfamily (SCOP id = 52058). This superfamily groups proteins containing repeat regions, which are regions of 20 to 30 amino acids unusually rich in leucine 64 . Repeat regions have strong implications for the biological role of protein, as they are often involved in protein-protein interactions in plant and mammalian immune responses 64 . A number of human diseases have been shown to be associated with mutations affecting leucine-rich repeat domains 64 . These repeat regions may therefore be of functional relevance.

Structural words SUQH, UQHS, QHSG,HSGI often occur in the same proteins, allowing the formation of longer motifs, like illustrated in Figure 7: in protein 1ogq A, SUQH and UQHS overlap to form the five-structural letter words SUQHS.

Figure 8A illustrates the example of the word UQHS. It is a recurrent word (seen 52 times in the initial data set), strongly over-represented in one superfamily (SCOP id = 52058), with a high maximal score (Lp_max = 75.07). The superimposition UQHS-fragments shows that they are very similar in terms of structures, with a turn conformation. The amino-acid logo indicates that UQHS presents amino-acid conservation at positions 1, 4 and 6, resulting in an amino-acid profile close to the consensus sequence of LRR (LxxLxLxxNxL or LxxLxLxxCxxL 65 ).

The comparison with Swiss-Prot annotations reveals that the four structural words SUQH, UQHS, QHSG and HSGI correspond to the "repeat" annotation with precision greater than 40% (see Table 5). According to our definition of functional words, these four words are thus functional. Some fragments encoded by these functional words, however, do not correspond to repeat annotations. For example, in the initial data set, 10 UQHS-fragments are unannotated. To determine whether these 10 fragments might still correspond to repeat regions unannotated in Swiss-Prot database (i.e., false negatives), we used the REP software to predict repeat regions. Two repeat regions are predicted: 1dce A:484-507 and 529-553. Region 1dce A: 484-507 actually contains the word UQHS, whereas the second region: 529-553 does not (see Table S2).

The sensitivity measure for the repeat annotation for the four structural words SUQH, UQHS, QHSG and HSGI ranges from 17 to 41%, meaning that repeat regions correspond to a variety of conformations, not only the ones encoded by SUQH, UQHS, QHSG and HSGI. By definition, repeat regions are formed by the repetition of a motif.

Two overlapping extreme superfamily-specific words, ZDOD and DODQ, are over-represented in only one superfamily: "EF-hand" (SCOP id = 47473). This superfamily contains proteins with EF-hand units, which consist of two helices connected by a calcium-binding loop. The words ZDOD and DODQ are frequently overlapping: in 66% of cases, DODQ is preceded by the letter Z, forming the word ZDODQ. Figure 8B presents the statistics, geometry and amino-acid sequence conservation of the word DODQ. The amino-acid logo shows that DODQ presents amino-acid conservation at positions 2, 3, 4, 5 and 7, with a strong conservation of an aspartic acid or asparagine residue at positions 2 and 4 and of a glycine residue at position 5. This conserved sequence is in close agreement with the consensus sequence of calcium-binding motifs [DxDxDG] 66 .

The two words ZDOD and DODQ correspond to the calcium-binding site annotation (CA_BIND) with precision greater than 65%, they thus are functional motifs. As shown in Figure 9A, DODQ contains residues directly involved in the binding of calcium ions. Five ZDOD-fragments and nine DODQ-fragments are not annotated as calcium-binding sites in Swiss-Prot. However, six of these unannotated DODQ-fragments are identified as putative calcium-binding sites by the SitePredict software (see Table S3). The sensitivity of the calcium-binding site annotations with respect to ZDOD and DODQ ranges from 58 to 75%, meaning that the majority of calcium-binding sites actually correspond to these structural words. These two structural words could thus be used to predict calcium-binding site candidates.

Five extreme superfamily-specific words are associated with nucleotide-binding site annotations (NP_BIND) with precision greater than 47%. Some correspond to ATP/GTP-binding sites, others to NAD(P)-binding sites. We discuss these two cases separately.

