The choice of the optimal length was guided by the following dilemma. On the one hand, it is desirable to consider long fragments, in order to better describe 3D conformation and capture the longest-range interactions. On the other hand, the amount of available data rapidly becomes insufficient when dealing with long fragments. To choose this optimal length, we computed the frequency of all structural words in our data set, with length from five residues (two-structural letters) to ten residues (seven-structural letters), see Additional file 1. We identified seven residues as the maximum length to avoid the problem of data sparsity. The number of different structural words sharply increases beyond that limit and 80% of structural words of 8 residues are seen at most 6 times in our data set, versus 34 times for words of 7 residues. For these reasons, we selected seven residues, i.e., four structural letters as the most meaningful length for systematic extraction.

We systematically extracted structural words of four structural-letters from protein loops and analyzed their properties: structural variability, amino-acid specificity and preference for particular loop types.

In the second part of this study, we complement our analysis of word properties by their statistical exceptionality in protein structures represented by strings of structural letters. Statistical exceptionality is traditionally used in genome analysis to extract functional motifs such as enzyme restriction sites or regulatory motifs 4445464748. Our goal was to explore if a statistical bias is also associated to specific properties in the case of protein structures. Statistical exceptionality does not measure the frequency of a word. It is an indicator of the discrepancy between observed and expected occurrence according to a background model that takes into account the first order Markovian process between structural letters. The statistical representation of words was assessed using the SPatt software that computes an exceptionality score L_p for each word (see Material and Methods). According to the value of L_p, words are classified as over-represented, under-represented or not significant. Hereafter, over-represented words are referred to OR_w, under-represented words as UR_w and not significant words as NS_w.

An extensive comparison with already existing loop classification schemes is extremely difficult because we do not consider the same objects, and pursue different objectives. Existing classifications cluster loops according to their length 1214151718, flanking region types 121417182021, flanking region geometry 12141718 and loop geometry 1718. Such classifications consider full length loops and are thus inherently limited to short loops. In the present study, we cluster fixed-length structural motifs within loops, independently of their lengths or flanking regions, thus also bringing information for long loops. Consequently, it is delicate to compare our loop analysis with existing loop classifications.

Other studies have previously investigated the use of seven-residue fragments to analyze protein structures 5556 whereas our study focuses on loop structural fragments. For this reason, the results are not directly comparable.

Other studies consisted in identifying functional patterns in whole proteins 5758. Such patterns, involved in protein function, are relatively rare. On the contrary, our approach considers recurrent structural motifs in loops. Alternatively, some groups have investigated the identification of 3D structural patterns linked to functions that are not necessarily made of consequent residues 5960616263. For example, Ausiello et al. (2009) 63 extracted some structural motifs from protein in different folds which recognize ligands presenting same features. In this case also, the studied objects are very different, making the comparison difficult. Another interesting analysis, MegaMotifBase, deals with structural motifs that are important for the preservation of the 3D structure in given families or superfamilies 64. These motifs were identified using both sequence conservation and preservation of important structural features. They mainly correspond to regular secondary structures, whereas we focused our analysis on loops. For all these reasons, any comparison between our approach and already existing classifications should be regarded with caution.

We analyzed structural and amino-acid properties of clusters, defined by structural words, using RMSd and different criteria to measure their amino-acid dependencies. We found an average intra-cluster RMSd_w equal to 0.85 Å versus 2.72 Å for the inter-cluster RMSd_dev, which confirms our previous results 40. In the loop classification ArchDB65 clusters grouping seven-residue loops present an average RMSd close to 1 Å. In Sander et al. 55, fragments were clustered according both to their structure and amino-acid sequence into 27 clusters with an average RMSd of 1.19Å. The most populated cluster groups α-helix fragments and probably largely contribute to the average RMSd.

Loop description by recurrent structural words permits a quantification of the loop structural redundancy: around 73% of loops are described by a limited number of accurate recurrent structural words. Thanks to the loop-structure simplification using HMM-SA, our method is the first one allowing a systematic mining of loops independently of their lengths and the study of all loops in terms of motif composition.

First, we demonstrate that the majority of the recurrent structural words have low structural variability and specific sequence signature. The simplification of loop structures using HMM-SA permits to analyze long loops. We can observe that 46% of loops are covered by words found both in short and long loops. These results show that short and long loops are composed of similar motifs. This is in agreement with the insertion/deletion process of loop evolution hypothesis made in 66. In addition to the identification of the shared structures, our analysis provides a quantification of how the same structural words are re-used in different loops. The existence of words found in both long and short loops could allow transposing some short-loop results into the long-loop analysis and decreasing the long-loop-analysis complexity.

