Molecular Biophysics Unit, Indian Institute of Science, Bangalore 560 012, India
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Abstract |
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Keywords: accessibility/conformation/dihedral angles/hydrogen bonds/motifs/side-chains
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Introduction |
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While the side-chain side-chain hydrogen bonds are a result of the tertiary arrangement of the structural components of proteins, the side-chain main-chain hydrogen bonds, by polar side-chains, present a case comparable with the main-chain main-chain hydrogen bonds. In other words, a majority of side-chain main-chain hydrogen bonds are also local in nature and involve less than six intervening residues on either side of the residue under consideration (Baker and Hubbard, 1984; Stickle et al., 1992
). Another factor of resemblance between these two types of hydrogen bond is the number of dihedral angles that define the conformation of the residues, which form the hydrogen-bonded ring and consequently the hydrogen bond itself. Though, in the latter case, a combination of the side-chain and the backbone torsion angles defines the hydrogen bond.
Side-chain main-chain hydrogen bonds have been observed as important stabilization motifs at the start sites of -helices (Bordo and Argos, 1994
; Doig et al., 1997
; Aurora and Rose, 1998
). Many recent analyses have been reported in the literature (Penel et al., 1999
; Vijayakumar et al., 1999
; Wan and Milner-White, 1999a
,b
) in which the focus has been restricted to those motifs involved in the formation of secondary structures. Other reports have been on specific types of motifs like the Asx motifs (Richardson and Richardson, 1981
; Richardson and Richardson, 1989
; Questal et al., 1993
; Wilson and Finlay, 1997
), backbone mimicry by selected residues (Eswar and Ramakrishnan, 1999
), etc. While many analyses on the backbone dependence of side-chain rotamers have also been reported (McGregor et al., 1987
; Dunbrack and Karplus, 1993
; Schrauber et al., 1993
; Stites and Pranata, 1995
; Bower et al., 1997
; Chakrabarti and Pal, 1998
), the results presented have been derived from either a statistical treatment of observed rotamers vis-à-vis the backbone conformation or based on homologous structures.
The analysis described in this paper presents a comprehensive characterization of those side-chain main-chain hydrogen bonds that are frequently observed in protein structures in terms of the combinations of the torsion angles defining the side-chain conformation and those of the backbone. In this sense, this work is complementary to those of Dunbrack and Karplus (1993) since a relationship between the side-chain torsion angles and the backbone is involved. The results are presented in the light of the consequent hydrogen bonds that might speculated to be the stabilizing motif for a particular rotamer of the polar residues.
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Materials and methods |
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1aan, 1aazA, 1abe, 1abk, 1acf, 1acx, 1afgA, 1ahc, 1ak3A, 1alc, 1ald, 1alkA, 1amp, 1ankA, 1aozA, 1apmE, 1arb, 1arp, 1ars, 1ast, 1bbhA, 1bbpA, 1bgc, 1bgh, 1bmdA,1brsD, 1bsaA, 1byb, 1cbn, 1ccr, 1cewI, 1cgt, 1chmA, 1cmbA, 1cot, 1cpcA, 1cpcB, 1cpn, 1cseE, 1cse I, 1csh, 1ctf, 1cus, 1ddt, 1dfnA, 1dmb, 1dri, 1dsbA, 1eca, 1esl, 1ezm, 1fas, 1fdn, 1fgvH, 1fiaA, 1fkf, 1flp, 1flv, 1fna, 1frrA, 1fus, 1fxl, 1fxd, 1gd1O, 1gia, 1gky, 1glqA, 1glt, 1gog, 1gox, 1gp1A, 1gpr, 1hel, 1hip, 1hleA, 1hleB, 1hoe, 1hpi, 1hsbA, 1hsbB, 1hslA, 1huw, 1hvkA, 1hyp, 1iag, 1ifb, 1isaA, 1isuA, 1lcf, 1lec, 1lib, 1lis, 1lldA, 1ltsA, 1ltsC, 1ltsD, 1mba, 1mbd, 1mdc, 1mjc, 1molA, 1mpp, 