Miguel M De Sousa

C R Munteanu

Alejandro Pazos

Nuno A Fonseca

Rui Camacho

A L Magalhães

Amino acid pair-and triplet-wise groupings in the interior of -helical segments in proteins

Keywords:

A statistical approach has been applied to analyze primary structure patterns at inner positions of α-helices in proteins. A systematic survey was carried out in a recent sample of non-redundant proteins selected from the Protein Databank which were used to analyze α-helix structures for amino acid pairing patterns. Only residues more than three positions apart from both termini of the α-helix were considered as inner. Amino acid pairings i, i + k (k = 1, 2, 3, 4, 5), were analysed and the corresponding 20 × 20 matrices of relative global propensities were constructed. An analysis of (i, i + 4, i + 8) and (i, i + 3, i + 4) triplet patterns was also performed.

These analysis yielded information on a series of amino acid patterns (pairings and triplets) showing either high or low preference for α-helical motifs and suggested a novel approach to protein alphabet reduction. In addition, it has been shown that the individual amino acid propensities are not enough to define the statistical distribution of these patterns. Global pair propensities also depend on the type of pattern, its composition and orientation in the protein sequence. The data presented should prove useful to obtain and refine useful predictive rules which can further the development and fine-tuning of protein structure prediction algorithms and tools.

Introduction

Understanding the formation, stability and function of protein structures requires the characterization of interaction preferences between amino acid residues in secondary structure motifs.

Helices, in particular α-helices, are the most commonly observed secondary structure motifs in folded proteins. Comprehension of the factors underlying the processes of helical formation and stability requires their exhaustive evaluation. A particularly relevant factor is the occurrence of intramolecular hydrogen bonds between C=O and N-H groups of amino acid residues in the protein backbone. This is especially true for (i, i + 4) amino acid pairings and, to a lesser extent, (i, i + 3). All the polar amide groups in the helix are hydrogen-bonded to one another except for the N-H group of the amino terminal end and the C=O group of the carboxy-terminal end.

The α -helix structure has a net dipole moment along its axis, with the N-terminus being positively polarized and the C-terminus negatively.

Both the formation of hydrogen bonds and the intensity of the helical dipole moment are conditioned by the occurrence and distribution of amino acids in the helix, with the different tendency of the various amino acids to form helices being well documented. [START_REF] Argos | Amino-Acid Distribution in Protein Secondary Structures[END_REF][START_REF] Chou | Conformational Parameters for Amino-Acids in Helical, Beta-Sheet, and Random Coil Regions Calculated from Proteins[END_REF][START_REF] Davies | Correlation Between Amino Acid Composition & Protein Structure[END_REF][START_REF] Malkov | A reexamination of the propensities of amino acids towards a particular secondary structure: classification of amino acids based on their chemical structure[END_REF][START_REF] Williams | Secondary Structure Predictions And Medium Range Interactions[END_REF] Each residue playing an individual part in stabilizing the helix chain, the amino acid distribution is different depending on whether one considers N-terminal, C-terminal or interior positions in the αhelix. [START_REF] Ermolenko | Noncharged amino acid residues at the solvent-exposed positions in the middle and at the C terminus of the alpha-helix have the same helical propensity[END_REF][START_REF] Petukhov | Position dependence of non-polar amino acid intrinsic helical propensities[END_REF][START_REF] Petukhov | Position dependence of amino acid intrinsic helical propensities II: noncharged polar residues: Ser, Thr, Asn, and Gln[END_REF] The distinction between these three types of positions is documented along with the importance of the first and last non-helical termini, the N-and C-caps: [START_REF] Chakrabartty | Helix Capping Propensities in Peptides Parallel Those in Proteins[END_REF][START_REF] Doig | N-and C-Capping Preferences for All 20 Amino-Acids in Alpha-Helical Peptides[END_REF][START_REF] Doig | Determination of Free-Energies of N-Capping in Alpha-Helices by Modification of the Lifson-Roig Helix-Coil Theory to Include N-Capping and C-Capping[END_REF]) N-cap is usually a polar residue with small side chain, positions N1 to N3 tend to be populated by negatively charged residues, Ala predominates in the interior of the helix, positions C3 to C1 are usually found to be positively charged amino acids, with Gly being very often found as C-cap.

It has been known for some time that particular sequences of amino acids may have significant roles in protein folding and stability [START_REF] Nagano | Logical Analysis Of Mechanism Of Protein Folding .1. Predictions Of Helices, Loops And Beta-Structures From Primary Structure[END_REF][START_REF] Nagano | Logical Analysis Of Mechanism Of Protein Folding .2. Nucleation Process[END_REF] and, more recent studies have shown how these patterns in pairs in β-sheets, [START_REF] Fooks | Amino acid pairing preferences in parallel beta-sheets in proteins[END_REF] loop sequences, [START_REF] Crasto | Sequence codes for extended conformation: A neighbor-dependent sequence analysis of loops in proteins[END_REF] particular (i, i + 4) pairs with helix-stabilizing effects [START_REF] Andrew | Stabilizing nonpolar/polar side-chain interactions in the alpha-helix[END_REF][START_REF] Andrew | Stabilizing interactions between aromatic and basic side chains in alpha-helical peptides and proteins. Tyrosine effects on helix circular dichroism[END_REF][START_REF] Butterfield | Contribution of aromatic interactions to alpha-helix stability[END_REF] and dipole-affecting triplets (Iqbalsyah and Doig, 2005a;[START_REF] Olson | Cooperative helix stabilization by complex Arg-Glu salt bridges[END_REF] may have a stabilizing or destabilizing influence.