We observe that only one third of short (resp. long) loops are covered by words that are specific to short (resp. long) loops. Moreover, words specific to short loops have higher amino-acid specificities than other words. That means that these short loop regions (30% of short loops) are more informative in terms of sequence than other regions. Interestingly, words that are specific to long loops are structurally less variable than others meaning that a part of long loops (34%) are structurally well defined.

We also analyze the dependence between recurrent words and the loop flanking-regions. We show that around 60% of words exhibit a significant preference. Most of these words are specific to βα and ββ loops. These results are in agreement with classification of short loops based on flanking region information as 12141517182021 and provide an identification and quantification of the structures with a dependence on the flanking regions. Moreover, this study allows identifying and quantifying regions with no preference for flanking-region types. Indeed, 31% of loops are covered by words with no preference for a flanking-region type.

The amino-acid specificities of structural words were also assessed. We observed that 97% of recurrent words, covering 70% of loops, have amino-acid specificities. Different studies have analyzed the amino-acid preferences of loops, particularly for short loops. Kwasigroch et al. (1997) have shown that amino-acid preferences were more frequent in the core of short loops 1516. Other studies have focused on the amino-acid preferences of β-turns and shown that these amino-acid preferences occurred at end positions 2567. This study provides an identification of regions with amino-acid specificities and a new quantification of the amino-acid specificity: we found an average number of three positions with significant amino-acid preference for Wset_≥30 motifs.

Most recurrent motifs exhibit significant amino-acid specificities: half of them display significant level of amino-acid conservation in at least four significant-positions. If we consider words with at least four significant-positions as predictable, we extract 1359 words covering 60% of the loops (on a per-structural letter basis). It is clear that this predictability index (at least four significant positions) is very basic and too optimistic. The predictability index of a word has to combine both its sequence informativity and sequence specificity. Indeed, one word can have several positions with high amino-acid preferences but close sequence from other words. Conversely, words with few informative positions can be clearly distinguishable from others in terms of sequence. Moreover, several words can be compatible with a same seven-residue sequence, involving several candidates per amino-acid sequence. A possible strategy for loop prediction would consist in splitting the query sequence into overlapping seven-residue fragments, and identifying subset of structural words compatible in terms of sequence profile with each fragment.

The successions of compatible overlapping word candidates would then be selected using a hidden Markov model taking into account the favorable transitions between structural words. This would result in a 1D structural letter trajectory set compatible with the target loop sequence. Then, the 3D reconstruction from this set of 1D trajectories could be achieved using an energy function as in PEPfold 68. This approach could yield a set of 3D structural conformation candidates for the target loop, in agreement with the flexibility of loops. Finally, for long loop prediction, a confidence index could be proposed for different parts of the predicted loop. Indeed, for a given loop, prediction of some regions could result in a limited number of word candidates while for other regions, the prediction could result in a large number of word candidates. This approach could be a way to decrease the complexity of long-loop prediction.

In Figure 5, we present an illustration of a long loop of 18 structural letters extracted from the protein structure with pdb code 3SIL, encompassing residues 120 to 140. Using the word extraction protocol, this loop was decomposed into 15 words of 4 structural letters. Among these 15 words, four words -namely UOGI, KHBB, IFFR and RPBQ- belong to Wset_≥30. These four words are seen in both short and long loops in the data set, as illustrated in Figure 5. Structural word KHBB is over-represented, with an L_p value equal to 39.5. It is characterized by a low structural variability (RMSd_w = 0.4 Å) and strong amino-acid preference (Z_max = 25), with conservation of hydrophobic amino acid at position 2 and Proline at position 3. These amino-acid conservation trends are derived from the analysis of every occurrence of a particular fragment.

