The molecular arrangement in α-keratin

J. Mol. Biol. (1963) 6, 474-482

The Molecular Arrangement in ex-keratin H. R. WILSONt The Children's Cancer Research Foundation and The Children's Hospital Medical Center, Boston, Massachusetts, U.S .A. (Received 5 October 1962, and in revised form 17 January 1963) X-ray analysis gives strong evidence in favour of the hypothesis that oc-kerabins are built up of coiled-coils of o-helices. However, it is not known how the coiledcoils are packed together. Recent electron microscope studies of transverse sections of wool fibres and porcupine-quill tips show that they consist of fibrils 70 to 80 A in diameter, separated by a distance of 80 to 90 A. These fibrils show substructure approximately 20 A in diameter. In this paper an analysis is made of the equator of the X-ray diffraction pattern from o-keratins, leading to an assessment of the agreement between the X-ray and electron microscope data. It is shown that the evidence from X-ray analysis and that from electron microscopy are not in conflict, and the best agreemcnt is obtained with a "9 + 2" arrangement of coiled-coils within the fibrils.

1. Introduction It was proposed by Crick (1952) and by Pauling & Corey (1953) that the k-m-e-f group of fibrous proteins is built up of coiled-coils of o-helices. Calculations by Crick (1953) and Lang (1956) showed that the 5·18 A and 1·49 A meridional spacings from
t

Present address: University of St. Andrews, Queen's College, Dundee, Scotland. 474

475

MOLECULAR ARRANGEMENT IN ex-KERATIN

sections of fibres examined in the electron microscope. Both the equatorial X-ray data and the electron microscopy of transverse sections should indicate how the molecules pack together. These studies alone, however, will not give information about the relative heights of adjacent molecules nor, at the low resolution with which we are concerned, the relative rotation of adjacent molecules.

2. Experimental Data (a) X -ray diffraction data The ex-fibrous proteins of the k-m-e-f group give a characteristic X-ray diffraction pattern with meridional spacings of 5·18 and 1·48 A, and a broad equatorial spacing at ~ 10 A. On high-resolution photographs the broad 10 A region shows variation of intensity. The ex-keratin X-ray pattern from wool, hair and porcupine quill is further characterized by three strong equatorial spots in the low-angle region between 25 and 90 A. The reported equatorial spacings for ex-keratins are given in Table 1. TABLE

1

Equatorial reflections from ex-keratins Porcupine quill Spacing (A) Intensity

83t 45t 28t

10 6 4

15·111

w (diff)

10'5211 9'2211 7-6411

vs vs w(diff)

Wool Spacing (A) Intensity

Human hair Spacing (A) Intensity

9 0t 47t 29t

80'\1 45§ 27§ 16·8§

w

12·2+ 11·2+ 10·4+ 9·2+ 7·8+

vw s s vs w

10 6 4

t Bear & Rugo (1951). + Sikorski quoted by Astbury (1955). § Fraser & MacRae (1957). & Rogers (1959). vw = very weak; w = weak; s = strong; vs = very strong; diff = diffuse.

II Happey (1955). '\I Fraser, MacRae

No quantitative intensity measurements of high-resolution photographs have been reported for ex-keratins. Bear & Rugo (1951) gave a qualitative estimate of the relative intensities of the three low-angle reflections from porcupine quill and hair. In order of decreasing spacing, the relative intensities are in the ratio 10 : 6 : 4. It is difficult to make even a qualitative comparison of the intensities of the low-angle spots with those in the 10 A region, owing to overlap of the true equatorial and nearequatorial layer lines. This overlap has the effect of increasing the apparent intensity of the 10 A equatorial region relative to the low-angle reflections. Photographs from very welloriented specimens are necessary to resolve these close layer lines and so make possible an accurate comparison of low- and high-angle equatorial intensities. (b) Electron micro8copy data

Recent electron microscope studies of transverse sections of wool keratin by Fraser, MacRae & Rogers (1962) have shown fibrils ~80 A in diameter separated by a distance of ~ 90 A. They further show that the fibrils have a substructure of diameter ~ 20 A, and these subunits appear to be arranged in a ring of nine surrounding two others. It is impossible to know whether all the subunits are of the same type. A "9 + 2" arrangement is also found at a higher order of magnitude in other biological structures such as cilia and flagella (Manton, 1952; Fawcett & Porter, 1954; Bradfield, 1955), and similar structures also occur in retinal rods and centrioles (De Robertis, 1956; Burgos & Fawcett, 31

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H. R. WILSON

1955; Porter, 1957). Fraser, MacRae & Rogers identified the subunits with three-stranded coiled-coils which their optical transform studies showed to be in agreement with the meridional X-ray data. Johnson & Sikorski (1962), in a study of porcupine quill, found fibrils of diameter -70 A, separated by a distance of - 83 A. These fibrils also showed substructure, in this case a ring of subunits separated by distances less than 20 A. Johnson & Sikorski were not able to count the number of subunits in the ring. By slightly defocusing the electron microscope they observed what appeared to be central subunits, but when the object was exactly in focus these disappeared. Johnson and Sikorski do not consider the subunits to be end-on projections of coiled-coils, and they suggest that the electron microscope and X-ray results on a-keratin are incompatible. It is unfortunate that these two groups did not examine both wool and porcupine quill, as it would then be possible to make definite conclusions as to whether or not there is a difference in the arrangement of subunits in the two keratins.

