Analysis of loop boundaries using different local structure assignment methods

Abstract

Loops connect regular secondary structures. In many instances, they are known to play important biological roles. Analysis and prediction of loop conformations depend directly on the definition of repetitive structures. Nonetheless, the secondary structure assignment methods (SSAMs) often lead to divergent assignments. In this study, we analyzed, both structure and sequence point of views, how the divergence between different SSAMs affect boundary definitions of loops connecting regular secondary structures. The analysis of SSAMs underlines that no clear consensus between the different SSAMs can be easily found. Because these latter greatly influence the loop boundary definitions, important variations are indeed observed, that is, capping positions are shifted between different SSAMs. On the other hand, our results show that the sequence information in these capping regions are more stable than expected, and, classical and equivalent sequence patterns were found for most of the SSAMs. This is, to our knowledge, the most exhaustive survey in this field as (i) various databank have been used leading to similar results without implication of protein redundancy and (ii) the first time various SSAMs have been used. This work hence gives new insights into the difficult question of assignment of repetitive structures and addresses the issue of loop boundaries definition. Although SSAMs give very different local structure assignments capping sequence patterns remain efficiently stable.

Introduction

The knowledge of the three-dimensional (3D) structures of proteins contributes to understand their biological functions. Protein 3D structures are often described as a succession of repetitive secondary structures (mainly α-helices and β-sheets^1,2). This mono-dimensional description helps to simplify coarsely this 3D information. It can also be used to describe more complex local 3D motifs, for example, the Greek key,³ or even complete 3D structures in 2D views, for example, HERA⁴ or TOPS.⁵

Numerous approaches exist to assign secondary structure and rely on various descriptors (see Table I).

Table I.

Secondary Structure Assignment Methods

Methods	Year	Assignment Based On
Greer and Levitt	1977	Distance
DSSP	1983	H-bond
DEFINE	1988	Distance
PCURVE	1989	Axis
SSTRUC	1989	H-bond
CONCENSUS	1993	Mean (DSSP, DEFINE, and PCURVE)
STRIDE	1995	H-bond/dihedral
PROMOTIF	1996	H-bond/dihedral
PSEA	1997	Distance/angle
PROSS	1999	Dihedral
XTLSSTR	1999	Distance/angle
DSSPcont	2002	H-bond
SECSTR	2002	H-bond
VORO3D	2004	Voronoï tessalation
KAKSI	2005	Distance/dihedral
SEGNO	2005	angle/multiple
Beta-Spider	2005	β-sheet + DSSP for α-helix
PALSSE	2005	Cα (vector similarity)
Delaunay tessellation	2005	Delaunay tessalation
SKSP	2007	Mean (STRIDE, DSSP, SECSTR, KAKSI, P-SEA, and SEGNO)
PROSIGN	2008	Cα deviation values

A first class of methods is based solely on H-bond patterns. In this category, DSSP⁶ remains the most popular secondary structure assignment methods (SSAMs). It identifies the secondary structures by particular hydrogen bond patterns detected from the protein geometry and an electrostatic model. DSSP is the basis of the assignment done by the Protein DataBank (PDB).^7,8 A recent version of DSSP called DSSPcont was proposed by Rost.⁹ SECSTR is also an evolution of DSSP method dedicated to improved π-helices detection.¹⁰

A second class of SSAMs add dihedral angle properties to H-bond patterns. In this category, STRIDE, developed in 1995, is the second widely used SSAM.¹¹ PROMOTIF derives also from the DSSP approach, namely the software SSTRUC,¹² but focus on the characterization of γ- and β-turns, β-hairpins, and β-bulges.¹³

The third class of secondary structure assignment methods relies on distances between residues inside protein structures. Additionally, this criterion has also been extended by taking into account angles. The DEFINE method,¹⁴ like the Levitt's and Greer's method,¹⁵ uses only the C_α positions. It computes inter-C_α distance matrix and compares it with matrices produced by ideal repetitive secondary structures. KAKSI is a new assignment method of assignation using the inter-C_α distances and dihedral angles criteria.¹⁶ PSEA assigns the repetitive secondary structures from the sole C_α position using distance and angles criteria.¹⁷ XTLSSTR uses all the backbone atoms to compute two angles and three distances.¹⁸

Fourth, some SSAMs are defined solely on angles. PROSS is based only on the computation of φ and Ψ dihedral angles. The Ramachandran map is divided into mesh of 30 or 60° and the secondary structures are assigned in regards to their successions of encoded mesh.¹⁹ SEGNO uses also the φ and Ψ dihedral angles coupled with other angles to assign the secondary structures.²⁰

Fifth, VoTap (Voronoï Tessellation Assignment Procedure) is a geometrical tool that associates with each amino acid a Voronoï polyhedron,²¹ the faces of which define contacts between residues.²² In the same way, Vaisman and coworkers have developed a simple five-element descriptor, derived from the Delaunay tessellation of a protein structure in a single point per residue representation, which can be assigned to each residue in the protein.²³

A sixth category of SSAM relies on geometrical definitions and Cα coordinates. PCURVE is based on the helical parameters of each peptide unit, generates a global peptide axis and makes use of an extended least-squares minimization procedure to yield the optimal helical description.²⁴ PALSSE delineates secondary structure elements from protein Cα coordinates, and specifically addresses the requirements of vector-based protein similarity searches²⁵; this approach leads to surprising assignment where a residue can be associated to a α-helix and also to a β-strand. Very recently, PROSIGN proposed a different approach based solely on Cα coordinates.²⁶ Hosseini and coworkers introduce four certain relations between Cα three-dimensional coordinates of consecutive residues, their method gives interesting information about helix geometry.

