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BIOINFORMATICS
Vol. 19 no. 1 2003
Pages 117–124
Search for structural similarity in proteins
Jacek Leluk 1, 2, Leszek Konieczny 3 and Irena Roterman 4,∗
1 Institute
of Biochemistry and Molecular Biology, University of Wrocław, Tamka 2,
50-137 Wrocław, Poland, 2 Interdisciplinary Centre for Mathematical and
Computational Modeling (ICM), Pawiłn skiego 5A, 02-106 Warsaw,Poland, 3 Institute
of Medical Biochemistry, Collegium Medicum, Jagiellonian University, Kopernika 7,
31-034 Krakow,Poland and 4 Department of Biostatistics and Medical Informatics,
Collegium Medicum, Jagiellonian University, Kopernika 17, 31-501 Krakow, Poland
Received on February 3, 2002; revised on May 27, 2002; July 11, 2002; accepted on July 15, 2002
ABSTRACT
Motivation: The expanding protein sequence and structure databases await methods allowing rapid similarity
search. Geometric parameters—dihedral angle between
two sequential peptide bond planes (V ) and radius of
curvature (R) as they appear in pentapeptide fragments
in polypeptide chains—are proposed for use in evaluating
structural similarity in proteins (VeaR). The parabolic
(empirical) function expressing the radius of curvature’s
dependence on the V -angle in model polypeptides is
altered in real proteins in a form characteristic for a
particular protein. This can be used as a criterion for
judging similarity.
Results: A structural comparison of proteins representing
a wide spectrum of structures was assessed versus sequence similarity analysis based on the genetic semihomology algorithm. The term ‘consensus structure’, analogous to ‘consensus sequence’, was introduced for the serpine family.
Availability: Semihom—sequence comparison freely
available on request from J. Leluk. VeaR—structural
comparison freely available on request from I. Roterman.
Contact: [email protected] for SEMIHOM program
[email protected] for VeaR program.
INTRODUCTION
Various properties of polypeptide chains in proteins can
be used as criteria for similarity estimation: superposition of two compared protein structures and RMS-D
calculation to measure the discrepancies in Cα location (Hubbard, 1999; Guda et al., 2001), contact maps
expressing inter-residue distances (Ortiz et al., 1999),
environmental properties (Jung and Lee, 2000) such as
solvent-accessible surface, and conformational properties
such as dihedral angles or the mutual orientation of
centres of masses (Shindyalov and Bourne, 1998). The
∗ To whom correspondence should be addressed.
c Oxford University Press 2003
increasing size of sequence and structure databases
demands methods that uniformly evaluate similarity for
homology-based structure prediction. In the postgenomic
era, when complete knowledge of the full proteome of
an organism is available, a theoretical method allowing
prediction of protein structure, especially one based on
homology, is urgently required (Fisher, 1999). This is
why the problem of similarity search is closely related to
all methods predicting protein structure and function on
the basis of the known amino acid sequence (Kolinski et
al., 2001; Irving et al., 2001; Fetrow et al., 2001).
The tools for sequence multiple alignment help to solve
the problem of homology search, while with 3D structure
comparison it is difficult to identify more than a pair of
proteins (Sauder et al., 2000; Leibowitz et al., 2001). A genetic algorithm has been proposed for use in protein alignment (Szostakowski and Weng, 2000). The Markov model
has been adapted for structure alignment (Kawabata and
Nishikawa, 2000; Bienkowska et al., 2000). Superposition
of Gaussian functions describing atoms in their so-called
‘fuzzy’ form produces a good description of the protein
body. The multiple alignment procedure has also been proposed for this model (Maggiora et al., 2001).
The parameters proposed here as criteria for similarity
search (VeaR program) express protein structure in the
form of linear profiles of the parameters characteristic of
the polypeptide treated as a ribbon. Subjective quantitative
criteria such as window size and score level are defined
by the user. The selected parameters allow units larger
than secondary structure units to be compared, including
loops and random coiled fragments. The proposed method
may be used also for comparison of structures as they
appear after dynamics simulation. A complex comparison
of the members of the serpine family, performed on the
basis of the presented parameters, supports one proposal
to adopt the notion of ‘consensus structure’, analogous to
‘consensus sequence’.