In particular for α-helices, these effects are consequence of several types of interactions between amino acid side chains -including aromatic interactions, [START_REF] Butterfield | Contribution of aromatic interactions to alpha-helix stability[END_REF][START_REF] Meurisse | Aromatic side-chain interactions in proteins: Near-and far-sequence Tyr-X pairs[END_REF]Thomas et al., 2002a;Thomas et al., 2002b) nonpolar/polar interactions, [START_REF] Andrew | Stabilizing nonpolar/polar side-chain interactions in the alpha-helix[END_REF] surface salt bridges (Iqbalsyah and Doig, 2005a;[START_REF] Olson | Cooperative helix stabilization by complex Arg-Glu salt bridges[END_REF] -and may be dependent on the relative positioning of the intervening side-chains. There is also the possibility of interactions between amino acid residue side chains and the α-helix backbone. [START_REF] Toth | Aromatic-backbone interactions in alpha-helices[END_REF] Intra-helical amino acid pairings may also be a factor in the formation and stabilization of supercoil motif structures, [START_REF] Beck | Supercoiled protein motifs: The collagen triple-helix and the alpha-helical coiled coil[END_REF][START_REF] Meier | Statistical analysis of intrahelical ionic interactions in alpha-helices and coiled coils[END_REF] with particular amino acid pair side chains being more suited than others for inter-helical interaction as well as having some influence in defining helixhelix crossover angles.

Similarly, triplets of side chains, especially of amino acids spaced (i, i + 4, i + 8), have been found to have an effect on the stabilization of α-helix structures, for example through the formation of salt bridges [START_REF] Olson | Cooperative helix stabilization by complex Arg-Glu salt bridges[END_REF][START_REF] Shi | Non-classical helixstabilizing interactions: C-H...O H-bonding between Phe and Glu side chains in alpha-helical peptides[END_REF] or via shared rotamer preferences, (Iqbalsyah and Doig, 2005b) though these pairwise couplings aren't always cooperative. (Iqbalsyah and Doig, 2005a) (FIGURE 1) Figure 1. Amino acid Triplets considered at the interior of α-helices:

a) (i, i + 4, i + 8) ; b) (i, i + 3, i + 4) .
As the tendency for individual amino acids to occur in α-helical structure varies and is related to their helix-forming properties, it is reasonable to consider that the same principle also applies to amino acid patterns, with different propensities to occur in α-helices being related to the formation and stabilization of the secondary structures. These correlations may be evaluated by statistical assessment of known protein 3D structures, information which is available in constantly updated databases [START_REF] Berman | Announcing the worldwide Protein Data Bank[END_REF][START_REF] Kabsch | Dictionary of Protein Secondary Structure -Pattern-Recognition of Hydrogen-Bonded and Geometrical Features[END_REF][START_REF] Wang | PISCES: a protein sequence culling server[END_REF] and which can be accessed and analysed by applications like the Prot-2S server. [START_REF] Munteanu | Prot-2S: A New Python Web Tool for Protein Secondary Structure Studies[END_REF] Constant updates to these databases create the necessity of regularly updating any statistical assessments. The first studies of this sort were conditioned by the availability of few completely solved protein 3D structures when compared to the amount of currently available data. In view of this, approaching this problem again may shed new light on the subject or allow a refinement of previously obtained results.

This work presents a comprehensive evaluation of the occurrence of amino acid pair and triplet patterns in the interior of α-helix structures, carried out on a recent set of α-helical protein segments. A further result of the statistical work performed in this study is the proposal of a potential novel approach to simplifying the protein alphabet, [START_REF] Etchebest | A reduced amino acid alphabet for understanding and designing protein adaptation to mutation[END_REF][START_REF] Murphy | Simplified amino acid alphabets for protein fold recognition and implications for folding[END_REF][START_REF] Wang | A computational approach to simplifying the protein folding alphabet[END_REF] grouping amino acids into classes of clusters based on their tendency to form doublet patterns in the inside of the α-helix.

Methods

The PISCES server [START_REF] Wang | PISCES: a protein sequence culling server[END_REF] was used to select a subset of protein chains from the Protein Data Bank-PDB [START_REF] Bernstein | Protein Data Bank -Computer-Based Archival File for Macromolecular Structures[END_REF] with structures solved at a resolution higher than 2Å, with a R-factor lower than 25%, and showing a maximum of 25% of sequence identity. The proteins chains considered for this study were chosen irrespectively of origin, structure or function -these are aspects to take into consideration in future work.

To avoid the use of incorrectly classified sequences, secondary structures were assigned with the Kabsch and Sander DSSP algorithm, [START_REF] Kabsch | Dictionary of Protein Secondary Structure -Pattern-Recognition of Hydrogen-Bonded and Geometrical Features[END_REF] using our own programs, written in Python using the BioPython [START_REF] Bassi | A primer on python for life science researchers[END_REF] module, to compare the initial set of data culled from PDB with recent DSSP sequences. We rejected PDB sequences where the secondary structure assignments did not agree with those obtained using DSSP. The α-helix content of the remaining HELIX and ATOM records from .pdb files was then analyzed by our own programs.

As we were interested in analysing pair interactions up to (i, i + 5) at the interior of the helices, only sequences with more than 12 residues were considered, from which the first three residues in both termini of each helix were excluded.