3. Analysis of the Equator of the X-ray Diffraction Pattern (a) General

The present analysis is similar to that carried out by Burge (1961) in his study of bacterial flagella. We consider n fibrils in a hexagonal arrangement of limited extent. The fibrils contain m subunits, circular in section, which we consider to be coiled-coils of a-helices. The normalized, cylindrically averaged intensity distribution along the equator, due to these fibrils, is given by (1)

where F(R) is the Fourier transform of the a-helix

ro R

= 2 sin OJ>,

T(u)

= 2

= radius of the major helix

1 m m

m

~ ~JO(21TRupq) p

q

1 n n

T'(u') = 2 ~ ~JO(21TRup'q')

n

P'

q'

The pth and qth units are separated by a distance u pq and the p'th and q'th units are separated by a distance uP ' q" (b) The packing of the fibrils

Burge (1961) has shown that if cylindrical units are packed in a hexagonal arrangement of limited extent, and provided the number of units is small (less than about twelve), then the maxima of the interference function T'(u') will be in the same position as the maxima of J O(21T Rv'), where v' is the distance between centres of nearest neighbors. Therefore, if n is small we should be able to determine v', the separation of the fibrils. To do this we plot the observed equatorial spacing, d, against the reciprocal of the position of the zero-order Bessel function maxima. The Bessel function maxima positions are given by values of i, 2w (British Association

MOLECULAR ARRANGEMENT IN a-KERATIN

477

Tables, 1937) and from the equation d = 2V'[jl,2W]-1 a value of v' is then obtained. Figure 1 shows a plot of spacing d against [jl.2W]-1. The plot is linear and passes through the origin. This gives a value of 92 A for Vi if we use the low-angle spacings of 83, 45 and 28 A (Bear & Rugo, 1951).

FIG. 1. The correlation of the
(c) The structure of the subunits

At this stage we consider the structure of the subunits because it should be simpler to analyse than the packing of the subunits in the fibrils. The structure of the subunits should give the general distribution of intensity along the equator. This is the squared term in equation (1). Crick (1953), Lang (1956) and Fraser & MacRae (1961) have shown that coiledcoils of three a-helices can account for the meridional intensity data. In order to determine the radius of the major helix, r o' which gives the best agreement with the observed equatorial data, it is not necessary to consider the number of a-helices in the coiled-coil. To simplify the calculations, we consider the a-helix to be a righthanded helix of a-poly-L-alanine. The cylindrically averaged intensity from a coiledcoil with r o = 5·5 A is shown in Fig. 2. This is in good agreement with observations, with the low-angle spots falling under the central maximum and the 10 A region spots falling under the first maximum. However, without accurate intensity measurement it is not possible to determine r o to a greater accuracy than ± 0·5 A. Thus, with the available equatorial data it is not possible to prove conclusively that the coiled-coil is three-stranded, although the value of 5·5 A for ro is in agreement with that used by Lang (1956) and by Fraser & MacRae (1961). Accurate intensity measurements should give a more precise value for ro' since the transform of the coiled-coil is zero at the positions of the minima.

478

H. R. WILSON 0'12

0·10

0·08

~0'06 c

'" E

0·04

0·02

o FIG. 2. The normalized, cylindrically averaged intensity of the equatorial X-ray scattering from a coiled-coil of poly-u-alanine, with To = 5·5 A. The arrows show the positions of the observed reflections.