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SYSTEMS AND METHODS
Structural similarity
A model based on a ribbon-like approximation was
described in detail (Roterman, 1995a). The main assumption of the model is that all structures of polypeptide
fragments in proteins can be treated as helix-like forms
with different radii of curvature, which for extended forms
are extremely large (theoretically infinite), so the radii
of curvature are measured as a logarithmic scale. The
pentapeptide appeared to be the proper unit to calculate
the radius of curvature. Analysis of model pentapeptides
revealed that the radius of curvature depends on and is
determined by the mutual orientation between two sequential peptide bond planes. The dihedral angle between
them is expressed by the second parameter—the V -angle.
The procedure for calculating R and V is as follows.
Before the R and V parameters can be calculated, all sequential pentapeptides in a polypeptide chain should be
oriented in a unified form to make comparison of their
values possible. The Z -axis for each sequential pentapeptide is determined by the averaged CO bond positions.
For this orientation the radius of curvature for the X Y plane projection of Cα atoms can be calculated. Two approaches will be adopted for this procedure. One of them
defines the centre of the helix by averaging the positions
of all (five) Cα atoms. In the second one the coordinates
of three Cα atoms (the 1st, 3rd and 5th in the pentapeptide) are taken into equations expressing the equal distance between the atoms and the centre of the circle. An
analytical solution can be found in this case. Both methods are applied for each analyzed structure of the pentatpeptide. The radius of curvature that satisfies the conditions of lower dispersion versus the theoretical curvature is accepted as the proper one for a particular pentapeptide structure. The procedure is described in detail in
(Roterman, 1995b). Vi —the tilt angle for the central peptide bond plane in the pentapeptide—is calculated versus
the Z -axis. The angle between the CO bond and X Y plane
is taken as the measure for tilt angle. The Vi+1 and/or
Vi−1 tilt is estimated in the same way. The difference between Vi and Vi+1 and/or Vi−1 (or the average of Vi+1 and
Vi−1 —this form is used here) expresses the dihedral angle
between two sequential peptide bond planes characteristic
for each pentapeptide fragment in the polypeptide chain.
The distribution of ln(R) and V along the polypeptide
chain (one amino acid step) can be represented as the
profile characteristic for a particular protein. The window
size for which the similarity is estimated can be defined
arbitrarily by the user. This size depends on the problem
being studied. In this paper the window size of 25 amino
acids was chosen to enable comparison of structure in
two polypeptide chains. This window size of 25 aa allows
comparison between two fragments longer than the usual
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secondary structure units. A window size equal to 10,
for example, allows identification of secondary structure
fragments as similar. A 5 aa window size usually finds the
loops linking the β-structural fragments of polypeptides to
be similar to helical fragments in the compared protein.
The similarity score (S) for fragments was calculated as
follows:
Si, j = (Pi − P j )/ min(Pi , P j )
where P expresses the parameter (ln(R) or V ) (ith amino
acid in one chain and jth amino acid in second chain).
A value of S below 50% discriminates similar pentapeptides for dot-matrix calculations, and S = 50% and 60%
for other similarity searches in this paper. The S parameter is user-defined, depending on the level of precision in a
similarity search. The 25 aa fragment was considered similar when more than half of the amino acids satisfied the
criteria presented above. The profile comparison was performed automatically, following the procedure producing
the dot-matrix.
The ln(R) value appeared to be dependent on the
V -angle for model pentapeptide structure representing the
low-energy area on the Ramachandran map. The mathematical relation can easily be defined as a second-degree
polynomial function (empirical function; Roterman,
1995a,b). The regular dependency that occurs for model
pentapeptides is not evident in real proteins. The deviation
versus the theoretical relation can be measured by the
DIS parameter, simply expressing the difference between
the expected and observed ln(R) values for a particular
V -angle. A positive value of DIS indicates a larger than
expected radius of curvature for a particular V -angle. A
negative DIS value describes a ‘spring’ more squeezed
than the relaxed form of the pentapeptide for a particular
V -angle. The profile of the DIS parameter in a particular
protein also appeared to be characteristic, and taken in
conjunction with the V -angle it may be used as a criterion
for comparison.
