LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS. PART 2. BY CONMAROBINSON, J. C. WARD AND R. B. BEEVERS Courtaulds Ltd., Research Laboratory, Lower Cookham Rd., Maidenhead, Berks Received 1 1 th February, 1957 The model previously published describing the arrangement of the molecular orientation in the cholesteric-like twisted structures found in solutions of poly-y-benzyl-L-glutamate and poly-y-methyl-L-glutamate has been confirmed. The relationship of this structure to that found in a racemic solution of the L and D enantiomorphs of poly-y-benzyl- glutamate is explained. A tentative model of the arrangement of the rnolecirles in the twisted structure is discussed in the light of X-ray and other evidence. In part 1 1 of this series a liquid crystalline structure which was found in bire- fringent solutions of poly-y-benzyl-L-glutamate (PBLG) and of poly-y-methyl-L- glutamate (PMLG) was described, This structure in a number of ways resembles that formed by various esters and ethers of cholesterol 2 and is characterized by a helical twist of very large and uniform pitch. A model describing the three- dimensional distribution of the molecular orientations in space was proposed as being consistent with the polarization-microscopic observations.This model, which has since received considerable confirmation, is shown in fig. 1. FIG. 1.-Model of the twisted structure. A', Y and 2 are Cartesian co-ordinates. 5 and r) are given by the equations : 2 n z 2 n z 8 = XCOS-+ P Ysin- P ' 2.572 2nZ P P y = Yccs--Xsin--, so that 5, r ) and 2 form a twisted co-ordinate system.The rod-like inolecules all lie at right-angles, or nearly at right-angles, to Z, the axis of torsion and parallel to 6. (The planes drawn in fig. 1 are not intended to indicate that the molecules are segregated into planes, the polarization microscope having provided no evidence on this point.) Since the highest refractive index is for light vibrating parallel to the long axes of the molecules, if the structure is observed in a direction parallel to Y, both the refractive index and the retardation will show a maximum value for every 2930 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS path for which 8 is at right-angles to Y and a minimum value where it is parallel to Y. This gives rise to periodic lines a distance S apart (where 2s = P, the pitch of the torsion) which are visible even in natural light, and similarly spaced bands of retardation colours when observed between crossed nicols.If the observation is made in a direction parallel to 2 no periodicities are seen but only the uniform areas described in part 1. For light travelling in this direction, however, the structure has a very high form optical rotatory power which can be shown to be a function of the torsional pitch. (This form optical rotatory power of the multi- molecular structure is distinct from, and greater by several powers of ten than, the form optical rotatory power arising from the a-helical configuration which the individual molecules of these polypeptides are known to assume.3s4) The value of S is dependent on solvent, concentration and temperature, but in any solution in which these are uniform, the structzrre will be the same and as shown in fig.1. On the other hand the orientation of the Cartesian frame of reference X, Y, 2 may change continuously from one part of the solution to another, and produce a particular macroscopic pattern of orientation which ex- tends throughout the birefringent phase. The texture * of a specimen of the material is the three-dimensional pattern thus produced, but the structzrre of any smallt cube of material will be the same throughout every texture though its orientation will be different. Fig. 10 and 11 of part 1 show two different textures which formed in glass capillaries. In the first the visible lines are everywhere parallel to the axis of the capillary; in the other they show a more complicated arrangement, but in each the structure is as in fig.1. When the concentration of the polypeptide does not exceed a concentration A (dependent on temperature and molecular weight) the solution is isotropic, while above a concentration B only the birefringent phase exists. Between A and B both the isotropic and the birefringent phase exist in different proportions, though the concentration of each phase remains constant in accordance with the phase rule. In this two-phase system the birefringent phase may be found dis- persed in the isotropic phase in the form of spherical droplets which show charac- teristic spiral patterns (fig. 5 and 6, part 1) when the microscope is focused on a plane through their centre) and