Conformation in Fibrous Proteins and Related Synthetic Polypeptides || The Alpha Helix

Chapter 9

The Alpha Helix

A. INTRODUCTION

Following the discovery of the α-helix (Pauling and Corey, 1950, 1951a; Pauling et al.y 1951) it was soon established that the overall distribution of intensity in the diffraction patterns of certain synthetic polypeptides was consistent with the presence of such a helix (Pauling and Corey, 1951b; Perutz, 1951a; Cochran et al.y 1952; Bamford et al.y

1952, 1954). As originally described, the α-helix embraced two distinct structures for residues other than glycine, and for L-amino acids these correspond either to a right-handed or to a left-handed helix. Early studies of synthetic polypeptides (Yakel et al.y 1952; Brown and Trotter, 1956) and proteins (Riley and Arndt, 1952) were held to favor the left-handed alternative, but Huggins (1952) pointed out that the distance between the C/ and O atoms in the same residue was only 2.64 A in the left-handed helix whereas no significant steric hindrance occurred in the right-handed alternative. It was concluded that the right-handed α-helix would be the more stable for amino acid residues with the L-configuration. This prediction has been largely borne out by subsequent studies. Confirmation of the occurrence of the α-helix in proteins was obtained in the 2-A Fourier synthesis of myoglobin calculated by Kendrew et al. (1960) and the screw sense was found to be right-handed in all the helical sections of the molecule.

If values are assumed for the bond angles and distances in the amide group and for r(N, Ca, C), the formulas given by Sugeta and Miyazawa (1967) can be used to generate atomic coordinates for the α-helix relative

179

180 9. THE ALPHA HELIX

Ζ

FIG . 9.1. The α-helical conformation of the polypeptide chain (Pauling and Corey, 1951a). Systematic hydrogen bonds of the type N tH t- - -O t_ 4 are formed.

to the helix axis for any permissible combination of unit height h and unit twist t. If the disposition of the bonds around Ο is assumed to be tetrahedral, that is, r(N, O , C ) = 109.47°, and the amide group is assumed to be planar and to have the "standard" dimensions given in Table 6.1, the coordinates of a "standard" α-helix with h = 1.5 A and

Β. DIFFRACTION STUDIES 181

t = 100° can be calculated. This helix is illustrated in Fig. 9.1 and the coordinates are given in Table 9.1 (Parry and Suzuki, 1969a).

TABLE 9.1

Atomic Coordinates of an L-Residue in a Right-Handed a-Helixa

Atom X y ζ r Φ (A) (A) (A) (A) (deg)

Ν 1.360 - 0 . 7 4 4 - 0 . 8 7 3 1.550 - 2 8 . 6 9 Η 1.485 - 0 . 5 5 9 - 1 . 8 4 7 1.586 - 2 0 . 6 3 C

a 2.280 0 0 2.280 0

&H

a 2.989 - 0 . 6 9 9 0.467 3.069 - 1 3 . 1 7

&c* 3.049 1.029 - 0 . 8 3 0 3.218 18.65 c 1.480 0.718 1.089 1.645 25.88 ο 1.765 0.579 2.288 1.858 18.15

° Unit height h = 1.5 A, unit twist t = 100°, r(N, C° 109.47°, and the "standard" planar amide-group geometry, the dimensions of which are given in Table 6.1. Other helix parameters are: axial period c = 27.0 A, pitch Ρ = 5.4 Α, φ — —51.45°, φ = —52.74°, ω = 180°, u = 18 residues in ν = 5 turns.

b Calculated assuming a tetrahedral distribution of bonds around C

a and b(C

a, H

a) =

1.1 A, &(Ca,C*) = 1.53 A.

In this chapter information which has been obtained on the α-helix from studies of ordered aggregates of synthetic polypeptides is reviewed in Sections Β and C and factors affecting the sense and geometry of the helix are considered in Section D. A discussion of the stability of the α-helix in relation to other conformations and the effects of composition and sequence on stability will be reserved for Chapter 12.

B. DIFFRACTION STUDIES

I. POLY(L-ALANINE)

Oriented specimens of [Ala]n in which the majority of the polymer has an α-helical conformation can be prepared by stretching spun fibers (Elliott, 1967). The X-ray diffraction pattern of such specimens was examined in detail by Brown and Trotter (1956) and a plot of the observed data in reciprocal space coordinates (Chapter 1, Section A.I.g) is shown in Fig. 9.2. The pattern consists mainly of sharp reflections characteristic of a three-dimensionally ordered structure (Chapter 1, Section A.I.e) but streaks are present on certain layer lines. The layer lines can be indexed on an axial period of c = 70.3 A and the sharp


60

55 52

42 39

34 31 29

26

21

18 16

13

s J

k t

i (

v Γ

• • <

\ f

/ t \ t k A k

<

\

\ 4

f \

\

r \

\ 4

r

k r \

f \

\ Γ

\ 4 \ 4 k f

(

' \ f

Κ > \ * ί: ι ι Κ

ι *

>—< γ

( ι *

>—< * S ) V

k * \ t κ * \ \ *

ψ \. \ *

V V κ

τ r—ν

< > < τ '

ι ο—< < Μ Η 10 11 20 21 30 2231 40 32 41 Hk

F I G . 9 . 2 . X-ray diffraction data obtained from the α form of [Ala]n . The pattern consists of discrete reflections (circles) together with layer-line streaks. The discrete reflections can be indexed on a hexagonal unit cell with a = 8 . 5 5 A and c = 7 0 . 3 A. (Redrawn from Brown and Trotter, 1956 . )

reflections fall on a set of vertical row lines which can be indexed on a hexagonal unit cell of side a = 8.55 A.

No evidence for a larger cell could be found and since the cross-sectional area of the cell perpendicular to the fiber axis was close to that expected for a single chain in the α-helical conformation, Brown and Trotter attempted to interpret the pattern in terms of a crystallite in which the repeating unit was a section of α-helix of length 70.3 A. This implied that all the chains in a crystallite had the same direction as regards the main-chain sequence —NH—CHR—CO—.

(i) Helical Parameters. From the theory of diffraction by helical structures (Chapter 1, Section A.III) the α-helix would be expected to produce a pattern consisting of a set of layer lines spaced about 1/5.4 A - 1

apart, centered on the origin, and similar sets centered on


a series of meridional reflections spaced about 1/1.5 A - 1 apart. The observed pattern can in fact be interpreted in these terms, which are summarized in the selection rule for Bessel function orders η contributing to a layer line (Chapter 1, Section A.III.b)

I = urn + vn (9.1)

where / is the layer-line index, u is the number of residues and ν is the number of turns in the repeat distance c> and m is an integer.

The only Bessel functions that can give rise to meridional reflections are those of order η = 0 (Fig. 1.10a) and since the meridional reflection of spacing about 1.5 A - 1, corresponding to m = ±1 , occurs on / = 47 (Fig. 9.2), the value of u must be 47. The first layer line of the origin set, corresponding to m = 0 and w = ±1 , has an index / = 13, and so from Eq. (9.1), ν = ±13. Thus it was concluded that a helix with u = 47 and ν = ±13 was present in the α-form of [Ala]n and since c = 70.3 A the unit height h = 70.3/47 = 1.496 A, the pitch Ρ = ±70.3/13 = ±5.41 A, and the unit twist t = ±360 X 13/47 = ±99.6°.

From the coordinates given in Table 9.1 it can be seen that the largest value of r for a nonhydrogen atom in the α-helical form of poly(L-alanine) is likely to be about 3.2 A. The observed data extend to R ~ 0.6 A

- 1 and so the maximum value of 2TTRT ~ 12. From Eq. (1.29) and Fig. 1.10 it can be seen that Bessel functions of order I η I > ~ 8 are unlikely to make any significant contribution to the observed pattern and in fact the indices / of the layer lines on which diffraction is observed (Fig. 9.2) all correspond to values of —7 < η ^ 7 in Eq. (9.1).

(ii) Helix Sense. With the exception of the meridional reflections in the vicinity of / = 16 and 31, and the layer-line streaks, the overall form of the diffraction pattern is in substantial agreement with that predicted for a hexagonally packed arrangement of helices with u = 47 and ν = ±13. However, the intensity distribution, except on the equator, was found to be in poor agreement with that calculated for either right-handed (v = 13) or left-handed (v = —13) α-helix models (Brown and Trotter, 1956). Of the two possibilities the left-handed helix was favored. It was also suggested that the unexpected meridional reflections could be explained in terms of distortion (Chapter 1, Section A.IV.c) of the methyl side-chain groups due to unfavorable interhelical contacts and the layer-line streaks were attributed to axial and azimuthal disorder (Chapter 1, Section A.IV.d).

Elliott and Malcolm (1956b, 1958) pointed out that the type of disorder involving random axial displacements and random azimuthal


rotations was sterically impossible with a fixed interchain distance due to the bulkiness of the protruding methyl side-chain groups and suggested that a different type of disorder was present in which the chain direction, with respect to the sequence — NH—CHR—CO—*, was random (Chapter 1, Section A.IV.e). The intensities of the sharp reflections in this case depend upon the sum of the Fourier transforms of the " u p " and "down" chains, while the layer-line streaks depend upon the difference between the two Fourier transforms. This packing model was explored by means of optical transforms using an optical diffractometer and it was found that within the limitations of accuracy imposed by this method the intensities of both the sharp reflections and the layer-line streaks could be explained by a crystal model in which right-handed α-helices were arranged with random chain sense.

An important feature of the studies by Elliott and Malcolm (1958) was the fact that the agreement between the observed and calculated intensities was significantly better for the right-handed than for the left-handed model, thus supporting Huggins's suggestion as regards their relative stabilities for L-amino acid residues.

(iii) Departures from Helical Symmetry. The reasons for the appearance in the observed diffraction pattern of "forbidden" meridional reflections has been investigated in detail by Elliott and Malcolm (1958) and Johnson (1959). Plausible explanations, which have been summarized by Elliott (1967), were given for these reflections in terms of regular distortions occasioned by intermolecular steric hindrance. Strictly speaking, the values for h and t calculated earlier from u and ν and the axial repeat of structure c must be treated, in the absence of strict helical symmetry, as average values although the variation in value from residue to residue for the main-chain atoms is probably small in the case of [Ala]n .

