Int. J. Peptidehotein Res. 10,1977, 129-138 Published by Munksgaard. Copenhagen, Denmark No part may be reproduced by any process without written permission from the author(s)
CONFORMATION O F POLYPEPTIDE CHAINS CONTAINING BOTH L- A N D D - R E S I D U E S 11. Double-Helical Structures of Poly-LD-Peptides B. V. VENKATRAM PRASAD and R. CHANDRASEKARAN
Molecular Biophysics Unit, Indian Institute of Science, Bangalore, India
Received 1 January, accepted for publication 4 March 1977 Polypeptides with alternating L - and D-amino acid residues can take up stereochemically satisfactory coaxial double-helical structures, both antiparallel and * 0 hydrogen parallel, which are stabilized by systematic interchain NH bonds. Semiempirical energy calculations over allowed regions of conformational space have yielded the characteristics of these double-helices. There are four possible types o f antiparallel double-helices - A3, A4, A5 and A g , with n. the number of L D peptide units per turn, around 2.8, 3.6, 4.5 and 5.5 respectively, while for the parallel double-helices there are two types, P3 and Pq, having similar helical parameters as in A 3 and A 4 . The hydrogen-bonding scheme restricts the pitch in all the models t o the narrow range o f 10.0 to 11.5 .k All these helices have large central cores whose radii increase proportionately with n In this respect, A 3 and A4 are suitable models for the structure o f gramicidin A. In terms o f their relative energies, antiparallel double-helices are marginally more stable than those with parallel strands. Our results indicate that the energy differences amongst the members in the antiparallel family are not significant and thus provide an explanation for the polymorphism reported for poly(ybenzyl-t D-ghtamate).
--
Several single-helical models for polypeptides with alternating L- and D-amino acid residues, which we may call poly-LDpeptides henceforth, have been proposed on the basis of conformational analysis (Ramachandran & Chandrasekaran, 1972; Hesselink & Scheraga, 1972; Urry, 1972). These helices were considered to be possible structures for the natural ion carrier gramicidin A, a linear pentadecapeptide in which L- and D-residues alternate. All of them, stabilized by regular NH . . . 0 Contribution No. 93 from the Molecular Biophysics Unit, Indian Institute of Science, Bangalore.
hydrogen bonds, display the successive carbony1 groups pointing in opposite directions relative to the helix-axis. Rarnachandran & Chandrasekaran (1972) predicted the LD4phelix (reD or g,3 according to Urry) to be a suitable structure for gramicidin A. And indeed, based on his niD-model and supported by specific conductance measurements and spectroscopic studies, Urry could explain the functioning of gramicidin A as a transmembrane channel, spanning the bilipid layer of biornembranes (Urry, 1972). Moreover, Heitz er al. (1975) have shown from X-ray and electron diffraction experiments that poly(y129
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
benzyl-LD-glutamate) can adopt any one of these helical models. Recently, for the first time, Veatch et al. (1974) from spectroscopic and chemical studies on gramicidin A, have suggested novel double-helices as alternatives for poly-LDpeptides. Until then, double-helices were a unique feature only for polynucleotides and polysaccharides. This has prompted us to investigate in detail the stereochemically feasible and energetically favourable polyLD-peptide double-helices using empirical energy calculations.
h D j shown in Fig. 1. Accordingly, we shall designate the antiparallel models as A3, A4, AS and A6 and the parallel models as P3, Pa, P5 and P6, corresponding to j being 3, 4, 5 and 6 respectively. A large central core is a persistent feature in all these double-helices? as was also reported for single-helices (Ramachandran & Chandrasekaran, 1972). The pitch remaining almost the same in all these double-helices, as we go from types A3 through A6 (or P3 through P6) the diameter of the molecule and hence the core size increases.
DESCRIPTION OF DOUBLE-HELICES The double-helix is formed by the association of two conformationally identical poly-LDpeptide strands wound about a common helixaxis. The two chains interact through systematic NH 0 hydrogen bonds analogous to the situation in orthodox polypeptide & structures. As in the poly-LD-peptide singlehelix, successive NH(or CO) groups are oriented in opposite directions relative to the helix-axis. There are two possible modes of intertwining the two strands coaxially to form a double-helix. In one such arrangement, the strands have opposite polarities and are related by a two-fold symmetry perpendicular to the helix-axis as observed in the well-known Watson-Crick DNA double-helix. Alternatively, the polarities of the strands can be retained to be the same. These two models are referred to as the antiparallel and parallel double-helices respectively. Hydrogen bonds are formed systematically, always between the L-residues in one strand and the D-residues in the other and vice versa in the former model, while they are only between like residues (L to L and D to D) in the latter. The details of the hydrogenbonding scheme are illustrated in Fig. 1. The very nature of this pattern is reminiscent of the &sheet polypeptide structures. This constrains the pitch of the helix to vary only within a narrow range of about 10.0 to 11.5.4. Model building shows that double-helices with this type of hydrogen-bonding scheme can be constructed for four different values of j, namely 3, 4, 5 and 6, for the repeating unit
---
130
FIGURE 1 : Schematic representations of the double-helix of polyLD-peptide. The interchain NH * * * 0 = C hydrogen bonds are shown by dotted lines. a) In the antiparallel, double-helix, hydrogen bonds are formed only between L and D peptide units. The four types A,, A,, A, and A, correspond to j = 3, 4, 5 and 6 respectively. Note that the hydrogen bonds marked 1 and 2 are equal and so are 3 and 4 because of dyad symmetry. b) In the parallel double-helix, the two strands are linked by hydrogen bonds - L to L and D to D. The two possible types P, and P, have j = 3 and 4 respectively.
COMPUTER MODEL BUILDING AND ENERGY CALCULATIONS In a poly-LD-peptide helical structure, the1 repeating unit is a pair of mns peptide units associated with an L- and a D-a-carbon atom' denoted by, say, L1 and D1. The successive units L2D2, L3D3, etc. in Fig. 1 can be gener-
L
w
e
*D
4.5
3.0
2.6 to 2.9
-28.8
-75 to -110
Range of axial rise per repeating unit.
5.5
4.0
3.35 to 3.65
-23.7
-95 to -125
100 to 180
100 to 180
QD
130 to 180
100 to 180
100 to 180
*L
6.5
5.0
4.35 to 4.65
-24.0
-130 to -145
130 to 180
-145 to -130
-160 to -125
7.5
6.0
5.40 to 5.60
-24.4
-180
-130 to
150 to 180
140 to 180
-165 to -155
Double-helices
-145 to -115
~
@L
* Ramachandran & Chandrasekaran (1972).