Data collection
Proteins representing serpine family were selected
for analysis: (PDB ID - 1OVA)—uncleaved ovalbumin (chain A), called OVA(A) here; 1ATT—cleaved
bovine antithrombin (chain A), called ATT(A); 2ACH—
cleaved human alfa-1-antichymotrypsin (chain A), called
ACH(A); 1AZX—human antithrombin (chain I), called
AZX(I); 2ANT—human antithrombin (chain L), called
ANT(L); and 7API—alfa-1-antitrypsin (chain A), called
API(A).
The proposed method was compared with another one
commonly used for the same purpose, the DALI program
(Guda et al., 2001).
Search for structural similarity in proteins
Fig. 1. Semihomologous relationships among proteinaceous amino
acids. Codons of residues along each axis differ by only one
nucleotide (Leluk, 1998). Diagram setting shows codon changes
at first (axis 1), second (axis 2) or third (axis 3) position in the
order A→G→C→U. Transition type of replacement is represented
by solid line at entire section; dashed line at any fragment of the
connection between two residues assigns transversion. This diagram
forms the basis of the genetic semihomology algorithm, instead
of a matrix of statistical parameters or replacement indices which
supports statistical algorithms.
Sequence similarity
We chose the algorithm of genetic semihomology (Leluk,
1998, 2000a,b) as the most appropriate and informative
tool for comparative analysis of the sequences. The
reason for using the genetic semihomology algorithm
was to improve the accuracy of the results of protein
sequence comparison, to avoid the wrong assumptions
and misinterpretation of the results, and to increase the
amount of information available from such a study. The
genetic semihomology has no stochastic scoring matrix
in its composition (Leluk, 1998, 2000a,b). The initial
assumptions are reduced to two dogmatic ones: the codon-
amino acid translation table, and the assumption that the
single transition/transversion is the most frequent mechanism of differentiation among homologous proteins.
Another significant feature distinguishing the genetic
semihomology approach from those based on statistical
matrices is that it considers both levels (genetic and
amino acid) simultaneously. Consequently the analysis is
more complete with respect to all significant processes
controlling evolutionary variability (the possible mutation
scale at the nucleotide sequence level and the selection
criteria at the amino acid level). Instead of PAM-like or
BLOSUM-like matrices, the principal component of this
algorithm is a three-dimensional diagram representing
all theoretically possible genetic relationships between
genetically encoded amino acids (Figure 1). It shows all
possible amino acid replacements as the effect of a single
transition/transversion, and the genetic distance between
amino acids depending on their codon sequence. Thus,
the semihomology approach enables thorough analysis,
reconstruction and/or prediction of the greatest number
of mechanisms of variability that refer to the existing
natural sequences. This nonstatistical approach has been
successfully used for theoretical analysis of several
protein families of different nature, origin and location
(Leluk, 2000a,b,c; Leluk et al., 2001, 2002; Hanus-Lorenz
et al., 2001; Leluk and Grabiec, 2001) with respect to:
(1) the locations of homologous and semihomologous
sites in compared proteins; (2) precise estimation of
insertion/deletion gaps in nonhomologous fragments; (3)
analysis of internal homology and semihomology; (4) the
precise locations of domains in multidomain proteins;
(5) estimation of the genetic code of nonhomologous
fragments; (6) construction of genetic probes; (7) studies
on differentiation processes among related proteins; (8)
estimation of the degree of relationship among related
proteins; (9) studies on the evolutional mechanism within
homologous protein families; and (10) confirmation of
actual relationships of sequences showing a low degree
of homology. The nonstatistical semihomology approach
for comparative analysis of protein primary structure has
been used successfully to discover, verify and/or describe
in detail some important mechanisms controlling protein
