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The crystal symmetry of DNA
W. FULLER ET AL.
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Trueblood, K. N., Horn, P. & Luzzati, V. (1961). Acta Cryst. 14, 965. Watson, J. D. & Crick, F. H. C. (1953). Nature, 171, 964. Wilkins, M. H. F. (1956). Cold Spr, Harb. Symp. Quant. Biol. 21, 75. Wilkins, M. H. F. (1957). Special Publications, N. Y. Acad. Sci. 5, 180. Wilkins, M. H. F. (1961). J. Chim. Phys. 891. Wilkins, M. H. F., Seeds, W. E., Stokes, A. R. & Wilson, H. R. (1953). Nature, 172, 759. Wilkins, M. H. F., Stokes, A. R. & Wilson, H. R. (1953). Nature, 171, 738. Wilkins, M. H. F. & Zubay, G., (1959). J. Biophys. Biochem. Cytol. 5,55. Wilkins, M. H. F., Zubay, G. & Wilson, H. R. (1959). J. Mol. Biol. 1, 179.
Appendix The Crystal Symmetry of DNA STRUTHER ARNOTT
Medical Research Oouncil Biophysics Research Unit King's Oollege, 26-29, Drury Lane, London, W.0.2
1. Introduction In their studies of highly crystalline sodium (A) and lithium (B) salts of DNA, Wilkins and his collaborators (Fuller, Wilkins, Wilson & Hamilton, 1965; Langridge et al., 1960; and Marvin, Wilkins & Hamilton, 1965) have assumed that A belongs to the monoclinic crystal class and B to the orthorhombic system. On the basis of systematically absent X-ray reflections and the presence of an asymmetric group in the deoxyribosyl parts of DNA, the space groups 02 and P2 1212 1 have been assigned. This assignment is compatible with the prevailing description of the conformational symmetries and molecular arrangements in the two DNA crystal forms. It is incompatible (loc. cit.; Wilkins, 1960), in particular, with any of the purine-pyrimidine base-pairing schemes described by Donohue (Donohue, 1956; Donohue & Trueblood, 1960), except those described by Watson & Crick (1953) and by Hoogsteen (1959). That no inconsistencies have arisen in the detailed analysis of the two crystal structures is the principal support for the space group assignment, since in neither case do the systematic absences alone provide adequate evidence for the symmetry elements assumed. In the A form, the systematically absent X-ray reflections which occur in hkl when (h + k) is odd are a consequence only of the lattice symmetry resulting from the choice of a 0 face-centred unit cell. In the B form, the presence of three mutually perpendicular 2-fold screw axes has to be inferred only from absences, 1, in hOO, OkO and OOl, for which there are few reflections. when h,k,l = 2n A more detailed analysis of the X-ray data was therefore undertaken to investigate whether an a priori space group determination could be made on the basis of the distribution of intensities alone, and therefore with minimum appeal to the structural details of particular molecular models. The method adopted was the N(z) test of Howells, Phillips & Rogers (1950), who have shown that the fraction, N(z), of intensities having a value less than a fraction z of the local average is erf (tz) for a centrosymmetric, and 1 - exp( - z) for a non-centrosymmetric distribution.