(outer radius)
C@atom in A
Mean radius of the helix for CQ atom in A (inner radius)
Range of n (Pitch: 10.0 to 11.5 A for doublehelices)
Lowest energy kcal/mol/LD unit
Allowed regions of conformational angles (")
Characteristics
~~
4.5
3.0
2.60 to 2.90
-23.3
5.5
4.0
3.35 to 3.65
-20.9
-110 to 100
145 to 160
160 to 180 -85 to -105
140 to 150
-150 to -140
120 to 140
-130 to -115
~~
4.0
2.8
2.24 to 2.31 (2.38 to 2.44)b
-19.4
-65 to -85
110 to 130
115
100 to
-100 to -80
5.4
3.9
3.12 to 3.17 (1.54 to l.58)b
-17.9
to
6.5
5.0
4.09 to 4.14 (1.16 to 1.20)b
-14.2
-142 to -148
132to 142
140 to 152 -124 -134
144 to 152
-128t0 -120 112 to 124
-112 to -102
Single-helices*
TABLE 1 Summary o f the relevant fentures of the double-helices (present study) and single helice? of ply-LDalanine
E
$
?5 6 2
%
v)
C
m
sr
0
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
ated from this by helix symmetry. This helix is then described by the two pairs of dihedral angles (@L, $L) and (@D, J / D ) which repeat themselves regularly. The conformational angles are defined following the rules of IUPAC-IUB Commission (1 970). The method of generating the double-helix involves two major steps. First of all, the coordinates (r, 8, z) of the repeating unit LIDl of the first chain for given (@L, J/L) and (GD, $D) are computed in the helical system whose x-axis passes through the first a-carbon atom, using the general matrix method (Ramachandran & Sasisekharan, 1968) and the helical parameters n and h are evaluated. The standard dimensions of the rruns planar peptide unit are used in the calculations. Throughout the analysis, the angle T(=N-C"-C) is maintained at the expected value of 110'. If the helical parameters are within the prescribed range amenable for the formation of required interchain hydrogen bonds, coordinates of additional peptide units spanning more than a turn of the helix are computed. Now the stage is set up for the interspersing of the second chain to create the double-helix - either antiparallel or parallel and the second step is as follows. For the antiparallel model, the repeating unit LkDk of the second coaxial strand of opposite polarity is generated by a rotation of 180" about the x-axis of the helical system from the corresponding coordinates of L1D1. It is further aligned with respect to the first chain by a rotation A0 about, and a translation Az along, the helix-axis (z-axis) in order that the four hydrogen bonds, two with LIDl and two with LjDj are formed as shown in Fig. la. The LkDk coordinates are then given by (r, -0 + AO, -z Az). Thus the repeating units LIDl and LkDk of the two strands are related by the dyad perpendicular to the helix-axis passing through (0, A8/2, Az/2). Also LjDj and LkDk are related by a similar dyad arising from the symmetry of the helix. Hence hydrogen bonds 1 and 2, and likewise 3 and 4, in Fig. l a are equivalent. Finer adjustments of A8 and Az, however, enable us to make 1 and 3, and so 2 and 4, very nearly equal, In the case of the parallel model, the pro-
+
132
cedure is virtually the same, excepting that the dyad symmetry does not exist. Consequently, the LkDk coordinates of the second coaxial strand (Fig. l b ) are computed as (r, O Ad, z + Az). The four hydrogen bonds here are quite independent of each other, but yet and 3 can be made nearly equivalent, and so, also 2 and 4, by a suitable choice of AO and Az values. For the double-helix having satisfactory hydrogen bonds, 12 peptide units in each1 strand with alanine side group (methyl h y d r q gens in staggered positions) at every a-carbon atom alternately in L- and D-configurations have been considered in the energy calculations. Non-bonded and electrostatic interactions and torsional potentials have been taken into account following the method of Ramachai dran & Sasisekharan (1968). Hydrogen bw energies have been evaluated using the potenti; function formulated by Ramachandran et al. (1971). Energy contributions from all those interactions arising from the repeating unit LIDl within itself and with the rest of the units in the double-helix have been summe up to get the total energy per LD unit o f t e double-helix. For the different types of double-helices (with j = 3, 4, 5 and 6 , as already mentioned7 the number of repeating units (n) per turn isapproximately 2.5, 3.5, 4.5 and 5.5 respectively. In the computational analysis, the ranges of n have therefore been centred around these values with suitable deviations on either side sE that none of the stereochemically acceptable, models have escaped our attention. The search has been made in the entire allowed conformational space by varying the four rotation angles generally at intervals of '5 and, in some instances at smaller intervals when necessary. The combination of (GL, $L) and (@D, $D) which produces rights handed helices alone has been analysed as the properties of these helices are implicitly related to the left-handed helices. This followa from the well-known fact that the inverse combination (-@L, -$L) and (-@D, I)$) for the DL-sequence leads to isoenergetic lef& handed helices. These two forms are mirror images of each other.
+
8
DOUBLE-HELICES OF POLY-LD-PEPTIDES
RESULTS AND DISCUSSION Poly-LD-peptides have large conformational possibilities viz., double-helices presently being discussed and single-helices previously reported '(Ramachandran & Chandrasekaran, 1972; Hesselink & Scheraga, 1972; Urry, 1972; Heitz et ul., 1975). Our computer model building a n d energy calculations have revealed the major features of these novel double-helices for poly-LD-peptides. The summary of these (features is given in Table 1 which also contains for comparison the important features of bhe single-helices as given by Ramachandran & Chandrasekaran (1972). A specific common feature, as can be seen from the mean radial coordinates of the CYcarbon atoms corresponding to the inner radius 'of the double-helical models, is that all of them, ke single-helices, possess large central cores ( able 1). Their sizes, by virtue of the hydrogen-bonding pattern as described earlier, increase from A3 t o A6 (or P3 to P6) in that order from 3.0A to 6.0A. The core sizes of the double-helices A3 and A4 (or P3 and P4) are comparable to those of single-helices LD3p and 4;D4p respectively (Ramachandran & Chandrasekaran, 1972) and hence, A3 and A4, which are more energetically favourable than P3 and P4, are the