Acta Chim. Slov. 2003, 50, 505-511.
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INCOHERENT RELATIONSHIP BETWEEN TORSION VALUES AND BOND LENGTHS IN ATOMIC RESOLUTION PROTEIN CRYSTAL STRUCTURES
Oliviero Carugo
Department of General Chemistry, Pavia University, Viale Taramelli 12, 27100 Pavia, Italy
and
Protein Structure and Bioinformatics Group, International Centre for Genetic Engineering and
Biotechnology, Padrice 99, 34012 Trst, Italy
Received 17-11-2002
Abstract
Deviations from planarity of the peptide C?-C(=0)-N moiety are expected to be accompanied by the lengthening of the C-N and the shortening of the C=0 bonds. Surprisingly, such a relationship cannot be detected by an analysis of the atomic resolution protein crystal structures deposited in the Protein Data Bank. This could be due to either an incorrect parameterisation of the refinement restraints or to the large mobility of the protein atoms, which could prevent their exact location
Introduction
The analysis of known protein three-dimensional structures produced marvellous results during the last few decades, both in allowing the development of new technologies, like for example theoretical modelling and protein design, ' and in improving our understanding of basic biological features, like for example the adaptation to high temperature and other extreme physical environments. ' Given that most of the known information about protein three-dimensional structure has been provided by crystallographic methods, structural bioinformaticians routinely filter out from the Protein Data Bank X-ray crystal structures with the characteristics desired for each particular analysis. The most usual filter is the crystallographic resolution which indicates how well defined the crystal structure is, i.e. how many experimental diffraction data have been measured relative to the number of variables that must be determined (positions of the atoms, atomic displacement parameters, etc). The crystallographic resolution is of course not the only criterion to select the “best” protein three-dimensional structures to be analyzed in a bioinformatic project. The R factor as well as the free R factor are useful indicators of the “quality” of a crystal structure. " The diffraction data completeness in the highest resolution shell is a further possible
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indicator of the structure “quality” as well as a critical assessment of the stereochemistry of the macromolecule or the comparison between the number of solvent molecules expected and experimentally located. Nevertheless, the crystallographic resolution is certainly the parameter most commonly used to select a three-dimensional protein structure subset from which to extract any trend to be related to any biological feature. The reason for this is very simple: contrary to other useful crystallographic parameters, the crystallographic resolution can be extracted very easily from the Protein Data Bank files.
O                                                           O

I
%
II
Figure 1. Mesomeric equilibrium that determines the planarity of the peptide unit. The rotation around the C-N bond is impossible because of the electron delocalisation that confers C-N a partial double bond character. The ? torsion around C-N is thus constrained to 0 or 180° (180° in the figure). Deviations from these values imply deviations from planarity of the peptide unit with consequent decrease of importance of the limit formula II. As a consequence, the peptide C-0 and C-N bonds are expected to shorten and lengthen, respectively.
For many years, the crystallographic resolution in protein crystallography has been limited to values, in the best cases, around 2 A. Recent improvements in both diffraction data acquisition at synchrotrons and data manipulation allowed the development of the so called “atomic resolution” protein crystallography. The resolution went down to values close to 1 A, and in some cases even below. The very large amount of experimental diffraction data available at this resolution allowed, in these cases, to treat a protein crystal structure nearly as chemists routinely do with small molecules. The quality of the crystallographic results is therefore expected to improve to such a level to allow very detailed interpretations of reaction mechanisms as well as structural trends. Some limitations, nevertheless, stili persist, as shown below.
In the present communication, the planarity of the peptide backbone moiety, monitored by the ? torsion around C-N, is correlated with the peptide C-0 and C-N bond lengths (Figure 1). It is expected that the electronic delocalisation within the
C
C
C
H
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peptide unit decreases when the peptide deviates from planarity, with a consequent shortening of the C-0 bond and a lengthening of the C-N bond. The mesomeric limit formula II of Figure 1 is thus less representative of a non-planar peptide. Atomic resolution protein crystal structures, found in the Protein Data Bank (Table 1), were analysed. Unexpectedly, deviations of the peptide unit from planarity are not associated with shortening and lengthening of the C-0 and C-N bonds, respectively.
Table 1. PDB identification codes of the protein atomic resolution crystal structures examined in the present work. They have resolution of at least 1.3 A, at least 99 percent of the atoms refined anisotropically, and at least 300 atoms. Given that the present work examines basic stereochemical features, the sequence similarity of these protein chains was disregarded as a criterion to define a representative data set.
Ia6k	la6m	la6n	la7s	lb0y	lb6g	lbkr	lbs9	lbx7	lbxo
lbyi	lbz6	lbzp	lbzr	lc5e	lc75	lc9o	lcc7	lcku	lctj
lcxq	lcy5	lcz9	lczb	lczp	ld4t	ldbf	lejg	leuw	lirn
liro	lixg	lixh	llkk	llks	lpsr	lqj4	lql0	lqlw	lqnj
lqow	lqt9	lqtw	lrb9	Irge	lrgg	lswu	2erl	2fdn	2igd
2nlr	2pvb	3chb	31zt	3pyp	3sil	41zt	7a3h	7fdl	8a3h
Results and discussion
The ? torsions and the C-0 and C-N bond lengths were computed for ali non-disordered residues (occupancy = 1) of the protein structures reported in Table 1. The first and the last residues within each chain were of course disregarded as well as residues surrounding disordered three-dimensional regions. For each residue the ?? parameter, defined as the minimal angular deviation from 0 or 180°, was then computed. These reference values of 0 and 180° correspond to the cis and the trans planar peptide conformation, respectively.