ATP/GTP-binding sites Structural words YUOD and UODO are strongly over-represented in the superfamily "P-loop-containing nucleotide triphosphate hydrolase" (SCOP id = 52540), grouping proteins with a phosphate-binding site. These two words are often found in the same proteins: in 90% of cases, the structural word YUOD is followed by the letter O, forming the word YUODO.

Figure 8C illustrates the statistics, geometry and amino-acid sequence conservation of the YUOD word. This word displays clear amino-acid conservation: glycine in positions 1 and 6, lysine in position 7, and threonine or serine in position 8, consistent with the consensus sequence of P-loops: [AG]XXXXGK[TS] 10 .

Structural words YUOD and UODO correspond to the nucleotide-binding site annotation with precision greater than 80%. YUOD and UODO are thus functional words with residues directly involved in ATP/GTP-binding sites, as shown in Figure 9B for YUOD word. In the initial data set, two YUOD-fragments and eleven UODO-fragments are unannotated. SitePredict indeed predicts ATP/GTP-binding sites for four of the eleven unannotated UODO-fragments (see Table S4). The sensitivity is equal to 35 and 38%, meaning that roughly one third of the ATP/GTP-binding sites adopt conformations described by these structural words.

NAD(P)-binding sites Two structural words, OEIJ and EIJU are strongly over-represented in the "NAD(P)-binding Rossmann-fold domain" superfamily (SCOP id = 51735) grouping proteins with NAD(P)-binding sites. These words are often overlapping: in 95% of cases, OEIJ is followed by the letter U.

Word OEIJ is associated with the NP_BIND annotation with precision equal to 86% and 47% respectively, they thus are functional words. One OEIJ-fragment and seven EIJU-fragments are unannotated. Two of the seven unannotated EIJU-fragments are predicted as NAD(P)-binding sites by SitePredict (see Table S5). The sensitivity is quite low, ranging from 14 to 20%, meaning that NAD(P)-binding sites probably adopt various conformations, and not only the ones encoded by OEIJ and EIJU.

The superfamily-specific word RUDO is strongly over-represented in the "S-adenosyl-L-methionine-dependent methyltransferase" superfamily (SCOP id = 53335), grouping proteins with SAH/SAM-binding sites. Figure 8D presents the geometry of the structural word RUDO and its amino-acid signature, with glycine residues preferred at positions 1, 3 and 5. Figure 9C presents an illustration of a SAH/SAM-binding site for a RUDO-fragment, showing the residues involved in the SAH/SAM-binding site. This word corresponds to the "binding" annotation with a precision equal to 50%, therefore it is a functional word. Three out of the five unannotated RUDO-fragments actually correspond to SAH/SAM-binding sites according to our analysis using LigPlot. The sensitivity is equal to 18%, suggesting that SAH/SAM-binding sites adopt other conformations than the one identified by the RUDO word.

Ten superfamily-specific structural words QXUS, ZSGI, GSUS, GZDO, USLG, UZCI, UGRU, EGZD, GRUD and SLGS, indicated in italics in Table 5 could not be validated as functional motifs because they have low precision values toward Swiss-Prot annotations. This could be due to (i) the limited number of proteins of the initial data set that are annotated in Swiss-Prot and (ii) the incomplete annotation of Swiss-Prot, since annotations for a given protein simply reflect our current knowledge about it.

The analysis of the correspondence between extreme superfamily-specific words and Swiss-Prot annotations revealed that some of superfamily-specific words are linked to functional sites. For example, we found superfamily-specific words associated to repeat annotations and binding sites to ATP/GTP, SAM/SAH, NAD(P), calcium and iron. Thus functional words allow a reliable prediction of some binding sites.