which show the same periodicities as the texture of the undispersed phase of equal concentration.Each of these spherulites shows a single radial line of dislocation, so that the sphere has polarity. A complete description of the molecular orientation in the spherulitic texture which would give rise to these patterns has been put forward by Prof. M. H. L. Pryce and Prof. F. C. Frank, as we shall explain in the appendix. It will be seen that their very elegant treatment is consistent with the supposition that every very small volume of the spherulite has the structure shown in fig. 1. This considerably strengthens our confidence in the correctness of our model. Further confirmation has been obtained from quantitative measurements of the optical rotatory power.Several attempts have been made to explain the optical rotatory power of cholesteric liquid crystals.5~ 6.7 De Vries7 has deduced a theoretical expression for this, a simplified form of which, in terms of observable quantities is 0 =- 4.5 x 104n2PfX2 where 8 is the optical rotation observed parallel to the axis of the twisted structure in deg. fmm, n is the birefringence of what we may refer to as the untwisted medium, h is the vacuum wavelength of light in microns and P is the pitch of the helix in microns. The negative sign indicates the optical rotation is in the opposite sense to the twist of the helix. No data were available to de Vries which would have allowed him to verify his relationship but the polypeptide solutions with their * This word has been used by Friedel in his description of liquid crystals.ti.e. small compared with the dimensions invoived in describing the pattern, but containing a large number of molecules.C. ROBINSON, J . C. WARD AND R . B . BEEVERS 31 large spacings which can conveniently be varied by altering the concentration or the solvent are suitable for providing such data. As has already been briefly reported by Robinson and Wards it has been possible to confirm this equation by measurements on 14 different solutions, covering a range of both concentra- tion and solvents. It was not possible to obtain a dependable value for n from the twisted structure in the optically active polypeptide solution, but it was found that a racemic mixture of the D and L enantiomorphs formed a birefringent solu- tion which, when introduced into a glass capillary, became highly oriented, and exhibited a constant birefringence throughout the solution (except near the menisci).The value of this birefringence was reproducible, the material in fact having formed a single uniaxial liquid crystal. This nematic structure which is obtained in the racemic mixture corresponds, we believe, to the untwisted form of the structure in the L enantiomorph solution. The value of the birefringence so obtained agrees with that calculated (using the above formula) from the optical rotatory power of the several solutions of PBLG. The results, therefore, not only show that de Vries's equation holds for the PBLG structures but demonstrates quantitatively that the " cholesteric " structure obtained with either enantiomorph may be looked upon as a twisted form derived from the nematic structure, the former arising as a result of the left- or right-handedness of the L or D enantio- morph.This work will be reported in more detail in a later paper. We may therefore have some confidence that our model correctly represents the distribution of molecular orientation within the structure. This in itself tells us little concerning the molecular distribution and how it varies with the concentration, but some insight into this has been obtained by other means as we shall explain later. Nine preparations of PBLG were used covering the range of molecular weight shown in table 1. The preparations were purified by dissolving in chloroform and precipitated by poured into a large excess of methanol. The specific preparation R 3 R 10 R 4 R 2 R S R 8 R 9 R 6 R 11 TABLE 1 'ISPJC 0-106 0.188 0.190 0.269 0.500 0.68 1.1 1 1 *22 1 -92 residues per molecule 60 90 102 135 274 385 673 728 1255 viscosities of their 0.5 % solutions were determined, and their molecular weights estimated by using Doty, Bradbury and Holtzer's 3 relationship connecting the molecular weight of this polypeptide with the limiting viscosity.The preparation of poly-y-benzyl-D-glutamate (PBDG), was of fairly low molecular weight as were the two samples of poly-y-methyl-L-glutamate (PMLG). All observations were made in a room thermostatted at 22" C. While not under observation solutions were kept in a water thermostat at this temperature.EXPERIMENTAL Solutions were made up by weighing the polymer and solvents into 2 ml stoppered bottles. After prolonged shaking on a slow stirrer and then standing until the regular structure appeared, the visible periodicity was measured with a low-power microscope while the bottle was immersed in a liquid of suitable refractive index. The time required for the regular structure to appear varied from hours to a few weeks according to the32 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS 5 0 - 4 0 c - E 8 30- --? - c 0 .