An unfortunate feature of the disorder in chain sense which appears to exist in crystallites of the α-helical form of [Ala]n is that a Fourier synthesis would yield an image of an " u p " chain superposed on a "down" chain and so far no means has been devised for overcoming this difficulty.

(iv) Refinement of the <x-Helical Model for Poly(h-alanine). Elliott and Malcolm (1958) attempted a limited empirical refinement of the atomic coordinates given by Brown and Trotter (1956) using optical diffraction methods and found that a better fit between calculated and observed intensities could be obtained if the radial coordinate of the oxygen atom was increased to 1.98 A and that of the nitrogen atom decreased to 1.49 A (cf. Table 9.1).


Arnott and co-workers (Arnott and Wonacott, 1966a,b; Arnott and Dover, 1967; Arnott, 1968) remeasured the diffraction pattern of [Ala]w

and obtained quantitative intensity data on 61 reflections. With this amount of information it was found possible to perform a limited least squares refinement (Chapter 1, Section D; Chapter 7, Section C) in which the number of independent variables was reduced by incorporating various assumptions about the stereochemistry of the amide group. The refined values of the bond and torsion angles are listed in Table 9.2 and the atomic coordinates are given in Table 9.3. In both

TABLE 9.2

Bond and Torsion Angles in the α-Helical Conformation of Poly(L-alanine)a

[Ala]ft "Standard"* [Ala]n

Angle (deg) (deg) Angle (deg)

T ( C « , C , O ) 1 2 1 . 0 1 2 1 τ(Ν, CA, C ) 1 0 9 . 7

T ( C « , C , N ) 1 1 5 . 4 1 1 4 r(N, CA, C*) 1 0 9 . 5

T ( 0 , C , N) 1 2 3 . 6 1 2 5 r ( H « , CA, C O 1 0 9 . 4

T ( C , N , C « ) 1 2 0 . 9 1 2 3 T ( H « , CA, C*) 1 0 9 . 5

T ( C , N , H ) 1 2 3 . 0 1 2 3 r(C*, CA, C O 1 0 9 . 4

r(H, N , C « ) 116 .1 1 1 4 Φ - 5 7 . 4 ω - 1 7 9 . 8 1 8 0 Φ - 4 7 . 5

β Arnott and Dover (1967). 6 Corey and Pauling (1953a).

TABLE 9.3

Atomic Coordinates of a Residue in the α-Helical Conformation of Poly(L-alanine)a

X y ζ r Φ Atom (A) (A) (A) (A) (deg)

Ν 1.375 -0 .711 - 0 . 9 0 6 1.548 - 2 7 . 3 5 Η 1.459 - 0 . 4 9 0 - 1 . 8 7 8 1.539 - 1 8 . 5 7 C

a 2.288 0 0 2.288 0

bH

a 2.929 - 0 . 7 0 5 0.485 3.013 - 1 3 . 5 4 3.139 0.998 - 0 . 8 0 8 3.294 17.63

c 1.481 0.760 1.054 1.664 27.16 ο 1.777 0.691 2.256 1.906 21.24

a Calculated from data given by Arnott and Dover (1967). Helix parameters: unit

height h = 1.495 A, unit twist t = 99.57°, repeat of structure c = 70.3 A contains u = 43 residues in ν = 17 turns of pitch Ρ = 5.41 A.

66 ( C

a, H

a) = 1.07 A.

c&(C

a,C0) = 1.54 A.


cases these must be regarded as average values in view of the departures, mentioned earlier, from perfect helical symmetry. According to Arnott and Dover (1967), there are no intramolecular contacts in the refined model less than the "fully allowed*' values given by Ramachandran et aL (1963) and the crystal packing parameters determined from the X-ray study were shown to be close to minima in the calculated intermolecular potential energy (Arnott and Wonacott, 1966b).

(v) Single Crystals of Poly(L-alanine). Padden and Keith (1965) examined the crystalline morphology of films of [Ala]w and found that platelets with a truncated hexagonal habit and sheaves of ribbonlike crystals were present. Selected-area electron diffraction patterns obtained from the sheaves resembled those obtained from the α form using X rays, and from the spatial orientation of the reflections it was concluded that the molecular chains were oriented transversely with respect to the long axis of the sheaves. The sheaves were found to consist of platelets about 150 A thick stacked on edge and since this dimension is too small to accommodate a complete molecule in the α-helical conformation (Keith et aL, 1969a), it can be concluded that crystal reentrant folding must occur. Lamellar single crystals about 100 A in thickness in which the chains fold back and forth on themselves have been prepared from a wide variety of synthetic polymers (Geil, 1963; Mandelkern, 1964, 1970; Keller, 1968).

I I . ESTERS OF POLY(L-GLUTAMIC ACID)

a. Poly(y-methyl-L-glutamate)

Early attempts to test the α-helix model centered on the diffraction pattern obtained from [Glu(Me)]n and the overall distribution of intensity was found to be consistent with this model (Cochran et aL, 1952; Bamford et aL, 1952; Yakel et aL, 1952). Diffraction patterns showing a high degree of orientation and crystallinity have been obtained from this polymer (Bamford et aL, 1953b, 1956), but so far it has not proved possible to develop a detailed model for the conformation of the side chain and so the conformation of the main chain has not been refined in the way that proved possible for the α form of [Ala]n . A curious feature of the crystal structure of [Glu(Me)]w is that the density calculated from dimensions of the unit cell is less than the observed density (Bamford et aL, 1953b). This is the reverse of the situation normally encountered in polymeric materials where the presence of an amorphous phase of density lower than the crystalline phase leads to a macroscopic density which is less than that calculated for the crystal.


Polymorphism occurs in the α form of [Glu(Me)]n: The crystalline form originally studied was hexagonal with a unit cell edge of a = 11.95 A and an axial repeat of structure c = 103 A corresponding to a helix with u = 69 and ν = ±19 (Brown and Trotter, 1956). However, Brown (1956) obtained specimens, from a different sample by different conditions of preparation, in which the axial repeat was c = 27 A, corresponding to a helix with u = 18 and ν = ±5. Both forms exhibit "forbidden" meridional reflections with spacings of 4.32 and 4.50 A, indicating a departure from perfect helical symmetry, and as with [Ala]n this can be attributed to distortions arising from intermolecular contacts (Johnson, 1959; Elliott, 1967).

Electron diffraction patterns have been obtained from [Glu(Me)]n

(Vainshtein and Tatarinova, 1967a) and the intensity data were used to compute a Fourier synthesis of the cylindrical average of the #-axis projection of the potential. The presence of a peak between r = 1 and 2 A was consistent with the axial projection of the main-chain atoms of an α-helix. A similar result had been obtained earlier (Bamford et al., 1956) for an electron density synthesis from the X-ray data.

b. Poly(y-benzyl-L-glutamate)

The α form of [Glu(Bzl)]n has been studied extensively using both X-ray diffraction (Bamford et al, 1951a, 1956; Tomita et al., 1962; A. Elliott et al., 1965) and electron diffraction (Parsons and Martius, 1964; Vainshtein and Tatarinova, 1967a) and a plot of the observed X-ray pattern is shown in Fig. 9.3a. This differs from the patterns obtained from [Ala]n and [Glu(Me)]n in that sharp reflections are observed only on the equator, all other layer lines consisting of streaks. From the discussion of the effects of disorder on diffraction patterns given in Chapter 1, Section A.IV it seems likely that disorders of chain rotation and translation and possibly also chain direction are present in crystallites of the α form of [Glu(Bzl)]n .

(i) Helical Parameters. With the exception of the meridional arcs with Ζ ~ 0.1 and 0.2 A - 1, the observed layer lines can be indexed on an axial repeat of structure of c = 27 A, suggesting that a distorted helix with 18 residues in five turns is present. Further evidence of regular distortion is contained in the fact that intensity appears on layer lines, for example, / = 2, 4, and 6, at values of R for which the predicted value for a perfect helix with u = 18 and ν = ± 5 would be negligible.

The mean unit heights (K) in normal and iV-deutero-[Glu(Bzl)]n

were measured by Tomita et al. (1962) and values of 1.494 and


Z(AH)

(a) (b )

FIG . 9 . 3 . (a) X-ray diffraction data obtained from the α form of poly(y-benzyl-L-glutamate). Discrete reflections are found on the equator (/ = 0 ) but only streaks are observed on other layer lines. The layer lines are indexed on an axial repeat of c = 2 7 . 0 A. (b) Data obtained from a mixture of equal parts of poly(y-benzyl-L-glutamate) and poly(y-benzyl-D-glutamate). The layer-line streaks can be indexed on an axial repeat of c = 1 0 6 A. Discrete reflections are indicated by circles, sharp layer-line streaks by full lines, and diffuse streaks are dotted. (Redrawn from A. Elliott et al., 1965 . )

1.501 ± 0 . 0 0 2 A, respectively, were obtained. This change was interpreted as being due to an increase in the hydrogen bond length of 0.025 A. An increase in the mean pitch <P> of 0.027 ± 0.008 A was also observed so that the mean unit twist <£> = 360<A>/<P> was not greatly affected by the increase in hydrogen bond length.

(ii) Liquid Crystals. [Glu(Bzl)]n forms liquid crystals in various solvents (Robinson, 1966) and these have been studied by X-ray diffraction (Luzzati et al, 1961, 1962; Parry and Elliott, 1965, 1967; Saludjian and Luzzati, 1967; Traub et al, 1967; Squire and Elliott, 1969; Go et al, 1969; Samulski and Tobolsky, 1971). The nature of the ordering is a function of solvent and of polymer concentration. A so-called "cholesteric" phase is observed in w-cresol at polymer con-


centrations of about 20-36% (w/w) which is characterized by the appearance of a diffuse ring in the X-ray diffraction pattern. On the basis of the variation of the observed spacing of this ring with concentration Luzzati et al. (1961, 1962) concluded that the main chain had a conformation similar to that of the 31 0-helix (Donohue, 1953). However, Parry and Elliott (1965) and Traub et al. (1967) succeeded in producing oriented specimens and the additional reflections observed in the diffraction pattern in both cases enabled an unequivocal assignment to the α-helix conformation to be made. A reappraisal of the original observations confirmed this conclusion (Saludjian and Luzzati, 1966, 1967).