expected models which can be correlated to the structure of gramicidin A in its ability to function as conductor of ions like Li, Na, K, Rb and Cs in biological systems. As mentioned already, the hydrogenbpnding network in these double-helical structures is very similar to conventional &structures of polypeptides with all L- or all D-residues. In fact, we can imagine the double-helices as being generated by wrapping two strands of a &structure around a cylinder so that its surface is lined with NH 0 = C groups. This may bk a pertinent factor in the functioning of gramicidin A. As a consequence, the conduction of an ion through the channel may be more prompted by dipolar interactions rather than van der Wads type of interactions. Another important feature of these structures is that the Ca-Cp bonds stick out of the cylinder and are almost perpendicular to the helix-axis as in single-helix models (Ramachandran & Chandrasekaran, 1972). Therefore, in gramicidin A, whether it adopts a single- or
$
---
double-helical structure, the hydrophobic side chains may not have a major role in ion conduction. On the contrary, they may shield the hydrogen-bonded network from external disturbances and thus protect the channel in the helix from being disrupted. The detailed conformational properties of the antiparallel and parallel double-helices of poly-LD-alanine are listed in Tables 2 and 3. These include, in addition to $, J/ and n, h values, the hydrogen bond lengths and angles and the parameters A0 and Az. In the last column the total energy, including that of hydrogen bonds, is given. In the antiparallel double-helical models listed in Table 2, the energy ranges from -21 to -29 kcal/mol/LD unit. The important observation here is, for A3 and A4, as q5L decreases, the corresponding J/,, increases in magnitude. Consequently, the more the difference in magnitude between these two, the larger is the number of sterically allowed conformations. On the other hand, for the other two types A5 and A6, the GL, difference is very small and therefore the number of conformations is also small. For the parallel double-helices, only two types, P3 and P4 with helical parameters similar as in A3 and &, are found feasible (listed in Table 3). Due to severe short contacts between the two strands, the P5 and P6 models cannot be generated. The energies of P3 and P4 are, however, higher than for the antiparallel counterparts and range from -19 to -23 kcal/mol/LD unit. The number of allowed conformations listed in Table 3 are indeed fewer than in the corresponding antiparallel cases. This is mainly due to difficulty encountered in making two satisfactory interchain hydrogen bonds for each repeating unit. The distribution of rotational angles is very similar to the behaviour of the antiparallel models mentioned earlier. Stereochemically satisfactory double-helical models with antiparallel chains could be built without any short contacts. However, for the parallel double-helices, a few short contacts were encountered in the model building for some conformations listed in Table 3. These short contacts range from 2.0 to 2.2 A between an Ha in one strand and a carbonyl oxygen just ,
133
P
w
c
*L
180 145 140 165 155 135 130 150 165 145 170 135 140
145 155 145 140 145 165 165 170 140 145 160 170 140 155 135 145
@L
-145 -140 -135 -135 -130 -130 -125 -125 -120 -120 -120 -115 -115
-160 -155 -150 -145 -145 -145 -145 -145 -140 -140 -140 -140 -135 -135 -130 -130
TYP@
A3
A4
2.93 2.82 2.81 2.88 2.86 2.80 2.80 2.85 2.63 2.84 2.73 2.89 2.83 3.58 3.37 3.61 3.60 3.35 3.59 3.45 3.62 3.62 3.37 3.58 3.64 3.64 3.57 3.63 3.54
- 75 - 80 - 85 - 85 - 90 - 90 - 95 - 95 - 85 -100 - 90 -110 -105
95 - 90 -105 -110 -100 -105 -100 -105 -115 -105 -110 -110 -120 -115 -125 -120
115 150 155 135 145 160 165 150 135 155 130 170 160
155 145 155 160 155 135 135 130 160 155 140 130 160 145 165 155 -
n
*D
2.75 3.14 2.77 2.79 3.17 2.92 3.11 2.89 2.81 3.19 2.97 2.91 2.85 3.02 2.87 3.07
3.53 3.70 3.70 3.89 3.93 3.70 3.69 3.96 4.25 3.98 4.13 4.07 3.99
h (A)
Helical parameters
@D
Conformational angles (")
85.5 84.3 79.6 78.3 80.6 76.0 79.4 72.7 74.6 78.7 73.5 74.0 67.1 69.8 70.0 66.2
101.6 99.5 94.6 91.8 87.8 93.5 89.1 86.4 94.7 82.6 89.6 69.3 76.5
A0 (o)a
-23.0 -22.3 -22.6 -2 1.9 -21.1 -23.3b -21.5 -23.1 -21.8 -20.2 -22.8b -21.3 -22.1 -22.3 -20.7 -21.8
29.5 21.8 24.8 25.0 24.5 9.1 12.5 8.7 22.0 22.4 7.4 14.6 16.2 6.0 20.0 9.9 3.07 3.14 3.00 2.95 3.10 3.00 3.12 3.02 2.94 3.11 2.99 3.06 2.9 2.99 2.95 3.00 7.99 8.32 8.01 8.02 8.38 8.12 8.37 8.04 8.02 8.44 8.16 8.20 7.92 8.17 8.08 8.17
-28.9 -24.2 -23.4 -26.4 -25.2 -21.3 -20.0 -23.5 -26.6 -22.3b -25.8 -20.4 -22.2b
28.6 32.6 31.8 20.5 20.3 34.3 34.3 22.5 21.5 22.2 18.3 24.3 20.1 2.94 2.95 2.87 2.93 2.89 2.87 2.81 2.88 2.84 2.84 2.81 3.05 2.80
8.36 8.53 8.44 8.69 8.68 8.48 8.4 1 8.73 8.86 8.71 8.74 8.94 8.62
kcal/mol/LD unit
Total energy
NHhNO(")
N * **O(A)
Az(A)~
Hydrogen bond parameters
TABLE 2 Conformational angles and characteristics of low energy structures of antiparallel double-helices of poly-LDalanine
*2
w
>
m 6
U 9
*z
0 3.
z P
>
U
g
P
+8
%
P
4
6
*
$ z
5
m
-165 -163 -161 -160 -159 -157 -155
-135 -130
-135
145
155
151 149 149 155 157
145 150 160 170 140 165 140
-140 -140 -140 -140
165 167 167 160 157 159 170
160 155 145 135 165 140 165
165 170
-130 -134 -136 -135 -134 -136 -140
-130 -140 -140 -145
-135
-135 -135
-130 -125
5.40 5.44
5.41
5.45 5.57 5.59 5.52
4.38 4.43 4.51 4.37 4.37 4.58 4.40
3.65 3.47
1.86 1.75 1.76 1.79 1.82 1.85 1.87
2.28 2.28 2.23 2.41 2.33 2.25 2.39
2.92 3.07
Helical parameters
52.2 45.9 45.2 47.1 53.1 54.5 53.9
58.5 54.2 58.5 62.1 58.4 50.9 58.9
62.8 63.8
7.54 7.19 7.27 7.23 7.36 7.49 7.69
7.50 7.40 7.42 8.03 7.68 7.52 7.89
8.00 8.15
16,3 22,4 21.5 15.4 8.8 9.8 16.8
12S 18.4 11.0
2.96 3.07 3.08 3.16 3.08 3.14 3.04 2.96 3.03 3.18
10.6 12,o 11.2 15.0
14.6 20.0
2.86 2.90 2.91 3.18
2.95 3.03
Hydrogen bond parameters
-21.lb -23.6 -22.1 -24.4 -24.3 -22.3 --18.7b
-22.3 -21.5 -19.3
-23.6 -24.1 -23.8b -17.6
-20.8
-21.8b
Total energy
a The
coordinates of the repeating unit LkDk (Fig. 1) in the second strand are given by (I, -8 + AO, -z + Az) where (I, 8 , z) are the cylindrical polar coordinates of the repeating unit L, D; of the first strand. These are the conformations whose helical parameters are close to those determined from X-ray diffractograms of poly(7-benzyl-LD-glutamate) (Lotz er al., 1976). The calculations are done at 2" interval.