differentiation pathways, as in the following studies:
the significant role of cryptic mutations in extending
the variability spectrum (Leluk, 2000a; Leluk et al.,
2001), the nonMarkovian nature of protein evolution
(Leluk, 2000b), asymmetry in replacement frequency
between amino acids, depending on their codons (Leluk,
2000b), analysis of the mutational variability mechanism
in protein differentiation (Leluk, 2000b,c; Leluk et al.,
2001), and the high occurrence of correlated mutations,
including spatially very distant amino acid residues
(Leluk et al., 2002). The correct multiple alignment and
consensus sequence construction achieved by the genetic
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Fig. 2. V -angle and ln(R) profiles and dot-matrix representing inter- and intra-molecular similarity for V and ln(R) as structural similarity
criteria. (A) V -angle distribution as it appeared in ATT(A) molecule; (B) V -angle distribution as it appeared in OVA(A) molecule; (C) ln(R)
distribution as it appeared in ATT(A) molecule; (D) ln(R) distribution as it appeared in OVA(A) molecule; (E) Upper right part of matrix
represents similarity distribution when V -angle is taken as criterion. Lower left part of matrix represents distribution of similarity when
ln(R) is taken as similarity criterion; (F) Similarity dispersion in and between OVA(A) and ATT(A) when simultaneous criteria of ln(R) and
V -angle are used
semihomology approach were also the starting point for
predicting the tertiary structure of the proteinase inhibitor
family from squash seeds (Leluk, 2000c). The algorithm
is assisted by some other useful approaches, such as
the significant similarity estimation method (Leluk and
Grabiec, 2001) and FEEDBACK program identifying the
allowed/forbidden sets at all sequence positions, which are
determined by the presence/absence of a particular residue
at a particular position (Leluk et al., 2002).
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IMPLEMENTATION
Structural similarity
The V and R parameter profiles, calculated according to
the procedure presented in Methods, were used to characterize the structure of OVA(A) and ATT(A) (Figure 2A–
2D). High values of V and ln(R) are present in β-structure
fragments of OVA(A) (150–250 aa) and ATT(A) (190–260
aa) proteins.
Search for structural similarity in proteins
Fig. 3. Relation between V -angle and ln(R). Thick line represents theoretical relation found for model pentapeptides. Dots represent V angle and ln(R) values for pentapeptides in real proteins. Thin line represents approximation curve obtained based on observed parameters.
Proteins taken for analysis are as follows: (a) OVA(A) protein; (b) ATT(A) protein. Plot representing magnitude of deviation of experimentally
observed values of V and ln(R) versus theoretical parabolic curve found based on model pentapeptides. (c) OVA(A); (d) ATT(A).
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The dot-matrix for two similar proteins [OVA(A) and
ATT(A)] looks as presented in Figure 2E and 2F. Besides
the internal similarity revealed in the dot-matrix, the intermolecular similarity is very easily distinguishable. Two
sub-diagonals can be seen in the upper right and lower left
quarters of the map, showing inter-molecular similarity.
Similarity for R and V in conjunction is observed rather
seldom; such a case is shown in Figure 2F. The origin of
this event is explained next.
MODEL AND REAL PROTEINS
The mathematical relation between ln(R) and V for
model pentapeptides exhibits parabolic form (Roterman, 1995a,b). Real proteins demonstrate a dispersion
versus the theoretical curve (Figure 3a,b). The thick
line represents the theoretical relation according to the
second-degree polynomial found for the model pentapeptides (Roterman, 1995a,b). The dots represent ln(R) versus V as observed in ATT(A) and OVA(A). The thin lines
represent the relation as an approximation curve for the
experimental points as they appeared in the analyzed proteins. The same relation is almost linear for OVA(A) and
ATT(A). The profile of DIS along the polypeptide chain
as it appeared in OVA(A) and ATT(A), is shown in Figure 3c,d.