At higher concentrations of polymer two further phases occur. In m-cresol a * hexagonal' ' phase appears and is characterized by sharp reflections which index on a hexagonal array (Luzzati et al., 1961, 1962; Parry and Elliott, 1965). In dimethylformamide and pyridine, on the other hand, a "complex" phase is observed at high concentrations and Luzzati et al. (1961, 1962) concluded from their diffraction data that three-stranded ropes of α-helices distorted into a coiled-coil conformation (Chapter 1, Section A.II.e) were present. Initially this conclusion was supported by Parry and Elliott (1965) but further studies on well-oriented specimens showed that it was incorrect (Parry and Elliott, 1967).

The observed pattern, which is depicted in Fig. 9.4, shows a number of features not previously observed with synthetic polypeptides. In particular there is a meridional reflection at Ζ = 1/5.06 A - 1

and a strong near-equatorial layer-line streak with Ζ = 1/55 A - 1. Although similar effects are produced by distortion of the α-helix into a coiled-coil conformation, other features of the pattern, such as the strong meridional reflection at Ζ = 1/1.50 A, are not consistent with this interpretation. An alternative departure from helical symmetry was suggested to account for the observed pattern, in which the main-chain atoms had an α-helical conformation while the side chains formed ordered arrays of different helical symmetry to the main chain (Parry and Elliott, 1967; Squire and Elliott, 1969).

The aggregates in the "cholesteric" phase of liquid-crystalline solutions of [Glu(Bzl)]n can be aligned by means of a magnetic field (Sobajima, 1967; Samulski and Tobolsky, 1968) to give a "nematic" structure which is retained when the solvent is evaporated (Go et al., 1969; Samulski and Tobolsky, 1971). The latter authors found that the X-ray diffraction patterns given by films cast in this manner from methylene dichloride or m-l,2-dichloroethylene suggested the presence of α-helices with u = 18 and ν = ± 5 .

Markedly different patterns were obtained, however, from films cast


from chloroform. These could be indexed on an axial repeat of c = 10.35 A and it was concluded that the helices present in these films had values of u = 7 and υ = ±2, that is, exactly 3.5 residues

R(A-')

F I G . 9 . 4 . X-ray diffraction data obtained from the "complex" phase of poly(y-benzyl-L-glutamate) which forms at high concentrations in solution in dimethylformamide. The full lines indicate data obtained at 5 5 % polymer concentration and the broken lines indicate additional data obtained at higher concentrations. (Redrawn from Parry and Elliott, 1967 . )

per turn. An interesting feature of these studies was the observation that the pattern reverted to the more usual one, with 3.6 residues per turn, when the films were heated.

(iii) Epitaxial Crystallization. Single crystals of the α form of [Glu(Bzl)]n have been prepared from dilute solution by epitaxial crystallization onto freshly cleaved alkali halide crystals (Carr et al., 1968). Electron diffraction studies were used to establish the orientation of the helical axes, and the crystallite dimensions parallel to these axes were found to be substantially less than the lengths of the individual molecules. It was concluded, therefore, that crystal reentering folds were present.


c. Racemic Polyiy-benzylglutamate)

Oriented fibers were prepared from a racemic solution containing equal parts of poly(y-benzyl-L-glutamate) and poly(y-benzyl-D-glutamate) by Tsuboi et al. (1961) and shown to have an unusual X-ray diffraction pattern which differed from that of fibers prepared from either of the enantiomorphs. The pattern was originally interpreted in terms of an α-helix with u = 1 and ν = ±2 , that is, exactly 3.5 residues per turn. More detailed studies (A. Elliott et aL, 1965) showed that the pattern was more complex than originally supposed and the observed layer lines (Fig. 9.3b) were tentatively indexed on an axial repeat of c = 106 A. Patterns obtained from better-oriented specimens (Squire and Elliott, 1972) showed that the true axial period was 320 A, but most of the reflections could be indexed on an orthogonal cell with a = 14.76 A, b = 25.40 A, and c = 64.11 A (fiber axis). The observed distribution of intensity was shown to be consistent with an α-helix having 43 residues in 12 turns, giving (K) = 1.491 A, (f) = ±100.5°, and <P> = ±5.34 A compared with the values <A> = 1.505 A, <f) = ±100°, and <P> = ±5.42 A for the enantiomorphic structure.

Appreciable intensity occurs on layer lines for which a helical structure with u = 43 and ν = ±12 would not be expected to diffract strongly and this is presumed to derive from a side-chain arrangement which has a symmetry that is different from the main chain. Mitsui et al. (1967) suggested a helical arrangement with three units per turn but this was discounted by Squire and Elliott (1972), who proposed a more complex model.

Racemic poly(y-benzylglutamate) forms liquid crystals in dimethyl-formamide and acetophenone (Squire and Elliott, 1969, 1972) and the observed reflections can be indexed on a tetragonal cell with a = 30.03 A and c = 64.16 A (fiber axis). An analysis of the distribution of intensity in the diffraction pattern suggested that the molecular conformation in the liquid crystalline forms is very similar to that which occurs in the dried fibers.

d. Other Esters of Poly(L-glutamic acid)

A series of polymers of y-glutamate esters prepared by Ledger and Stewart (1965, 1966) were examined by X-ray diffraction (Fraser et aL, 1967b) in a study of the effects on the α-helix of intermolecular and intramolecular interactions between the outer portions of the side chains. Significant differences were found between the helical parameters for the ortho and meta isomers and the para isomer of poly(y-nitrobenzyl-L-glutamate) and the values, together with those for other polymers


studied, are included in Table 9.8a (see p. 214). On the basis of these and other values obtained from studies of synthetic polypeptides and proteins a correlation between unit height h and unit twist t was established which is discussed further in Section D.

I I I . ESTERS OF POLY(L-ASPARTIC ACID)

a. Poly(ji-benzyl-w-aspartate)

Blout and Karlson (1958) found that the constant b0 in Eq. (8.1) for the dispersion of optical rotation for solutions of [Asp(Bzl)]n in chloroform was of opposite sign to that of other polymers of L-amino acid derivatives in the α conformation. Further studies (Karlson et al., 1960; Bradbury et al., 1960a) established with reasonable certainty that the helix sense in solution was left-handed, that is, opposite to that established for solid films of [Ala]n by Elliott and Malcolm (1958).

When [Asp(Bzl)]n is cast from chloroform solution at room temperature a film is obtained which yields a poorly developed X-ray diffraction pattern of the α-helix type. After heating the film in vacuo to 160°C, however, a different pattern with sharp crystal-like reflections is obtained (Bradbury et al., 1959, 1962a). The observed reflections can be indexed on an axial repeat of structure c = 5.30 A and a tetragonal unit cell (which has a square base) of side a = 13.85 A.

(i) Helix Parameters. The absence of layer lines requiring a value of c larger than 5.30 A indicates that the helix has an integral number of residues in one turn of a helix of pitch Ρ = 5.30 A. The density calculated for four residues in one turn agreed satisfactorily with the observed density and the main-chain conformation was assumed to be a left-handed α-helix so distorted that each turn contained four rather than around 3.6 residues per turn as in the α form of [Ala]n and [Glu(Me)]n . This modification of the α-helix, termed the ω-helix, was superficially similar to a model which had been suggested earlier as a possible conformation of the polypeptide chain by Bragg et al. (1950).

(ii) Refinement of Model Structure. A model for the arrangement of the atoms in a residue was developed by Bradbury et al. (1962a) from a consideration of the infrared dichroism of various localized vibrational modes of the side chain combined with studies of scale atomic models of the molecular framework. The model was refined by comparison of optical diffraction patterns (Chapter 4) with the observed X-ray diffraction data. As with [Ala]n , it was found necessary to assume that a random distribution of "up" and "down" chains was present (Section B .II) in order to obtain satisfactory agreement between the predicted and


observed intensity distribution. The coordinates quoted for the main-chain atoms and for C0 in the refined model are given in Table 9.4.

TABLE 9.4

Atomic Coordinates of a Residue in the ω-Helical Conformation of Poly(j8-benzyl-L-aspartate)

e

X y ζ r Φ Atom (A) (A) (A) (A) (deg)

Ν - 0 . 4 1 1.75 - 0 . 8 0 1.80 103.2 C

a 0.56 2.48 0 2.54 77.3

c* - 0 . 1 7 3.66 0.70 3.66 92.7 c 1.19 1.54 1.05 1.95 52.3 ο 1.27 1.90 2.25 2.29 56.2

a Calculated from data given by Bradbury et al. (1962a). Helix parameters: unit height

h = 1.325 A, unit twist t = —90°, repeat of structure c = 5.30 A contains u = 4 residues in ν = —1 turn of pitch Ρ = —5.30 A. Bond angles and bond distances calculated from these coordinates are: 6 (N , C

a) = 1.45 A; 6(C

a, C

0) = 1.55 A; o(C

a, C ) =

1.54 A; b(C'tO) = 1.26 A; b{C\ N ) = 1.37 Α; τ(Ν, Ca, C ) = 109.9°; r(C

a, C , N ) =

114.2°; r(Ca, C , O) = 120.1°; T ( C , N , C

a) = 123.1°. Torsion angles calculated from

these coordinates: φ = 62.8°, φ = 54.9°, ω = 175.4°.

Because the refinement was limited to adjustments of the side-chain conformation and molecular rotation, the main-chain conformation is that arrived at by a consideration of the stereochemistry of a left-handed helix with four residues per turn. According to Bradbury et ah (1962a), the amide group in the model structure has nonplanar amide groups with ω = 175°, a hydrogen bond length 6(Nt., O i - 4) = 2.9 A, and τ(Η,, N<, Of_4) = 25°.

The refinement of this model for the ω form of [Asp(Bzl)]n is incomplete since there are some residual discrepancies between the predicted and observed intensity distributions. One problem which must be overcome before further refinement can be carried out is the fact that the diffraction pattern is not unique and varies slightly from specimen to specimen. It should also be noted that the assignment of a left-handed screw sense to the helix in the solid state is based on indirect evidence.