Finally, some SSAMs like Beta Spider could be considered more as hybrid or consensus methods. For instance, Beta Spider focuses only on β-sheet (the α-helix assignment is performed by DSSP) by considering all the stabilizing forces involved in the β-sheet phenomenon.²⁷

As a consequence, these different assignment methods have generated specific weaknesses. For example, DSSP can generate very long helices that can be classified as linear, curved or kinked.^28–30 This was one of the motivations of KAKSI methodology to define linear helices instead of long kinked helices.¹⁶ Moreover, the disagreement between the different SSAMs is not negligible, leading to only 80% of agreement between two distinct methods.^16,31–33 Consensus methods have been proposed using (i) DEFINE, P-CURVE, and DSSP³² and (ii) more recently, P-SEA, KAKSI, SECSTR, and STRIDE,³⁴ to diminish such features.

The coil state is in fact composed of really distinct local folds,^35–38 such as turns.^13,39–44 Several studies have attempted to analyze conformation of loops linking specific secondary structures forming distinct subsets.^45–51 They are biologically essential regions,⁵² for example, loops of protein kinases.^53,54 They are also used to analyze protein homology,^55–60 for example, for structure-based phylogenetic study.⁶¹ Because of their flexible nature they raise crucial questions in protein docking approaches,^62–64 to predict protein loop conformations,^65–78 to enhance protein thermostability,⁷⁹ to design proteins,⁸⁰ or to obtain protein structures.⁸¹ According to the repetitive secondary structures of their extremities, connecting loops are of four distinct classes (α-α, α-β, β-α, and β-β).^46,82–84 The research on loops has always been limited by the number of available loops in protein structures from the Protein DataBank (PDB,^7,8), so most of the works focus on loops of less than nine residues.^85,86

Analyses have shown that capping regions of repetitive structures have specific amino acid compositions. George Rose analysis of helix signals in proteins highlighted the hydrophobic capping,⁸⁷ an hydrophobic interaction that straddles the helix terminus is always associated with hydrogen-bonded capping. From a global survey of protein structures, they identified seven distinct capping motifs, three at the helix N-terminus and four at the C-terminus.⁸⁸ Recently, Kruus and coworkers have studied helix-cap sequence motifs. Their study is based on a very innovative approach. Indeed, they firstly assigned the helix of well-determined protein structures. Then, they searched for the sequence motifs corresponding at best to the capping regions. This search is based on Gibbs sampling method. They showed an important number of frameshifts of ±1 amino acid residue.⁸⁹ To date, no similar properties have been reported directly on β-strands.

In this article, we focus on the analysis of loop boundaries, that is, capping regions of repetitive structures. We analyzed the disagreement between SSAMs for the definition of these capping regions and evaluated if the structural disagreement is associated with clear frameshift at the sequence level.

Results

Protein databanks

The constitution of the protein dataset is always crucial for protein structure analysis and prediction. In the case of loop predictions, another major problem is the right choice of the sequence similarity cut-off used to construct training datasets. Indeed, a 30% sequence identity nonredundant dataset corresponds to 10–20% sequence identity in coil regions. Thus, we have used different cut-off criteria ranging from 20 to 90% and constructed 10 different datasets (see Supporting Information 1) to sample different sequence identity rates and analyze the influence of sequence identity on capping regions. Crystallographic structures in these datasets were selected at two resolution levels: three datasets were filtered for high resolution quality (resolution better than 1.6 Å) and seven were filtered for good resolution quality (resolution better than 2.5 Å). The datasets have been extracted from PISCES database.^90,91

Table II summarizes, for each of the 10 datasets in our study, the secondary structure assignment done by different secondary structure assignment methods (SSAMs). The classical differences observed between (SSAMs) are found again,³³ that is, α-helices frequency ranges mainly between 28 and 34% and β-strand between 18 and 24%. Some SSAMs have particular behaviors like KAKSI¹⁶ that is associated to a high β-strand frequency (∼28%) or DEFINE¹⁴ with a low α-helix frequency (∼24%). Nonetheless, for each SSAM, both mean frequency of secondary structures and length of repetitive structures remain surprisingly highly comparable for all the datasets; neither number of residues, nor sequence identity rate, nor resolution quality had an effect on the secondary structure features. In the following, the presented results will concern DB0 except when noted.

Table II.