- L E! 2 0 - QI c 0 10- system being observed. The volume of the solution was calculated from the density of the solvent and the density of the polymer (taken as 1.3), any contraction on dissolving being neglected. Some of the smallest values of S were measured by filling a glass capillary with the solution and observing the sealed capillary in an immersion liqJid under higher magnification. The optical rotation was measured in fused glass cells fitted with ground glass stoppers ar,d having parallel sides 1 mm apart.A polarization micro- scope was used for this purpose. - DEPENDENCE OF A AND B POINTS ON MOLECULAR WEIGHT Fig. 2 and 3 show how the A point (the concentration above which the isotropic phase cannot exist) and the B point (the lowest concentration at which the birefringent phase can exist) depend on the molecular weight. A and B are in m1/100ml. The A points S I I * I C * ~ * ~ ~ ~ 0 - Apoints 8- Bpoints FIG. 2.-Molecular weight dependence of the A and B points. PBLG in dioxan.1 I . a . . . . . . . 0 2 200 4 0 0 bOO 8 0 0 1000 1 2 0 0 residues per molecule FIG. 3.-Mo~ecdar weight dependence of the A and B points. PBLG in methylene chloride.C . ROBINSON, J . C . WARD A N D R . B . BEEVERS 33 could be determined with little difficulty within rather wide limits, but the B points could only be determined approximately owing to the difficulty of detecting small amounts of the isotropic phase when dispersed in the birefringent phase, and because of the long period required to bring about separation. It will be seen that A and B have much the same values for either dioxan or methylene chloride as the solvent. A similar impression was obtained with the other solvents less systematically studied : chloroform, rn-cresol, dichloracetic acid.The results show how increasing the molecular length extends the concentration range over which the birefringent phase is stable. Bernal and Fankuchen 9 suggested that for aqueous birefringent solutions of tobacco mosaic virus which will be discussed in a later section, the A point might be inversely proportional to I and the B point to I*, where I is the length of the molecule. It is clear that these relationships do not hold for the polypeptide solutions. DEPENDENCE OF s ON CONCENTRATION Fig. 4 and 5 show the dependence of S, the visible periodic spacing, on concentration, sol- vent and molecular weight. The B point determined the lower concentration limit of obser- vation (the spacing as stated remaining constant between A and B) while the upper limit O \ , , , , , , 2:o 2 0 4 0 b 0 8 0 100 concentra tion(m>lOOml) FIG.4.-Double logarithmic plot of S against concentration. PBLG in dioxan. was determined by the viscosity preventing observations being made within a reasonable time. The results for dioxan (fig. 4) show that S is proportional to l/C2 and independent of molecular weight. Similar results obtained for PBLG (R5) and for the two samples of PMLG in rn-cresol are shown in fig. 5. The value of S obtained at a given concentration depends to a marked extent on the solvent used. Thus, for a concentration of 20 m1/100 ml the values of S for PBLG were (approximately) : CHC13 0.10, CHC12 0.04, dichloracetic acid 0.03 and rn-cresol0-007 mm. The results obtained in chloroform and methylene chloride between 20 and 30 m1/100 m! were, however, too erratic to allow the slope of the curve to be determined, sometimes a comparatively large spacing being obtained which after a few days changed to a lower B34 LIQUID CRYSTALLINE STRUCTURE I N POLYPEPTIDE SOLUTIONS value.It is not yet clear whether this was due to impurities or to the structure being less stable in these solvents. Yang and Doty 10 have shown from the dispersion of the optical rotation that the molecules of PBLG are in the randomly coiled configuration in isotropic solutions in dichloracetic acid. It was therefore interesting to find the regular periodicities and optical rotation associated with the twisted structure in the more concentrated solutions (see plate la). However, Downie, Elliott, Hanby and Malcolm 11 have shown that if such a 8 - R 5 0 - PMLC,I 0 - PMLC,2 I I -I * r'o 2 0 4 0 concentration (m1;/10ornl.) FIG. 5.