Consequently, we obtained a working sample consisting of 12821 reduced sequences extracted from 4068 protein chains (the complete list of PDB entries is available as supplementary material) which corresponds to a total number of 125297 amino acid residues.

Starting at the first residue, all the pairs of the type (i, i + k) (k = 1, 2, 3, 4, 5) were considered along each complete sequence and we counted the total number of intra-helical pairs for each type and obtained 111779,99117,86470,73853,61192 respectively for k = 1, 2, 3, 4, 5. The trend in these numbers reflects our methodology for establishing the sample and the order of magnitude is high enough to discard differences in statistical significance between samples -especially because propensities are normalized statistics.

The preference of a particular amino acid pair (X i , Y i+k ) to occur at the interior of the helical motifs was evaluated by means of a statistic called global propensity ( g k XY P ), defined in a similar study on the termini positions of α-helices: [START_REF] Fonseca | Amino acid pairing at the N-and C-termini of helical segments in proteins[END_REF] ∑ ∑ From the above definitions, the larger/smaller the value of g k XY P , the higher/lower the preference of the pair (X i , Y i+k ) to occur in the interior of α-helices (a value close to 1 means no preference at all, reflecting similar distributions inside and outside the helices).

Using a similar procedure on the same working dataset, the global propensities for amino acid triplets, g Z XY n k P

, were also determined for (k = 4, n = 8) and (k = 3, n = 4), corresponding to the triplets (i, i + 4, i + 8) and (i, i + 3, i + 4), respectively (see Fig. 1).

To investigate the existence of correlations between pair of residues with high propensity, we applied association rule learning, a popular and well researched method in data mining for discovering interesting relations between variables in large databases. We used the Apriori [START_REF] Agrawal | Mining Association Rules Between Sets Of Items In Large Databases[END_REF] algorithm implementation for learning association rules described by Borgelt [START_REF] Borgelt | Efficient Implementations of Apriori and Eclat[END_REF][START_REF] Borgelt | Recursion Pruning for the Apriori Algorithm[END_REF]) and available at http://www.borgelt.net/apriori.html. The following settings were used to learn the association rules: minimum number of items/pairs in a rule was set to 2 (-m2); minimum support was set to 1 (-s1); and minimum confidence was set to 75% (-c75).

Results and discussion

The large and unbiased sample used ensures a strong statistical support to the observations presented here. The global propensities were calculated for all the 400 possible cases of each type of amino acid pairings i, i + k (k = 1, 2, 3, 4, 5) and the data was collected in five 20 × 20 matrices, all of which are available at http://www.requimte.pt:8080/Prot-2S/HelicalAA.php. The propensity values of these five matrixes allowed us to evaluate and compare the different tendencies of the amino acids to occupy the five next helical positions in relation to a certain residue.

Pairing differentiation

We initially evaluated how different are the abilities of the five relative helical positions to distinguish the amino acids concerning their tendencies for pairing. The hypothesis underlying this analysis is that each amino acid in position i will influence the relative occurrence of a certain amino acid in position (i + k). Therefore, the first position i can be seen as a variable to which a particular amino acid responds with a characteristic value of propensity. We rearranged the data in a 400 × 5 matrix -rows for amino acid pairs and columns for the type of pairs. Then, we ran a hierarchical clustering algorithm over these 400 cases and five variables using unweighted pair- The results show undoubtedly the formation of two clusters. One contains the pairings (i, i + 3) and (i, i + 4), and the other includes the three remaining variables. In the latter one, it is still possible to distinguish (i, i + 1) from the other two variables.

This statistical result supports intuitive considerations that can be put forward by simple inspection of the geometry of α-helices. In fact, the three positions i, i + 3 and i + 4 appear on the same side of the helix which has, at least, two important consequences. On one hand the spatial proximity allows the two side chains of the pair to interact and, on the other hand, being on the same side of the helix the molecular environment is similar for both residues. These facts may condition the probability of pairing, thus allowing a differentiation of the amino acids by their properties, in a distinct manner from the other pairs. It is also interesting to observe that the variable (i, i + 1) joins the [(i, i + 2), (i, i + 5)] cluster later, i.e. for bigger Euclidean distances. Though somewhat similar to the (i, i + 2) and (i, i + 5) situations, the two amino acids in the (i, i + 1) pair are immediate neighbours in the protein primary structure linked by a peptide bond, which may condition the pairing in a different way even if their side chains are unlikely to interact.

Global pair propensity matrices

The global propensity matrices corresponding to the five types of amino acid pairings are presented in supplementary material. The columns and the rows correspond to the first and k th amino acid in the pair (k = 1, 2, 3, 4 and 5), respectively, ordered by a criterion of roughly increasing polarity. For sake of clarity, a gradient colour code was introduced, ranging from blue for the lowest value to red for the highest one. The (i, i + 4) matrix is shown in Table 1 as the most illustrative example, with the values rounded to one decimal place.

(Table 1)

A first inspection of Table 1 allows some general features to be suggested. The results indicate that pair propensities in the interior of the α-helix depend on the nature of the amino acids involved as was verified for amino acid pairings in helical N-and C-termini. [START_REF] Fonseca | Amino acid pairing at the N-and C-termini of helical segments in proteins[END_REF] If the distribution of the pairs were uniform along the whole protein sequence, we would expect the sample to present a normal distribution centered at the value 1 (a global propensity 1 = g k XY

P

reflects similar preference for helices and elsewhere in the protein chain). However, the corresponding histogram reflects a different distribution (see Figure 3), which is confirmed by the highly significant p-value = 0.0002, obtained by the Shapiro-Wilk test of normality. The same is observed with the remaining pair combinations (see supplementary material). On the other hand, if no correlation between the residues of the pair existed, the elements of all these five matrices would be obtained merely by the product , 1988) In fact, this is not the case, and all the matrices show significantly different distributions from that reference matrix, as was concluded by paired sample t-tests. The largest two-tailed p-value found was 3.6% for (i, i + 2), which confirms that in all the cases the occupancies of the two positions in the pair are not independent.