10 Protein Databanks

		DB0		DB1		DB2		DB3		DB4
		freq	lg	freq	lg	freq	lg	freq	lg	freq	lg
DSSP	α	33.17	10.66	34.51	11.21	34.46	11.14	34.07	11.09	33.70	11.02
	β	21.52	5.30	21.60	5.44	21.64	5.42	21.85	5.41	21.86	5.39
	coil	45.3		43.88		43.91		44.08		44.44
STRIDE	α	30.78	11.12	34.15	11.76	34.07	11.69	33.74	11.63	33.47	11.56
	β	19.7	5.34	20.89	5.47	21.10	5.45	21.38	5.44	21.39	5.42
	coil	49.51		44.96		44.83		44.88		45.14
SECSTR	α	31.38	10.93	32.72	11.56	32.62	11.48	32.25	11.43	31.88	11.36
	β	20.32	4.98	20.22	5.11	20.29	5.10	20.48	5.09	20.57	5.07
	coil	48.3		47.06		47.10		47.27		48.75
XTLSSTR	α	32.13	10.64	32.83	11.18	32.62	11.10	32.23	11.04	31.87	10.98
	β	19.57	4.91	19.05	5.02	19.14	5.01	19.34	5.00	19.38	4.99
	coil	48.3		48.12		48.24		48.44		48.75
PSEA	α	34.04	10.78	35.56	11.30	35.48	11.23	35.09	11.17	34.68	11.11
	β	24.01	5.16	24.49	5.27	24.48	5.26	24.72	5.25	24.84	5.24
	coil	41.95		39.94		40.04		40.18		40.48
DEFINE	α	28.35	10.95	25.60	11.42	26.25	11.36	26.38	11.30	26.12	11.24
	β	25.89	5.39	22.39	5.47	23.12	5.47	23.48	5.46	23.48	5.45
	coil	45.76		52.01		50.63		50.14		50.40
KAKSI	α	29.66	11.12	27.36	11.57	28.25	11.51	28.45	11.45	28.83	11.40
	β	28.91	5.53	25.87	5.59	26.69	5.59	27.12	5.58	27.84	5.58
	coil	41.43		46.78		45.06		44.43		43.34
SEGNO	α	30.17	10.99	31.64	11.43	31.71	11.37	31.32	11.31	30.92	11.27
	β	21.26	5.58	21.26	5.65	21.36	5.65	21.50	5.63	21.52	5.63
	coil	48.58		47.10		46.93		47.17		47.56
PBs	α	31.39	10.65	33.02	11.11	32.84	11.05	32.45	10.99	32.05	10.94
	β	18.25	5.39	18.64	5.46	18.64	5.45	18.77	5.44	18.85	5.44
	coil	50.35		48.35		48.51		48.79		49.10
Nb res		162,830		565,364		712,075		870,094		1,132,639
Nb chains		887		2722		3325		3983		5081
pc		20		20		25		30		40
res		1.6		2.5		2.5		2.5		2.5
R factor		0.25		1.00		1.00		1.00		1.00
		DB5		DB6		DB7		DB8		DB9
		freq	lg	freq	lg	freq	lg	freq	lg	freq	lg
DSSP	α	32.18	10.69	33.60	11.10	33.37	10.99	33.17	10.98	31.56	10.70
	β	21.77	5.31	22.03	5.45	21.76	5.37	21.90	5.37	22.18	5.31
	coil	46.05		44.37		44.87		44.93		46.25
STRIDE	α	29.96	11.15	33.60	11.66	33.25	11.54	33.09	11.53	29.60	11.18
	β	19.88	5.34	21.57	5.47	21.37	5.40	21.53	5.40	20.34	5.34
	coil	50.16		44.83		45.38		45.38		50.06
SECSTR	α	30.41	10.96	31.90	11.46	31.58	11.34	31.40	11.34	29.83	10.98
	β	20.73	4.99	20.67	5.13	20.53	5.06	20.67	5.06	21.15	4.99
	coil	48.86		47.43		47.89		47.93		49.02
XTLSSTR	α	31.13	10.65	31.95	11.08	31.63	10.96	31.45	10.96	30.61	10.68
	β	19.83	4.92	19.48	5.04	19.32	4.97	19.44	4.97	20.21	4.93
	coil	49.05		48.57		49.05		49.10		49.18
PSEA	α	32.96	10.80	34.47	11.22	34.30	11.10	34.11	11.09	32.41	10.83
	β	24.37	5.17	25.00	5.28	24.80	5.22	24.97	5.23	24.86	5.18
	coil	42.67		40.52		40.90		40.93		42.73
DEFINE	α	28.02	10.95	26.70	11.34	26.52	11.22	26.41	11.22	26.91	10.97
	β	26.10	5.39	24.29	5.49	23.91	5.44	24.01	5.44	26.12	5.40
	coil	45.89		49.01		49.57		49.58		46.97
KAKSI	α	29.45	11.14	29.14	11.49	28.84	11.38	28.66	11.38	27.98	11.14
	β	30.00	5.56	28.27	5.82	28.29	5.58	28.23	5.58	29.16	5.56
	coil	40.55		42.58		42.88		43.11		42.86
SEGNO	α	29.41	11.00	31.34	11.36	30.61	11.24	30.43	11.24	28.24	11.00
	β	21.28	5.61	22.06	5.68	21.49	5.64	21.66	5.64	21.55	5.62
	coil	49.31		46.60		47.91		47.92		50.21
pBs	α	30.62	10.65	32.04	11.02	31.71	10.91	31.54	10.91	32.08	10.65
	β	18.59	5.41	18.88	5.48	18.78	5.45	18.90	5.45	18.87	5.42
	coil	50.79		49.09		49.51		49.56		51.05
Nb res		276,586		415,360		1,513,629		1,572,412		312,219
nb chains		1425		5847		6823		7141		1630
pc		50		50		70		80		90
res		1.6		2.5		2.5		2.5		1.6
R factor		0.25		1.00		1.00		1.00		0.25

This table summarizes all the 10 protein databanks (noted from DB 0 to DB 9) used in this study. Each databank is analyzed using different SSAMs, are given the frequencies of secondary structure (freq) and average length of repetitive structures (lg), with the total number of amino acids (NB res), the number of protein chains (nb chains), the maximum percentage of sequence identity (pc), the resolution (res) and R factor.