-Double logarithmic plot of S against concentration.PBLG and PMLG in m-cresol. birefringent solution is heated until it becomes isotropic, the solution shows positive optical rotation ; while the more dilute solutions which Yang and Doty studied showed negative optical rotation. Downie, Elliott, Hanby and Malcolm interpreted this as indicating that the more concentrated solutions were in the a-helical configuration. It would seem, then, that here as in the other polypeptide solutions showing the twisted structure, the molecules are in the a-helix co&uration. X-RAY INVESTIGATIONS One preparation, R 5, of PBLG was used throughout. Dioxan was used as a solvent on account of its relatively high transparency to X-rays.The solutions were introduced into 1-0 mm or 0.5 mm diameter Pantak capillaries having a wall thickness of 0.01 mm. Two distinct methods of filling the capillaries were used. In the fmt the solution was sucked into the capillary with the aid of a micro-syringe and the capillary then sealed ; in the second the desired amount of solid PBLG and solvent were introduced into the capillary, which was sealed, and only used for X-ray irradiation when the uniformity of the microscopic spacings showed that equilibrium had been reached. In either case some solvent was liable to be lost during the manipulation, so S was measured microscopically and C determined from the S against C relationship of fig.4. In the racemic solution of PBLG and PBDG which showed no visible periodicity, the original concentration of the solution was used.PLATE la.-?BLG (R 5 ) in dichloracetic acid ; natural light ; concn. 33-3 rn1/100 ml ; s = 18.4 >: 10-4 crn. [To face page 34PLATE 1 (b), (c), (d). PLATE 1b.-X-ray diffraction pattern ; PBLG in dioxan ; capillary vertical ; concn. PLATE ]lc.-X-ray diffraction pattern ; PBLG in dioxan ; capillary vertical ; concn. 46 m1/100 ml. PLATE Id.-X-ray diffraction pattern ; racemic solution of PBLG and PBDG ; capillary 38.0 ml/l00 ml. (The outermost ring is due to the solvent.) vertical ; total concn. 20.8 m1/100 ml.C. ROBINSONy J . C. WARD AND R . B . BEEVERS 35 The first method of filling generally gave some limited area of the capillary where the visible lines were parallel to the capillary axis (cf, part 1, fig.10). With the second method there was no shearing to produce orientation, and the appearance more resembled fig. 11 of part 1. We shall refer to the first of these arrangements as the oriented texture and the second as the unoriented texture. The photographs were taken in Z I ~ C U O on flat film, the capillaries being vertical. Nickel-filtered copper Ka radiation was used in conjunction with a collimator and a 0.5 mm pinhole. The X-ray photographs of the isotropic solutions of PBLG showed no reflections in- dicating spacings of less than 508, that were not given by the solvent. The birefringent solutions all showed a ring, the diameter of which depended on the concentration, indicating a spacing d which changed continuously with concentration from 18 to 29A (see plates l b and lc).As the concentration increased, this ring became less diffuse. The prepara- tions with oriented texture showed in addition two more or less pronounced equatorial FIG. 6.-Double logarithmic plot d against concentration. R5 in dioxan. spots or arcs on this ring. In no case was a photograph obtained showing only equatorial spots, and in no case were reflections indicating any other spacing which varied with the concentration observed. Although efforts were made to focus the beam on the best oriented portion of the structure, this, especially in the more fluid preparations, often deteriorated or changed its position before the experiment was complete, and it is therefore doubtful if any of the pictures corresponded to a completely oriented texture.The experimental data showing how this X-ray spacing, dy depended on the concentration are given in fig. 6 as a double logarithmic plot. A racemic solution containing equal proportions of PBLG and PBDG (total poly- peptide concentration = 21 m1/100 ml), showing very regular orientation in the polar- ization microscope,8 gave a ring with more pronounced equatorial spots (plate Id), in- dicating a value 23 8, for d. This does not quite fall on the curve for PBLG (fig. 6), but the discrepancy may be due to accepting too low a figure for the concentration which may have increased by evaporation while filling the capillary. There was some reason to suspect that the orientation when actually irradiated was not as perfect as that shown in the microphotograph previously published.