1nar, 1nbaA, 1nlkR, 1npc, 1nscA, 1olbA, 1onc, 1opaA, 1ovaA, 1pda, 1pgb, 1phc, 1php, 1pii, 1pk4, 1pmy, 1poc, 1poh, 1ppa, 1ppbH, 1ppbL, 1ppfE, 1ppt, 1prn, 1ptf, 1ptsA, 1r69, 1rbp, 1rdg, 1rec, 1ris, 1rnh, 1ropA, 1sacA, 1sbp, 1sgt, 1shaA, 1shfA, 1shg, 1sim, 1sltA, 1smrA, 1srdA, 1stn, 1tca, 1ten, 1tfg, 1tgn, 1tgsI, 1tgxA, 1thbA, 1tml, 1ton, 1trb, 1trkA, 1ubq, 1utg, 1whtA, 1whtB, 1xib, 1ypiA, 256bA, 2acq, 2act, 2alp, 2apr, 2bbkH, 2bbkL, 2bmhA, 2cab, 2ccyA, 2cdv, 2chsA, 2ci2I, 2cmd, 2cpl, 2ctvA, 2cy3, 2cyp, 2end, 2fcr, 2gbp, 2gstA, 2had, 2hbg, 2hmqA, 2lh7, 2lhb, 2ltnA, 2ltnB, 2lzm, 2mcm, 2mltA, 2mnr, 2msbA, 2ohxA, 2ovo, 2pabA, 2pia, 2plt, 2por, 2prk, 2rhe, 2rspA, 2sarA, 2scpA, 2sga, 2sn3, 2spcA, 2trxA, 2tscA, 2wrpR, 2ztaA, 351c, 3app, 3b5c, 3bcl, 3blm, 3c2c, 3chy, 3cla, 3cox, 3dfr, 3dni, 3drcA, 3ebx, 3est, 3grs, 3il8, 3mdsA, 3psg, 3rp2A, 3rubL, 3rubS, 3sdhA, 3tgl, 4azuA, 4bp2, 4cpv, 4enl, 4fxn, 4gcr, 4i1b, 4icb, 4insC, 4insD, 4mt2, 4tnc, 5chaA, 5cpa, 5fd1, 5p21, 5pti, 5rubA, 6ldh, 7acn, 7rsa, 8dfr, 8fabA, 8fabB, 9wgaA.
Hydrogen bond criteria
Hydrogen bonds were identified using the criteria of the well known hydrogen bond length l (donor...acceptor) and angle (hydrogen-donor...acceptor) in the case of the N-H...O hydrogen bond, where the amide group comes from the peptide backbone (Ramakrishnan and Prasad, 1971
). The position of the hydrogen atom was always fixed assuming standard geometry at the peptide nitrogen.
In the cases of hydrogen bonds involving (a) side-chain amides (as in Asn/Gln examples) and backbone oxygen atoms or (b) side-chain hydroxyl oxygens (as in Ser/Thr examples) and backbone oxygen atoms, the lengths were calculated as described above. However, due to the ambiguity of positioning of the side-chain hydrogen atoms, the following angles were calculated: µ(C-N
...acceptor) for Asn residues, µ(C
-N
... acceptor) for Gln residues and µ(Cß-O
...acceptor) for Ser/Thr residues. The limits used for identifying the hydrogen bonds are 2.4 Å
l
3.5 Å for all types of hydrogen bonds (Mitra and Ramakrishnan, 1981
), 0°
40° for N-H...O hydrogen bonds where N-H is the backbone amide, 80°
160° for N-H...O hydrogen bonds where N-H is the side-chain amide and 70°
150° for O-H...O hydrogen bonds (Mitra and Ramakrishnan, 1977
).
Nomenclature
Throughout the text SC-MC hydrogen bonds have been denoted by the sequential positions of the residues providing donor and acceptor atoms respectively (for example, i/i4, i+2/i, etc.) with respect to the residue `i', which always refers to the residue whose side-chain is involved in the hydrogen bond.
Backbone dihedral angles are denoted by the following convention when the (,
)s fall into the indicated ranges:
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Results and discussion |
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Inclusion of the above said criteria in the analysis further shows that the short range SC-MC hydrogen bonds are mainly restricted to the window ranging from i4 to i+3 (indicated by the bold-faced numbers in Table I occurring only in this region). It is noteworthy that the frequency of occurrence of short-range hydrogen bonds made by the small polar residues is remarkably higher than those of the others. Another interesting point arising out of Table I
is that for these residues (Asn, Asp, Ser and Thr), the prominent hydrogen bonds (shown in boldface) made to the first half of the window (i5 to i) are all those in which the side-chain atom of residue i is the donor, in contrast to those in the window (i+1 to i+5) where they are acceptors. This fact presents a case of directional hydrogen bonds, similar to the main-chain main-chain hydrogen bonds (preponderance of N
1 hydrogen bonds over 1
N), and are probably analogously restricted by the local stereochemistry.