A9
A,
135 130
-125 -125
Conformational angles (")
TABLE 2 (continued)
v1
m
U
z%
?
?
2
$!
j: m
! i m
8
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
FIGURE 2: Perspective drawing of the double-helix (a) antiparallel model A, and (b) the corresponding parallel model P,, viewed perpendicular to the helixaxis. The hydrogen bonds are indicated by dashed lines. The acarbon atoms in the L- and &configurations are denoted by L and D respectively. Smail circle for hydrogen, medium circle for carbon, striated medium circle for nitrogen and large circle for oxygen.
above it in the other strand. The orientations of the Ca-Ha bonds and the carbonyl groups are suggestive of possible weak CH * 0 hydrogen bonds. Such interactions have been reported, for example, in the structures of polyglycine I1 (Krimm et al., 1968) and collagen (Ramachandran & Chandrasekaran, 1968). The hydrogen bonds in general are nonlinear with bond lengths varying from 2.8 to 3.2 A in all the double-helices given in Tables 2 and 3. The NHAN 0 angle is generally over lo', but never exceeds 35'. These hydrogen bonds are slightly slanted, i.e. not parallel to the helix-axis. This is more pronounced in parallel double-helices as can be seen from the perspective diagrams of the models for A4 and P4 shown in Fig. 2. These trends are very similar to observations in single-helices of polyLD-peptides (Ramachandran & Chandrasekaran, 1972).
- -
---
136
While our energy calculations were in progress, Lotz et al. (1976) published doublehelical models for poly(ybenzy1-DL-glutamate from X-ray and electron diffraction studies. In an earlier paper Heitz et al. (1975) also reported possible single-helices for the same polymer using similar studies. It is in fact remarkable that this polymer can adopt any one of the various single- or double-helical models that have been proposed from the0 retical analysis of our own and those of Ramachandran & Chandrasekaran (1972) and from experimental studies of Lotz el al. (1976) and Veatch et al. (1974). In Table 3 of Lotz et al. (1976) are presented the coordinates of their double-helical models. Making use of the procedure suggested by them, we generated the duplex-chain in order to analyse the hydrogen bond interactions. But in none of the models could we find satisfactory interstrand
-130 -130 -125 -120 -120 -115
-147 -147 -145 -145 -145
P,
',P
144 148 144 146 152
125 130 135 i40 135 125
$t
157 151 155 155 147
175 170 170 160 170 175
OD
3.56 3.52 3.51 3.58 3.55
2.67 2.68 2.88 2.82 2.78 2.78
- 85 - 85 -100 -100 -100 -105
-106 -104 -106 -108 -106
n
$D
2.92 2.88 2.89 2.93 2.88
3.96 3.99 4.01 3.97 4.14 3.91
h(A)
Helical parameters
-28.3 -27.2 -26.5 -28.9 -27.5
-44.7 -46.0 -54.7 -53.0 -50.6 -50.5
AO(")'
4.38 4.30 4.32 4.40 4.33
3.97 3.97 4.01 3.94 4.13 3.89
Az(A)'
3.18 3.10 3.10 3.18 3.10
3.00 3.00 3.10 2.95 3.16 2.81
N - . - O (A)
(1)
30.5 32.7 31.5 28.0 30.3
32.0 30.6 15.2 14.5 22.2 17.9
NHhNO(O)
N
(2)
3.00 2.83 2.84 3.02 2.87
2.91 2.81 3.15 2.83 2.98 3.08
- - -0(A)
Hydrogen bond parameters
21.7 20.5 19.5 21.5 23.0
33.7 27.0 22.5 17.0 19.4 29.1
NHANO(")
-19.8 -20.4 -20.9 -19.7b -20.1
-20.1 -21.0 -20.7 -23.3b -21.6 -21.2
kcal/mol/ LD unit
Total energy
* The coordinates of the repeating unit LkDk (Fig. 1) in the second strand are given by (r, 8 + A8, z + Az) where (r, 8 , z) are the cylindrical polar coordinates of the repeating unit L, D, of the first strand. These are conformations whose helical parameters are close to those determined from X-ray diffractograms of poly(y-benzyl-LD-glutamate) (Lotz etal., 1976). Calculations are done at 2" interval.
-
OL
Type
angles (")
Conformational
TABLE 3 Conformational angles and characteristics of low energy structures of parallel double-helices of poly-LD-alanine
U
4 3
5
~
41
: el m
F z
C
0
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
NH
---
0 hydrogen bonds for the listed values of P and 7. However, all of them show the presence of good hydrogen bonds with our A9 and Az values appropriate for each type. The experimental results of Lotz et al. (1976) are extremely appealing. These authors have demonstrated that heat treatment, followed by solvent conditions, are the major determining factors which dictate the type of double-helix amenable for poly(y-benzyl-DLglutamate). Although our energy calculations are for poly-LD-alanine, our results can be extended to polymers with longer side chains as well, for we believe that the conformation of side chains will have little influence on backbone geometry. The energies of doublehelical conformations of poly-LD-Ala (in Tables 2 and 3) corresponding to the experimentally determined helical parameters of poly(y-benzyl-LD-glutamate) (Lotz et al., 1976) are nearly the same (-23 kcal/mol/LD unit). Hence, the transformation from one form to the other can take place easily. It is thus not the least surprising that poly(ybenzyl-LD-glutamate) is able to exist in different double-helical forms (Lotz et al., 1976) depending mainly on the size of the solvent molecules.
ACKNOWLEDGEMENTS The authors thank Professor G.N. Ramachandran for his keen interest. This work was supported by the Science and Engineering Research Council of the Department of Science and Technology, Government of India.