* Unfortunately owing to the very small quantity of PBDG available only one concentration of the racemic solution was investigated. The value for 100 % PBLG included in fig.6 was taken from the data of Bamford, Hanby and Happey.12 The full line is the best straight line drawn through this and the other experimental points. The data, though insufficient to allow us to determine the structure, may be discussed in relation to models which are suggested by the other properties of PBLG solutions and our general knowledge of liquid crystalline solutions. The molecules of PBLG and PBDG being in the a-helical configuration may be looked upon as rigid rods from which the side chains, when fully extended,36 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS project radially.The length of each molecule (in A) is equal to the number of residues it contains multiplied by 1-5,13 while the diameter 2r of the cylinder described by the side chains when the molecule rotates about its axis is 28.2A, a value obtained from atomic models and the known dimensions of the cc-helix. It seemed a reasonable possibility that the uniaxial liquid crystalline structure of uniform birefringence given by the racemic solutions might have the molecules arranged parallel and in a two-dimensional hexagonal array, as was found by Bernal and Fankuchen19 to be the case in solutions of tobacco mosaic virus (T.M.V.). Sufficiently concentrated oriented solutions of T.M.V.give four re- flections on the equator corresponding to the first four reflections of planes parallel to the axis of orientation having the spacings d, d / d 3 , d / 4 4 , d/2/7. On dilution this relationship is maintained as long as the diminished intensity of the higher order reflections allows them to be observed, and d remains proportional to C-4. These relationships would be expected from the arrangement shown in fig. 8 or 9 (when there is no twist about the Z-axis) if no measurable dilution takes place parallel to the length of the molecules, the molecules moving apart in direc- tions at right-angles to their axes so as to fill the available space uniformly. It should be remembered, however, that the birefringent polypeptide solution is neither simply a liquid nor a crystal, but may be looked upon as either a some- what disordered crystal, or as a liquid arranged in a partially ordered way, so that even if dilution parallel to the length of the molecules was negligible, the arrange- ment in the plane at right-angles to their length (the 7, Z plane) might have any degree of order between hexagonal and the completely random.It follows that the twisted structure of the PBLG solutions might similarly be found to be a structure in which the torsion is superimposed on a hexagonal array of parallel molecules, 2, the axis of torsion lying, for instance, either as in fig. 8 or 9. The amount of torsion per molecule required to produce the observed values of S, and of the optical rotation is very small and its effect on the structure of a small region which is nevertheless sufficiently large to give sharp X-ray re- flections may be neglected.Thus only the orientation of the hexagonally packed rods, and not the distance between the planes, is affected by the structural twist. The broken line in fig. 6 is calculated on the assumption of a two-dimensional hexagonal array with no dilution parallel to the long axes of the molecules. Its equation is w1/3 x 1024 - 1-61 x 104 - 2Nd2qP d2 C = where C is the concentration in m1/100; W = 219, the residue weight; N = Avogadro’s number ; d is the distance between the (1010) planes in A ; q = 1.5 A, the length of the projection of one residue on the axis of the a-helix 13 and p = 1-3, the assumed density of the polymer.The full straight line through the experi- mental values has a slope of approximately - 2.3 instead of - 2.0, but is nowhere far removed from the calculated curve. If this difference in the slope is considered to be significant, in spite of the considerable size of the experimental errors, it may indicate that there is some dilution along the 6 axis. It is of interest to examine theoretically the X-ray diagrams which would be expected from some more fully defined twisted and untwisted structures and to compare these with the observed patterns. We shall assume that the spacings of between 18 A and 29 A which are indicated by the strong X-ray reflection arise from planes or approximations to planes which lie parallel to the direction ( of preferred orientation.We shall further assume (throughout this discussion) that the molecular axes lie exactly parallel to the 6 axis, Fig. 7 summarizes the expected patterns. An oriented texture of the twisted structure is defined to be