Figure 1 shows an example of Hhai Methyltransferase⁹² assigned by different SSAMs, it highlights visually how the differences can be important (see also Supporting Information 2). In the same way, the computation of C₃, that is, the agreement rates between SSAMs (see Methods section), gives also similar results to previous works^16,33,93 (see Fig. 2). Briefly, SSAMs based on hydrogen bond assignments (DSSP, STRIDE, and SECSTR) produced nearly identical assignments, with C₃ more than to 90%. Otherwise, a mean C₃ of 80% was observed, with SEGNO displaying a closer C₃ value to hydrogen bond assignments than the others. DEFINE remains very different from the other methods with C₃ values close to 60%. Comparison of all theses SSAMs clearly highlights the intricacy of obtaining a simple consensus between all the methods.

Figure 1.

SSAMs of Hhai Methyltransferase. Example of secondary structure assignments for the Hhai Methyltransferase (PDB code :10MH⁹²) with (a) DSSP, (b) STRIDE, (c) PSEA, (d) DEFINE, (e) PCURVE, (f) XTLSSTR, and (g) SECSTR. All the methods have been reduced to three states with the helical states in red ribbons, the extended state in green arrows, and the coil in blue line. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 2.

C₃ values for different SSAMs (DB0 dataset). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Analyses of the structural agreement between the capping regions of repetitive secondary structures

These results highlight the difficulties to define an appropriate length for α-helices, β-strands, and coils and locating their extremities.^87,88,94-98 Inaccuracies in defining the repetitive structures have direct repercussions on the definition of loops. Thus, we have analyzed the positions of capping positions of repetitive structures as assigned by DSSP and systematically looked for their counterparts in assignments performed by another SSAM (only long repetitive structures of more than six residues have been used). Figure 3 shows some examples of this systematic comparison (see Supporting Information 3 for all the examples). Each figure compares a SSAM with DSSP. On the x-axis are given the positions of the N- and C-caps of α-helices (top) and β-strands (bottom) obtained by each method with respect to reference DSSP assignments (labeled “N-cap” or “C-cap” on this x-axis). On the y-axis are given the corresponding observed frequencies. For instance, C-cap position of α-helix assigned by DSSP corresponds to 43% of C₁, 42% of C_cap and 4% of C₁′ positions assigned by STRIDE (see Fig. 3, pattern 2). Five characteristic patterns could be identified:

• pattern 1, the capping position of the SSAM is the same than DSSP (in red),

• pattern 2, same capping position as DSSP and an adjacent positions are found,

• pattern 3, No preferred capping positions could be identified, they are distributed over the whole window range,

• pattern 4, it is another position that is considered preferably as the capping residue by the other SSAM,

• pattern 5, due to the definition of repetitive structures, the capping position is not within the range −4 to +4 around the capping position of DSSP.

Figure 3.

Examples of discrepancies between N or C cap positions assigned by DSSP with other SSAMs. Examples of the four kinds of differences are shown. (x-axis) the position of the capping region, (y-axis) frequencies of N or C cap central positions of SSAMs according to DSSP. Central positions are in red color. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Using the above categorization scheme, we can conveniently classify assignment methods based on how their capping positions differ from DSSP (see Supporting Information 4). It can also be used to show how well the four different capping regions are resolved. Hence, α-helix N cap displays four patterns 1, whereas β-sheet N cap displays only two patterns 1, but also two patterns 3 and two patterns 5, that is, the capping regions of β-sheet are more variably described than those of α-helix for which the correspondence between SSAMs is quite easily found. For the C caps, it goes to a higher level of complexity. Thus, α-helix C cap has only one pattern 2, two patterns 3 and three patterns 4, while the β-sheet C cap is characterized by four patterns 4, that is, the correspondence between SSAMs are quite complex. Surprisingly, even the SSAM related to DSSP are not strictly equivalent to it, for example, β-sheet N cap of STRIDE and SECSTR are shifted by (−1) residue. These results highlight greatly the difficulties to assign the β-strand extremities, while α-helix is in comparison more “conserved.” Previous works done using other SSAMs as standard gave similar results.