The V -angle and DIS profiles were used to compare
analyzed serpine family members and shown in Figure 4
together with the results of sequence (Figure 4a) and
structure (Figure 4c) comparison based on Cα-Cα atoms
overlaping (according to DALI procedure—(Guda et al.,
2001)). Each point on the thick line in Figure 4b represents
a 25 aa fragment in which more than 50% of the residues
Fig. 4. Similarity between serpine family members (ACH(A), ANT(L), API(A), AZX(I), OVA(A)) as it appears using: (a) Sequence similarity
as obtained according to Semihom algorithm; (b) V and DIS parameter similarity in serpine family members. Thick lines represent similarity
for S = 50%, thin lines for S = 60%. (c) DALI procedure (Cα–Cα distance between overlapped protein molecules). ATT(A) structure was
taken as template structure for comparison in all methods. Horizontal axis represents sequence of template molecule (ATT(A)). Vertical axis
represents sequence (in relative numbers versus sequence of target molecule) of compared chain. Line parallel to horizontal axis (0 on vertical
axis scale) represents the situation when two chains are similar without any shift in their sequences. Such a line represents the situation that
in a dot-matrix is represented by a diagonal. Negative values on a vertical line represent deletion in second compared chain, while a positive
value represents insertion
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Search for structural similarity in proteins
Fig. 4. Continued.
represent a V -angle varying no more than 20% (calculated
according to the expression of S) and the DIS parameter
satisfies the condition of having the S value lower than
50%. Each point on the thin line represents a 25 aa
fragment satisfying the V -angle similarity condition and
having DIS similarity measured with the S parameter
below 60%.
The ATT(A) protein was taken as the template protein
structure to which all others were compared pair-wise.
The diagrams shown in Figure 4 reveal the same V angle distribution and the same deformation in the sense
of radius curvature measured versus the expected ln(R)
values.
DISCUSSION
The analysis presented in this paper shows that the
proposed geometric parameters can be used to search
for structural similarity in proteins, although the criteria
selected for this search differ from the standard ones.
The profiles of ln(R) and V as they appear in proteins
really express the visual characteristics of the polypeptide
ribbon. They are correlated in model peptides (in the
model peptide all five amino acids represent the same Phi,
Psi angles). In real proteins this correlation is somewhat
disturbed, as is shown in Figure 3. The explanation
for this is that the V -angle parameter is rather the
backbone attribute, while the R-value describes the shape
of the polypeptide adopted for its particular fragment.
The empirical function expressing the dependence of
ln(R) on the V -angle describes structures with agreement
between the mutual orientation of the peptide bond planes
(backbone structure) and the resulting radius of curvature
for the particular fragment. The radius of curvature
is influenced by the V -angle, on the one hand, and
depends on inter-side-chain interactions on the other.
The latter force allows the backbone to adopt a nonrelaxed radius of curvature for the polypeptide ribbon
fragment. The deviation from the theoretical curve in
real proteins can be explained as the consensus between
these two factors: backbone structure and side-chain
interactions. The characteristic distribution of polypeptide
chain fragments deviating from the relaxed form reveals
the specificity of inter-side-chain interactions.
The Semihom and DALI programs revealed the high
similarity of the patterns representing sequence and 3D
structural similarity in the analyzed proteins (Figure 4).
The similarity distribution found using the newly introduced method agrees only partially with the results obtained using the standard method DALI—pair-wise alignment distance-based score. The disagreement is due to differences in the criteria of comparison. The fragments that
appeared similar in both the DALI and VeaR methods represent the situation in which the fragment adopted a similar V and R system and in consequence represents a similar spatial arrangement. The fragments revealed as similar
by DALI criteria and dissimilar by the VeaR method are
fragments whose similarity is not based on the same structural origin, although for each similar (according to DALI)
fragment a sort of incipient similarity based on V and R
characteristics can be found.
The term ‘consensus structure’, analogous to ‘consensus sequence’, can be proposed. Since the structural parameters can be expressed in quantitative form, the ‘averaged’ structure with averaged V -angles and R-radii for
structurally similar fragments can be described.
V and R profile comparison between the target molecule
and the predicted form of protein structure could be useful
in the CASP project (Hubbard, 1999), especially since the
proposed parameters are somehow related to polypeptide
chain folding (Xu et al., 1999). Random coiled fragments,
which usually are difficult to identify, can also be easily
analyzed uniformly with secondary structure fragments
when the proposed parameters are used.
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ACKNOWLEDGEMENT
Many thanks to Anna Smietanska for technical support.
This study was partially supported by ICM grant BST
783/2002.
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