an arrangement of the structure in which the Z-axis (fig. 1) lies radially in the capillary, the X-axis longitudinally, and the Y-axis tangentially. A disoriented texture is one in whichC. ROBINSON, J. C. WARD AND R . B. BEEVERS 37 these axes, although still rectangular at any point, are oriented in a random way in different parts of the capillary. A hexagonal arrangement is defined to be a hexagonal arrangement of parallel rods as shown in fig. 8 or 9. A random P B LC (twisted structures) o r ie n ted tex r u re arranqement -, hexaqonal random case ,@ -@ (d 1 f fuse) (ii) @ case 2 PBLC+PBDC (untwisted structure’) oriented texture hexaqonal a rra nqe men t random arranqement (d i f f u J e) (iii) disorien red texture hexaqonal random disoriented texture (diffuse) (4 FIG.7a and b.-Expected X-ray diffraction patterns from some arrangements of parallel rod-like molecules.38 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS arrangement is defined to be an arrangement of parallel rods in which the nearest neighbour distance in the 7 2 plane varies in a random manner. An oriented texture of the untwisted structure is one in which the [ (or X ) axis is parallel to the axis of the capillary. Since only one spacing has been observed, only the first hexagonal spacing d has been considered, and only the corresponding principal maximum for random arrangements. The special simple case of the untwisted mixture of D and L FIG.8.-Hexagonal arrangement Case 1. The axis of torsion, Z, to the (1010) plane. of rods. is normal 3 FIG. 9.-Hexagonal arrangement of rods. Case 2. The axis of torsion, 2, lies along the crystallographic axis u. polypeptides is first assumed to exist as a perfectly hexagonal arrangement of rods, and secondly as a random arrangement. There are two likely twisted hexagonal arrangements (case I and case 11) which will be considered. CASE THE AXIS OF TWIST (2) BISECTS THE ANGLE BETWEEN THE CRYSTALLO- GRAPHIC AXES (x AND - u, SAY) (fig. 8). The (1010) planes give equatorial spots. The (1100) and (0110) planes give equatorial arcs extending 60" on either side of the equator (fig.7a (i)). CASE 2 . T H E AXIS OF TWIST (2) LIES ALONG ONE CRYSTALLOGRAPHIC AXIS (SAY U) (fig. 9). The (1100) planes give rise to a continuous ring. The (1010) and (Olio) planes give equatorial arcs which extend only to 30" on either side of the equator (fig. 7a (v)). (The Z-axis mentioned above is as defined earlier in the paper and not the conventional z crystallographic axis.) The experimental patterns obtained with the more oriented textures of the twisted structure (given by the first method of filling the capillary) are composed of a continuous circle showing greater density over two equatorial arcs (plate lb and c). This is in good qualitative agreement with that predicted by the hexagonal structure, case 2 (fig. 7a(v)). The diffuseness of the patterns decreased within, creasing concentration. The disoriented textures (second method of filling)C .ROBINSON, J . C . WARD AND R. B . BEEVERS 39 only gave a diffuse ring as predicted. The untwisted structure in the racemic solution showed diffuse equatorial spots on a fainter continuous ring which would be predicted from a somewhat disoriented texture of an imperfect hexagonal arrangement. We may conclude that all the X-ray pictures we have are consistent with the models we have put forward. The absence of the higher-order reflections in the photographs is not evidence against the possibility of a hexagonal arrangement. In T.M.V., Bernal and Fankuchen found only one, and at most two, reflections in comparable concentra- tions, four reflections only being obtained in the dried gel.It is understandable that the reflections from the higher order planes would be less intense the more fluid the system. On the other hand the absence of any other reflection of com- parable intensity which would have indicated a primary spacing which differed from that expected from hexagonal spacing accords with the models we have put forward while the presence of the equatorial spots in the photographs of the more oriented textures shows that the arrangement in the 72 plane is far from completely random. In the analysis presented, it has been assumed that the molecules are parallel to the &axis. The fact that the birefringence of the untwisted structure as cal- culated from the optical rotatory power of the twisted structure is (at least ap- proximately) independent of the concentration supports this assumption, as do the considerations in the next section which show how closely packed the molecules lie in the oriented birefringent solutions. Further observations under more