138
REFERENCES Heitz, F., Lotz, B. & Spach, G. (1975) J. Mol. Biol. 9291-13 Hesselink, F.T. & Scheraga, H.A. (1972) Macromolecules 5,455-463 IUPAC-IUB Commission on Biochemical Nomenclature (1970) Biochemistry 9,3471-3478 Krimm, S . , Kuroiwa, K. & Rebare, T. (1968) in Conformation of Biopolymers (Ramachandran, G.N., ed.), vol. 2, pp. 439-448, Academic Press, New Y ork Lotz, B., Colonna-Cesari, F., Heitz, F. & Spach, G. (1976) J. Mol. Biol. 106,915-942 Ramachandran, G.N. & Chandrasekaran, R. (1968) Biopolymers 6,1649-1658 Ramachandran, G.N. & Sasisekharan, V. (1968) Advan. Protein Chem. 23,283-437 Ramachandran, G.N., Chandrasekaran, R. & Chidambaram, R. (1971) Roc. Ind. Acod. Sci. A74, 270-283 Ramachandran, G.N. & Chandrasekaran, R. (1972) Ind. J. Biochem. Biophys. 9,1-11 Urry, D.W. (1972) R o c . Notl. Acod. Sci UXA. 69, 1610-1614 Veatch, W.R., Fossel, E.T. & Blout, E.R. (1974) Biochemistry 13,5249-5256
Address: R. Chandrosehran Molecular Biophysics Unit Indian Institute of Science Bangalore 560012 India
CONFORMATION O F POLYPEPTIDE CHAINS CONTAINING BOTH L- A N D D - R E S I D U E S 11. Double-Helical Structures of Poly-LD-Peptides B. V. VENKATRAM PRASAD and R. CHANDRASEKARAN
Molecular Biophysics Unit, Indian Institute of Science, Bangalore, India
Received 1 January, accepted for publication 4 March 1977 Polypeptides with alternating L - and D-amino acid residues can take up stereochemically satisfactory coaxial double-helical structures, both antiparallel and * 0 hydrogen parallel, which are stabilized by systematic interchain NH bonds. Semiempirical energy calculations over allowed regions of conformational space have yielded the characteristics of these double-helices. There are four possible types o f antiparallel double-helices - A3, A4, A5 and A g , with n. the number of L D peptide units per turn, around 2.8, 3.6, 4.5 and 5.5 respectively, while for the parallel double-helices there are two types, P3 and Pq, having similar helical parameters as in A 3 and A 4 . The hydrogen-bonding scheme restricts the pitch in all the models t o the narrow range o f 10.0 to 11.5 .k All these helices have large central cores whose radii increase proportionately with n In this respect, A 3 and A4 are suitable models for the structure o f gramicidin A. In terms o f their relative energies, antiparallel double-helices are marginally more stable than those with parallel strands. Our results indicate that the energy differences amongst the members in the antiparallel family are not significant and thus provide an explanation for the polymorphism reported for poly(ybenzyl-t D-ghtamate).
--
Several single-helical models for polypeptides with alternating L- and D-amino acid residues, which we may call poly-LDpeptides henceforth, have been proposed on the basis of conformational analysis (Ramachandran & Chandrasekaran, 1972; Hesselink & Scheraga, 1972; Urry, 1972). These helices were considered to be possible structures for the natural ion carrier gramicidin A, a linear pentadecapeptide in which L- and D-residues alternate. All of them, stabilized by regular NH . . . 0 Contribution No. 93 from the Molecular Biophysics Unit, Indian Institute of Science, Bangalore.
hydrogen bonds, display the successive carbony1 groups pointing in opposite directions relative to the helix-axis. Rarnachandran & Chandrasekaran (1972) predicted the LD4phelix (reD or g,3 according to Urry) to be a suitable structure for gramicidin A. And indeed, based on his niD-model and supported by specific conductance measurements and spectroscopic studies, Urry could explain the functioning of gramicidin A as a transmembrane channel, spanning the bilipid layer of biornembranes (Urry, 1972). Moreover, Heitz er al. (1975) have shown from X-ray and electron diffraction experiments that poly(y129
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
benzyl-LD-glutamate) can adopt any one of these helical models. Recently, for the first time, Veatch et al. (1974) from spectroscopic and chemical studies on gramicidin A, have suggested novel double-helices as alternatives for poly-LDpeptides. Until then, double-helices were a unique feature only for polynucleotides and polysaccharides. This has prompted us to investigate in detail the stereochemically feasible and energetically favourable polyLD-peptide double-helices using empirical energy calculations.
h D j shown in Fig. 1. Accordingly, we shall designate the antiparallel models as A3, A4, AS and A6 and the parallel models as P3, Pa, P5 and P6, corresponding to j being 3, 4, 5 and 6 respectively. A large central core is a persistent feature in all these double-helices? as was also reported for single-helices (Ramachandran & Chandrasekaran, 1972). The pitch remaining almost the same in all these double-helices, as we go from types A3 through A6 (or P3 through P6) the diameter of the molecule and hence the core size increases.
DESCRIPTION OF DOUBLE-HELICES The double-helix is formed by the association of two conformationally identical poly-LDpeptide strands wound about a common helixaxis. The two chains interact through systematic NH 0 hydrogen bonds analogous to the situation in orthodox polypeptide & structures. As in the poly-LD-peptide singlehelix, successive NH(or CO) groups are oriented in opposite directions relative to the helix-axis. There are two possible modes of intertwining the two strands coaxially to form a double-helix. In one such arrangement, the strands have opposite polarities and are related by a two-fold symmetry perpendicular to the helix-axis as observed in the well-known Watson-Crick DNA double-helix. Alternatively, the polarities of the strands can be retained to be the same. These two models are referred to as the antiparallel and parallel double-helices respectively. Hydrogen bonds are formed systematically, always between the L-residues in one strand and the D-residues in the other and vice versa in the former model, while they are only between like residues (L to L and D to D) in the latter. The details of the hydrogenbonding scheme are illustrated in Fig. 1. The very nature of this pattern is reminiscent of the &sheet polypeptide structures. This constrains the pitch of the helix to vary only within a narrow range of about 10.0 to 11.5.4. Model building shows that double-helices with this type of hydrogen-bonding scheme can be constructed for four different values of j, namely 3, 4, 5 and 6, for the repeating unit
---
130
FIGURE 1 : Schematic representations of the double-helix of polyLD-peptide. The interchain NH * * * 0 = C hydrogen bonds are shown by dotted lines. a) In the antiparallel, double-helix, hydrogen bonds are formed only between L and D peptide units. The four types A,, A,, A, and A, correspond to j = 3, 4, 5 and 6 respectively. Note that the hydrogen bonds marked 1 and 2 are equal and so are 3 and 4 because of dyad symmetry. b) In the parallel double-helix, the two strands are linked by hydrogen bonds - L to L and D to D. The two possible types P, and P, have j = 3 and 4 respectively.
COMPUTER MODEL BUILDING AND ENERGY CALCULATIONS In a poly-LD-peptide helical structure, the1 repeating unit is a pair of mns peptide units associated with an L- and a D-a-carbon atom' denoted by, say, L1 and D1. The successive units L2D2, L3D3, etc. in Fig. 1 can be gener-
L
w
e
*D
4.5
3.0
2.6 to 2.9
-28.8
-75 to -110
Range of axial rise per repeating unit.