McGuire et al. (1971) attempted to refine the structure proposed by Bradbury et al. (1962a) on the basis of a minimization of the sum of the calculated intramolecular and intermolecular potential energies. Bond angles and distances were maintained at standard values used in earlier work (Scott and Scheraga, 1966; Ooi et al., 1967) except for


i(C, H), which was increased to 1.07 A for aliphatic CH bonds in the side chain, and minimization was carried out with respect to the torsion angles φ, φ, ω, and χ1 to χ 4 (Chapter 6) and the orientation df the molecule about the helix axis. It was claimed that the conformation and packing of minimum calculated potential energy were similar to those proposed by Bradbury et al. (1962a) on the basis of X-ray diffraction and infrared studies, but even allowing for the fact that the diagrams seem to be incorrectly drawn, the two conformations appear to be significantly different.

Several aspects of the refinement are open to criticism since no account was taken of the random chain sense believed to be present in the crystal (Bradbury et al.y 1962a) or of the possibility that the bond angles, in particular τ(Ν, Ca, C), have values different from the "standard" values. In view of the distortion present in the ω-helix, this possibility cannot be excluded and the results obtained by Gibson and Scheraga (1966) indicate that the energy penalty due to steric hindrance is likely to be overestimated if no flexibility in bond angles and distances is allowed. An unexplained feature of the calculations was the fact that the total potential energy decreased rapidly with decrease in h when this parameter was allowed to vary, that is, the observed axial period does not coincide with a minimum in the sum of the intramolecular and intermolecular potential energies.

(iii) Monolayers. Malcolm (1970) prepared molecular monolayers of [Asp(Bzl)]n at the air-water interface and examined collapsed films by electron diffraction. Air-dried specimens were poorly crystalline but the diffraction patterns showed the main features expected for an α-helical conformation. Parallel studies using infrared spectra indicated that the amide frequencies were appropriate to a right-handed helix (Section C.I) rather than a left-handed helix as observed in solution. A transformation to a left-handed helical form, again as evidenced by infrared spectra, could be induced without loss of orientation by exposing the dried film to the vapor of chloroform containing 10% (v/v) dichloroacetic acid.

A transition to an ω form, yielding a diffraction pattern in many respects similar to that obtained from bulk specimens with X rays, occurred when films were heated briefly to 160°C. In addition to the reflections observed in the X-ray diffraction pattern, a meridional reflection on the first layer line was recorded. This reflection is forbidden in a helix with u = 4 residues in ν = ±1 turns (Chapter 1, Section A.III) and it must be concluded that the four residues are not completely equivalent.


(iv) Liquid Crystals. Saludjian and Luzzati (1967) reported that [Asp(Bzl)]n forms liquid crystals in m-cresol solutions. At about 60% (w/w) concentration of polymer a "hexagonal" phase was observed, while at higher concentrations a phase with a tetragonal cell was observed in equilibrium with the "hexagonal" phase. When the solvent was removed the tetragonal form persisted and the spacings of the observed reflections suggest that the unit cell was essentially similar to that observed by Bradbury et al. (1962a) in the heated films containing the ω form. b. Poly(ji-p-chlorobenzyl-L-aspartate)

Hashimoto and co-workers (Hashimoto and Aritomi, 1966; Hashimoto and Arakawa, 1967) found that in contrast to [Asp(Bzl)]n the polymer [Asp(/>OBzl)]n formed right-handed α-helices in solution and Takeda et al. (1970) have obtained X-ray diffraction patterns from films of this polymer.

(i) oc-Helical Form. After heating for two hours in vacuo at 150°C highly crystalline specimens were obtained which yielded a diffraction pattern rich in sharp reflections together with a few layer-line streaks. The sharp reflections can be indexed on a hexagonal unit cell of side a = 14.9 A and axial repeat c = 27.0 A. A strong meridional reflection was observed on / = 18 and a strong off-meridional reflection on / = 5 as predicted for a helical conformation with 18 residues in five turns (Chapter 1, Section A.III). The appearance of additional meridional reflections on / = 6 and 12 indicates, however, that there is some departure from perfect helical symmetry and a plausible explanation was given in terms of a repeating unit consisting of three residues.

The layer-line streaks were interpreted as indicating a random distribution of chain directions as regards the sequence —NH—CHR—CO—. This conclusion was supported by the better agreement obtained between the observed intensities and those calculated for models with random chain sense compared with the agreement obtained when a uniform chain sense was assumed.

The location of the chlorine atoms was determined by applying helix diffraction theory (Chapter 1, Section A.III) and models for the side-chain conformations arrived at by combining this information with observations of infrared dichroism and with stereochemical data. The helix was assumed to be right-handed. Refinement of the model on the basis of the X-ray data was attempted and reasonable agreement between calculated and observed intensities was obtained for the equator. The agreement on other layer lines, however, was generally poor and the atomic coordinates cannot be regarded as being fully refined.


(ii) ω-Helical Form. Takeda et aL (1970) further reported that when the α-helical form of [Asp(/>ClBzl)]n was heated to 190°C a different X-ray pattern was obtained which could be indexed on a tetragonal cell with side a = 23.3 A and an axial repeat of c = 5.20 A. It was concluded that the structure contained right-handed helices with exactly four residues per turn of pitch Ρ = 5.20 A and that the unit cell contained one "up" and one "down" chain. In view of the aforementioned change in helix sense in [Asp(Bzl)]n observed by Malcolm (1970), the assumption that the ω-helical form of [Asp(/>ClBzl)]n is right-handed is open to question.

IV. OTHER POLYMERS

a. Poly(S-benzylthio-L-cysteine)

The polymer poly(S-benzylthio-L-cysteine), in which the side chain is —CH2—S—S—CH2—C6H5 , was studied by Fraser et aL (1962a). No solvent could be found but oriented films were prepared by rolling and examined by X-ray diffraction. The pattern contained sharp reflections which could be indexed on a tetragonal cell with edge a = 14.28 A and an axial repeat of c = 5.55 A. The tetragonal symmetry, together with the absence of meridional reflections except on the fourth layer line, indicated that the chains had a helical symmetry with u = 4 and ν = ±1 . From density considerations only one chain could be accommodated in the unit cell and the conformation of the main chain was presumed to be similar to that observed in the ω form of [Asp(Bzl)]n . The helix sense in this polymer is not known.

b. Poly(L-tryptophan)

Peggion et al. (1968) studied oriented films of [Try]n , cast from dimethylformamide, by X-ray diffraction and found a pattern characteristic of the α-helical conformation with a sharp meridional reflection with Ζ = 1/1.49 A - 1 and strong near-meridional reflections on a layer line with Ζ = 1/5.42 A" 1. Thus the unit height is h = 1.49 A and the unit twist is t = 360 X 1.49/5.42 = 99.0°.

The determination of the helix sense of [Try]TO by optical methods is complicated by the presence of side-chain chromophores and Peggion et al. (1968) studied the circular dichroism spectra in solution of a series of copolymers of Try and Glu(Et). Since no abrupt transition occurred with increasing proportions of Try, it was reasoned that both [Try]n and [Glu(Et)]n had a right-handed α-helical conformation in solution. A similar conclusion was reached by Damle (1970) and Engel et al. (1971).


c. Poly(L-lysine) and Poly{L-arginine)

Studies of hydrohalides of [Lys]n by a variety of methods have established that this polymer can exist in a range of conformations depending upon the state of ionization and degree of hydration of the side-chain amine group (Blout and Lenormant, 1957; Elliott et al, 1957a; Applequist and Doty, 1962).

(i) Films. The structure of films of the hydrochloride of [Lys]w has been studied using X-ray diffraction by Johnson (1959) and Shmueli and Traub (1965). The pattern obtained was found to depend upon the water content of the specimen. The dried material gave a pattern characteristic of the β conformation (Chapter 10) and with increasing relative humidity, the intersheet distance gradually expanded, but above 84% relative humidity a transition to a pattern characteristic of the α-helix was observed. In this pattern sharp equatorial reflections were observed which could be indexed on a hexagonal lattice with cell edge a = 16.8 A, but on other layer lines there were continuous distributions of intensity, suggesting that random axial displacements and rotations of the molecules were present (Chapter 1, Section A.IV.d). The cell dimensions at 84% relative humidity correspond to about five water molecules per residue and the cell was found to expand laterally with increasing relative humidity. Above a water content equivalent to about 15 water molecules per residue, however, the regular packing of the helices disappeared. The conformational change from a β form to an α form was found to be reversible.

The structure of films of the hydrochloride of [Arg]n has also been investigated by X-ray diffraction (Suwalsky and Traub, 1972). Specimens containing up to about five water molecules per residue gave diffraction patterns showing features characteristic of an α-helical conformation, while specimens containing 5-20 water molecules per residue gave a β pattern.

(ii) Single Crystals. Padden et al. (1969) succeeded in obtaining crystals from aqueous solutions of [Lys]n in the presence of divalent anions. Single crystals of the monohydrogen phosphate were obtained in the form of hexagonal lamellae about 150 A thick (Fig. 9.5) in which the conformation was shown both by electron and X-ray diffraction to be α-helical. The electron diffraction data indicated that the chain axes were perpendicular to the plane of the lamellae and since the average length of the molecule in the α-helical conformation was predicted to be about 1100 A, it was concluded that the molecules must be folded.


FIG . 9.5. Portion of a single crystal of poly(L-lysine) monohydrogen phosphate freeze-dried from the mother liquor (Padden et al.y 1969).

The packing in the crystal was found to be hexagonal, with a cell edge a = 19.55 A, and a lateral contraction of the cell was observed in water/ethanol mixtures as the proportion of ethanol was increased. A transformation to the β conformation occurred at high ethanol concentrations and this could be reversed by resuspending the crystals in the mother liquor. A transformation to the β conformation was also observed when crystals of the α form were dried.

d. Sequential Polypeptides

Diffraction patterns characteristic of the α-helical conformation have been obtained from a number of polymers containing ordered sequences of residues (sequential polypeptides). These include [Glu(Me)Glu(Me) Glu(Me)ValGlu(Me)]n (Fraser et aly 1965b), [Glu(Et)Glu(Et)Glu(Et) Cys(Bzl)Glu(Et)]n , [Glu(Et)Cys(Bzl)Glu(Et)]n , and [Glu(Et)Cys(Bzl) Glu(Et)Glu(Et)]n (Fraser et al, 1965d).