precisely defined conditions are clearly re- quired but on the present evidence an arrangement of molecules in the 7 2 plane, not completely hexagonal and not completely random seems most probable for PBLG solutions, the whole structure being twisted about the Z-axis so as to give the observed microscopic periodicity.Some comparatively small dilution may take place along the &axis but no regular spacings in this direction are observed. FREEDOM OF MOVEMENT OF THE MOLECULES Although this picture must remain tentative it may be fruitful to consider certain consequences which follow if the spacing given by a hexagonal arrange- ment is assumed as a first approximation. The distance in the 7 2 plane between the molecular centres is (see fig. 8) 2 , 4 4 3 ~ 4 .. The diameter 2r of the cylinder described by the PBLG molecule with side chains fully extended by rotating about its axis is 28.2A. (This was obtained by adding the known distance of the /3 carbon atom from the axis of a-helix, 9.50& to the length of the remainder of the side chain obtained from measurements with Courtauld atomic models.) Hence D = (2d/1/3) - 28*2A, where D is the nearest approach of two side chains in neighbouring parallel molecules at a given concentration. Table 2 shows how the value of D at the B point depends on the molecular weight of PBLG.The molecular axes can approach still nearer, since as can be shown with models the side-chains are just far enough apart to allow interleafing. There is also the possibility of the side chains becoming folded. In column 5, 4 = tan-1 (DIZ), where I is the length of the molecule, is given. This is the angle which a molecule must rotate through at the concentration of the B point in order to come in contact with the extended side chains of a neigh- bouring molecule. These values show that even at the lowest concentration at which the birefringent phase exists for each molecular weight, very little dis- placement, from the parallel position could bring two neighbouring molecules into contact. It is easy to see how the parallel array once formed will not readily be destroyed.In the last column is given 8 (= mils) which is the angle of twist40 LIQUID CRYSTALLINE STRUCTURE I N POLYPEPTIDE SOLUTIONS per molecule in the 2 direction. Since, for the concentrations of dioxan solutions which have been investigated, S = kl/C2 and d = k2/C3, where kl and k2 are constants, we see that 8 = k3CQ. So we find that the angle of deviation from the parallel position is not only very small even in the higher concentrations, but decreases on dilution. preparation TABLE 2 . 4 AND 0 AT B POINT FOR PBLG IN DIOXAN I = mean length of molecules A B point (ml/ 100 ml) D at B point A d = tan-l(D/Z) e = g x 180" R 4 156 32.6 - 3.8 - 5.4' R 5 311 13.9 + 7.0 1" 36' 1.5' R 9 1010 10.1 + 12.2 0" 42' 0.9' R 11 1883 9.1 + 14-4 0" 26' 0.7' If we consider a polypeptide molecule in the a-helix configuration as presenting a helical arrangement of dipoles, then in the PBLG solutions where all the spirals are of one sense (right-handed) we can expect that the forces of attraction between molecules arising from these dipoles would tend to impose a unidirectional twist on the array of parallel molecules. The smallness of the angle and the fact that it decreases continuously on dilution suggests that it arises from a dynamic equilibrium.No accurate figures for the temperature coefficient of S have been obtained owing to the marked hysteresis, but it would seem that the value of S is approx- imately doubled on heating a dioxan solution from 20 to 40°C.The twisted structures which we have described as forming spontaneously in certain polypeptide solutions seem to be very similar to those formed by choles- terol derivatives. The much longer rigid molecules of the polypeptides, however, allow the structure to exist even at considerable dilution, while the larger periodicity which is then observed lends itself more readily to quantitative observation. Although more work is needed before the structure is fully understood, its general nature and its relationship to the nematic or untwisted structure now seems to be clear. The twisted structure is more highly organized than other liquid crystalline systems which have been described. It combines a high degree of organization with a left- or right-handed twist which is characteristic of its composition and environment. The solutions may nevertheless be surprisingly fluid 1 and may dissolve other components without the qualitative nature of the structure being changed. It is conceivable that such highly organized, yet reproducible, liquids may play a role in chemical reactions