Amino acid distributions in capping regions

Table III shows the over- and under-representation of amino acid of the different SSAMs in terms of Z-scores.⁹⁹ Thus, at each position of each SSAM is given the important amino acids. KLd¹⁰⁰ values were also computed to locate the most informative positions (see Supporting Information 5). For the following paragraphs, we use a notation (x/y)^pz that corresponds to the amino acid (x) over- and (y) under-represented at the position z. N capping regions of α-helices (Table III) show a strong pattern (PSTND/IVLMAFYQERK)^p1 (PE/GN)^p2 (AQDE/IGN)^p3 where p1 corresponds to position N₁′ for DSSP, STRIDE, SECSTR, PSEA, and SEGNO and N_cap for XTLSSTR and KAKSI. This position p1 is associated to a high KLd value.

Table III.

Amino Acid Over- and Under-Representation at Capping Regions

C cap betaa		C2	C1	Ccap	C1′	C2′	C3′
DSSP	(+)	G	M	PSTND	WPE	AQDE	QDE
STRIDE	(+)	PG	M	PGSTND	P	ADE	QDE
SECSTR	(+)	PG	MP	STND	PE	ADE	AQDE
XTLSSTR	(+)	G	P	STND	PSTND	APE	QDE
PSEA	(+)	G	MG	GSTND	PE	AQDE	AQDE
DEFINE	(+)		D	PSD	AE	E	AE
KAKSI	(+)	P	G	P	PSTAND	APE	ADE
SEGNO	(+)	G	MP	GSTND	WPE	AQDE	AQDE
PBs	(+)	PSTND	PD	DE	QDE	ILAF	LAQERK
DSSP	(−)			IVLMAFYQERK	GN	IVLFG	PGN
STRIDE	(−)			IVLAFYWQERK	GN	IVLFG	PGN
SECSTER	(−)			IVLMAFYERK	GN	IVLFG	PGN
XTLSSTR	(−)			VAEK	IVLAF	VGTN	IPGN
PSEA	(−)			IVLAFQERK	GN	IVLG	PGN
DEFINE	(−)			IV	N		PG
KAKSI	(−)				IVLMAFK	GN	IVG
SEGNO	(−)			IVLMAFYQERK	GTN	IVLG	PGN
PBs	(−)	IVLAFQERK	IVL	IVLC	IP	PGTD	PGS
C cap alphaa		C2	C1	Ccap	C1′	C2′	C3′
DSSP	(+)	LAERK	LAERK	LAERK	GN	PG	PK
STRIDE	(+)	LAERK	AQERK	LAN	GN	P	PDK
SECSTR	(+)	LMA	AERK	LAQERK	LAGN	PGN	K
XTLSSTR	(+)	LAEK	AERK	LAE	GN	PK	K
PSEA	(+)	ILAERK	AQERK	LAHNRK	GN	PG	PD
DEFINE	(+)			G	P	P	V
KAKSI	(+)	LAQERK	LARK	GN	PG	PGD	P
SEGNO	(+)	ILA	LAERK	LAQERK	GHN	PHN	PGD
PBs	(+)	LA	LMAC	AQERK	QERK	LTN	PGN
DSSP	(−)	VPGT	PGSTD	IVPGD	IVWPTE	IVLMAFYE	V
STRIDE	(−)	PGTN	IVPGT	IVPGD	IVLAPTE		VL
SECSTR	(−)	VPGT	PGST	VPGD	IVPTD	IVLMFYWTE
XTLSSTR	(−)	PG	PG	VPG	IVPT		V
PSEA	(−)	PGSTD	IVFPGT	IVPGD	IVLAF		A
DEFINE	(−)
KAKSI	(−)	VPGT	VPGD	IVP		IVL
SEGNO	(−)	PGSTND	VPGTD	IVFPGD	IVPT	IVF	IVLFYT
PBs	(−)	PGST	VPGTD	VGT	IVG	IVG	IVLMAFYWTE
N cap betab		N3′	N2′	N1′	Ncap	N1	N2
DSSP	(+)	PGND	PGND	PGND	IVFYT	IVLFY	IVFY
STRIDE	(+)	PGSND	PGND	PGND	IVFYT	IVLFY	IVFY
SECSTR	(+)	PGN	PGND	PGND	IVFYWT	IVLY	IVLFY
XTLSSTR	(+)	PG	PGNK	PGN	G	IVFYT	IVLFY
PSEA	(+)	GNK	PN	GND	VG	IVYPT	IVFY
DEFINE	(+)	G	G	G		IVP	V
KAKSI	(+)	PGNDK	PGND	GN	VPT	IVFY	IVLFY
SEGNO	(+)	GNK	PGN	GND	PG	IVFYT	IVLFYW
PBs	(+)	GN	GDK	VP	IVFYP	IVFY	IVFYPT
DSSP	(−)	IVLA	IVLMFWT	IVLAFE	APND	AQPGSNDEK	AQPGNDERK
STRIDE	(−)	IVLAF	IVLMFWT	IVLAE	APGND	APGSNDEK	QPGNDERK
SECSTR	(−)	LAF	VLMAFYW	IVLAFE	APNDE	AQPGSNDEK	AQPGNDEK
XTLLSTR	(−)	IL	ILAY	E	A	APGNDE	AQPGNDEK
PSEA	(−)	IVL		IVLAFYC	LPD	AGNDE	AQPGSNDEK
DEFINE	(−)					A
KAKSI	(−)	IVLY	IVLMAFYW	LAF	E	APGNDE	AQPGSNDEK
SEGNO	(−)	IVL	LYW	IVLAFYW	LND	APGNDE	AQPGSNDEK
PBs	(−)	ILMAYE	LAP	LD	AGSNDE	AGSNDEK	AQGDERK
C cap betab		C2	C1	Ccap	C1′	C2′	C3′
DSSP	(+)	IVLFYW	IVFYWC	IVFYD	GSND	PGSND	GSND
STRIDE	(+)	IVFYW	IVFYWC	IVYD	GND	PGSND	GSND
SECSTR	(+)	IVLFYW	IVFYWCT	IVFY	GND	PGSND	GSND
XTLLSTR	(+)	IVF	IVFYWT	IVFYTD	PGND	PGSD	PGSND
PSEA	(+)	IVLFY	IVFYCT	PSTD	PND	GSND	GSD
DEFINE	(+)		P	PSD	PD	GD	G
KAKSI	(+)	IVLFY	IVFYW	ND	PGND	PGSND	GSND
SEGNO	(+)	IVLFYW	IVFYWC	IVCTD	PGND	GSND	GSND
PBs	(+)	IVF	IVFY	IVFY	PSTND	P	GSND
DSSP	(−)	AQPGSNDERK	APGSNDEK	AGE	IFQER	IVLMAFY	IVLAF
STRIDE	(−)	AQPGSNDERK	APGNDEK	AGE	VFYQER	IVLMAFY	IVLAF
SECSTR	(−)	AQPSNDERK	APGNDE	AQGEK	AFYQEK	IVLMAFY	IVLAF
XTLSSTR	(−)	APNDE	AQPGNDEK	APGE	IVAQR	IVLF	IVLMAF
PSEA	(−)	AQPGNDEK	AQGNDEK	LAERK	IVLAFY	IVLAF	IVLAF
DEFINE	(−)			I	L	IV
KAKSI	(−)	AQPGSNDEK	APGNDE	AEK	IVLF	IVLMAFY	IVLAF
SEGNO	(−)	AQPGSNDEK	APGSNDE	APGEK	IVLMAFYQR	IVLMFY	IVLAF
PBs	(−)	GNDERK	AGSNDE	AQGNDE	LAQERK	G	IVLMAFYP