In order to assess the statistical significance of the numbers shown in boldface in Table I, the propensity of a polar atom of residue i to form the indicated hydrogen bonds was calculated and is shown in Table II
, which shows that the types of hydrogen bonds shown in boldface in Table I
, are indeed statistically significant and are not the effect of a random distribution.
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i/i4 hydrogen bonds
Hydrogen bonds of the type i/i4, when formed between the main-chain atoms (51 hydrogen bonds) are typical of
-helices which bring residue i and i4 proximal to each other. However, these types of hydrogen bonds are also found to occur between the side-chain and main-chain atom of these residues (Baker and Hubbard, 1984
; Lyu et al., 1990
; Armstrong and Baldwin, 1993
; Aurora et al., 1997
). There are a total of 945 examples of such hydrogen bonds in the data-set and as shown in Table I
more than 10% of the SC-MC hydrogen bonds made by the residues Ser, Thr, Asn and His (shown in boldface in Table I
) fall into this type. On the other hand, propensity of these residues to form these hydrogen bonds (Table II
) indicates that only the N
atom of Asn and the donor O
atom of Ser/Thr show high preference to form such hydrogen bonds, with Thr showing the maximum (P = 2.85) preference to participate in such hydrogen bonds.
Ser/Thr residues
These i/i4 hydrogen bonds involving Ser/Thr residues are of a O(H)...O type with their -hydroxyl oxygen playing the role of a donor atom. These form 16-membered closed ring structures which are conformationally defined by the (
,
)s at residues i3, i2 and i1 and the
of residue i along with its
1 angle. In order to ease the interpretation of the distributions of these dihedral angles, the
of residue i is also considered, although a rotation about it does not affect the hydrogen bonded ring. There are 608 examples of such hydrogen bonds in the data-set, of which 242 examples are of Ser and 366 examples are of Thr. The distribution of backbone dihedral angles of residues in the window between residues i3 and i (data not shown) reveals that there is an almost complete clustering of the angles in the
R-region. It is found that almost 93% (N = 567) of the examples are indeed part of
-helices. In order to investigate the position of these hydrogen bonds within the helix, the secondary structure flanking the residue i was analysed. Results indicate that in more than 50% (N = 326) of the examples the residue i is flanked by at least one complete turn of an
-helix on either side, indicating that these hydrogen bonds are predominantly found in the middle of
-helices. Also, just over one-third (~35%) of the examples occurring in
-helices, 199 examples out of 567, occur at the last turn at the C-terminal end of the helices. On the other hand, there are only 28 examples where they occur in the first turn of the
-helix. Figure 1a
shows a representative example of an intra-helical i/i4 hydrogen bond. The distribution of
1 angles in these residues show populations in only the g and g+ conformation, with none in the t-conformation (Figure 1b
). Close to 72% (N = 439) of the examples have the g rotamer and 27% (N = 163) have the g+ rotamer leading to two types of conformational motifs, namely,
R
R
R(g) and
R
R
R(g+), respectively.
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The -nitrogen atoms of the Asn and His side-chains too show a tendency to form i/i4 hydrogen bonds. Compared with the earlier examples of Ser/Thr, these residues have an extra atom (the
-nitrogen atom) and consequently result in 17-membered SC-MC hydrogen bonded rings. There are a total of 154 examples of such hydrogen bonds and the (
,
) distribution of the residues in the window (i3 to i) again show near complete clustering at the
R-region (data not shown). A majority of the examples, 132 out of the 154, are indeed part of
-helices. Investigation of the intra-helical position of these hydrogen bonds reveals that these hydrogen bonds are more often found at the C-terminal end of helices than at the middle or the N-terminus. It is found that close to 54% (N = 72) of the examples occur at the C-terminus against just 52 examples in the middle and just five examples at the N-terminus. The distribution of
1/
21 of residue i in these examples shows that the
1 angle is almost always restricted to the g conformation and the
21 angles are clustered around ±60°. A closer examination of the results shows that, surprisingly, all except one example of His have positive values for the
21 angle.