C. INFRARED STUDIES 199

The pattern obtained from the polymer [Glu(Et)Cys(Bzl)Glu(Et)]n

contained sharp reflections characteristic of a crystalline phase and these could be indexed on a hexagonal unit cell with side a = 13.2 A and an axial repeat c = 26.8 A (Fraser et al., 1965c). These dimensions are consistent with an α-helical conformation of the main chain in which the mean unit height is <Λ> = 26.8/18 = 1.489 A and mean unit twist is = ±100°. Intensity was observed on layer lines for which the contribution from a perfect helix with u = 18 units in ν = ± 5 turns would be negligible and this was correlated with the fact that the chemical repeating unit of the polymer is a group of three residues. If all groups were equivalent in the crystal, the expected helical symmetry of the chains would be u = 6, ν = ^ 1 , and the observed pattern is consistent with this symmetry. An unexplained feature of the observed pattern was the absence of meridional reflections with 1 = 6 and 12 which are permitted with a helix in which u = 6 and ν = = p l .

e. Liquid Crystals

Luzzati and co-workers (Luzzati et al., 1961, 1962, 1966; Saludjian and Luzzati, 1966, 1967; Saludjian et al., 1963a,b) have studied the X-ray diffraction patterns of unoriented liquid crystalline forms of a number of synthetic polypeptides and the results obtained with [Glu(Bzl)]n have been discussed in Section B.II.b. The interpretation of the diffraction patterns of unoriented specimens is more difficult than for oriented specimens but the α-helical form was reported to be present in the "hexagonal" phase (Section B.II.b) of [Glu]n and [Lys(Cbz)]n in dimethylformamide, and ω-helical forms were reported to be present in [Glu]n , [Lys(Cbz)]n , and [Asp(Bzl)]n at high concentrations of polymer. More recently Squire and Elliott (1969) have questioned the assignment of an ω conformation on the basis of a tetragonal (square-based) cell. Working with oriented specimens, they were able to show that under certain circumstances liquid crystals with tetragonal cells are formed which contain α-helices. Thus the observation of a square-based cell does not automatically imply the presence of a helix with four residues per turn.

C. INFRARED STUDIES

The infrared spectra of synthetic polypeptides in the α form have been studied extensively and useful reviews of this topic have been given by Miyazawa (1962, 1967) and Susi (1969). Much of this work has been concerned with the detailed interpretation of infrared spectra


on the basis of knowledge gained primarily from X-ray diffraction studies. In the present context the question of what useful information about the α-helix can be gained from these studies is considered with particular reference to features which have been or may be of value in studies of the conformation in fibrous proteins.

I. FREQUENCIES OF AMIDE BANDS

Elliott and Ambrose (1950) established a correlation between the frequencies of the amide vibrations and the conformation of the polypeptide chain in [Glu(Me)]n and found that the α form was characterized by frequencies of 1658 cm - 1 for the parallel component of amide I and 1550 cm - 1 for the perpendicular component of amide II. A small shift in the frequency of the amide A vibration was also noted between the α and β forms of this polymer. This work was extended to other enantiomorphic synthetic polypeptides (Ambrose and Elliott, 1951a; Elliott, 1953a; Bamford et aL, 1956) and narrow ranges of 1652-1657 and 1545-1551 cm - 1 were reported for the frequencies of the amide I and II bands, respectively (Elliott, 1953a). Further studies (Elliott et aL, 1957a) showed that it was necessary to exercise caution in the use of the amide I frequency in the diagnosis of the α form, because the frequency for unordered material was close to that for the α form.

An explanation of the dependence of the vibrational frequencies of the amide modes on conformation was provided by the analysis given by Miyazawa (1960a), which was discussed in detail in Chapter 5. In the case of the α-helix each mode of the isolated amide group gives rise to two infrared-active modes with frequencies

",,(0) = v0 + D1 + D3 (9.2)

v±(t) = v0 + D1 cos t + D 3 cos 3t (9.3)

where v0 is the unperturbed frequency, Dx is a coefficient which depends on the interaction between adjacent groups in the helix, and D3 is a coefficient which depends on the interaction between groups coupled by hydrogen bonds. Miyazawa and Blout (1961) suggested values of vQ = 1658 cm - 1, D1 = 10 cm - 1, and Z>3 = —18 cm - 1 for the amide I mode of the α form of [Glu(Bzl)]n , giving predicted values of y„(0) = 1650 cm - 1 and i>±(100°) = 1647 cm - 1 compared with observed values of 1650 and 1652 cm - 1, respectively. For the amide II mode values of v0 = 1535 cm - 1, D1 = —21 cm - 1, and Dz = 2 cm - 1 were suggested, giving predicted values of ν„(0) = 1516 cm - 1 and v±( 100°) = 1540 cm - 1

C . INFRARED STUDIES 201

compared with the observed values of 1516 and 1546 cm - 1, respectively. In both cases the agreement between the calculated and observed values of v„(0) is not significant since this value was used in the determination of Dx. Other amide bands exhibit frequency differences between v„(0) and v±(t) but so far these have not been studied in detail.

Potentially the frequencies of the amide vibrations provide information, through the values of v0 , Dx, and Z)3 , on a number of important molecular parameters which cannot be obtained readily by other means. The unperturbed frequency v0 depends upon the spatial configuration of the atoms in the repeating unit of the polymer, the electronic structure of the bonds, and the nature of the hydrogen bond, while the interaction coefficients depend upon the mutual relationships of the interacting amide groups. To date, explicit interpretation in such terms has not proved possible but differences between the amide I frequencies and amide II frequencies in the α forms of various synthetic polypeptides have been observed and these are summarized in Tables 9.5a and 9.5b.

The ranges for esters of [Glu]n are quite small even though the unit height h and unit twist t of the helix vary somewhat from polymer to polymer (see Table 9.8a). On the other hand, the ranges for esters of [Asp]n are considerably greater and this can be attributed to three main effects. First, t varies over a considerably greater range (see Table 9.8a) and the values for the perpendicular component predicted from Eq. (9.3) vary from v±(90°) = v0 to v±(\00°) = v 0 — 0.\1D1 + 0.5Z>3

for the ω and α forms, respectively. Second, distortion of the amide-group geometry and changes in hydrogen bond strength will affect v0 , while changes in the spatial relationships of the amide groups will affect Dx and Z)3 .

For the ω form, t = 90° and so from Eqs. (9.2) and (9.3) ν „(0)—v±(t) = Dx + Z)3 . From the values given in Table 9.5a an estimate of Dx + D3 = 7 cm - 1 is obtained for the amide I modes of [Asp(Bzl)]n in the ω form, which may be compared with the value of —8 cm - 1 suggested by Miyazawa and Blout (1961) for the α form. The coefficient D3 depends upon interactions between hydrogen-bonded residues in adjacent turns and thus might be expected to be more sensitive to changes in t than Dx . The discrepancy between the observed and calculated values for Dx + Z)3 probably arises from this effect, particularly since Z)3 has a large magnitude for amide I. In contrast, the estimate of —18 cm - 1

obtained from Table 9.5a for Dx + D3 applicable to the amide II modes of the ω form is close to the value of —19 cm - 1 predicted for the α-helix by Miyazawa and Blout (1961). This is perhaps to be expected since the dominant term is Dx. The predicted value of Z)3 in the α-helix is small (2 cm - 1) and would be expected to be even less in the ω form


Amide I Amide II

Confor ",,(0) ",,(0) "Λ0 Polymer" mation

6 (cm-

1) (cm-

1) (cm"

1) (cm-

1) Ref.

[Ala]n 1658 — — 1548 1 [Glu]n a R 1650 1650 1515 1550 2

Esters of [Glu]n

[Glu(Me)]n <*R 1654 1659 1519 1550 1 [Glu(Bzl)]n <*R 1652 1655 1518 1549 3 [Glu(oN02Bzl)]n «R 1653 1657 — 1552 4 [Glu(mN02Bzl)]n <*R 1652 1656 — 1550 4 [Glu(£N02Bzl)]n a R 1654 1657 — 1546 4 [Glu(£lBzl)]n «R 1655 1658 1516 1549 4 [Glu(N PMe)] n <*R 1654 1656 1518 1550 4 [Glu(Me3Bzl)]n <*R 1656 1658 1517 1550 4 [Glu(Et)]n <*R 1658 — 1522 1550 1 [Glu(isoAm)]n <*R 1656 — — 1550 1

Range 1652-1658 1655-1659 1516-1522 1546-1552

Esters of [Asp]n [Asp(Bzl)]n

WL 1677 1670 1520 1538 5

[Asp(Bzl)]n <*R 1658 — — 1552 6 [Asp(Bzl)]n <*L 1664 — — 1561 5 [Asp(Bzl)]n <*L 1668 — — 1560 7 [Asp(/>MeBzl)]n <*R 1656 — — 1555 7 [Asp(/>ClBzl)]n a R 1657 — — 1556 7 [Asp(PhEt)]n a R 1657 — — 1554 7 [Asp(«Pr)]n a 1662 — — 1554 8 [Asp(/>IBzl)]n a 1660 1660 1525 1555 4

Copolymers <*R 1657-1661 — — 1551-1555 9 Copolymers «L 1664-1668 — — 1555-1559 9 Copolymers CD 1667-1673 — — 1534-1538 9

Range 1656-1677 1660-1670 1520-1525 1534-1561

a Abbreviations defined on p. xvii. b The assignment of helix sense as left (L) or right (R) is in most cases based on indirect

evidence. c References: 1, Masuda et aL (1969); 2, Miyazawa and Blout (1961); 3, Tsuboi (1962);

4, Suzuki (1971); 5, Bradbury et al. (1962a); 6, Malcolm (1970); 7, Hashimoto and Arakawa (1967) (values for solution in chloroform); 8, Bradbury et al. (1960b); 9, Bradbury et al. (1968b).