(d) The packing of subunits in the fibrils

It is not possible to determine the packing of the subunits in the fibrils directly from the X-ray data. We can, however, use the electron microscope results to calculate T(u), which enables us to calculate the equatorial intensity, and in turn to compare this with the observed X-ray pattern. Assuming that all the subunits are identical, we can calculate the T(u) function for the "9+2" arrangement observed by Fraser, MacRae & Rogers (1962) and we can also calculate the T(u) function for a ring of nine subunits and ascertain whether it would be possible to detect any difference between these two arrangements from the X-ray data. Figure 3(a) shows the T(u) function for a "9+2" arrangement of cylindrical units. Two "9 + 2" arrangements containing a plane of symmetry are possible, but the interference function is to all intents and purposes the same for both. The fourth order of diffraction has not been reported for o-keratin and must be absent or very weak. Since there is no minimum of the coiled-coil transform at the position of the fourth-order reflection, there must be a minimum of the T(u) function at this point. If we make the third minimum of the T(u) function coincide with the position of the fourth-order reflection we find that this gives a value of 19·5 A for the separation of the subunits. This is about what we would expect if we have coiledcoils with ro = 5·5 A. Moreover, the first and second maxima of the T(u) function are close to the second and third maxima of the T'(u') function, and there is a high maximum of the T(u) function at 9·2 A, which is the strongest part of the high-angle region. The resultant calculated intensity due to a group of three fibrils, with a "9 + 2" arrangement of coiled-coils, is shown in Fig. 4. For this calculation ro = 5·5 A, v = 19·5 A and v' = 92·0 A.

479

MOLECULAR ARRANGEMENT IN ex-KERATIN

11

1\

0-20

0-15 T(u)

0-10

0-05

o

10 (0)

15

o

20 (27TRv)

~

..

5

10

V\ ~

v

V 15

20

(b)

FIG. 3. (a) The interference function, T(u), for a "9 + 2" arrangement of cylindrical units. (b) The interference function, T(u), for a ring arrangement of nine cylindrical units.

OOB -

0·06 »

:!

.& E 0.04

002

a

0·14

FIG. 4. The normalized, cylindrically averaged intensity of the equatorial X-ray scattering by an aggregate of three fibrils, with a "9 + 2" arrangement of coiled-coils within each fibril. The ordinates of the right-hand curve should be divided by ten. The arrows show the positions of the observed reflections. r Q = 5·5 A, v = 19·5 A, v' = 92·0 A.

H. R. WILSON

480

The interference function, T(u), for nine subunits arranged in a ring is shown in Fig. 3(b). The main differences between Fig. 3(a) and 3(b) are in the height of the first maximum and in the position of the first minimum. Using the same argument as before for the "9 + 2" arrangement, we find v = 19·5 A. However, using this value for v and 92 A for Vi, the first and second maxima in the final calculated intensity are nearly equal, and this is contrary to observation. Also, the calculated first maximum position is at '" 105 A which is much larger than the observed value. In order to improve both these factors, and at the same time to keep the fourth order low, v and Vi were reduced by the same fractional amounts. The calculated equatorial intensity for a group of three fibrils with ro= 5·5 A, v = 18·5 A and Vi = 87·5 A is shown in Fig. 5.

0-06

0·02 -

o FIG. 5. The normalized, cylindrically averaged intensity of the equatorial X-ray scattering by an aggregate of three fibrils, with a ring arrangement of nine coiled-coils within each fibril. The ordinates of the right-hand curve should be divided by ten. The arrows show the positions of the observed reflections. TO = 5·5 A, v = 18·5 A, Vi = 87·5 A.

Calculations have been made for a ring arrangement of seven, eight and ten coiledcoils, but the calculated intensities show very poor agreement with the observed pattern. Interference functions have also been calculated for "9+1", "9+3" and "9+4" arrangements of coiled-coils to see whether it would be possible to distinguish between such arrangements from the X-ray data. These calculations show that if only the X-ray data were available, it would need accurate intensity measurements to distinguish between a "9 + 2" and a "9 + 3" arrangement. The "9 + 1" and "9 + 4" arrangements, however, do not give the correct intensity distribution for the lowangle reflections.

4. Discussion The over-all agreement between the calculated intensity for the "9+2" arrangement and the observed pattern is reasonably good. There are three strong low-angle spots in the calculated and in the observed patterns, and the absent fourth order is explained. The spacing at 16·8 A, which Fraser & MacRae (1958) found difficult to explain, is also accounted for. The calculated first maximum occurs at 100 A and not at the observed value of 83 A, but there are two ways of improving the calculated position. One way is to

MOLECULAR ARRANGEMENT IN ex-KERATIN

481

decrease the separation of the fibrils, Vi, and simultaneously to decrease v by the same fractional amount in order to keep the fourth order low. Figure 6 shows the calculated intensity distribution when ro = 5·5 A, v = 18·5 A and Vi = 87·5 A. The calculated first maximum position now occurs at ",95 A, and also the over-all agreement has slightly improved.

0·08

0·06

0·02

FIG. 6. The normalized, cylindrically averaged intensity of the equatorial X-ray scattering by an aggregate of three fibrils with a "9 + 2" arrangement of ooiled-ooils within each fibril. The ordinates of the right-hand curve should be divided by ten. The arrows show the positions of the observed reflections. TO = 5·5 A, v = 18·5 A, v' = 87·5 A.