The over (+)(respectively under (−))− representation have been selected using a Z-score more than 4.4(respectively less than −4.4). The first part of the table presents the N and C capping regions of α-helix. Results have been obtained with DB0.

The over (+)(respectively under (−))− representation have been selected using a Z-score more than 4.4(respectively less than −4.4). The second part of the table presents the N and C capping regions of β-sheet. Results have been obtained with DB0.

At the opposite, KLd values of C capping regions of α-helices are weaker; multiple positions are in the same range of values. Repeated patterns (LAERK/IVPG) are found before p1, then (GN/IV)^p1, (PG/-)^p2, and (PK/-)^p3 where p1 corresponds to position C₁′ for DSSP, STRIDE, SECSTR, XTLSSTR, PSEA, and SEGNO and C_cap for DEFINE and KAKSI. It is noteworthy that the different positions, even if they are related, cannot be interchanged. The pattern of over-represented amino acids ([LAERK], [LAERK], [LAERK], [GN], [PG], [PK]) can correspond for instance, to the sequence (L A L N P K). The succession LAL of C₂, C₁, C_cap cannot be shifted as they are mainly under-represented at positions C₁′, C₂′, and C₃′.

N capping regions of β-strand (Table III) are more informative than C capping regions, they are characterized by a strong succession of patterns (PGND/IVL), followed by a pattern (IVFYT/APND)^p1 followed by compatible patterns (IVFY/AQPGNDERK); this latter corresponding to the β-strand; position p1 correspond to N_cap for DSSP, STRIDE, SECSTR, and KAKSI, and to N₁ for PSEA, DEFINE, and SEGNO.

C capping regions of β-strand are less informative, but are also clearly cut into two successive patterns, the first is the one characteristic of β-strand (IVLFYN/AQPGNDERK) followed by (GND/IVLAF)^p1. The final position of p1 is harder to define than previously, but correspond most of the time to C₁′ that is also the less informative position in terms of KLd. Analysis of the position informativity with KLd values, emphases the results seen on Table III. Positions C₂, C_1, and C₂′ have a strong amino acid distribution associated with high KLd values, whereas the boundary region, that is, C_cap and C₁′, have fewer amino acids over and under-represented and low KLd values.

Finally, every amino acid distributions of DSSP capping regions with the other SSAMs have been compared (see Supporting Information 6). N capping α-helix regions of DSSP is strictly equivalent to SECSTR, STRIDE, PSEA, and SEGNO. A light difference at N₂′ position (associated to a low informative position) is found between DSSP and DEFINE and a clear frameshift from N_cap of DSSP to N₁ for XTLSSTR and KAKSI.

For the C capping regions of α-helix, the situation is more complex, the only strict equivalent amino acid matrices is find between DSSP and SECSTR. A limited divergence is found at position C₁ for PSEA and at C_2′ for XTLSSTR. Surprisingly, STRIDE has only three strict corresponding positions with DSSP, but it remains highly comparable as C₂ and C₁ positions have very close amino acid distributions as C_2′ and C_3′. Concerning KAKSI, we observe a shift of (+1) for the positions ranging from C₂ to C_cap. For SEGNO, only the central positions are equivalent to DSSP. C₂ and C₁ positions of SEGNO correspond to C₁ and C_cap positions of DSSP, but all these amino acid distributions are very close. Only position C_3′ of SEGNO is particular due to an over representation of Glycine not found in any other SSAM and thus more related to C_2′ position of DSSP than C_3′ position.