Figure 2 reports the distribution of the ?? values for solvent exposed and buried residues and for residues in various secondary structures. A residue was considered buried if its total solvent accessible area, computed with DSSP, was less than 5 A . The secondary structure types, also assigned with DSSP, were simplified as helix (H), strand (B), turn (T), and coil (C), as described by Heringa and Argos. Most of the residues have ?? values close to 0°, indicating a substantially planar peptide unit. The
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distributions of Aco values are statistically independent of the degree of burial within the protein core. Residues in helical backbone conformations show the greatest resistance from distorting planar peptide units. Only about 17-19% of them have Aco values higher than 5°, while 35-45% of the residues in other backbone conformations have Aco values over 5°. This clearlv reflects the higher steric requirements of helical segments, whose (f> and \|/ torsions are known to be little variable.
Figure 2. Distributions of the Aco values for buried and solvent exposed residues associated with various secondary structure types (H = helix, B = strand, T = turn, C = coil).
The relationships between Aco and the amide C-0 and C-N bond lengths are depicted in Figure 3. Single observations are indicated with small circles while large black starš indicate mean bond length values for Aco bins of 1 degree. The mean C-0 bond lengths oscillate from a minimum of 1.232 A to a maximum of 1.236 A. Analogouslv, the mean C-N bond distances range from 1.327 to 1.332 A. The standard
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deviations of these mean bond distances are not reported in Figure 3, for clarity, but range from 0.001 to 0.004 A. The variability of the mean C-N and C-0 distances is therefore statistically insignificant. The linear-least-squares fit of the C-N and C-0 bond lengths versus the ?? values results in slopes statistically identical to 0.0. Analogous results were obtained by considering separately buried and solvent exposed residues as well as different secondary structural types. The correlation between ?? values and C-0 and C-N bond distances was also examined separately in each of the protein structures reported in Table 1. Only in 19% of the structures the C-0 bonds were statistically shorter in the ?? range 15-20° than in the 0-5° range. Only in 2% of the structures the C-N bond was statistically longer in the 15-20° ?? range than in the 0-5° range. Similar results were obtained also by analyzing only 9 crystal structures determined at resolution better that 0.95 A (lb0y, ldy5, lgci, lnls, lrb9, 2fdn, 2pvb, 31zt, 3pyp) where, as expected, a modest, statistically significant correlation between the C-0 and C-N bond distances has been recently observed. For each these 9 ultra-high resolution structures, the slopes of the relationships of the C-0 and C-N bond distances with the ?? values were statistically identical to 0.0. It must therefore be concluded that distortions from planarity are not accompanied by bond length modifications.
The above results contrast observations on small molecule crystal structures. For example, ?? values close to 15° are expected to be associated with C-N distances close to 1.38-1.40 A, much longer than those observed in the proteins of Table 1 {ca. 1.33 A). Such an observation is particularly significant because there are not statistically relevant relationships between the rotameric state of the main-chain peptide bond and the residue atomic displacement parameter values (data not shown), i.e. between the rotameric state and the mobility and flexibility of the atom subset.
Amongst the possible reasons for this discrepancy between observations and expectations, two are worth noting. On one side, crystallographic refinements are rather different in small and large asymmetric unit crystallography. While the application of stereochemical restraints is very unusual in small molecule crystallography (with the exception of the hydrogen atom positions), it is nearly always necessary in protein crystallography. Even at very high resolution, like for the structures considered here, the experimental diffraction data are usually insufficient to allow refinements completely unrestrained. As a consequence, it might be possible that the weights applied to the
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peptide planarity restraint and to the peptide bond distance restraints are inconsistent. Deviations of the bond distances from their target values might be penalized more than
deviations from planarity.
Figure 3. Relationships between the Aco values and the peptide C-0 and C-N bond lengths. Single occurrences are indicated with small circles while large black starš indicate the mean bond lengths for Aco bins of 1 degree.
On the other side, the overall mobility of protein atoms is considerably high and could prevent the detection, even with diffraction data at very high resolution, of subtle features. One must remember that a quite usual atomic displacement parameter value of 20 A (in B units) corresponds to a mean square displacement of 0.25 A from the average atom position, a value not much minor than most of the covalent bonds. It might be possible that such an intrinsic flexibility of the protein molecules in their crystals will never allow very accurate, stereochemical characterizations. The fact that the Aco values
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are similar, on average, for both buried and exposed residues (Figure 2) actually supports this hypothesis.
Although it is not clear which are the ultimate reasons for the discrepancy between observations and expectations, it is nevertheless important for both crystallography and structural bioinformatics to consider that experimental results could be, at least in part, rather inaccurate. Crystallographic improvements must be achieved and caution in data mining still remains.
Experimental
All data were taken from the Protein Data Bank.5 60 crystal structures with resolution of at least 1.3 A, at least 99 percent of the atoms refined anisotropically, and with at least 300 atoms were retained. Residue solvent accessible area values were determined with DSSP14 (probe sphere radius = 1.4 Angstroms), as well as the secondary structural assignments and the omega angles.
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Povzetek
Pričakovali bi, da bo odmik od planarnosti vezi C?-C(C=O)-N v peptidni skupini spremljalo podaljšanje C-N vezi in skrajšanje C=O vezi. Presentljivo pa z analizo proteinskih kristalnih struktur z atomsko ločljivostjo, ki so v zbirki proteinskih struktur PDB, take relacije ne moremo pokazati. Razlog za to je nepravilna parametrizacija omejitev, uporabljenih pri piljenju proteinskih struktur ali pa velika gibljivost proteinskih atomov, ki preprečuje določitev njihovega natančnega položaja.
O. Carugo: Incoherent Relationship Between Torsion Values and Bond Lengths