It is well-known that a major cause for α-helix stabilization is the network of (i, i + 4) H-bonding between carbonyl and amino groups of the protein backbone but, even though all amino acids are able to establish such interactions, these statistical results definitely confirm that the type of side chains plays an important role in α-helix stabilization.

( In the (i, i + 3) and (i, i + 4) matrices the regions of higher propensities are roughly located at the upper-left and bottom-right quadrants. The remaining two quadrants are regions of neutral or low propensities. In contrast, the (i, i + 2) and (i, i + 5) pairings show approximately the opposite trend (see supplementary material).

The (i, i + 3) and (i, i + 4) pairs correspond to both residues on the same side of the helix, and the (i, i + 2) and (i, i + 5) concern residues on the opposite sides of the helix. Therefore, it is not surprising that in the former two cases there is a preference of amino acids with similar polarity to pair, and the opposite happens for the other two pairs.

Knowing the different propensities for individual amino acids to populate the distinct regions of the α-helix, one would expect to observe differences in (i, i + 4) pair propensities between those regions and, consequently, differences in amino acid pair patterns. A comparison of our data and previously published results [START_REF] Fonseca | Amino acid pairing at the N-and C-termini of helical segments in proteins[END_REF] clearly confirmed this, indicating that a particular amino acid pair may have different roles in helix formation and stabilization, similarly to what happens with individual amino acids. [START_REF] Argos | Amino-Acid Distribution in Protein Secondary Structures[END_REF]Cochran and Doig, 2001;Cochran et al., 2001;[START_REF] Ermolenko | Noncharged amino acid residues at the solvent-exposed positions in the middle and at the C terminus of the alpha-helix have the same helical propensity[END_REF][START_REF] Kumar | Dissecting alpha-helices: Position-specific analysis of alpha-helices in globular proteins[END_REF][START_REF] Penel | Side-chain structures in the first turn of the alpha-helix[END_REF][START_REF] Richardson | Amino-Acid Preferences for Specific Locations at the Ends of Alpha-Helices[END_REF] For example, pairings H-M, H-F, H-L, H-I and H-V show global propensities at inner α-helical positions of 1.1, 0.8, 1.1, 0.9 and 1.0 respectively but, if H occupies the N1 of an α-helix, the values increase to 2.4, 2.4, 2.1, 2.5 and 3.1. An opposite trend can be illustrated with the pairings E-Q, E-R, E-K and E-E which, respectively, show global propensities of 1.6, 1.7, 1.6 and 1.4 at the interior of helices and of 0.7, 0.6, 0.5 and 0.6 when E is located in the N1 position of the α-helix. [START_REF] Fonseca | Amino acid pairing at the N-and C-termini of helical segments in proteins[END_REF] Similar conclusions are possible for the other four (i, i + k) pairing cases, with some pairs having effectively high propensities to occur in the interior of α-helices and others exhibiting opposite tendencies.

Side-chain polarity/charge and pair orientation

The observed predominance of apolar/apolar and polar/polar combinations observed for the (i, i + 4) case in Table 1 is to be expected given the frequently amphipatic nature of the α-helix structure.

There are also some polar/apolar (i, i + 4) amino acid combinations which show high propensity to appear in α-helix structures. This provides further indication that hydrophobic interactions between some polar and nonpolar side chains may have a positive influence in helix stability. [START_REF] Andrew | Stabilizing nonpolar/polar side-chain interactions in the alpha-helix[END_REF] = 1.9). These pairs may contribute to the stabilization of the α-helix due to the simultaneous effect of hydrophobic interactions between side chains and the solvation of their polar heads. Pairings involving these amino acids and the much less flexible H, show lower propensities and, in the case of pairing between H and R or K, the pair orientation with the helical axis is statistically relevant, with H showing a higher tendency to be closer to the C-terminal of the helix.

The propensities of pairings of amino acids with negatively-charged chains, D and E, show that these are not particularly frequent in α-helices. However, the E-E pair does show some tendency to be observed with P = 1.4; the weak hydrophobic interactions between the relatively flexible side-chain may compensate for the charge repulsion between the carboxylic groups. yielding a p-value of 3.5%. Additionally, a Shapiro-Wilk test of normality was done for the differences distribution, and a p-value of 2.0% was obtained. These statistics show that, assuming the usual limit of 5%, the differences are indeed significant and the corresponding distribution deviates somehow from the Normal. Under this statistic error range a propensity difference of 0.4 is considered significant and the list of the most relevant cases are collected in Table II. Noteworthy is the case of Aspartate (D) that has an overall low helix propensity. However, when paired with highly polar Glutamine (Q) the propensities increase substantially but only when D is in position k = 4, i.e. the one in the pair closer to the C-terminus of the helix, g

(Table 2)

For the most part, the orientation of apolar/apolar pairings is not dependent in relation to the α-helix axis but there are exceptions which exhibit statistically different propensities (see Table 1 andTable 2). These may be explained considering volume constraints caused by the orientation of side chains towards the N-terminal in α-helices, with smaller residues occupying the i position and larger residues occupying the i + 4 being the most sterically favourable situation, as both side chains can occupy preferred N-oriented conformations without serious steric hindrances.