i/i3 hydrogen bonds
The i/i3 hydrogen bonds are similar to the i/i4 hydrogen bonds in that, at first sight, these also appear to be typical intra-helical hydrogen bonds owing to the fact that the periodicity of -helices (3.6 residues per turn) roughly brings residues i4 and i3 spatially close to the residue i. From Table I
it can be seen that a large number of SC-MC hydrogen bonds made by the residues Ser/Thr and Glu/Gln are of this type. Notwithstanding the h-bonds marked in boldface in Table I, Table II
shows that only the Ser/Thr residues show a really high preference to make such hydrogen bonds. Glu shows a propensity of P
1 which neither indicates a preference nor a disfavour and Gln has a propensity P < 1, indicating a disfavour to form such hydrogen bonds. Consequently, only the Ser/Thr residues have been chosen for further analysis. There are a total of 451 examples of Ser/Thr residues participating in such hydrogen bonds out of which 247 examples are of Ser and 204 of Thr. These residues form closed ring structures comprising 13 atoms through a O(H)...O hydrogen bond, which has been known to be a mimic of the main-chain main-chain 5
1 hydrogen bonded
-turn (Eswar and Ramakrishnan, 1999
). Investigation of the distribution of the backbone dihedral angles of the residues in the window i2 to i, which defines the conformation of the hydrogen bond along with the side-chain dihedral angles at residue i, shows a clustering very similar to that of the i/i4 hydrogen bonds. Out of the 451 examples, almost close to 75% (N = 338) of the examples fall into the
R-region of the Ramachandran map (Ramachandran et al., 1963
; Ramakrishnan and Ramachandran, 1965
) and 106 examples into the ß-region. It was found that close to two-thirds of the total number of examples (301 out of 451) and also 89% (301 out of 338) of the examples occurring in the
R-region, are indeed part of
-helices. Investigation of the position of these hydrogen bonds within the helix showed that there are only 69 examples in which the i/i3 hydrogen bond is in the middle of a helix. In contrast, more than 77% (N = 234) of the examples occur at the C-terminal end of
-helices and the remaining 104 examples occur at the N-terminal end. This enforces the fact that a majority of examples occur at the ends of
-helices.
Investigation of the 1 rotamer distribution of the residues involved in the i/i3 SC-MC hydrogen bonds reveals that the prominent clustering is at the g+ conformation (Figure 1d
). Almost close to 85% (N = 383) of the examples have the
1 values in the range of the g+ conformation. Figure 1c
shows an example of an i/i3 hydrogen bond from the middle of a helix and it is evident from Figure 1ad
that, in comparison, the i/i4 and i/i3 SC-MC hydrogen bonds show peaks at complimentary
1 positions (g and g+ respectively) owing to the periodicity of the helix. A combination of the side-chain rotamers and the main-chain angles of the residues in the window i2 to i yields two conformational motifs of this hydrogen bond which are
R
R
Rg+ and
R
R
Rg.
i/i type hydrogen bonds
These types of hydrogen bond are unique since they occur between the side-chain and peptide backbone of the same residue. From Table I it can be seen that there are a total of 1259 examples of such intra-residue hydrogen bonds in the data-set. A major fraction of the examples comes from Thr (38% or N = 482 out of 1259), Ser (29% or N = 359) and Glu residues (13% or N = 164). It can also be seen that 28.8% (N = 482 out of 1672) of the SC-MC hydrogen bonds made by the Thr side-chain, 27.3% (N = 359 out of 1314) of Ser, 24.6% (N = 164 out of 667) of Glu and 12.6% (N = 33 out of 262) of Gln are of this type. Propensities of the residues to form such hydrogen bonds can be seen from Table II
, which highlights the fact that only Thr, Ser and Glu show high propensities to form such hydrogen bonds. Though more than 10% of the SC-MC hydrogen bonds made by the Gln side-chain are of the i/i type (shown in boldface in Table I
), the propensity of the residue to form such hydrogen bonds is very low (P = 0.38).
The Ser and Thr residues form these i/i hydrogen bonds through a O(H)...O type of interaction resulting in a six-membered closed ring conformation, while the Glu and Gln residues form a N(H)...O
type of hydrogen bond, consisting of seven atoms in the ring, through their side-chain
-carbonyl oxygens. Accordingly, the number of degrees of freedom that defines the hydrogen bonded conformation varies between the two sets of residues, Ser/Thr and Glu/Gln. A representative example from each of these two sets is shown in Figure 2a and d
. It can be seen that in the Ser/Thr examples, the hydrogen bonded conformation is independent of the value of
, while for the Glu/Gln examples they are independent of the value of
at residue i.