Contrary to the α-helix, the β-strand capping regions show few strong amino acid distribution divergences as the α-helix. Thus, we find that SECSTR, STRIDE, and DEFINE are equivalent to DSSP N capping region of β-strand. For the others, only the clear cut between [N_3′ − N_1′] and [N_cap − N₂] positions of DSSP are found. For instance, [N_3′ − N_1′] of XTLSSTR correspond to N_2′ position of DSSP.

For the C capping regions of β-strand, SECSTR, STRIDE and KAKSI are equivalent to DSSP. For XTLSSTR and SEGNO, only their C₁′ positions is not equivalent to C₁′ of DSSP. PSEA adds to this, a shift of positions C₁ and C_cap; it is mainly due to lower informativity at these positions.

Discussion

Analysis of different SSAMs based on diverse structural protein databanks gave results that are in line with previous studies including our own.^{16,32,33,34,101} Indeed, each SSAM—based on different criteria—gives a different assignment. Thus no simple consensus of secondary structure assignments could be done. Repetition of over- and under-represented amino acids are found as expected within the regular secondary structures, that is, positions N_cap, N₁, N₂ and positions C₂, C₁, C_cap.⁹⁹ Analysis of position of N and C cap of DSSP in regards to capping positions given by other SSAMs lead to a similar view. Even the SSAM closely related to DSSP could have systematically a very different N or C cap position.

Amino acid distributions surprisingly do not reflect this fact: A structural frameshift does not imply a “sequence” frameshift. α-helix capping regions possess a true amino acid patterns (see Table III), the classical over- and under- representations of amino acids are found again. For the N cap α-helix, we observe a clear frameshift of (+1) for KAKSI & XTLSSTR assignment method and for the C cap α-helix, we observe a clear frameshift of (−1) for KAKSI. Thus, the sequence informativity characterizing “the” α-helix capping regions is found for all the SSAMs with some slight sliding. Only DEFINE assignment does not correspond. However, its KLd values are 20–50 times less informative than other SSAMs. For the β-strands capping regions as classically noted, a simple differentiation exists between the central regions mainly composed of aliphatic hydrophobic residues and “outside” regions with polar and “breakers.” This very simple rule is found for all the SSAMs.

The capping regions are the most important differences between SSAMs, but they do not create different amino acid patterns, only minor shift, for example, DSSP and KAKSI helices. These results are in agreement with the results of Kruus and coworkers⁸⁹ that elegantly analyze the question of capping regions of α-helices. They have shown that strong patterns are found in these regions, but on the structure, even if does not correspond perfectly, they shift often in a very close vicinity. We observe the same kind of results, but in our case, the average created by the use of one occurrence matrix each time gives a global view of the amino acid patterns.

We have also analyzed the repetitive structures assigned by our structural alphabet,³⁸ namely the Protein Blocks.^{93,99,101-112} Their results are a bit different from the SSAMs, for example, N_cap and C_cap have always lower KLd values than other positions. Contrary to the SSAMs, they approximate even the nonrepetitive states, that is, loops, so they can be used to predict them from the knowledge of sequence.

Secondary structure assignment is too often considered as a finished research field with only one golden standard DSSP. As noted by Arthur M. Lesk,¹¹³ “What is unfortunate is that people use these secondary structure assignments unquestioningly; perhaps the greatest damage the programs do is to create an impression (for which [authors of SSAMs] cannot be blamed) that there is A RIGHT ANSWER. Provided that the danger is recognized, such programs can be useful.” SSAMs lead to different assignments, and, to different analysis of protein structures.

Robson and Garnier have written: “In looking at a model of a protein, it is often easy to recognize helix and to a lesser extent sheet strands, but it is not easy to say whether the residues at the ends of these features be included in them or not.¹¹⁴” Indeed, the discrepancies are often found at the extremities of repetitive structures and loop boundaries are essential in loop conformation prediction.⁶⁵ Nonetheless, we have shown here that systematically differences do not appear in terms of sequence. This result reinforce the results of Kruus and coworkers.⁸⁹ This study is also related to the elegant research done by Zhang and coworkers.³⁴ They have proposed to assess secondary structure assignment using recognized pairwise sequence-alignment benchmarks. They have so highlighted the interest of two assignment methods and also underline the repetitive structure extremities. Here, we went further and quantified the discrepancies in terms of amino acid propensities in a very systematic way using various SSAMs. We showed that, though SSAMs give different local structure assignments, capping sequence patterns remain in fact surprisingly stable. In someway, it emphasized the idea of Grishin with PALSSE, that focus on the sequence property as on the structure properties to assign the repetitive structure.²⁵

Moreover, the definition of assignment of secondary structure has a direct impact on the quality of the prediction. Cuff and Barton have used three different SSAMs (DSSP, STRIDE, and DEFINE) and combined their assignments to improve secondary structure prediction rate (using assignment done by DSSP as reference).¹¹⁵ Recently, Zhang and coworkers showed that the consensus of STRIDE, KAKSI, SECSTR, and P-SEA improves assignments over the best single method in each benchmark by an additional 1%.¹¹⁶ Our analysis underlines that the amino acid contents of capping regions is encompassed by numerous various SSAMs. Thus, the amino acid contents of capping regions could help to define more precisely the assignments by helping to find a consensus between divergent assignment methods. Thus, this new consensus SSAM encompassing different SSAMs and amino acid behaviors would help the prediction.