In this particular protein, a Lysine and a Threonine occupy positions 2 and 3 of word KHBB. This region does not appear to be particularly conserved in the multiple alignment of homologous sequences retrieved from a BLAST search in Swiss-Prot (data not shown). When aligned with sequences retrieved from a BLAST search in PDB sequences, this region exhibits three positions with equivalent residues (see alignment in Additional file 1). We attempted to further explore the functional implication of this long loop. 3SIL is a sialidase from Salmonella typhimurium. It corresponds to Swiss-Prot entry NANH_SALTY, and is responsible for the cleavage of terminal sialic acid from glycoproteins. There is no functional annotation in Swiss-Prot for the 120-140 region, but the catalytic and substrate-binding sites are annotated. They are highlighted in pink and blue in Figure 6. Furthermore, a structure of sialidase co-crystallized with an inhibitor is available in the PDB: structure 1DIL, with sequence identical to 3SIL. The inhibitor is thus shown in red in Figure 6. It can be seen that loop 120-140 is spatially close to functional residues and inhibitor molecules. This observation suggests that this loop could be important for the substrate stabilization, but only the observation of the enzyme co-crystallized with a substrate could confirm this hypothesis.

This example shows that some motifs extracted from loops seem to be involved in protein function. It is not surprising due to the fact loops are often involved in protein function.

In genomic sequences, functional motifs are often characterized by particular frequencies (rare or very frequent). Therefore, the search for functional motifs is successfully guided by the search for exceptional motifs 4445. Inspired by this singularity, we explored the properties of structural words in proteins to see if the over- or under-representation of particular conformations can be linked to particular features. Contrary to classic methods that were primarily developed for DNA sequences, statistics are here computed by a method that takes into account the large number and short length of sequences of our data set 69. We considered the intrinsic properties of structural words and their relationship with the statistical exceptionality status of words, classified as over-represented, under-represented, or not significant. The comparison of the three statistical word types showed that over-represented words have indeed specific properties: they are highly conserved in terms of structure or sequence and highly dependent on loop types. By setting a RMSd_w cut-off equal to 0.74 Å and a Z-max cut-off equal to 14, we found that 89% of over-represented words present either a low RMSd or a high Z_max or a significant dependence to a loop type defined by eight types according to the KLD criterion. This ratio is only 62% for other words. This indicates that statistical exceptionality results from a complex process combining word frequency, sequence and/or structure properties. The consideration of statistical exceptionality thus enhances the signal-to-noise ratio in protein loops. Most of the time, the relationship between local structures and protein function is not straightforward. Our findings open new perspectives to the use of over-representation in order to detect functional motifs in loops. It is the subject of an ongoing study (Regad et al, in preparation) where we suppose that functional motifs could correspond to over-represented motifs in a protein family.

We used a data set of protein structures corresponding to chains presenting less than 50% of sequence pairwise identity extracted from PDB of May 2008. The data set is composed of 8186 protein chains of at least 30 residues, obtained by X-ray diffraction with a resolution better than 2.5 Å. Proteins for with missing residues or alternate conformations were removed.

Our structural alphabet, HMM-SA, is a library of 27 structural prototypes of four residues, called structural letters, established using a hidden Markov model 4270. Thanks to HMM-SA, the 3D structure of a protein backbone is simplified into a sequence of structural letters. The simplification relies on Cα positions only: each four-residue fragment of the protein structure is described by four inter-Cα distances. Consecutive four-residue fragments are overlapping on three residues resulting in one common distance. The resulting distances are the input of a hidden Markov model, and the 3D structure is translated as a sequence of 1D structural letters. This translation is made using the Viterbi algorithm 71 and takes into account both the structural similarity of the fragments with the 27 structural letters of the structural alphabet and the preferred transitions between structural letters. A protein structure of n residues is then simplified as a sequence of (n - 3) structural letters. The 27 structural letters, named [A-Z, a] are shown in Figure 1. It has been shown previously 51, that four structural-letters, [a, A, V, W], specifically describe α-helices, and five structural letters, [L, M, N, T, X], specifically describe β-strands. The remaining 18 structural letters [B, C, D, E, F, G, H, I, J, K, O, P, Q, R, S, U, Y, Z] allow accurately describing loops. Some transitions between structural letters are not possible, which results in a limited number of pathways between letters and in a limited number of short patterns of structural letters.

Following our previous study 40, loops are identified as series of structural letters linking simplified regular secondary structures (α-helices and β-stands) that are defined using regular expressions of structural letters. This approach permits to extract a bank of 93396 simplified loops ranging from 4 to 82 structural letters with an average length of 8.5 ± 5.5 structural letters, corresponding to an average length of 11.5 ± 8.6 residues. A loop of l structural letters corresponds to (l + 3) residues. Long loops -more than 12 residues- represent 28% of the loops in our data set. 39% of the loops are linking two β-strands, 23% are linking a β-strand to an α-helix, 22% an a-helix to a β-strand, and 16% two α-helices. The extraction of structural motifs in loops is illustrated in Figure 1. Simplified loops are split into series of overlapping words of four structural-letters, i.e., seven residues. A loop of l structural letters is then split into (l - 3) words. As we focus on structural motifs within loops, words beginning or ending with a structural letter specific to regular secondary structures [AaVWLMNTX] are excluded. This results in a global set of 28274 structural words describing all loops in the simplified structural alphabet space. The structural words thus define a partition of the structural diversity of loops, where each four-structural-letter word is a cluster of seven-residue fragments.