TABLE 9.5a

Amide I and II Frequencies of Homopolymers and Random Copolymers in the α Form


TABLE 9.5b Amide I and II Frequencies of Sequential Polymers in the α Form

Amide I Amide II

".(0) vJO) *.(0) "±(0) Polymer" (cm-

1) (cm"

1) (cm"

1) (cm-

1) Ref.

b

[{Glu(Me)}m-Val-Glu(Me)]n , m ι _i

1654-1656 1655-1657 — 1546-1549 1

τη — i—j

[{GluiEt^-CyaiBzD-GluiEt)],, 1656-1657 1658 — 1548-1550 2 m = 0-3

[Glu(Et)-Cys(Bzl)-{Glu(Et)}2]„ 1656 1657 — —1550 2 [Cys(Bzl)-{Glu(Et)}2]n 1659 1661 — 1550 2 [Glu(Et)-{Cys(Bzl)-Glu(Et)}2]n 1657 1658 — 1549 2 [Glu(Et)-{Cys(Bzl)}2-{Glu(Et)}2]n 1657 1658 — 1550 2 [{Glu(Et)}m-Gly]n,ro = 3-4 1657 1658 — 1548 3 [{Glu(Et)}2-Gly-{Glu(Et)}3]„ 1657-1658 1658 — 1548-1557 3 [{Glu(Me)}m-Ser(Ac)-Glu(Me)]w , 1654-1656 1656-1657 1515-1518 1547-1548 4

m = 2-3

Range for all polymers6

1650-1677 1650-1670 1515-1525 1534-1561

a Indirect evidence suggests that all these polymers exist as right-handed α-helices.

Symbols defined on p. xvii. b References: 1, Fraser et al. (1965b); 2, Fraser et al. (1965d); 3, Fraser et al. (1967a);

4, Fraser et al. (1968a). e This table and Table 9.5a.

since the angle between the planes of the bonded amide groups is greater than in the α form (Miyazawa and Blout, 1961).

The third factor which operates to increase the range of values for esters of [Asp] n is the occurrence of both right- and left-handed helical forms. For L-residues these two forms cannot be transformed one into the other by reflection or any other symmetry operation and so would be expected a priori to have different normal modes of vibration. Miyazawa et al. (1967) calculated the vibrational frequencies for the left-handed and right-handed forms of [Ala]n and reported that the amide I and II frequencies were higher for the left-handed form by 8 and 2 c m - 1, respectively. The senses and magnitudes of these differences are in reasonable agreement with those observed by Hashimoto and Arakawa (1967) and Bradbury et al. (1968b) quoted in Table 9.5a.

It is clear from the range of values reported for the α forms of various synthetic polypeptides that while correlations exist between the frequencies of the amide I and II vibrations and the α-helical conformation,


these must be applied with circumspection in dealing with materials of unknown conformation. In addition to the variability of frequency, overlap occurs with the frequency ranges for unordered and for collagenlike conformations. In view of these difficulties considerable attention has been given to a search for other conformation-sensitive amide bands, and the amide V band in particular has been studied in considerable detail (Miyazawa et aL, 1962; Masuda and Miyazawa, 1967; Miyazawa et aL, 1967; Masuda et aL, 1969). Although the frequency for the α form is well separated from that of the β form, the bands associated with the oc and unordered forms overlap.

The frequencies of NH and OH bond stretching vibrations are generally lowered and the absorption bands broadened and intensified when the group acts as donor in the formation of a hydrogen bond. The magnitude of the frequency change from the nonbonded to the bonded state has been correlated with the length of the hydrogen bond (Pimentel and Sederholm, 1956; Pimentel and McClellan, 1960) and this correlation is potentially of value in the study of the conformations of regular arrangements such as the α-helix. It cannot be applied directly, however, since the NH stretching mode of the amide group and the overtone of the amide II vibration have comparable frequencies and similar symmetries and interact through Fermi resonance (Chapter 5). The frequencies of the resulting amide A and Β components vA and vB are related to the true stretching frequency v NH and the

3.1

3.0

e< 2.9 u c ο

. Ϊ 2.8 a Ο

± 2.7

2.6

3KX) 3200 3300 3400

NH Stretching frequency (cm'1)

F I G . 9 . 6 . Relationship between 6 ( N T , 0 < _ 4) in the α-helix and the N H stretching frequency assuming that v^H in Eq. ( 9 . 5 ) has a value of 3 4 5 7 c m

- 1.


frequency of the amide II vibration vu by the expression (Miyazawa, 1960c)

^ N H = V A +V

B — 2vn (9.4)

Some calculated values of v NH for different synthetic polypeptides are given in Table 9.6. It should be noted that these values refer to the v„(0) mode and need to be corrected by subtracting the appropriate value of Dx + Z)3 . The values of Dx and Z)3 for the NH stretching vibration are unknown but the available evidence suggests that they are small (<10 cm - 1).

In order to assess the hydrogen bond length ό(Ν, Ο) in the α-helix it is also necessary to know for the non-hydrogen-bonded state. The value of has been determined for a range of N-substituted amides by Jones (1966) and of the compounds investigated the most appropriate model would appear to be iV-ethylpropionamide, C2H5CONHC2H5 , for which v£H = 3457 cm"1. With this value the relationship given by Pimentel and Sederholm (1956)

"°NH - " N H = 548[3.21 - *(N, O)] (9.5) yields

δ(Ν, Ο) = 0.001825vNH - 3.1 (9.6)

This relationship is illustrated in Fig. 9.6. When Eqs. (9.4) and (9.6) are applied to the observed data for [Ala]n

(Table 9.6) a value of 6(N, O) = 2.85 A is obtained, which is close to the measured value of 2.86 A derived from the X-ray diffraction data by Arnott and Dover (1967). The error incurred in neglecting to correct for the interaction coefficients Dx and Z>3 is 0.002 A/cm - 1. The values of 6(N, O) in the esters of [Glu]n are generally similar to that in [Ala]n , except for the />-nitrobenzyl ester, for which the calculated hydrogen bond length is appreciably longer (Table 9.6). This can be correlated with the greater value of the unit height h in this particular polymer (see Table 9.8a). The values of 6(N, O) in esters of [Asp]n are generally greater than in the esters of [Glu]n , suggesting that the hydrogen bonding is weaker in esters of [Asp]n .

II. DICHROISM OF AMIDE BANDS

Measurements of the dichroism of the amide bands of synthetic polypeptides provide information about the spatial orientation of the amide groups relative to the molecular axis. Originally the dichroic ratios observed for the amide A and amide I bands of synthetic


TABLE 9.6

Values of the Hydrogen Bond Distance 6(N, O) for Synthetic Polypeptides in the α Form Calculated from the Observed Values of vA , vB , and v\\

'NH E b(N, oy

Polymer" Conformation6

(cm-1) (cm"

1) (cm"

1) (cm-

1) (A) Ref."

[Ala], AR 3293 3060 1545 3263 2.85 1

[Glu(Bzl)]„ AR 3291 3065 1549 3258 2.85 2

[Glu(oN02Bzl)]„ a R 3291 3062 1550 3253 2.84 2 [Glu(mN02Bzl)]n <*R 3292 3065 1549 3259 2.85 2 [Glu(i>N02Bzl)]„ A

R 3313 3065 1548 3282 2.89 2 [Glu(/>IBzl)]„ A

R 3294 3063 1549 3259 2.85 2 [Glu(NpMe)]n a R 3292 3061 1550 3253 2.84 2 [Glu(Me3Bzl)]„ A

R 3294 3065 1550 3259 2.85 2 [Asp(«Pr)]„ a 3305 3075 1554 3272 2.87 3 [Asp(Bzl)]B <*L 3308 3082 1561 3286 2.90 4 [Asp(Bzl)]„ 3298 3075 1538 3301 2.92 4

a Abbreviations defined on p. xvii. 6 Assignment of helix sense based on solution studies. c v„(0) measured from parallel spectrum.

d v±(t) measured from perpendicular spectrum. * Calculated from Eq. (9.4) assuming Dx -\- Dz = 0. / Calculated from Eq. (9.6). • References: 1, Elliott (1954); 2, Fraser et al. (1967b); 3, Bradbury et al. (1960b);

4, Bradbury et al. (1962a).

polypeptides were thought to be incompatible with the α-helix (Bamford et al., 1952) but recognition of the complex nature of amide-group vibrations enabled the observed ratios to be reconciled, in a qualitative manner, with the α-helix (Fraser and Price, 1952). However, lack of precise knowledge about directions, relative to the amide group, of the transition moments associated with these and other amide group vibrations precluded a quantitative test (Elliott, 1953b). Subsequent measurements on crystals of simple model compounds provided estimates for the transition moment directions of several in-plane amide vibrations relative to the CO direction (Chapter 5, Section A.I), and the information obtained from crystalline iV,AT-diacetylhexamethylenediamine (Sandeman, 1955) was used by Tsuboi (1962) to calculate the inclination of the transition moment directions to the axis for the model of the α-helix described by Bamford et al. (1956). These were compared with the values deduced from measurements of dichroism in [GluiBzl)]^ , but the agreement was generally poor (Table 9.7). It was noted by Tsuboi (1962) that some improvement could be obtained if the amide


TABLE 9.7

Amide vibration (deg)

Method A I II I l l V

Calculated for an a-helixb with h = 1.50 A 22.7 34.6 87.5 45.6 86.7

Observed in [Glu(Bzl)]n (Tsuboi, 1962) 28 39 75 40 > 8 0 Observed in [Glu(Bzl)]n (Suzuki, 1971) 17.3 27.6 75.3 — 76.4 Calculated for an a-helix

c with h = 1.525 A 22.9 34.9 87.9 45.1 88.5

Observed in [Glu(/>N02Bzl)]n (Suzuki, 1971) 19.0 31.2 — — 80.5

β The sense of the transition moment direction cannot be determined from infrared

measurements; of the two possibilities, the angle in the range 0-90° has been given. b Calculated from the coordinates given in Table 9.1 and the transition moment direc

tions, relative to the CO group of 8° for amide A, 20° for amide I, 73° for amide II, and — 60° for amide III. The transition moment for amide V was assumed to be normal to the plane of the amide group.

c Calculated from the coordinates of an α-helix with the standard amide-group geometry

(Table 6.1), r(N, Ca, C ) = 109.47°, h = 1.525 A, t = 99.6°. The values of h and t

correspond to those observed in [Glu(/>N02Bzl)]n (Table 9.8a). The transition moment directions were assumed to be the same as given in footnote b.

group was rotated through an angle of 10° about the normal to the plane of the group.

Although the work of Tsuboi (1962) represented a considerable advance over earlier studies in that a quantitative assessment was made of the effects of imperfect orientation, several other factors need to be considered. The procedure for estimating the inclination of a transition moment direction to the axis of the α-helix involves the following:

(1) Determination, usually by X-ray diffraction studies, of the type of orientation texture present in the specimen. This texture determines the way in which the observed dichroism must be interpreted (Chapter 5, Section B.II).

(2) Analysis of the spectra into individual absorption bands and a baseline (Chapter 5, Section C).