Some annotations, such as metal-binding sites (cadmium, lithium, mercury, potassium, vanadium) are very rare and not represented in our data set. This explains why these functional sites are not detected at all by superfamily-specific words. Moreover, only a fraction of the annotation data set is covered by Swiss-Prot annotations (2% of seven-residue fragments) and the step of mapping annotations to PDB structures using the PDB/UniProt Mapping database further reduces significantly the data available for comparison. The link between structural words and functional sites is thus established on a limited amount of data and is probably under-estimated by our analysis. For example the structural word UGRU, over-represented in the "S-adenosyl-L-methionine-dependent methyltransferase" superfamily (SCOP id = 53335), is not characterized as "functional word" in the annotation or validation data sets (precision = 33% and 36%). The manual analysis of the functional annotations of UGRU-fragments show that 69% of them are actually involved in SAH/SAM-binding sites, see Table S6. This illustrates the case of a functional motif missed by our analysis due to a defect of biological annotations.

In this paper, the link between superfamily-specific words and functional sites is established only for the 23 extreme superfamily-specific words. These 23 words cover 1% of residues in loops and they are seen in 17% of proteins. If we consider superfamily-specific words with moderate scores (565 words with Lp_max ≥ = 10, see Table 2), the coverage can be increased to 10% of residues and 90% of proteins. From these moderately superfamily-specific words, 13 words are clearly associated with a functional Swiss-Prot annotation ("binding site" or "active site" annotations), 17 correspond to a repeat annotation and 16 to a disulfide annotation (data not shown). For example, word ZCLH is over-represented in the superfamily SCOP id = 53474 with a Lp_max equal to 12. This word has a precision for the detection of "active site" annotation of 67% (see Table S7). This suggests that over-represented words with moderate Lp_max score may be functional too.

However, some functional sites were not detected by structural words. To be identified by our structural word approach, a functional site must meet two conditions: (i) at least one part of the functional site must be located in protein loops and (ii) it must correspond to recurrent structures across different proteins. Indeed, structural words can only identify a functional motif if structural conformation spanning at least seven or more consecutive residues. Thus, superfamily-specific words cannot detect DNA-binding sites or zinc finger motifs because these functional sites are preferentially seen in α-helices. In the same way, some metal binding sites (cobalt, copper, magnesium, canganese, colybdenum, nickel, sodium) are not detected because they display a high flexibility 67 or a structural conservation restricted to few residues.

To quantify the correspondence between extreme superfamily-specific words and Swiss-Prot annotations, we computed the precision and sensitivity of annotation detection by these words. We observed that sensitivity values depend on the functional sites and structural words. For example, two overlapping words DODQ, ZDOD present a high sensitivity for calcium-binding sites, meaning that most of these binding sites can be detected by these two structural words. Other structural words have lower sensitivity, e. g. YUOD detects only one third of ATP/GTP-binding sites. However, we checked, on randomized data sets, that these sensitivity measures are significantly greater than expected by chance (see Table S8). Indeed, random sensitivities are very low and the sensitivity of structural words reported in this study are higher in any case. Thus, even if the sensivity measures reported in this sudy may seem modest, they are still significant, meaning that all the superfamily-specific structural words presented here are significantly enriched in functional sites. These low sensitivity values indicate that some functional sites actually correspond to several conformations encoded by different structural words. These different conformations of a functional site could be explained by (i) its flexibility or (ii) the fact that it can span several segments in a protein. Figure 10 presents an illustration of flexibility of binding-site through the four calcium-binding sites of protein Calcium-dependent protein kinase 3 (pdb code 3k21). This flexibility results in the encoding of these functional sites into two close words: ZDOD and WDOD, with a RMSD of 0.419 Å. A way to take into account the flexibility of binding-site could be to consider "degenerated words" (for example [W/Z]DOD) instead of "exact" word. This would certainly increase the ability to detect functional sites.