+
CONFIGURATION OF DEOXYRIBONUCLEI C ACID
77
2. Procedure N on- centrosymmetric crysta ls may po ssess a variet y of symmet ry elements which give rise to a centric di stribution of int ensity in part icular reflect ion classes. Conversely, a com p ar ison of the intensit y di stributions in various lines and zon es of r eflections wi th t h e ove r -all distribution can b e us ed t o diagnose the presence of particular symmetry eleme nts. F or exam ple, the space gro u p 0 2 requires a centric d istribution of intensity in hOl and ac entric distributions in Okl, hkO and hkl, while in P212121 hkO, hOl, Okl should all have cen t r ic distributions, and hkl an ac entric di stribution. The 222 l o(hk l) values for t h e A form which had l « 6 and no index zero were divided into 5 equal gr oups ac cording to their distance fr om the reciprocal lattice origin. In each group the average inten sity , was ob t a ine d and used to derive values of z = 1/<1> . The values of N(z) for z = 0,1, 0·2, .. . 1·0 were calculated an d the five values for each z
z
z
FIG. 1. The N(z) axis is marked off in intervals of 0·1; z = 0(0·1) 1·0. The full lines show the th eoretical values for a centric (upper) and acentric (lower) distribution of intensit ies. The circles show the distributions of intensity: (a) in hkl for NaDNA; (b)in hklfor model I; (c) in hkO and Okl for NaDNA; (d) in hkO and Okl for model I; and the intensity distributions in hOI for: (e) NaDNA ; (f) model I; (g) model II; (h) model III. aver aged to give the result s illu strated in Fig. l(a). The zones hOl, hkO and Okl contain 27, 28 and 31 sp ectra, respectively. In eac h case the r eflections were di vided in t o t wo groups a nd t he average d istribution ca lculated. The first d istribution is shown in Fig. l(e) and t he m ean of t he secon d two, which are sim ilar, in Fig. l(c) . This statistical t est is rigor ou sly valid only when t he an alysis is m ade u sing all t he p oint s of reciprocal sp ace , but it is a characteristic of crystalline fibre d iffraction di agrams t hat only a limited region of reciprocal space n ear the origin is recorded. The theory als o r equires t he distribution of at omic p osi tions in the unit cell t o b e effect ive ly random, a situation which cannot be as sumed t o ex ist in DNA. For these r eas ons it was decided to det ermine the d istribution of intensities for a number of model systems, in the sam e regions of reciprocal space and in exactly t h e same manner as in t he in vestigation of t he observed
W. FULLER ET AL.
78
intensit.ies. Thereby most of the theoretical objections could be anticipated and the sensitivity of such low resolution to the presence or absence of the symmetry elements in question determined. The most symmetrical model chosen, I, containing all the symmetry elements of 02, had the structure already described for NaDNA (Fuller, Wilkins, Wilson &
CI
(I
FIG. 2. The Donohue-type base-pairing scheme of NaDNA models II and III. The bases in models I, II, III lie on the same planes and have Cl '" Cl coincident.
z
z
FIG. 3. The averaged intensity distribution in LiDNA: (a) observed in hkO, Okl, hOI; (b) calculated in hkO, Okl, hOI for Watson-Crick type model BIII; (c) observed in hkl; (d) calculated in hkl for the model. The error bars have a total length equal to twice the root mean square deviation in the various groupings.
Hamilton, 1965). Model II retained all the features of I except that the average WatsonCrick base pairs, which have a dyad in the plane of the bases, were replaced by a Donohue set possessing a dyad axis perpendicular to the base plane (see Fig. 2). In model III the bases were of the Donohue kind as in model II, but the second sugar-phosphate chain was related to the first by a dyad parallel to the molecular helix axis. No attempt was made to
CONFIGURATION OF DEOXYRIBONUCLEIC ACID
79
make models II and III stereochemically reasonable, since intensity statistics are grossly insensitive to co-ordinate errors and reflect only the symmetry of the system chosen. Figure l(b) and (d) show the intensity distributions calculated from model I and corresponding to the observed distribution shown in Fig.l (a) and (c), respectively. The distributions for the unique hOl zone for models I, II and III are shown in Fig. l(f),(g),(h). In a similar way the distributions of the observed intensities with l <;;: 8 in LiDNA were calculated and compared with those provided by the model system BIll described elsewhere (Arnott, 1964). The results are shown in Fig. 3 and were derived for 27 reflections in hOl, 31 in Okl, 28 in hkO and 113 in hkl.