In the same way, Dovidchenko and coworkers showed that loop boundary prediction methods relying on sequence specificities seem to be more efficient that methods based on physical properties of amino acids.¹¹⁷ Actually, the PSIPRED prediction method (based on assignment performed by DSSP) achieved 73% correct prediction rates from the single sequence that is between 7 and 9% better than physics based methods. Thus, protein sequence conservation is critical for predicting loop boundaries. Our contribution is substantial in the sense that equivalent sequence patterns were found for most of the SSAMs. Thus prediction from these patterns could provide a unified decision of loops boundaries. Furthermore, this pattern stability, despite of assignment shifts, enlightens an interesting property of protein sequences that allow some fuzziness at loop boundaries. This phenomenon might physically support the conformational adaptations of proteins for function or for stability in variable cell environments.

Methods

Data sets

The 10 sets of proteins are based on the PISCES database^90,91 and represents between 162,830 and 1,572,412 residues. They are available at http://www.dsimb.inserm.fr/~debrevern/DOWN/DB/new. The sets are defined as containing no more than x% pairwise sequence identity with x ranging from 20 to 90%. The selected chains have X-ray crystallographic resolutions less than 1.6 Å with an R-factor less than 0.25 or less than 2.5 Å with an R-factor less than 1.0. Each chain was carefully examined with geometric criteria to avoid bias from zones with missing density. Table II presents all the details of these databanks.

Secondary structure assignments

They have been done with five distinct software: DSSP⁶ (CMBI version 2000), STRIDE,¹¹, SECSTR¹⁰ (version 0.2.3-1), XTLSSTR,¹⁸, PSEA¹⁷ (version 2.0), DEFINE¹⁴ (version 2.0), KAKSI¹⁶ (version 1.0.1), and SEGNO²⁰ (version 3.1). PBs⁹³ have been assigned using in-house software (available at http://www.dsimb.inserm.fr/~debrevern/DOWN/LECT/), it follows similar rules to assignment done by PBE web server (http://bioinformatics.univ-reunion.fr/PBE/).¹¹⁸ DSSP, STRIDE, SECSTR, XTLSSTR, and SEGNO give more than three states, so we have reduced them: the α-helix contains α, 3₁₀ and π-helices, the β-strand contains only the β-sheet and the coil everything else (β-bridges, turns, bends, polyproline II and coil). Default parameters are used for each software. The first residue of a repetitive structures is noted N_cap and the following N_n (n = 1–3 in this study), while the previous residues are noted N′_n (n = 1 is so the closest residue to N_cap position). In the same way, the last residue of repetitive structure is noted C_cap and the following C′_n, while the previous residues are noted C_n. The N_n and C_n residues are so inside the repetitive structures, N′_n and C′_n residues belongs to coil regions.

Agreement rate

To compare two distinct secondary structure assignment methods, we used an agreement rate which is the proportion of residues associated with the same state (α-helix, β-strand, and coil). It is noted C₃.³³

To compare capping regions of repetitive secondary structures, we have taken as standard the capping regions of repetitive secondary structures defined by DSSP. Then, we simply search the positions corresponding to N and C cap defined by DSSP with other assignments. In the same way, we have compared the amino acid distribution of capping regions of repetitive secondary structures defined by DSSP with the amino acid distribution of capping regions of repetitive secondary structures defined by other SSAMs.

Z-score

The amino acid occurrences for each secondary structure have been normalized into a Z-score:

with n_i,j^obs the observed occurrence number of amino acid i in position j for a given secondary structure and n_i,j^th the expected number. The product of the occurrences in position j with the frequency of amino acid i in the entire databank equals n_i,j^th. Positive Z-scores (respectively negative) correspond to over-represented amino acids (respectively underrepresented); threshold values of 4.42 and 1.96 were chosen (probability less than 10⁻⁵ and 5 × 10⁻², respectively).

Asymmetric Kullback-Leibler measure

The Kullback-Leibler measure or relative entropy,¹⁰⁰ denoted by KLd, evaluates the contrast between two amino acid distributions, that is, the amino acid distribution observed in a given position j and the reference amino acid distribution in the protein set (DB). The relative entropy KLd(j|S_x) in the site j for the secondary structure S_x is expressed as:

where P(aa_j = i|S_x) is the probability of observing the amino acid i in position j (j = −w, …,0, …, +w) of the sequence window (15 residue long, w = 7) given a secondary structure S_x, and, P(aa_j = i|DB) the probability of observing the same amino acid in the databank (named DB). Thus, it allows one to detect the “informative” positions in terms of amino acids for a given secondary structure.⁹⁹