5.5
4.0
3.35 to 3.65
-23.7
-95 to -125
100 to 180
100 to 180
QD
130 to 180
100 to 180
100 to 180
*L
6.5
5.0
4.35 to 4.65
-24.0
-130 to -145
130 to 180
-145 to -130
-160 to -125
7.5
6.0
5.40 to 5.60
-24.4
-180
-130 to
150 to 180
140 to 180
-165 to -155
Double-helices
-145 to -115
~
@L
* Ramachandran & Chandrasekaran (1972).
(outer radius)
C@atom in A
Mean radius of the helix for CQ atom in A (inner radius)
Range of n (Pitch: 10.0 to 11.5 A for doublehelices)
Lowest energy kcal/mol/LD unit
Allowed regions of conformational angles (")
Characteristics
~~
4.5
3.0
2.60 to 2.90
-23.3
5.5
4.0
3.35 to 3.65
-20.9
-110 to 100
145 to 160
160 to 180 -85 to -105
140 to 150
-150 to -140
120 to 140
-130 to -115
~~
4.0
2.8
2.24 to 2.31 (2.38 to 2.44)b
-19.4
-65 to -85
110 to 130
115
100 to
-100 to -80
5.4
3.9
3.12 to 3.17 (1.54 to l.58)b
-17.9
to
6.5
5.0
4.09 to 4.14 (1.16 to 1.20)b
-14.2
-142 to -148
132to 142
140 to 152 -124 -134
144 to 152
-128t0 -120 112 to 124
-112 to -102
Single-helices*
TABLE 1 Summary o f the relevant fentures of the double-helices (present study) and single helice? of ply-LDalanine
E
$
?5 6 2
%
v)
C
m
sr
0
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
ated from this by helix symmetry. This helix is then described by the two pairs of dihedral angles (@L, $L) and (@D, J / D ) which repeat themselves regularly. The conformational angles are defined following the rules of IUPAC-IUB Commission (1 970). The method of generating the double-helix involves two major steps. First of all, the coordinates (r, 8, z) of the repeating unit LIDl of the first chain for given (@L, J/L) and (GD, $D) are computed in the helical system whose x-axis passes through the first a-carbon atom, using the general matrix method (Ramachandran & Sasisekharan, 1968) and the helical parameters n and h are evaluated. The standard dimensions of the rruns planar peptide unit are used in the calculations. Throughout the analysis, the angle T(=N-C"-C) is maintained at the expected value of 110'. If the helical parameters are within the prescribed range amenable for the formation of required interchain hydrogen bonds, coordinates of additional peptide units spanning more than a turn of the helix are computed. Now the stage is set up for the interspersing of the second chain to create the double-helix - either antiparallel or parallel and the second step is as follows. For the antiparallel model, the repeating unit LkDk of the second coaxial strand of opposite polarity is generated by a rotation of 180" about the x-axis of the helical system from the corresponding coordinates of L1D1. It is further aligned with respect to the first chain by a rotation A0 about, and a translation Az along, the helix-axis (z-axis) in order that the four hydrogen bonds, two with LIDl and two with LjDj are formed as shown in Fig. la. The LkDk coordinates are then given by (r, -0 + AO, -z Az). Thus the repeating units LIDl and LkDk of the two strands are related by the dyad perpendicular to the helix-axis passing through (0, A8/2, Az/2). Also LjDj and LkDk are related by a similar dyad arising from the symmetry of the helix. Hence hydrogen bonds 1 and 2, and likewise 3 and 4, in Fig. l a are equivalent. Finer adjustments of A8 and Az, however, enable us to make 1 and 3, and so 2 and 4, very nearly equal, In the case of the parallel model, the pro-
+
132
cedure is virtually the same, excepting that the dyad symmetry does not exist. Consequently, the LkDk coordinates of the second coaxial strand (Fig. l b ) are computed as (r, O Ad, z + Az). The four hydrogen bonds here are quite independent of each other, but yet and 3 can be made nearly equivalent, and so, also 2 and 4, by a suitable choice of AO and Az values. For the double-helix having satisfactory hydrogen bonds, 12 peptide units in each1 strand with alanine side group (methyl h y d r q gens in staggered positions) at every a-carbon atom alternately in L- and D-configurations have been considered in the energy calculations. Non-bonded and electrostatic interactions and torsional potentials have been taken into account following the method of Ramachai dran & Sasisekharan (1968). Hydrogen bw energies have been evaluated using the potenti; function formulated by Ramachandran et al. (1971). Energy contributions from all those interactions arising from the repeating unit LIDl within itself and with the rest of the units in the double-helix have been summe up to get the total energy per LD unit o f t e double-helix. For the different types of double-helices (with j = 3, 4, 5 and 6 , as already mentioned7 the number of repeating units (n) per turn isapproximately 2.5, 3.5, 4.5 and 5.5 respectively. In the computational analysis, the ranges of n have therefore been centred around these values with suitable deviations on either side sE that none of the stereochemically acceptable, models have escaped our attention. The search has been made in the entire allowed conformational space by varying the four rotation angles generally at intervals of '5 and, in some instances at smaller intervals when necessary. The combination of (GL, $L) and (@D, $D) which produces rights handed helices alone has been analysed as the properties of these helices are implicitly related to the left-handed helices. This followa from the well-known fact that the inverse combination (-@L, -$L) and (-@D, I)$) for the DL-sequence leads to isoenergetic lef& handed helices. These two forms are mirror images of each other.