3. Discussion The irregularities in the distributions are not unexpected when one considers the relatively small number of data available. Inaccuracy also arises in dividing observed intensities between reciprocal lattice points where the g-values are almost equal and therefore the reflections overlap. Nevertheless, the observations for NaDNA show (Fig. l{e)) the centric distribution in (hOl), and the acentric distribution in the other reflection classes (Fig l{a),{c)) characteristic of 02. Sampling errors in the model distributions should be of the same kind as in the observed distributions. It can be seen by comparing the information from models with varying degrees of symmetry that, even with data of small number and low resolution, the method is sensitive enough to allow a space group assignment to be made, since the distribution of the intensities in hOl changes from centric to acentric when the Watson-Crick dyad is absent. The further possibility that the dyad along b results from a statistical arrangement of polar Donohue-type DNA molecules with "up" and "down" molecules occurring randomly in the crystals is ruled out, since this would give centric intensity distributions in Okl, which is not the case (cf. Fig. l{c) and (g)). The analysis of the LiDNA observations shows quite conclusively that the intensity distributions in the hkO, Okl and hOl zones are of the same type, distinct from that of the rest of the reflections, and are of the kind expected in space group P2 12 121 • There is a systematic departure from the theoretical curves in this case, which is undoubtedly due to the very non-random atomic distribution, which results in a higher proportion than usual of accidental absences. This hypersymmetry is not surprising, since the two molecules passing through the unit cell have forty interdigitating dyads perpendicular to c. It is interesting that in spite of the violations of the theoretical requirements of the analysis, the distributions are similar to the conventional patterns. That this is not fortuitous is demonstrated by the model systems. The presumed crystal symmetry in both forms of DNA, and the consequent constraints in the symmetries allowed in DNA molecular models, are therefore supported in a very direct way by the X-ray diffraction data. This appendix was improved by the helpful criticism of Professor David Rogers. REFERENCES Arnott, S. (1964). Bull. Inst, Phys. 15, 169. Donohue, J. (1956). Proc. Nat. Acad. Sci., Wash. 42,60. Donohue, J. & Trueblood, K. N. (1960). J. Mol. Biol. 2, 363. Fuller, W., Wilkins, M. H. F., Wilson, H. R. & Hamilton, L. D. (1965). J. Mol. Biol. 12, 60. Hoogsteen, K. (1959). Acta Cryst. 12, 822.
80
w.
FULLER ET AL.
Howells, E. n., Phillips, D. C. & Rogers, D. (1950). Acta Cryat. 3, 210. Langridge, R., Marvin, D. A., Seeds, W. E., Wilson, H. n., Hooper, C. w., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. Mol. Biol. 2,38. Marvin, D. A., Wilkins, M. H. F. & Hamilton, L. D. (1965). Acta Cryat. in the press. Watson, J. D. & Crick, F. H. C. (1953). Nature, 171, 737. Wilkins, M. H. F. (1960\. Biological Structure and Function, vol. 1. New York: Academic Press.
76
Trueblood, K. N., Horn, P. & Luzzati, V. (1961). Acta Cryst. 14, 965. Watson, J. D. & Crick, F. H. C. (1953). Nature, 171, 964. Wilkins, M. H. F. (1956). Cold Spr, Harb. Symp. Quant. Biol. 21, 75. Wilkins, M. H. F. (1957). Special Publications, N. Y. Acad. Sci. 5, 180. Wilkins, M. H. F. (1961). J. Chim. Phys. 891. Wilkins, M. H. F., Seeds, W. E., Stokes, A. R. & Wilson, H. R. (1953). Nature, 172, 759. Wilkins, M. H. F., Stokes, A. R. & Wilson, H. R. (1953). Nature, 171, 738. Wilkins, M. H. F. & Zubay, G., (1959). J. Biophys. Biochem. Cytol. 5,55. Wilkins, M. H. F., Zubay, G. & Wilson, H. R. (1959). J. Mol. Biol. 1, 179.
Appendix The Crystal Symmetry of DNA STRUTHER ARNOTT
Medical Research Oouncil Biophysics Research Unit King's Oollege, 26-29, Drury Lane, London, W.0.2
1. Introduction In their studies of highly crystalline sodium (A) and lithium (B) salts of DNA, Wilkins and his collaborators (Fuller, Wilkins, Wilson & Hamilton, 1965; Langridge et al., 1960; and Marvin, Wilkins & Hamilton, 1965) have assumed that A belongs to the monoclinic crystal class and B to the orthorhombic system. On the basis of systematically absent X-ray reflections and the presence of an asymmetric group in the deoxyribosyl parts of DNA, the space groups 02 and P2 1212 1 have been assigned. This assignment is compatible with the prevailing description of the conformational symmetries and molecular arrangements in the two DNA crystal forms. It is incompatible (loc. cit.; Wilkins, 1960), in particular, with any of the purine-pyrimidine base-pairing schemes described by Donohue (Donohue, 1956; Donohue & Trueblood, 1960), except those described by Watson & Crick (1953) and by Hoogsteen (1959). That no inconsistencies have arisen in the detailed analysis of the two crystal structures is the principal support for the space group assignment, since in neither case do the systematic absences alone provide adequate evidence for the symmetry elements assumed. In the A form, the systematically absent X-ray reflections which occur in hkl when (h + k) is odd are a consequence only of the lattice symmetry resulting from the choice of a 0 face-centred unit cell. In the B form, the presence of three mutually perpendicular 2-fold screw axes has to be inferred only from absences, 1, in hOO, OkO and OOl, for which there are few reflections. when h,k,l = 2n A more detailed analysis of the X-ray data was therefore undertaken to investigate whether an a priori space group determination could be made on the basis of the distribution of intensities alone, and therefore with minimum appeal to the structural details of particular molecular models. The method adopted was the N(z) test of Howells, Phillips & Rogers (1950), who have shown that the fraction, N(z), of intensities having a value less than a fraction z of the local average is erf (tz) for a centrosymmetric, and 1 - exp( - z) for a non-centrosymmetric distribution.