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There are a total of 841 examples of Ser/Thr (359 examples of Ser and 482 examples of Thr) i/i SC-MC hydrogen bonds. The (,
) and
1 distributions for these examples are shown in Figure 2b and c
. It can be seen that the (
,
) points of these examples are clustered around the usual ß- or the
R-regions of the Ramachandran map. The
-values form two distinct clusters, one close to
= +150° and the other close to
= 40°. The dependence on the
-value is evident here since there are almost no points near the left-handed
-helical (
L) region, which is characterized by
+40°, indicating that only those backbone conformations which have
in one of the two clusters favours formation of this hydrogen bond. Close to 87% (N = 733) of the examples fall into the ß-region and 12% (N = 99) into the
R-region. More than 50% of the examples in the two clusters are part of standard secondary structures; 401 examples out of the 733 which occur in the ß-region are part of ß-strands and 77 out of the 99 which occur in the
R-region are part of
-helices. The distribution of the
1 angles also shows a distinct clustering only around the t or the g+ rotamers. Investigation of the two distinct clusters of the backbone dihedral angles and the side-chain torsion angles revealed that, only two kind of motifs, namely,
R(t) and ß(g+), favour the formation of such a hydrogen bonded conformation.
Glu/Gln residues
The Glu/Gln residues also exhibit a preference to participate in i/i hydrogen bonds. These residues form seven-membered rings that are closed by a hydrogen bond between its own backbone amide and the -carbonyl oxygen of the side-chain. As can be seen from Figure 2d
, in contrast to examples of the Ser/Thr residues, the i/i hydrogen bonded motif of Glu/Gln side-chains is dependent on the
-angle instead of the
as is in the Ser/Thr examples. There are 197 examples of such motifs in the data-set of which 164 are of Glu and 33 are of Gln. Though the Gln residues do not show a propensity to form such hydrogen bonds (Table II
) they are considered here since the mode of hydrogen bonding, namely the acceptor
-oxygen, is the same as Glu residues. The (
,
) distribution of these examples, shown in Figure 2e and f
, clearly shows the restriction of the
-angle to the interval 90°
45°. Almost all of the examples have their
-values confined to this interval. Further, there are only two regions of clustering for the backbone dihedral angles. 159 out of the 197 examples have (
,
)s in the
R region and 38 fall into the ß-region. The side-chain torsion angles
1 and
2 are confined to either of the g+ or g conformation with the t-conformation completely absent (Figure 2f
). The
31 angle is almost completely restricted to the interval 90°
31
+90° (indicated as the t'-conformation) with only 26 out of the 197 examples having the
31 near the trans region. The 197 examples can be grouped into well defined motifs. The most populated conformational motif is the
R(gg+t') motifs with 47% (N = 91) examples followed by the
R(g+gt') having 24% (N = 47) examples. Majority of the examples falling under the ß-region of the backbone dihedral angle space (24 out of 38 examples), belong to the ß(gg+t') motif.
i+2/i hydrogen bonds
In contrast to the previously discussed types of SC-MC hydrogen bonds, the i+2/i hydrogen bonds are different in the sense that these hydrogen bonds are directed towards the main-chain polar groups succeeding residue i, unlike in the former cases where they were all towards residues earlier in the chain. The most predominant of these hydrogen bonds are the ones made by the -carboxyl groups of Asp/Asn or the
-hydroxyl groups of Ser/Thr. Another remarkable point of difference between these hydrogen bonds to the successive residues in the chain and those towards the preceding residues, is the fact that the polar atoms of the Asp/Asn and Ser/Thr side-chains act as an acceptor for hydrogen bonds. These four residues contribute to a total of 1033 examples of such hydrogen bonds out of which 637 examples comprise the
-carboxyl group of Asn/Asp and the remaining 396 examples involve the acceptor
-hydroxyl group of Ser/Thr residues. It can also be seen from Table II
that out of these four residues, Asp, Asn and Ser show a high propensity to form such hydrogen bonds, for which the Thr residues neither show a preference nor a disfavour with P
1.