In Figure 10, we also present an example of protein Translation initiation factor if2/eif5b (pdb code 1g7s) data, illustrating a binding site involving different 3D regions. This protein contains a GTP-binding site involving three regions, which two are annotated by one NP_BIND annotation, resulting in two NP_BIND annotations for this protein. Each annotated region is detected by a superfamily-specific word: YUOD and UGBB. This indicates each word can detect one part of the GTP-binding site, thus each word is expected to detect to 50% of the NP_BIND annotations at most. Thus, the weak sensitivity value of some functional words shows that these words can detect one part of the functional site. To identify the entire functional sites, we could couple the different functional words associated to the same annotation.

Several approaches address the link between local structures and protein function. These methods can be clustered into three groups.

The first group corresponds to the characterization of structural motifs specific to functional sites 22 23 24 25 26 27 28 . Such methods consist in learning the structural motifs of known functional sites and are therefore dedicated to the prediction of those sites.

The second group corresponds to the discovery of conserved structural motifs in proteins with the same function. These methods start from protein superfamilies and search for structural motifs specific to superfamilies 20 21 68 . They can identify conserved motifs in different proteins with the same function. In these approaches, the extraction of structural motifs is based on the comparison of structural fragments using RMSD. These methods are able to discover new functional sites within superfamilies. However, they cannot identify functional motifs common to several superfamilies.

The third group corresponds to structural classification of local conformations, followed by an analysis of the association between clusters and functional sites 14 17 18 69 . These methods do not focus on the description of a particular functional site, or restrict the analysis to a particular superfamily. Instead, they analyze a posteriori the association between fragment clusters and protein superfamilies or GO annotations. Our approach is based on the same philosophy as these methods.

Compared to Espadaler et al. 14 , Tendulkar et al. 17 , and Manikandan et al. 18 , our method is original in three ways: (i) the extraction of structural motifs is based on a structural alphabet, which allows defining structural motifs without using geometrical thresholds or extensive pairwise structural comparison, (ii) the functional role of a motif in a particular superfamily is assessed by its statistical over-representation within the superfamily, and (iii) it can deal with all loops, irrespective of their length or secondary structure types. This last point is particularly important: in a previous study, we have shown that 64% of structural words display no specificity for loop length 39 . It is also the case of the functional motifs identified in the present study: for example, 60% fragments of the word DODQ, involved in calcium-binding sites are extracted from short loops, and 40% from long loops. The fact that we made a systematic decomposition of loops into structural words, instead of clustering full-length loops as done by Espadaler et al. 14 makes the comparison with their study difficult.

Two studies by Tendulkar et al. 17 and Manikandan et al. 18 aimed at the extraction of structural motifs specific to a protein function. Contrary to our approach, they considered all structural motifs including α-helices and β-strands. In these two studies, structural motifs were extracted by a systematic classification of eight-residue fragments based on geometric invariants 17 or dihedral angles 18 . They then analyzed the association between structural clusters and protein functions provided by SCOP superfamilies 17 or GO terms 18 . Tendulkar et al. 17 defined a cluster as functional if at least 70% of its fragments are found in a same SCOP superfamily. Manikandan et al. 18 identified functional clusters on the basis of the over-representation of GO terms in clusters. These two definitions restrict the definition of functional motifs to motifs specific of one superfamily or GO term. By contrast, the statistical treatment presented here allows the extraction of motifs shared by several families, even if the superfamily contains few members.

Recently, Wu et al. 69 have proposed an approach to extract functional structural motifs from DNA-binding proteins using a structural alphabet. As in our approach, the structural alphabet is used to simplify 3D structures into uni-dimensional sequences. The structural alphabet used in 69 is composed of 16 structural letters, named protein blocks. Wu et al. focused on DNA-binding sites by searching structural words present in DNA-binding proteins binding and absent in others, and considered long and degenerated structural words (26 residues) without secondary structure restriction. In the present study, we discarded helices and strands. In addition, our statistical treatment is radically different from theirs, and allows retrieving structural words shared by several superfamilies, even in superfamilies with few proteins. Even if based on a similar method of protein structure simplification, both these works thus pursue quite different objectives and consider different structural motifs.