+
CONFIGURATION OF DEOXYRIBONUCLEI C ACID
77
2. Procedure N on- centrosymmetric crysta ls may po ssess a variet y of symmet ry elements which give rise to a centric di stribution of int ensity in part icular reflect ion classes. Conversely, a com p ar ison of the intensit y di stributions in various lines and zon es of r eflections wi th t h e ove r -all distribution can b e us ed t o diagnose the presence of particular symmetry eleme nts. F or exam ple, the space gro u p 0 2 requires a centric d istribution of intensity in hOl and ac entric distributions in Okl, hkO and hkl, while in P212121 hkO, hOl, Okl should all have cen t r ic distributions, and hkl an ac entric di stribution. The 222 l o(hk l) values for t h e A form which had l « 6 and no index zero were divided into 5 equal gr oups ac cording to their distance fr om the reciprocal lattice origin. In each group the average inten sity , was ob t a ine d and used to derive values of z = 1/<1> . The values of N(z) for z = 0,1, 0·2, .. . 1·0 were calculated an d the five values for each z
z
z
FIG. 1. The N(z) axis is marked off in intervals of 0·1; z = 0(0·1) 1·0. The full lines show the th eoretical values for a centric (upper) and acentric (lower) distribution of intensit ies. The circles show the distributions of intensity: (a) in hkl for NaDNA; (b)in hklfor model I; (c) in hkO and Okl for NaDNA; (d) in hkO and Okl for model I; and the intensity distributions in hOI for: (e) NaDNA ; (f) model I; (g) model II; (h) model III. aver aged to give the result s illu strated in Fig. l(a). The zones hOl, hkO and Okl contain 27, 28 and 31 sp ectra, respectively. In eac h case the r eflections were di vided in t o t wo groups a nd t he average d istribution ca lculated. The first d istribution is shown in Fig. l(e) and t he m ean of t he secon d two, which are sim ilar, in Fig. l(c) . This statistical t est is rigor ou sly valid only when t he an alysis is m ade u sing all t he p oint s of reciprocal sp ace , but it is a characteristic of crystalline fibre d iffraction di agrams t hat only a limited region of reciprocal space n ear the origin is recorded. The theory als o r equires t he distribution of at omic p osi tions in the unit cell t o b e effect ive ly random, a situation which cannot be as sumed t o ex ist in DNA. For these r eas ons it was decided to det ermine the d istribution of intensities for a number of model systems, in the sam e regions of reciprocal space and in exactly t h e same manner as in t he in vestigation of t he observed
W. FULLER ET AL.
78
intensit.ies. Thereby most of the theoretical objections could be anticipated and the sensitivity of such low resolution to the presence or absence of the symmetry elements in question determined. The most symmetrical model chosen, I, containing all the symmetry elements of 02, had the structure already described for NaDNA (Fuller, Wilkins, Wilson &
CI
(I
FIG. 2. The Donohue-type base-pairing scheme of NaDNA models II and III. The bases in models I, II, III lie on the same planes and have Cl '" Cl coincident.
z
z
FIG. 3. The averaged intensity distribution in LiDNA: (a) observed in hkO, Okl, hOI; (b) calculated in hkO, Okl, hOI for Watson-Crick type model BIII; (c) observed in hkl; (d) calculated in hkl for the model. The error bars have a total length equal to twice the root mean square deviation in the various groupings.