Pair propensity and ΔG for helix stabilization

The observed propensity values for the pairing of amino acids with oppositely charged side-chains (R, K, H and E, D) reveal that pairs with the positively-charged side-chain closer to the N-terminal and negatively charged side-chain closer to the Cterminal are more frequent than the reverse. The few ΔG measurements available for these cases seem to be in agreement with our observations.(HuyghuesDespointes and [START_REF] Huyghuesdespointes | Ion-pair and charged hydrogen-bond interactions between histidine and aspartate in a peptide helix[END_REF][START_REF] Huyghuesdespointes | Measuring the Strength of Side-Chain Hydrogen-Bonds in Peptide Helices -the Gln-Center-Dot-Asp-(I,I+4) Interaction[END_REF][START_REF] Scholtz | The Energetics of Ion-Pair and Hydrogen-Bonding Interactions in a Helical Peptide[END_REF][START_REF] Smith | Energetics of polar side-chain interactions in helical peptides: Salt effects on ion pairs and hydrogen bonds[END_REF][START_REF] Taylor | The synthesis and study of side-chain lactam-bridged peptides[END_REF] A comparison of the propensities determined for the (i, i + 4) combinations and the experimentally determined free energies of several (i, i + 4) amino acid sidechain interactions indicates a reasonable correlation between these two sets of values.

Although the experimental free energies corresponding to pairs with higher than neutral propensities (P > 1.0) are usually stabilizing values (ΔG 0), the correlation between the two is not linear. However, modest values of ΔG can make large contributions to the observed helicity of model peptides, [START_REF] Smith | Energetics of polar side-chain interactions in helical peptides: Salt effects on ion pairs and hydrogen bonds[END_REF] an effect which may be reflected in proteins and influence the observed propensity values. The documented interaction free energy values were determined with model situations, generally using modified poly-A peptides which may not accurately represent the reality of amino acid side-chain interactions in vivo, where intra-helical side chain interactions are not regularly used to increase stability. [START_REF] Fernandez-Recio | Intrahelical side chain interactions in alpha-helices: poor correlation between energetics and frequency[END_REF] This may be illustrated by the observation that pairings V-F, V-Y, V-W, V-H, I-Y, I-W (potentially helix destabilizing with ΔG > 0) [START_REF] Creamer | Interactions between Hydrophobic Side-Chains within Alpha-Helices[END_REF] show relatively neutral propensities (P = 0.8 -1.3) while I-F has a positive propensity (P I-F = 1.5). On the other hand, potentially stabilizing pairs Y-W, W-W, H-F, K-F (ΔG < 0) [START_REF] Andrew | Stabilizing interactions between aromatic and basic side chains in alpha-helical peptides and proteins. Tyrosine effects on helix circular dichroism[END_REF][START_REF] Creamer | Interactions between Hydrophobic Side-Chains within Alpha-Helices[END_REF][START_REF] Fernandez-Recio | Energetics of a hydrogen bond (charged and neutral) and of a cation-pi interaction in apoflavodoxin[END_REF][START_REF] Meurisse | Aromatic side-chain interactions in proteins. Near-and far-sequence His-X pairs[END_REF][START_REF] Meurisse | Aromatic side-chain interactions in proteins: Near-and far-sequence Tyr-X pairs[END_REF]Thomas et al., 2002a;Thomas et al., 2002b) also show neutral propensities (P = 0.8 -1.1).

i, i + n pair correlations

Further analysis of our pool of sequence data revealed the existence of a series of pair association rules which appear to indicate the existence of correlations between pairings in α-helices (rule confidence being the number of cases in which the rule is correct relative to the number of cases in which it is applicable) with the presence of a given pair suggesting the presence others in an α-helix. The other way around, the presence of a set of pairs that make a given rule may indicate that the segment where those pairs are to be found may be an α-helix. Selected results are shown in Table 3 and the full list is available as supplementary material.

(Table 3)

Consequence of the tendency of alanine to form α-helical structures, most relevant correlation rules involve pairs containing alanine and other hydrophibic amino acids; also, a significant part involves only (i, i + n) alanine pairs (see supplementary material). Of particular interest are association rules involving pairs with polar or charged amino acids (aspartic acid, arginine and lysine), which frequently indicate the possible existence of 'less-common' pairs (i.e., not as common as the frequent (i, i + n) apolarapolar pairings indicated in the majority of other rules). The combination of these association rules and amino acid pair propensities has potential to be applied to pattern detection algorithms in fine-tuning the prediction of occurrence of α-helical structures from the determined probabilities of amino acid pairing patterns in known primary sequences. Our own data and a previous study [START_REF] Fonseca | Amino acid pairing at the N-and C-termini of helical segments in proteins[END_REF] suggest that different pairing patterns may occur with different degrees of statistical significance in the interior of the α-helix, similarly to amino acid patterns described in previous works(de [START_REF] De Brevern | Bayesian probabilistic approach for predicting backbone structures in terms of protein blocks[END_REF][START_REF] Etchebest | A structural alphabet for local protein structures: Improved prediction methods[END_REF] and also open a possible novel approach to the problem of amino acid alphabet reduction.