(3) Correction of the observed dichroism for the effects of imperfect orientation.

If the v„(0) and v±(t) modes are well separated then the corrected dichroic ratio R0 , in the case of fiber orientation, can be calculated from the expression

(9.7)

Comparison of Calculated and Observed Transition Moment Directions0

Relative to the Axis of the α-Helix


where [ A 0 ] n is the integrated area beneath the ν „ (0) band in the parallel ( 7 7 ) spectrum and [ Α 0 ] σ is the integrated area of this component in the perpendicular (σ) spectrum, e tc If the texture is such that the molecular axes all lie in a plane perpendicular to the incident radiation but have azimuthal dispersion, the coefficients 2 and \ are omitted from Eq. (9.7) (Miyazawa and Blout, 1961). This method, which relies on a result obtained by Higgs (1953), is only applicable when the vH(0) and v ± ( t ) components are well resolved, as is the case, for example, with the amide II components.

If the components are not well separated, the overlapped pair must be treated as a single band and a correction applied for the effects of disorientation. The orientation parameter / (Chapter 5, Section B.II) can be determined from the X-ray diffraction pattern (Chapter 5, Section B.III) or from the observed absorbances for a well-separated component such as the v ± ( t ) component of amide II (Miyazawa and Blout, 1961; Miyazawa, 1962; Tsuboi, 1962). For fiber orientation the value of / in the case of a v ± ( t ) mode is given by

/ = 2([At]„ - [A].)/(2[A]. + (9.8)

and in the case of a ν „ (0) mode by

/ = ([A], - [AL)/([A]„ + 2[Λ]σ) (9.9)

[see Eq. (5.52)]. The value of R0 is then calculated from the expression

R0 = [f(R + 2) + 2(R - l)]l[f(R + 2)-(R- 1)] (9.10)

where R = ([Air + [Α].)/([Α]σ + [Α]α) (9.11)

The numerator in Eq. (9.11) is simply the observed integrated intensity of the overlapped pair in the parallel spectrum and the denominator is the integrated intensity in the perpendicular spectrum.

(4) Assuming that all amide groups are equivalent, the inclination of the transition moment direction to the helix axis can then be calculated from Eq. (5.51), giving

« = c o t - i [ ± ( W ] (9.12)

It should be noted that the correct choice of sign in Eq. (9.12) cannot be determined from dichroism measurements alone. Thus if α is the principal value of cot

- 1[ ( | i?o)

1 / 2] then 180° — α is also a solution of

Eq. (9.12).


If values of α can be obtained for two amide modes, information can also be obtained about the inclination to the helix axis of the normal to the plane of the amide group. If a x and a 2 are values in the range 0-90° for the inclinations of two transition moments to the helix axis and φ is the angle between them (Table 5.2), it can be shown that the inclination of the normal to the helix axis a N is given by

The plus and minus signs give two complementary solutions which reflect an uncertainty of 180° in the directions of the transition moments, which is discussed later. In addition, two solutions are in general obtained, one of which is incorrect, depending on whether φ is taken in the range 0-90° or 90-180°. If a value of α for a third mode can be obtained, the correct solution can be found by comparing the results obtained by using a x and a 2 with those obtained by using a x and a 3

or a 2 and a 3 .

According to Beer (1956), both the orientation parameter / and the spatial orientation of the amide group can be uniquely determined directly from measurements of R for three bands together with the information given in Table 5.2. However, the fact that olx , <x2 , α 3 , and φ cannot be distinguished from their complements appears to have been overlooked and in general a fourth observation would be required to eliminate incorrect solutions. Even then there would be ambiguity, since two solutions would remain, corresponding to the correct spatial orientation and its reflection in the xy plane.

The dichroism in the spectrum of oriented films of [Glu(Bzl)]n has been reinvestigated by Suzuki (1971) and interpreted along the lines just indicated. The inclinations of the transition moments, calculated from the observed data (Table 9.7), differ from those calculated for the "standard" α-helix and it seems likely that some refinement of the atomic positions in the model is required. Measurements were also made on [Glu(/>N02Bzl)]n and the results obtained with both polymers are included in Table 9.7. In this case the observed transition moment directions for the amide A and amide I bands agree, within experimental error, with those calculated for an α-helix having the "standard" amide geometry and h = 1.525 A. The agreement in the case of the amide V transition moment direction is less satisfactory.

III. SIDE-CHAIN BANDS

Studies of the dichroism of absorption bands associated with vibrational modes localized in side chains have been used in a number of

(9.13)


instances to devise models for the conformation of the side chains in synthetic polypeptides in the α form (Tsuboi, 1962; Mitsui et al., 1967; Takeda et al., 1970) and the ω form (Bradbury et al., 1962a). As explained earlier, the conformation cannot be determined uniquely from infrared measurements, and stereochemical and other data must be used to reduce the number of possibilities. Changes in the frequencies and dichroisms of side-chain bands have also been used to detect side-chain rearrangements (Tsuboi et al., 1961; Bradbury et al., 1962a, 1968b; Tsuboi, 1964; Mitsui et al., 1967).

Many side-chain localized vibrations have slightly different frequencies in spectra obtained with the electric vector vibrating respectively parallel and perpendicular to the fiber axis. These frequency differences suggest that vibrations in different residues are coupled through weak interactions and that frequencies are related by equations similar in type to those used in the analysis of the amide vibrations (Miyazawa and Blout, 1961).

D. FACTORS AFFECTING HELIX SENSE AND GEOMETRY

I. HELIX SENSE

Shortly after the announcement of the discovery of the α-helix Huggins (1952) pointed out that with L-amino acid residues there would be a short contact between Ot- and C/ in the left-handed form of the α-helix which was not present in the right-handed form. Accordingly, it was suggested that the right-handed form should be preferred for polymers of L-amino acids. This prediction has largely been borne out in practice and the only exceptions which have been observed are in [Asp(Bzl)]n (Blout and Karlson, 1958; Karlson et al., 1960; Bradbury et al., 1960a), [Asp(Me)]n (Goodman et al., 1963a; Bradbury et al., 1968a), and [Asp(oClBzl)]n and [Asp(mClBzl)]n

(Erenrich et al., 1970), which appear to exist in the left-handed form. The preference for the left-handed form is not an intrinsic property of esters of [Asp]n , since closely related polymers such as [Asp(/>MeBzl)]n

and [Asp(Et)]n form right-handed helices (Hashimoto and Aritomi, 1966; Hashimoto, 1966; Bradbury et al., 1968a). In addition, a transition from a right-handed to a left-handed helical form with increase in temperature has been observed in [Asp(wPr)]n by Bradbury et al. (1968a,b), and [Asp(Bzl)]n can be isolated in the right-handed helical form from molecular monolayers (Malcolm, 1968b, 1970).

Calculations of intramolecular potential energies per mole residue have been carried out for helical conformations of [Ala]n (Liquori, 1966;

D. FACTORS AFFECTING HELIX SENSE AND GEOMETRY 211

Ramachandran et aL, 1966b; Scott and Scheraga, 1966; Ooi et aL, 1967; Brant, 1968) and deep minima are observed in regions of the (φ9 φ) conformational maps corresponding to the left-handed and right-handed forms of the α-helix. According to Ooi et aL (1967), the minimum for the right-handed helix is 0.38 kcal mole -1 lower than that for the left-handed helix, the difference in energy being attributable to differences in the contributions of the nonbonded interactions. Similar calculations have been carried out for other homopolypeptides (Ooi et aL, 1967; Yan et aL, 1968, 1970) and in some instances the conformation of lowest energy was found to be a left-handed α-helix. It is difficult to test these predictions experimentally since the most stable helix sense will depend upon the difference in free energy between the right-handed and left-handed forms rather than the difference in intramolecular potential energy. In many cases the observed helix sense corresponds to the helix sense of the conformation of lowest calculated potential energy but this would appear to be partly fortuitous since the side-chain conformation, which plays an important part in determining the differences between the calculated potential energies, appears to be different in the actual polymer from that of the calculated minimum-energy conformation (Bradbury et aL, 1972).

A feature of the energy calculations that calls for comment is the highly empirical nature of the potential functions that are used. For example, Ooi et aL (1967) calculated minimum-energy conformations for helical forms of [Asp(Me)]n and found that with the potential functions used, the minimum for the right-handed form was lower than that for the left-handed form. The experimental data discussed earlier indicate that the opposite is true for the free energies. However, it was found that the calculated depths of the minima for the intramolecular potential energy could be brought in line with the observed data by empirical adjustment of the constants in the nonbonded potential functions used in the energy calculation. These amended functions were then used in subsequent calculations.

Despite the lack of a secure theoretical basis for the formulation of potential functions, the calculations of intramolecular potential energy have been developed to the stage where some of the factors which influence helix sense can be appreciated. In [Ala]n the contribution of the main chain to the potential energy exceeds that of the side chain but as the length of the side chain increases, the contribution from the side chain becomes progressively more important. For example, in [Glu(Bzl)]n the side-chain contribution is twice that of the main chain (Yan et aL, 1968) and more than half of the total energy arises from nonbonded interactions in the side chain.


In esters of [Asp]n an unfavorable interaction occurs between the dipole of the ester group and the main-chain amide group which is less for a left-handed helix than for a right-handed helix (Ooi et al., 1966, 1967; Yan et al., 1968). Against this must be balanced the remaining contribution from the side-chain terms which may outweigh this effect in some instances (Yan et al., 1968). In esters of [Glu]n the interaction between the dipole of the ester group and the main-chain amide group is favorable in the right-handed helical conformation of lowest energy and unfavorable in the left-handed form. No evidence was found to support an earlier suggestion by Goodman et al. (1963b) that there is competition between the side-chain and main-chain C = 0 groups for hydrogen bond formation with the main-chain Ν—Η group in the right-handed form which destabilizes it relative to the left-handed form.

The helix sense in solution of several polypeptides has been shown to be temperature-sensitive (Bradbury et al., 1968a,b; Toniolo et al., 1968) and Lotan et al. (1969) suggested that the observed inversions of helix sense with increasing temperature could be explained on the basis of an increased amplitude of intramolecular motions. This effect was simulated in calculations of potential energies by increasing the effective radius of the hydrogen atoms and it was found that the helix sense of the lowest-energy conformations of several homopolypeptides inverted with increasing temperature.