The coverage rate of loops by a word set corresponds to the percentage of loop structural-letters covered by these words.

For example, given two loops of 11 (l₁₁) and 15 (l₁₅) structural letters and a set of recurrent 4-structural-letter words (S_w). Loop l₁₁ contains two words of S_w on positions 1 to 4 and 8 to 11. As these two words are not overlapping, they cover 8 structural letters. Loop l₁₅ contains three words of S_w on positions 1 to 4, 3 to 6 and 9 to 12. As the first two words are overlapping, these three words cover 10 structural letters. Thus, the coverage rate of these two loops by S_w is equal to = 69%.

This coverage rate is used in order to provide information on loop description by a set of structural words.

Although the structural-alphabet decomposition into structural word is purely geometrical, it is still possible to analyse the sequence-to-structure dependence a posteriori. This is achieved using Z-score computation.

To study the preference of structural words for particular ℓ loop types (defined by length and/or flanking regions with ℓ, 1 ≤ ℓ ≤ N_ℓ) the word distribution in different loop types is compared to the global distribution of loop types using a relative entropy measure, called the Kullback-Leibler asymmetric divergence, Kullback distance or relative entropy, denoted KLD 52. The KLD quantifies the preference of a word w for the loop types, as:

where p_{w, ℓ}, denotes the relative frequency of word w in loop type ℓ and p_ℓ, the relative frequency of loop type ℓ among all loops. The KLD is equal to 0 if is w is similarly distributed in every loop type and increases with loop type dependence. The significance of KLD value is assessed by a chi-square test, since the quantity 2 × N_w × KLD(w) follows a chi-square with N_w - 1 degrees of freedom. Thus, words associated to specific loop types have significant KLD values. A correction is introduced using False Positive Rate (FPR) to take into account multiple testing. A correspondence analysis is used to visualize the main relationships between words and loop types.

The principle is to compare the actual frequency of a word in the data set and its expected frequency under a background reference model. A word seen significantly more (respectively less) than expected is then classified as over-represented (respectively under-represented). The expected frequency is computed using a Markov model for which the parameters are estimated from the global set of loops. This is performed using the software SPatt 74 available at http://stat.genopole.cnrs.fr/spatt, with a first order Markov chain used as reference. SPatt approach is based on the Pattern Markov Chain (PMC) notion 75. This software has been adapted to the case of data sets with a large number of short sequences 43. The statistical significance of the exceptionality is quantified by a p-value. To facilitate the analysis, p-values are translated into scores using equations:

where N(w) is the expected frequency of the word w, and N_w its observed frequency. An over-represented word has a positive L_p value and an under-represented word has a negative L_p value. For example, an L_p equal to 21.3 means that the word is over-represented with a p-value equal to 10^-21.3. A L_p equal to -17.7 means that the word is under-represented with a p-value equal to 10^-17.7. The L_p threshold for statistical significance is set to 5.94, using the Bonferroni adjustment to take into account multiple tests. This permits to classify words as over-represented (L_p > 5.94), under-represented (L_p < -5.94) or not significant (-5.94 ≤ L_p ≤ 5.94).

As explained in 75, pattern significance scores tend to increase with the considered database size. This is due to the fact that a tail distribution event like the one we usually consider in pattern problems (i.e. pattern with small p-value) falls within the range of the Large Deviations theory 7677 which means that its probability p to occur can be approximated by p ≃ exp(-ℓI) where I is a real positive rate and ℓ is the database size. As a consequence we have log p ≃ -ℓI which is exactly the pattern score we consider (up to a constant multiplier). It is hence obvious that extreme pattern scores will increase in magnitude linearly with database size. If this is not a problem when we perform a pattern analysis on a single database, this bias has obviously to be corrected in order to compare results from two different databases. The correction simply consists in using one of the database as a reference and rescaling the pattern scores obtained on the second database by the appropriate ratio of sizes.