Protein alphabet reduction by propensity response

The (i, i + 4) pairing is of particular importance because this is the case where the two amino acids are better aligned with the helix macrodipole, and spatial proximity enables their side chains to interact more easily. A hierarchical clustering algorithm was applied to the 20 amino acids using the global propensity values, in order to classify them in terms of their pairing response at position i + 4. Each row of the propensity matrix corresponds to a particular amino acid (20 cases are thus defined) whose response to a particular residue four positions backwards in the helix (20 variables are thus defined) is evaluated by the global propensity value. The corresponding dendrogram for case clustering, using unweighted pair-group average and squared Euclidean distances, is shown in Figure 4.

The number of clusters was defined by carrying out a series of one-way ANOVA analyses with an increasing number of clusters. The proportion of variation explained by the clustering increases rapidly up to R 2 = 85 % which corresponds to a set of five clusters. The further partition of the space improves the value of R 2 at a slower rate, thus the five clusters are {P, G}, {C, V, Y, W, F}, {I, M, L, A}, {D, H, N, S, T} and {E, K, R, Q } -respectively designated as Class 1, 2, 3, 4 and 5.

The results of clustering expectedly suggest that P and G (both small, nonpolar and neutral amino acids) are special cases -in fact, both have low helix forming tendency, with P being a helix breaker. Other clusters are somewhat intuitive following chemical/structural properties of side chains and others less so.

The cluster {E, K, R, Q} is comprised of amino acids with relatively large and very flexible alyphatic side chains which are either charged (E, K, R) or polar (Q).

The side chains of amino acids in the {D, H, N, S, T} cluster are hydrophilic and highly polar (D being negatively charged) and share comparable values of relatively low flexibility. Large and with an aromatic group in the side-chain, H is another exceptional member of this cluster of otherwise small amino acids with aliphatic side chains.

The cluster {I, M, L, A} is formed by amino acids with hydrophobic non-polar aliphatic side chains. All are relatively large and have flexible hydrocarbon chains, with the exception of the rather small A and the sulphur-containing M.

Ranging in volume from relatively small (C) to the large (W), the hydrophobic amino acid side chains of the {C, V, Y, W, F} cluster show reduced degrees of flexibility. The cluster is divided into two sub-groups, one composed by F, Y and W which have large aromatic side chains and another by the small amino acids C and V.

(FIGURE 4) Figure 4. Dendrogram for case (amino acid type) clustering in pairing (i, i + 4).

Global triplet propensities

Particular arrangements of three residues (see Figure 1) have been suggested previously as important structural motifs in the stabilization of helices. (Iqbalsyah and Doig, 2005b;[START_REF] Olson | Cooperative helix stabilization by complex Arg-Glu salt bridges[END_REF] The synergy they achieve in such arrangements is difficult to predict on the basis of individual or even amino acid pair analysis.

The evaluation of the calculated values of global propensities for the triplets (i,

i + 4, i + 8) or (i, i + 3, i + 4), g Z XY n k P
, reveals that they cannot be immediately and confidently used to assign the tendency of a given triplet to occur in α-helix. In fact, propensities with values greater than 4 often reflect cases in which the associated triplets are observed too few times, so that their relative frequency of occurrence in and outside of α-helices can differ by an order of magnitude, originating extreme propensity values which cannot be deemed significant. The obtained results may nevertheless prove of use for future research into the stabilization properties of intrahelical amino acid triplet groupings. Sorting triplet results, first by the number of occurrences inside α-helix and then by propensities, suggests that some triplet combinations have a greater tendency to appear in α-helical structures. Table 3 shows the top 25 cases of such sorting for both triplets considered, and the full list is also available online at http://www.requimte.pt:8080/Prot-2S/HelicalAA.php.

(Table 4)

Applying the amino acid clustering classification described above to those 100 cases, one finds that, though Class 3 amino acids appear more frequently than others in the most common triplets, there isn't a clear difference between their occurrence inside and outside of helices. Triplets containing Class 5 amino acids (the second most represented cluster) are somewhat more frequently observed in α-helices. Class 1 is expectedly under-represented inside α-helices while Class 2 amino acids seem similarly presented in and out of α-helices, with a relatively low number of occurrences. Class 4 amino acids were observed in only a few occasions in the top 100 more frequent triplets with the results suggesting that triplets containing amino acids belonging to this cluster have a greater tendency to be found outside of αhelices.

We observed that (i, i + 4, i + 8) triplets formed by Class 3 and Class 5 amino acids appear to be relatively common among the more frequently observed triplets in α-helices. While contrary to the expected when considering the amphiphilic nature of the α-helix, with residues of similar polarity usually found on the same face of the helix, the longer side chains of amino acids like E, K, R and Q simultaneously exhibit polar and hydrophobic character and thus interact favourably with the short and markedly hydrophobic aliphatic side chains of amino acids like A, L, I and M stabilizing the α-helix structure and interacting with other polar groups or water, similar to what is observed for micelles. [START_REF] Andrew | Stabilizing interactions between aromatic and basic side chains in alpha-helical peptides and proteins. Tyrosine effects on helix circular dichroism[END_REF]

Conclusion

Based on the results presented here and by other investigations before, it is accepted that the occurrence of amino acids pairings in helical positions, both in termini and inner positions, is not random. We present the most comprehensive analysis of amino acid sequence patterns ever done for the interior locations of α- The information presented here and in a previous study [START_REF] Fonseca | Amino acid pairing at the N-and C-termini of helical segments in proteins[END_REF] represents steps in the creation of a comprehensive, and constantly updated, online mapping of amino acid side-chain interactions in α-helical structures, both in terminal and inner helical positions. Detailed analysis data is periodically updated in our own public server which can be accessed at http://www.requimte.pt:8080/Prot-2S/HelicalAA.php and the latest versions are also supplied as supplementary material.