Asn/Asp residues
The hydrogen bonds between the -carboxyl oxygen of Asn/Asp of residue i to the amide hydrogen of residue i+2 results in a hydrogen bonded ring of 10 atoms. This hydrogen bonded conformation has particularly evoked a lot of interest since it mimics the type II' ß-turn while also stabilizing the type I and type I' ß-turns (Richardson and Richardson, 1989
; Ramakrishnan et al., 1996
; Eswar and Ramakrishnan, 1999
) and is also believed to be crucial at the initiating sites of
-helices (Wan and Milner-White, 1999a
). The distribution of the 637 examples of such hydrogen bonds between Asp and Asn is 423:214, the former being almost double that of the latter. The backbone dihedral angle distribution of the residues i and i+1, which provides the conformational definition of the hydrogen bond, is shown in Figure 3
and it can be seen that the conformation of residue i is restricted to mostly the ß-region with almost 86% (N = 545) of the examples occurring in this region, with only a small fraction of the examples (N = 87) occurring in the bridge region of the Ramachandran map (
= 0°). The clustering of (
,
) points of residue i+1, on the other hand, shows that they are restricted to the bridge regions of the Ramachandran map on either side of the
-axis. Out of the 637 examples, almost as many as 545 examples are followed by an
R-conformation at i+1 and 90 examples are followed by an
L-conformation.
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Ser/Thr residues
The i+2/i hydrogen bonds involving the -hydroxyl oxygen of the Ser/Thr residues results in a 12-membered closed hydrogen bonded ring with the side-chain oxygen atom acting as an acceptor to the hydrogen bonds from backbone amide groups ahead in the sequence (Wan and Milner-White, 1999b
). There are a total of 396 examples of such hydrogen bonds out of which 227 are by Ser and 169 are by Thr residues. An examination of the backbone conformations of residues i and i+1 of these examples reveals that a majority (81%, N = 321) of the examples adopt the ß-conformation at i and at residue i+1, the majority occurs in the bridge/
R region of the Ramachandran map with as many as 323 examples adopting this conformation and 71 examples adopting the
L conformation.
The 1 values of the examples show clear clustering at only the g+ and t rotamers. 209 examples out of 396 adopt the t rotamer and 187 adopt the g+ rotamer. And investigation of the secondary structures following residues i indicate that only 45 examples function at helix initiators.
The fact that the clustering of the backbone dihedral angles of residue i at the ß-conformation and the side-chain torsion angle of these examples at g+ is similar to the clustering of these angles in the case of the i/i SC-MC hydrogen bonds prompted us to investigate the existence of any additional hydrogen bonds through the -hydroxyl atom. It was found that in 110 examples, the i+2/i hydrogen bonds had an additional i/i hydrogen bond in which
-hydroxyl oxygen of Ser/Thr residues additionally act as a donor to the carbonyl oxygen of its own peptide backbone. In order to ascertain if these i+2/ii/i hydrogen bonds are characteristic of the helix initiating examples, the secondary structures following the motif were analysed. It was found that there are only 18 examples out of the 45, which function as
-helix start sites, which had this additional hydrogen bond.
i+3/i hydrogen bonds
The i+3/i hydrogen bonds are closely related to the previous i+2/i type hydrogen bonds in that the side chain atoms function as an acceptor to polar groups of the backbone ahead in the sequence. From Table I it can be seen that the Asp/Asn and Ser/Thr residues contribute the maximum number of examples to this type of hydrogen bond. In total, there are 640 examples of such hydrogen bonds out of which the Asp/Asn account for 298 examples and the Ser/Thr residues account for a further 299 examples. Table II
also shows that these are the only four residues which show high propensity to form such hydrogen bonds.
Asp/Asn residues
Asp/Asn residues form i+3/i hydrogen bonds through the -carboxyl oxygen atoms and the backbone amide hydrogens three residues ahead in the chain. They form 13-membered hydrogen bonded rings which mimics the 13-membered main-chain main-chain hydrogen bonded conformation of an
-turn (Eswar and Ramakrishnan, 1999
). There are 298 examples of Asp/Asn participating in such hydrogen bonds in the data-set out of which 190 examples are of Asp and 108 examples are of Asn.