The experimental data on synthetic polypeptides which have been gathered from optical and X-ray diffraction studies indicate that the right-handed α-helix is in general the more stable conformation for L-amino acid residues. In the case of esters of [Asp]n , however, an unfavorable dipole-dipole interaction is present which tends to destabilize the right-handed form of the α-helix relative to the left-handed form. In the protein structures so far determined by X-ray crystallography no evidence has been obtained for the occurrence of left-handed α-helices.

II. HELIX GEOMETRY

Values of unit height h and unit twist t in the α-helical forms of various synthetic polypeptides, as determined by X-ray diffraction studies, are collected together in Tables 9.8a and 9.8b. Several polypeptides, including [Ala]n , have values of h and t close to those originally suggested by Pauling and Corey (1951a) but appreciable departures from these values are evident, with h varying from 1.325 A in the ω form of [Asp(Bzl)]n to 1.525 A in the α form of [Glu(/>N02Bzl)]n, while 111 varies from 90° in [Asp(Bzl)]w to 102.8° in nematic films of [Glu(Bzl)]n .


Some correlation is evident between h and t (Fig. 9.7) and the general trend suggests that the number of residues per turn can be varied over a small range without appreciable increase in energy, provided any increase in h is accompanied by a compensating increase in t. This behavior suggests that, to a first approximation, the polypeptide chain can be thought of as a ribbon of width w wrapped around a cylinder of radius r equal to the radial coordinate of Ο (Fig. 9.8). A relationship between h and t can be derived (Fraser et al.y 1967b) in terms of the distance d between successive Ο atoms and the width of the ribbon as follows:

¥ - h*{d2 + («>/360)2|>2 - 4 sin2(£*)]} + («>Λ/360)2 = 0 (9.14)

For the "standard peptide" geometry (Table 6.1) d = 3.80 A and if w is chosen so that the α-helix with h — 1.50 A and t = 100° is a solution of Eq. (9.14), the relationship shown in Fig. 9.7 is obtained. Although the treatment is an oversimplification of the problem, the general trend in both synthetic polypeptides and proteins, also included in Fig. 9.7, is well represented.

Another correlation which can be made is with the normal and extreme limits of allowed conformations for [Ala]n given by Ramachandran and Sasisekharan (1968). The relevant regions in the (φ, φ) steric map (Chapter 6, Section B.III) corresponding to right-handed helices with Ν ^ Η ^ - Ό ^ hydrogen bonding have been transformed to h and t values by means of Eqs. (6.14) and (6.15) and the result is shown in Fig. 9.9. Again the general trend is well represented but a comprehensive analysis on this basis is not possible without a detailed study of the effect on the steric map of variation in r (N, Ca, C) and other parameters. The range of allowed values of h and t is very sensitive to the choice of T ( N , Ca, C ) (Ramakrishnan and Ramachandran, 1965).

As regards the detailed structure of the α-helix, it must be recognized that the only synthetic polypeptide for which the atomic positions and helix sense have been satisfactorily established is [Ala]n . In no other case is the agreement between the calculated and observed intensity transforms sufficiently good to place any reliance on the precise value of the atomic coordinates given for model structures. On the contrary, the lack of agreement is sufficiently great in some instances to indicate either that the coordinates are significantly in error or that the packing model is incorrect.

All the synthetic polypeptides in the α form so far examined in detail by X-ray diffraction show departures from strict helical symmetry in the solid state. These departures can be attributed to the fact that

214 9. T H E A L P H A H E L I X

T A B L E 9.8a

Symbol5 in

Figs. 9.7 Pitch Unit height Unit twist and 9.9 Polymer

0 Ρ (A) h (A) t (deg)

1 18-residue/5-turn a-helixd

[Glu(Bzl)]n and related polymers 2 [Glu(Bzl)]n 3 [Glu(Bzl)]n nematic 4 [Glu(Bzl)]n racemic* 5 [Glu(Bzl)]n racemic' 6 [Glu(oN02Bzl)]n 7 [Glu(mN02Bzl)]n 8 [Glu(£N02Bzl)]n 9 [Glu(£lBzl)]n

10 [Glu(NpMe)]n 11 [Glu(Me3Bzl)]n 12 [Glu(/>N02Bzl)-Glu(Bzl)]n

Other synthetic polypeptides 13 [Ala]n 14 [Glu(Me)]n

15 [Try]n

16 [Lys(Cbz)]n 17 [Asp(/>ClBzl)]n , α form 18 [Asp(/>ClBzl)]n , ω form 19 [Asp(Bzl)]n , α form 20 [Asp(Bzl)]n , ω form 21 [Cys(BzlTh)]n 22 [Glu(Et)-Cys(Bzl)-Glu(Et)]n 23 [Leu, DL-Phe]n

5.40 1.50 100.0

5.42 1.505 100.0 5.25 1.50 102.9 5.30 1.495 101.5 5.35 1.492 100.4 5.34 1.495 100.8 5.32 1.485 100.5 5.51 1.525 99.6 5.35 1.51 101.6 5.39 1.505 100.5 5.47 1.50 98.7 5.42 1.50 99.6

5.41 1.496 99.6 5.43 1.493 99.1 5.42 1.49 99.0 5.38 1.495 100.0 5.40 1.50 100.0 5.20 1.30 90.0

1.496 5.30 1.325 90.0 5.55 1.39 90.0 5.36 1.489 100.0 5.36 1.47 98.7

° Helix parameters derived from unit cell: 2, 5, 13, 14, 16-22. Helix parameters derived from ratio of the Ζ coordinates of the "turn" layer line (= 1/P) and the "1.5 A reflection" (= 1/Λ): 3, 4, 6-12, 15, 23. Where the helix is left-handed, the values given for Ρ and t are magnitudes. b

References: 2, 4, Elliott, A. et al. (1965); 3, Samulski and Tobolsky (1971); 5, Squire and Elliott (1969); 6-12, Fraser et al. (1967b); 13, Brown and Trotter (1956); 14, 23, Bamford et al. (1956); 15, Peggion et al. (1968); 16, Yakel (1953); 17, 18, Takeda et al. (1970); 19, 20, Bradbury et al. (1962a); 21, Fraser et al. (1962a); 22, Fraser et al. (1965c).

c Abbreviations defined on p. xvii. d Coordinates given in Table 9.1. * Mixture of equal parts of D and L polymers. ' Mixture of equal parts of D and L polymers, liquid crystal.

Observed Values of Pitch, Unit Height, and Unit Twist in the α-Helical Conformation in Synthetic Polypeptides

0

TABLE 9.8b

Observed Values of Pitch, Unit Height, and Unit Twist in the α-Helical Conformation in Myoglobin and Lysozyme

Symbol in Figs. 9.7 Helical Number of Pitch Unit height Unit twist and 9.9 segment residues Ρ (A) h (A) t (deg)

Myoglobin" 24 A 16 25 Β 16 26 D 7 27 E1 10 28 E 2 10 29 F 9 30 G 19 31 Η 24

Lysozyme6

32 A 11 33 Β 11 34 C 6 35 D 9

5.45 1.50 99.1 5.47 1.47 96.8 5.27 1.45 99.1 5.49 1.52 99.7 5.47 1.49 98.0 5.40 1.46 97.4 5.49 1.53 100.3 5.41 1.49 99.1

5.42 1.51 100.2 5.44 1.485 98.3 5.61 1.66 106.6 5.41 1.455 96.7

Kendrew (1962). b

Blake et al. (1967).

1.7 ~ ' — Γ

95 100 Unit twist f (deg)

105

FIG . 9.7. Unit height h and unit twist t of α-helices in synthetic polypeptides and proteins. A correlation between these quantities is evident and the fitted curve t = 52.43Λ + 21.08 is compared with the curve predicted from the simplified ribbon model shown in Fig. 9.8. A key to the individual compounds is given in Tables 9.8a and 9.8b.

215


FIG . 9.8. Simplified model of the α-helix to explain the correlation between unit height h and unit twist t. The polypeptide chain is visualized as a ribbon wrapped around a cylinder so as to form a continuous tube. Any variation in h results in a change in t and these changes are related by Eq. (9.14). This relationship is illustrated in Fig. 9.7.

ι 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , 1 1 1 1 I

Unit twist f (deg)

FIG. 9.9. Correlation of unit height h and unit twist t of α-helices in synthetic polypeptides and proteins with * 'allowed'' conformations for [Ala]n (Chapter 6). The relevant regions of the (φ, φ) steric map in Fig. 6.7a for τ(Ν, C

a, C ) = 110° have been trans

formed to give ''normal'' (full line) and "extreme" (broken line) limits in terms of h and t. The allowed regions are sensitive to the value assumed for τ(Ν, C

a, C ) .


a homopolypeptide with the screw symmetry of the α-helix cannot be packed in a crystal in such a manner that all residues have equivalent environments. The impression has been gained from the polymers studied so far that the departure from strict helical symmetry increases with distance from the helix axis and in extreme cases (Parry and Elliott, 1967; Squire and Elliott, 1969, 1972) the symmetries of the main chain and side chains are only tenuously related. Again it should be emphasized that these conclusions are based on plausible arguments rather than an objective test by comparison of observed and calculated intensity transforms.

In summary the geometry of the α-helix in [Ala]n appears to be very close in all respects to that originally suggested by Pauling and Corey (1951a) but appreciable variations in both unit height and unit twist have been observed. Similar variations have been found in globular proteins (Blake et aL, 1967; Watson, 1970) and it can be concluded that the α-helix is capable of some flexibility. Appreciable departures from strict helical symmetry occur in crystals of synthetic polypeptides and regular distortion patterns of long period have been observed (A. Elliott et aL, 1965; Parry and Elliott, 1967). A further result from the study of synthetic polypeptides which has considerable relevance to conformation in fibrous proteins is the observation that in single crystals the α-helix is regularly folded (Padden and Keith, 1965; Padden et aL, 1969). This leads to an approximately equal number of "up" and "down" chains in the crystal and provides convincing support for the finding, from X-ray studies, that models with a single chain direction are not adequate to explain the observed intensity transforms (Elliott and Malcolm, 1958; Bradbury et aL, 1962a; Arnott and Wonacott, 1966b; Takeda et aL, 1970).

Conformation in Fibrous Proteins and Related Synthetic Polypeptides || The Alpha Helix

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