helices
The large amount of information collected will be extremely useful for further analysis using Inductive Logic Programming algorithms, which will allow us to obtain and refine predictive rules based on amino acid physicochemical characteristics and global propensities, both individually as well as pair and triplet propensities.

i P G F A V L I M C Y W T N S Q R K H E D
i + 4 P 0.0 0.0 0.0 0.2 0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.2 0.1 G 0.1 0.3 0.4 0.8 0.4 0.6 0.4 0.5 0.4 0.4 0.5 0.4 0.4 0.4 0.6 0.7 0.4 0.5 0.5 0.3 F 0.1 0.5 1.6 1.7 1.3 1.6 1.5 1.6 1.1 0.9 1.2 0.7 0.6 0.7 1.0 1.0 0.9 0.8 0.8 0.5 A 0.1 0.9 1.3 2.5 1.5 2.0 1.6 2.0 1.3 1.3 1.4 1.1 1.2 1.1 1.8 1.8 1.7 1.1 1.4 1.0 V 0.0 0.4 1.6 1.5 1.4 1.7 1.7 1.7 1.3 1.4 1.2 0.7 0.6 0.6 0.8 1.1 0.5 1.0 0.7 0.4 L 0.1 0.8 1.9 2.0 1.8 2.2 2.1 2.1 1.5 1.7 1.5 1.2 0.9 0.9 1.6 1.6 1.2 1.1 1.2 0.5 I 0.1 0.4 1.6 1.9 1.7 2.3 2.3 2.0 1.6 1.4 1.6 1.1 0.7 0.6 1.3 1.4 1.0 0.9 1.0 0.4 M 0.2 0.8 1.9 2.0 1.7 2.3 1.6 2.5 1.2 1.7 1.7 1.2 0.9 0.9 1.3 1.5 1.2 1.1 1.1 0.7 C 0.0 0.6 1.5 1.5 1.1 1.5 1.1 1.7 1.0 1.2 1.3 0.6 0.6 0.6 0.6 0.9 0.5 0.8 0.5 0.5 Y 0.1 0.5 1.2 1.8 1.2 1.7 1.2 1.5 1.1 0.9 0.9 0.9 0.6 0.8 1.1 1.2 1.1 0.9 0.9 0.5 W 0.1 0.4 1.4 1.7 1.1 1.9 1.4 1.6 1.0 0.9 1.1 0.6 0.6 0.7 1.0 1.3 1.1 0.8 1.1 0.7 T 0.0 0.4 0.6 1.2 0.8 1.2 0.8 0.9 0.7 0.5 0.7 0.6 0.6 0.6 1.1 1.1 0.9 0.7 0.9 0.7 N 0.1 0.4 0.4 0.9 0.7 0.8 0.9 1.1 0.5 0.7 0.7 0.8 0.7 0.6 1.2 1.2 1.0 0.6 1.2 0.7 S 0.1 0.4 0.6 1.1 0.6 0.9 0.7 0.9 0.7 0.6 0.7 0.5 0.7 0.6 1.0 1.0 0.9 0.7 0.9 0.7 Q 0.2 0.5 1.1 1.7 1.1 1.5 1.3 1.6 0.6 1.4 1.2 1.0 1.2 1.0 2.2 1.8 1.9 1.2 1.6 1.0 R 0.2 0.5 1.0 1.8 1.1 1.6 1.3 1.4 1.0 1.3 1.5 0.9 1.0 0.8 1.8 1.7 1.5 0.9 1.7 1.0 K 0.2 0.4 0.9 1.5 1.0 1.3 1.2 1.2 0.8 1.0 1.1 0.9 0.8 0.9 1.7 1.4 1.3 0.5 1.6 1.0 H 0.1 0.4 0.8 1.3 0.8 1.2 1.0 1.1 0.6 0.8 0.8 0.8 0.7 0.8 1.1 1.3 1.1 0.9 1.0 0.8 E 0.2 0.5 0.8 1.6 0.9 1.3 1.1 1.2 0.8 0.8 0.8 0.9 1.1 0.9 1.9 2.0 1.8 1.0 1.4 1.0 D 0.1 0.3 0.4 0.8 0.4 0.6 0.5 0.8 0.4 0.4 0.5 0.5 0.9 0.7 1.6 1.4 1.4 0.7 0.8 0.6

  the tendency of the particular pair of amino acids XY to integrate helices when they are k (k = 1, 2, 3, 4, 5) positions apart between each other. It is the ratio of the relative frequency of occurrence of the pair XY k at the interior of helices and the relative frequency of occurrence of that pair in all protein sequences. The term helix k XY nis the number of occurrences of the particular pair XY k inside the helices; in ∑ extended to all amino acids and it represents the total number of pairs found in helices where the second residue is always found k positions after the first one; all k XY n is the number of observations of the particular pair XY k in all the protein sequences; in ∑ to all amino acids, and it represents the total number of pairs observed in all the working dataset.

Figure 2 .

 2 Figure 2. Dendrogram for variable (pair position) clustering.

  acid propensities, which were calculated previously.(McCaldon and Argos

3 )Figure 3 .