+
8
DOUBLE-HELICES OF POLY-LD-PEPTIDES
RESULTS AND DISCUSSION Poly-LD-peptides have large conformational possibilities viz., double-helices presently being discussed and single-helices previously reported '(Ramachandran & Chandrasekaran, 1972; Hesselink & Scheraga, 1972; Urry, 1972; Heitz et ul., 1975). Our computer model building a n d energy calculations have revealed the major features of these novel double-helices for poly-LD-peptides. The summary of these (features is given in Table 1 which also contains for comparison the important features of bhe single-helices as given by Ramachandran & Chandrasekaran (1972). A specific common feature, as can be seen from the mean radial coordinates of the CYcarbon atoms corresponding to the inner radius 'of the double-helical models, is that all of them, ke single-helices, possess large central cores ( able 1). Their sizes, by virtue of the hydrogen-bonding pattern as described earlier, increase from A3 t o A6 (or P3 to P6) in that order from 3.0A to 6.0A. The core sizes of the double-helices A3 and A4 (or P3 and P4) are comparable to those of single-helices LD3p and 4;D4p respectively (Ramachandran & Chandrasekaran, 1972) and hence, A3 and A4, which are more energetically favourable than P3 and P4, are the expected models which can be correlated to the structure of gramicidin A in its ability to function as conductor of ions like Li, Na, K, Rb and Cs in biological systems. As mentioned already, the hydrogenbpnding network in these double-helical structures is very similar to conventional &structures of polypeptides with all L- or all D-residues. In fact, we can imagine the double-helices as being generated by wrapping two strands of a &structure around a cylinder so that its surface is lined with NH 0 = C groups. This may bk a pertinent factor in the functioning of gramicidin A. As a consequence, the conduction of an ion through the channel may be more prompted by dipolar interactions rather than van der Wads type of interactions. Another important feature of these structures is that the Ca-Cp bonds stick out of the cylinder and are almost perpendicular to the helix-axis as in single-helix models (Ramachandran & Chandrasekaran, 1972). Therefore, in gramicidin A, whether it adopts a single- or
$
---
double-helical structure, the hydrophobic side chains may not have a major role in ion conduction. On the contrary, they may shield the hydrogen-bonded network from external disturbances and thus protect the channel in the helix from being disrupted. The detailed conformational properties of the antiparallel and parallel double-helices of poly-LD-alanine are listed in Tables 2 and 3. These include, in addition to $, J/ and n, h values, the hydrogen bond lengths and angles and the parameters A0 and Az. In the last column the total energy, including that of hydrogen bonds, is given. In the antiparallel double-helical models listed in Table 2, the energy ranges from -21 to -29 kcal/mol/LD unit. The important observation here is, for A3 and A4, as q5L decreases, the corresponding J/,, increases in magnitude. Consequently, the more the difference in magnitude between these two, the larger is the number of sterically allowed conformations. On the other hand, for the other two types A5 and A6, the GL, difference is very small and therefore the number of conformations is also small. For the parallel double-helices, only two types, P3 and P4 with helical parameters similar as in A3 and &, are found feasible (listed in Table 3). Due to severe short contacts between the two strands, the P5 and P6 models cannot be generated. The energies of P3 and P4 are, however, higher than for the antiparallel counterparts and range from -19 to -23 kcal/mol/LD unit. The number of allowed conformations listed in Table 3 are indeed fewer than in the corresponding antiparallel cases. This is mainly due to difficulty encountered in making two satisfactory interchain hydrogen bonds for each repeating unit. The distribution of rotational angles is very similar to the behaviour of the antiparallel models mentioned earlier. Stereochemically satisfactory double-helical models with antiparallel chains could be built without any short contacts. However, for the parallel double-helices, a few short contacts were encountered in the model building for some conformations listed in Table 3. These short contacts range from 2.0 to 2.2 A between an Ha in one strand and a carbonyl oxygen just ,
133
P
w
c
*L
180 145 140 165 155 135 130 150 165 145 170 135 140
145 155 145 140 145 165 165 170 140 145 160 170 140 155 135 145
@L
-145 -140 -135 -135 -130 -130 -125 -125 -120 -120 -120 -115 -115
-160 -155 -150 -145 -145 -145 -145 -145 -140 -140 -140 -140 -135 -135 -130 -130
TYP@
A3
A4
2.93 2.82 2.81 2.88 2.86 2.80 2.80 2.85 2.63 2.84 2.73 2.89 2.83 3.58 3.37 3.61 3.60 3.35 3.59 3.45 3.62 3.62 3.37 3.58 3.64 3.64 3.57 3.63 3.54
- 75 - 80 - 85 - 85 - 90 - 90 - 95 - 95 - 85 -100 - 90 -110 -105
95 - 90 -105 -110 -100 -105 -100 -105 -115 -105 -110 -110 -120 -115 -125 -120
115 150 155 135 145 160 165 150 135 155 130 170 160
155 145 155 160 155 135 135 130 160 155 140 130 160 145 165 155 -
n
*D
2.75 3.14 2.77 2.79 3.17 2.92 3.11 2.89 2.81 3.19 2.97 2.91 2.85 3.02 2.87 3.07
3.53 3.70 3.70 3.89 3.93 3.70 3.69 3.96 4.25 3.98 4.13 4.07 3.99
h (A)
Helical parameters
@D
Conformational angles (")
85.5 84.3 79.6 78.3 80.6 76.0 79.4 72.7 74.6 78.7 73.5 74.0 67.1 69.8 70.0 66.2
101.6 99.5 94.6 91.8 87.8 93.5 89.1 86.4 94.7 82.6 89.6 69.3 76.5
A0 (o)a
-23.0 -22.3 -22.6 -2 1.9 -21.1 -23.3b -21.5 -23.1 -21.8 -20.2 -22.8b -21.3 -22.1 -22.3 -20.7 -21.8
29.5 21.8 24.8 25.0 24.5 9.1 12.5 8.7 22.0 22.4 7.4 14.6 16.2 6.0 20.0 9.9 3.07 3.14 3.00 2.95 3.10 3.00 3.12 3.02 2.94 3.11 2.99 3.06 2.9 2.99 2.95 3.00 7.99 8.32 8.01 8.02 8.38 8.12 8.37 8.04 8.02 8.44 8.16 8.20 7.92 8.17 8.08 8.17
-28.9 -24.2 -23.4 -26.4 -25.2 -21.3 -20.0 -23.5 -26.6 -22.3b -25.8 -20.4 -22.2b
28.6 32.6 31.8 20.5 20.3 34.3 34.3 22.5 21.5 22.2 18.3 24.3 20.1 2.94 2.95 2.87 2.93 2.89 2.87 2.81 2.88 2.84 2.84 2.81 3.05 2.80
8.36 8.53 8.44 8.69 8.68 8.48 8.4 1 8.73 8.86 8.71 8.74 8.94 8.62
kcal/mol/LD unit
Total energy
NHhNO(")
N * **O(A)
Az(A)~
Hydrogen bond parameters
TABLE 2 Conformational angles and characteristics of low energy structures of antiparallel double-helices of poly-LDalanine
*2
w
>
m 6
U 9
*z
0 3.
z P
>
U
g
P
+8
%
P
4
6
*
$ z
5
m
-165 -163 -161 -160 -159 -157 -155
-135 -130
-135
145
155
151 149 149 155 157
145 150 160 170 140 165 140
-140 -140 -140 -140
165 167 167 160 157 159 170
160 155 145 135 165 140 165
165 170
-130 -134 -136 -135 -134 -136 -140
-130 -140 -140 -145
-135
-135 -135
-130 -125
5.40 5.44
5.41
5.45 5.57 5.59 5.52
4.38 4.43 4.51 4.37 4.37 4.58 4.40
3.65 3.47
1.86 1.75 1.76 1.79 1.82 1.85 1.87
2.28 2.28 2.23 2.41 2.33 2.25 2.39
2.92 3.07
Helical parameters
52.2 45.9 45.2 47.1 53.1 54.5 53.9
58.5 54.2 58.5 62.1 58.4 50.9 58.9
62.8 63.8
7.54 7.19 7.27 7.23 7.36 7.49 7.69
7.50 7.40 7.42 8.03 7.68 7.52 7.89
8.00 8.15
16,3 22,4 21.5 15.4 8.8 9.8 16.8
12S 18.4 11.0
2.96 3.07 3.08 3.16 3.08 3.14 3.04 2.96 3.03 3.18
10.6 12,o 11.2 15.0
14.6 20.0
2.86 2.90 2.91 3.18
2.95 3.03
Hydrogen bond parameters
-21.lb -23.6 -22.1 -24.4 -24.3 -22.3 --18.7b
-22.3 -21.5 -19.3
-23.6 -24.1 -23.8b -17.6
-20.8
-21.8b
Total energy
a The
coordinates of the repeating unit LkDk (Fig. 1) in the second strand are given by (I, -8 + AO, -z + Az) where (I, 8 , z) are the cylindrical polar coordinates of the repeating unit L, D; of the first strand. These are the conformations whose helical parameters are close to those determined from X-ray diffractograms of poly(7-benzyl-LD-glutamate) (Lotz er al., 1976). The calculations are done at 2" interval.