Hamilton, 1965). Model II retained all the features of I except that the average WatsonCrick base pairs, which have a dyad in the plane of the bases, were replaced by a Donohue set possessing a dyad axis perpendicular to the base plane (see Fig. 2). In model III the bases were of the Donohue kind as in model II, but the second sugar-phosphate chain was related to the first by a dyad parallel to the molecular helix axis. No attempt was made to
CONFIGURATION OF DEOXYRIBONUCLEIC ACID
79
make models II and III stereochemically reasonable, since intensity statistics are grossly insensitive to co-ordinate errors and reflect only the symmetry of the system chosen. Figure l(b) and (d) show the intensity distributions calculated from model I and corresponding to the observed distribution shown in Fig.l (a) and (c), respectively. The distributions for the unique hOl zone for models I, II and III are shown in Fig. l(f),(g),(h). In a similar way the distributions of the observed intensities with l <;;: 8 in LiDNA were calculated and compared with those provided by the model system BIll described elsewhere (Arnott, 1964). The results are shown in Fig. 3 and were derived for 27 reflections in hOl, 31 in Okl, 28 in hkO and 113 in hkl.
3. Discussion The irregularities in the distributions are not unexpected when one considers the relatively small number of data available. Inaccuracy also arises in dividing observed intensities between reciprocal lattice points where the g-values are almost equal and therefore the reflections overlap. Nevertheless, the observations for NaDNA show (Fig. l{e)) the centric distribution in (hOl), and the acentric distribution in the other reflection classes (Fig l{a),{c)) characteristic of 02. Sampling errors in the model distributions should be of the same kind as in the observed distributions. It can be seen by comparing the information from models with varying degrees of symmetry that, even with data of small number and low resolution, the method is sensitive enough to allow a space group assignment to be made, since the distribution of the intensities in hOl changes from centric to acentric when the Watson-Crick dyad is absent. The further possibility that the dyad along b results from a statistical arrangement of polar Donohue-type DNA molecules with "up" and "down" molecules occurring randomly in the crystals is ruled out, since this would give centric intensity distributions in Okl, which is not the case (cf. Fig. l{c) and (g)). The analysis of the LiDNA observations shows quite conclusively that the intensity distributions in the hkO, Okl and hOl zones are of the same type, distinct from that of the rest of the reflections, and are of the kind expected in space group P2 12 121 • There is a systematic departure from the theoretical curves in this case, which is undoubtedly due to the very non-random atomic distribution, which results in a higher proportion than usual of accidental absences. This hypersymmetry is not surprising, since the two molecules passing through the unit cell have forty interdigitating dyads perpendicular to c. It is interesting that in spite of the violations of the theoretical requirements of the analysis, the distributions are similar to the conventional patterns. That this is not fortuitous is demonstrated by the model systems. The presumed crystal symmetry in both forms of DNA, and the consequent constraints in the symmetries allowed in DNA molecular models, are therefore supported in a very direct way by the X-ray diffraction data. This appendix was improved by the helpful criticism of Professor David Rogers. REFERENCES Arnott, S. (1964). Bull. Inst, Phys. 15, 169. Donohue, J. (1956). Proc. Nat. Acad. Sci., Wash. 42,60. Donohue, J. & Trueblood, K. N. (1960). J. Mol. Biol. 2, 363. Fuller, W., Wilkins, M. H. F., Wilson, H. R. & Hamilton, L. D. (1965). J. Mol. Biol. 12, 60. Hoogsteen, K. (1959). Acta Cryst. 12, 822.
80
w.
FULLER ET AL.
Howells, E. n., Phillips, D. C. & Rogers, D. (1950). Acta Cryat. 3, 210. Langridge, R., Marvin, D. A., Seeds, W. E., Wilson, H. n., Hooper, C. w., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. Mol. Biol. 2,38. Marvin, D. A., Wilkins, M. H. F. & Hamilton, L. D. (1965). Acta Cryat. in the press. Watson, J. D. & Crick, F. H. C. (1953). Nature, 171, 737. Wilkins, M. H. F. (1960\. Biological Structure and Function, vol. 1. New York: Academic Press.