A second method of improving the agreement between the calculated and observed positions of the first maximum is to increase the number of fibrils in the diffracting unit, which in the present calculations we have assumed to be three. The position of the first maximum is very sensitive to the number of fibrils diffracting coherently because of the rapid variation of the T(u) function in this region. However, the greater the number of fibrils diffracting coherently, the sharper will be the T'(u /) maxima, giving rise to a fourth-order maximum. In any specimen we would expect to find regions with different numbers of fibrils diffracting coherently, but no attempt has been made in the present analysis to consider possible distributions. The agreement in the high-angle region is difficult to assess because of the overlap of the near-equatorial lines which have strong intensities in the 10 A region (Crick, 1953; Cohen & Holmes, 1963). The highest calculated intensity, however, occurs close to the position of the highest observed intensity. Without accurate intensity measurements from well-oriented specimens to resolve the layer lines, further comparison of this region is difficult. For the case of a ring of nine coiled-coils V and Vi have already been decreased in order to improve the ratio between the intensities of the first and second maxima. Even after this decrease, the calculated first maximum occurs at '" 100 A. It is not possible to decrease v and Vi much further as this would produce too large a displacement of the other maxima. Increasing the number of fibrils in the diffracting unit will improve the position of the first maximum, but will reduce its intensity, which

482

H. R. WILSON

is already relatively low. The agreement between the calculated and observed positions of the reflections is, therefore, not as good as for the "9 + 2" arrangement. The final value of 18·5 A for the separation of the coiled-coils suggests that there may be some interpenetration taking place, but if the coiled-coils are segmented (Fraser & MacRae, 1961) the interpenetration may be less than if they are continuous. It is finally concluded that at present there is no conflict between the X-ray and electron microscope results. The "9 + 2" arrangement of coiled-coils within fibrils gives better correlation between the X-ray and electron microscope data than does a ring arrangement of seven, eight, nine or ten coiled-coils; but of the ring arrangements, the one with nine coiled-coils is the most favourable. I should like tothank Dr, Carolyn Cohen for drawing my attention to the problem and for discussions, Drs. D. L. D. Caspar, R. C. G. Killean and R. Langridge for discussions, and Dr. Sidney Farber and the Staff of The Children's Cancer Research Foundation for their kind hospitality. A generous allocation of time on the IBM 7090 by the Massachusetts Institute of Technology Computing Center is gratefully acknowledged. I also wish to acknowledge, with thanks, the award of a Fulbright Travel Grant. This investigation was supported in part by National Cancer Institute, N.I.H., USPHS grant C-4696 (C-3) to Dr. D. L. D. Caspar. Similar calculations to those described in the present paper were carried out independently by Dr. R. E. Burge, and similar conclusions were reached. I am grateful to Dr. Burge for showing me his unpublished results. REFERENCES Bear, R. S. & Rugo, H. J. (1951). Ann. N.Y. Acad. Sci. 53,627. Bradfield, J. R. G. (1955). Proc. Symp. Soc. Exp. Biol. 9, 306. British Association (1937). Mathematical Tables, 6, Bessel functions, part 1. Burge, R. E. (1961). Proc. Roy. Soc. A, 260, 558. Burgos, M. H. & Fawcett, D. W. (1955). Biophys. Biochem. Cytol. I, 287. Cohen, C. & Holmes, K. C. (1963). J. Mol. Biol. 6, 423. Crick, F. H. C. (1952). Nature, 170, 882. Crick, F. H. C. (1953). Acta Cryst. 6, 689. De Robertis, E. (1956). Biophys. Biochem. Cytol. 9, 211. Fawcett, D. W. & Porter, K. R. (1954). J. Morph. 94, 221. Fraser, R. D. B. & MacRae, T. P. (1957). Nature, 179, 732. Fraser, R. D. B. & MacRae, T. P. (1958). Biochim. biophys. Acta, 29, 229. Fraser, R. D. B. & MacRae, T. P. (1961). J. Mol. Biol. 3, 640. Fraser, R. D. B., MacRae, T. P. & Rogers, G. E. (1959). Nature, 183, 592. Fraser, R. D. B., MacRae, T. P. & Rogers, G. E. (1962). Nature, 193, 1052. Happey, F. (1955). Proc. Int. Wool Text. Res. Coni. B, p. 149. Melbourne, Australia: C.S.I.R.O. Johnson, D. J. & Sikorski, J. (1962). Nature, 194, 31. Lang, A. R. (1956). Acta Cryst. 9, 436. Manton, I. (1952). Proc. Symp. Soc. Exp. Biol. 6, 306. Pauling, L. & Corey, R. B. (1953). Nature, 171, 59. Porter, K. R. (1957). Harvey Lect. 51, 175. Sikorski, J. (1955). Reported by Astbury, W. T. (1955), Proc. Int. Wool Text. Res. Conj. B, p. 202. Melbourne, Australia: C.S.I.R.O.