A9
A,
135 130
-125 -125
Conformational angles (")
TABLE 2 (continued)
v1
m
U
z%
?
?
2
$!
j: m
! i m
8
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
FIGURE 2: Perspective drawing of the double-helix (a) antiparallel model A, and (b) the corresponding parallel model P,, viewed perpendicular to the helixaxis. The hydrogen bonds are indicated by dashed lines. The acarbon atoms in the L- and &configurations are denoted by L and D respectively. Smail circle for hydrogen, medium circle for carbon, striated medium circle for nitrogen and large circle for oxygen.
above it in the other strand. The orientations of the Ca-Ha bonds and the carbonyl groups are suggestive of possible weak CH * 0 hydrogen bonds. Such interactions have been reported, for example, in the structures of polyglycine I1 (Krimm et al., 1968) and collagen (Ramachandran & Chandrasekaran, 1968). The hydrogen bonds in general are nonlinear with bond lengths varying from 2.8 to 3.2 A in all the double-helices given in Tables 2 and 3. The NHAN 0 angle is generally over lo', but never exceeds 35'. These hydrogen bonds are slightly slanted, i.e. not parallel to the helix-axis. This is more pronounced in parallel double-helices as can be seen from the perspective diagrams of the models for A4 and P4 shown in Fig. 2. These trends are very similar to observations in single-helices of polyLD-peptides (Ramachandran & Chandrasekaran, 1972).
- -
---
136
While our energy calculations were in progress, Lotz et al. (1976) published doublehelical models for poly(ybenzy1-DL-glutamate from X-ray and electron diffraction studies. In an earlier paper Heitz et al. (1975) also reported possible single-helices for the same polymer using similar studies. It is in fact remarkable that this polymer can adopt any one of the various single- or double-helical models that have been proposed from the0 retical analysis of our own and those of Ramachandran & Chandrasekaran (1972) and from experimental studies of Lotz el al. (1976) and Veatch et al. (1974). In Table 3 of Lotz et al. (1976) are presented the coordinates of their double-helical models. Making use of the procedure suggested by them, we generated the duplex-chain in order to analyse the hydrogen bond interactions. But in none of the models could we find satisfactory interstrand
-130 -130 -125 -120 -120 -115
-147 -147 -145 -145 -145
P,
',P
144 148 144 146 152
125 130 135 i40 135 125
$t
157 151 155 155 147
175 170 170 160 170 175
OD
3.56 3.52 3.51 3.58 3.55
2.67 2.68 2.88 2.82 2.78 2.78
- 85 - 85 -100 -100 -100 -105
-106 -104 -106 -108 -106
n
$D
2.92 2.88 2.89 2.93 2.88
3.96 3.99 4.01 3.97 4.14 3.91
h(A)
Helical parameters
-28.3 -27.2 -26.5 -28.9 -27.5
-44.7 -46.0 -54.7 -53.0 -50.6 -50.5
AO(")'
4.38 4.30 4.32 4.40 4.33
3.97 3.97 4.01 3.94 4.13 3.89
Az(A)'
3.18 3.10 3.10 3.18 3.10
3.00 3.00 3.10 2.95 3.16 2.81
N - . - O (A)
(1)
30.5 32.7 31.5 28.0 30.3
32.0 30.6 15.2 14.5 22.2 17.9
NHhNO(O)
N
(2)
3.00 2.83 2.84 3.02 2.87
2.91 2.81 3.15 2.83 2.98 3.08
- - -0(A)
Hydrogen bond parameters
21.7 20.5 19.5 21.5 23.0
33.7 27.0 22.5 17.0 19.4 29.1
NHANO(")
-19.8 -20.4 -20.9 -19.7b -20.1
-20.1 -21.0 -20.7 -23.3b -21.6 -21.2
kcal/mol/ LD unit
Total energy
* The coordinates of the repeating unit LkDk (Fig. 1) in the second strand are given by (r, 8 + A8, z + Az) where (r, 8 , z) are the cylindrical polar coordinates of the repeating unit L, D, of the first strand. These are conformations whose helical parameters are close to those determined from X-ray diffractograms of poly(y-benzyl-LD-glutamate) (Lotz etal., 1976). Calculations are done at 2" interval.
-
OL
Type
angles (")
Conformational
TABLE 3 Conformational angles and characteristics of low energy structures of parallel double-helices of poly-LD-alanine
U
4 3
5
~
41
: el m
F z
C
0
B.V. VENKATRAM PRASAD AND R. CHANDRASEKARAN
NH
---
0 hydrogen bonds for the listed values of P and 7. However, all of them show the presence of good hydrogen bonds with our A9 and Az values appropriate for each type. The experimental results of Lotz et al. (1976) are extremely appealing. These authors have demonstrated that heat treatment, followed by solvent conditions, are the major determining factors which dictate the type of double-helix amenable for poly(y-benzyl-DLglutamate). Although our energy calculations are for poly-LD-alanine, our results can be extended to polymers with longer side chains as well, for we believe that the conformation of side chains will have little influence on backbone geometry. The energies of doublehelical conformations of poly-LD-Ala (in Tables 2 and 3) corresponding to the experimentally determined helical parameters of poly(y-benzyl-LD-glutamate) (Lotz et al., 1976) are nearly the same (-23 kcal/mol/LD unit). Hence, the transformation from one form to the other can take place easily. It is thus not the least surprising that poly(ybenzyl-LD-glutamate) is able to exist in different double-helical forms (Lotz et al., 1976) depending mainly on the size of the solvent molecules.
ACKNOWLEDGEMENTS The authors thank Professor G.N. Ramachandran for his keen interest. This work was supported by the Science and Engineering Research Council of the Department of Science and Technology, Government of India.
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Address: R. Chandrosehran Molecular Biophysics Unit Indian Institute of Science Bangalore 560012 India