Figure 5 shows the (
,
) plots of the backbone dihedral angles at residues i, i+1 and at i+2. It can be seen that the residue i is mostly clustered at the ß-region and there are only very few examples elsewhere. Indeed, 276 examples out of the 298 have a ß-conformation at the residue i and only 18 examples possess an
R-conformation. Inspection of the plots for the residue at i+1 indicates that there is a very strong clustering near the
R-region. And the residue at i+2 shows almost complete clustering in the same region. Analysis of the examples reveals that almost 93% (N = 276) of the examples possess the main-chain motif of ß
R
R. This repeated occurrence of clusters at the
R-region prompted us to investigate the secondary structure of the residues following i. Close to 180 examples were indeed at the initiating positions of
-helices with the hydrogen bond serving to satisfy the unsatisfied polar amide groups of the N-terminus of the helices (Penel et al., 1999
; Vijayakumar et al., 1999
; Wan and Milner-White, 1999a
).
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Ser/Thr residues
Out of a total of 640 examples of such i+3/i hydrogen bonds, 299 examples correspond with those made by Ser/Thr residues. There are 172 examples of Ser and 127 examples of Thr residues which participate in such hydrogen bonds. These hydrogen bonds result in a 12-membered closed ring with the hydrogen bond between the -hydroxyl oxygen and the amide hydrogen three residues away. The backbone dihedral angle distribution of the residue i shows that an overwhelming majority of the examples (295 out of 299) possess the ß-conformation and only four examples possess the
R-conformation. The secondary structure of the following residues (i+1, i+2, etc.) reveals that in 80% (N = 240) of the examples the following residues are part of
-helices. This confirms the fact that this hydrogen bonded motif is a strong helix initiator.
Distribution of the side-chain rotamers of the examples, shown in Figure 6, reveals a preference for the g+ and the t rotamers. Almost close to 84% (N = 251) of the examples adopt the g+ rotamer while there are only 48 examples which adopt the t rotamer. An investigation similar to the one described earlier (in the case of i+2/i) for an additional i/i hydrogen bond revealed that 66% (N = 202 out of the 299) of the examples form an i+3/ii/i type hydrogen bond. Interestingly, a large majority of 74% (N = 178 out of 240) of the examples which are found at the start sites of
-helices possessed this motif.
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The accessibility of the residue i participating in each of these hydrogen bonds was calculated using the Lee and Richard algorithm (Lee and Richards, 1971). Since this analysis involved only polar residues it was expected that these hydrogen bonds will all be surface features in globular proteins. But contrary to expectations, it was found that the majority of each of these hydrogen bonded interactions were in fact buried from the solvent. Figure 7
shows the distribution of the accessibilities of the residue i in each of the five hydrogen bonds analysed. It can be seen that in all the cases, the accessibility profile drops from the left to the right indicating that a majority of the residues participating in these hydrogen bonds are indeed buried (Chothia, 1976
; Miller et al., 1987
). It can be calculated that 81.5% of the residues participating in i/i4 hydrogen bonds, 79.6% of those participating in i/i3, 71.9% of those engaged in i/i, 83% of those in i+2/i and 80.3% of those in i+3/i hydrogen bonds have accessibilities of less than 45%.
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In summary, the analysis of the side-chain main-chain hydrogen bonds made by the polar side-chains reveals that these hydrogen bonds are well ordered and can indeed be characterized by the torsion angles enclosed by the hydrogen bonded ring similar to the case of the regular main-chain main-chain hydrogen bonds. The predominant motifs identified by this analysis are given in Table III.
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Conclusions
The analysis seeks to establish the fact that side-chain main-chain hydrogen bonds do indeed form regular patterns of conformational motifs. These can be compared with the main-chain main-chain hydrogen bonds like the -, ß- or the
-turns which are identified based on the clustering of the backbone dihedral angles. Fixing of the side-chain rotamers in both theoretically generated models as well as unrefined X-ray crystal structures is largely based on the principle of maximizing the hydrogen bonds (McDonald and Thornton, 1994a
). The results of this analysis, which establish a strong conformational relationship between the backbone and side-chain dihedral angles, can be used to identify the rotamers based on the backbone (
,
) angles. The analysis also establishes the fact that SC-MC hydrogen bonds are crucial elements at the start sites of
-helices where they play the role of the protein backbone to initiate the secondary structure. And the fact that these hydrogen bonds are predominantly buried indicates that they play very important roles in the interior of the protein where the side-chains probably contribute to satisfy the hydrogen bonding potential of the backbone polar groups.
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Received October 5, 1999; revised January 12, 2000; accepted January 19, 2000.