 33 Figure 3. Histogram of the global propensity values for the (i,i+4) case

  This is particularly noticeable for (i, i + 4) pairings involving the polar and charged amino-acids Q, R, K and E with the small apolar A, L and M -especially in pairs involving A.Pairings between the highly polar Q and positively charged R, K exhibit high propensities and the pair orientation is statistically indifferent (

  same values, suggesting that orientation of some pairs with the helical axis may be important. In order to evaluate how significant the differences g paired sample T-test was run with all the 190 possible pairs XY k (X≠Y),

  . A similar phenomenon happens with pairing of D with the positively charged Arginine (R) and Lysine (K).

  Apolar/polar pairing combinations are, for the most part also orientationindependent. Notable exceptions, K-V ( 6) arise for the same reasons mentioned for apolar/apolar pairings.

  in proteins, as different pairs and triplets. A systematic and exhaustive study of 12821 α-helices allowed us to determine the frequency of occurrence of all possible (i, i + k) (k = 1, 2, 3, 4, 5) amino acid side-chain pairings and (i, i + k, i + n) (k = 4, n = 8) ; (k = 3, n = 4) triplets, in interior positions, and to evaluate their relative propensities to occur in such positions. This study represents a broad approach and further work using different and narrower subsets of proteins as sampling material (taking into account their origin, structure and function) should provide more detail into amino acid pattern trends in the interior or α-helices. The obtained results were compared with past experimental research corroborating the existence of possible correlations between those amino acid patterns and their effect on the stability of α-helical structures. Based on a statistical assessment of the results it is possible to propose a novel amino acid alphabet reduction, clustering amino acids according to their pairing propensities. This clustering also reflects chemical and structural properties of isolated amino acids but there are some less intuitive clusters. These groups may indicate possibilities for amino acid replacements and may give additional insight into the comparison of homology sequences.

  from grant Ref. PIO52048 and RD07/0067/0005 funded by the Carlos III Health Institute.

  Figure 1. Amino acid Triplets considered at the interior of α-helices: a) (i, i+4, i+8) ,

Fig. 2

 2 Fig.2 Dendrogram for variable (pair position) clustering.

Fig. 3 Fig. 4

 34 Fig.3 Histogram of the global propensity values for the (i,i+4) case and results of the Shapiro-Wilk test of normality.

Table I

 I

	is not a symmetric matrix, as g XY k

Table 1

 1 Global propensities for the (i, i + 4) pairing.

Table 2

 2 (i, i+4) residue pairs with statistically relevant propensity differences.

	i+4	i	P	i+4	i	P	Abs( P)
	H	K	1.1	K	H	0.5	0.59
	D	Q	1.6	Q	D	1.0	0.53
	Y	A	1.8	A	Y	1.3	0.52
	C	M	1.7	M	C	1.2	0.50
	K	V	1.0	V	K	0.5	0.48
	C	I	1.1	I	C	1.6	0.46
	W	L	1.9	L	W	1.5	0.45
	C	F	1.5	F	C	1.1	0.45
	T	Y	0.5	Y	T	0.9	0.44
	D	K	1.4	K	D	1.0	0.44
	M	I	1.6	I	M	2.0	0.42
	H	R	1.3	R	H	0.9	0.41

Table 4 .

 4 Selected global propensities (P) for the (i, i + 4, i + 8) and (i, i + 3, i + 4) triplets.

	i, i + 4, i + 8				i, i + 3, i + 4
		Class P	Cases in α-helix	Total cases		Class P	Cases in α-helix	Total cases
	AAA 333	3.7	121	850	ALA	333	3.7	224	756
	AAL	333	3.4	94	708	LAL	333	3.5	219	795
	LLL	333	2.9	75	672	AAA 333	3.1	211	846
	LLA	333	3.2	69	566	AAL	333	3.5	188	677
	LAA	333	2.9	65	589	LLA	333	3.7	187	643
	VAA 233	3.3	61	480	LLL	333	3.2	174	673
	ALL	333	2.4	59	624	AEA 353	3.2	140	557
	LIL	333	3.9	58	382	ALL	333	3.0	135	567
	LVL	323	3.2	56	449	AVA 323	3.3	130	491
	LAL	333	2.6	56	567	LAA	333	3.1	130	530
	ALA	333	2.5	53	554	LAI	333	4.2	123	367
	AAV 332	2.8	52	485	VAL	233	2.9	123	526
	LLR	335	3.2	51	418	LLE	335	2.6	119	572
	ALI	333	4.1	50	319	AIA	333	3.3	116	437
	IVL	323	4.3	48	289	AKA 353	3.3	113	434
	AAE 335	3.0	48	416	LLV	332	3.2	112	438
	LLE	335	2.3	48	533	ARA 353	3.3	111	422
	VLL	233	2.6	47	460	IAL	333	3.3	107	401
	KAA 533	3.3	45	349	LAV	332	2.7	106	489
	KEK 555	3.2	45	362	VLL	233	2.8	104	466
	AGA 313	2.0	44	563	LEL	353	2.4	103	531
	AAI	333	3.1	43	362	AAV 332	2.8	101	448
	RLL	533	2.9	42	379	LLK	335	2.5	101	506
	VLA	233	2.7	42	400	LLI	333	3.5	99	351
	LVA	323	2.6	42	418	ALV	332	3.0	99	412

Acknowledgements

De Sousa M. thanks the Fundação para a Ciência e a Tecnologia for funding this work (PhD grant SFRH/BD/45821/2008). Munteanu C. R. acknowledges the funding for a research position by the Isidro Parga Pondal Programme, Xunta de Galicia (Spain) and for the stage fellowship IN809 A 2010/81 by Galician Ministry of Econonmy and Industry, Xunta de Galicia (Spain). The authors thank for the partial financial support