involving some of the highly specific, optically active molecules present in biological systems.However, a periodicity of the same order as that found in PBLG solutions would easily be overlooked in biological units having a diameter not much greater than S, the repeat distance, while the form optical rotation would also be overlooked in a thin specimen. It might therefore be rewarding to re-examine some biological systems with these points in mind. All the polypeptides used in this research were synthesized by Mr.W. E. Hanby of this laboratory. The X-ray photographs were taken by and discussed with Mr. L. Brown of Courtaulds' Acetate and Synthetic Fibres Laboratory, Coventry. We are grateful to Prof. M. H. L. Pryce and Prof. F. C. Frank for discussions which led to the interpretation of the spherulite structure given in the appendix, and to Prof. J. D. Bernal for further discussions. Our thanks are due to Dr. C. H. Bamford for valuable criticism. We are much indebted to Mr. J. P. Hetherington for much painstaking assistance throughout this research.C . ROBINSON, J . C . W A R D AND R . B . BEEVERS 41 APPENDIX THE SPHERULITIC TEXTURE A model of the way in which the molecules are arranged to form the special “ texture ” of the twisted structure which arises in the spherulite has been put forward in a private communication from Prof.M. H. L. Pryce and Prof. F. C. Frank. This was described by them in the following words. “ Consider a spherical surface, and the family of small circles and one great circle on this sphere which are all tangent to a line PQ itself tangent to the sphere at P. This family of circles corresponds to the intersections of the sphere and all planes passing through PQ. It also corresponds to a stereographic projection on to the sphere, for the pro- jection point P, of a family of parallel straight lines ruled on a plane normal to the diameter through P, all these straight lines being parallel to PQ. Now repeat the construction using a second line PQ’, likewise tangent to the sphere at P, but making an angle a with FIG.10. FIG. 11. PQ. Now, by the conformal property of the stereographic projection, at every inter- section of a circle of the first family with a circle of the second, the angle at the intersection is ci. We may make a sequence of such families numbered n = 1, 2, 3, . . . making angles nr with the first. If now, instead of doing this on one sphere, we do it on a suc- cession of concentric spheres of radius YO + nc, with the singular point P moving out along a radius, then in each spherical shell we may arrange the molecules with their long axes parallel to the directions of its appropriate family of circles. Then every molecule will be nearly parallel to its neighbours in the same shell (the error being small everywhere except near to the singular radius) and will be inclined at an angle a to neighbours on the same radius in neighbouring shells.On any cross-section of this model, except cross- sections through the singular radius OP, the locus on which molecules make any given constant angle to the plane of section is a spiral. If the angles 8 and 180” f B are equivalent, as they are for this case, it is a double spiral.” Fig. 10 and 11 are tracings obtained by photographing a ball on which a family of circles had been constructed in accordance with this scheme. All the microscopically observed properties of the spherulites are accounted for by the Frank-Pryce model if linear propagation of light through the spherulite is assumed, and if we merely need to42 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS consider a thin slab of material coincident with the plane of sharp focus of the microscope objective. Such an assumption is not quite as drastic as it might seem, since we are here only concerned with tracing the path of the visible spacings, and not with their origin. If we consider a median section of the spheres shown in fig. 10 cut parallel to the plane of the paper and consider light propagated in a direction perpendicular to this plane, then at points A and B the birefringence of the section will vanish. The locus of A and B on successive concentric spheres will appear between crossed plane-polarizers as a dark double spiral, as was observed. When the plane-polarizers were replaced by crossed circular-polarizers, the spiral remained dark, showing that the lack of birefringence on the spiral is not due to a coincidence between the principal directions of the structure and the planes of polarization of the polarizers, but to the fact that the light was pro- pagated parallel to the optic axis of the structure. The above agrument predicts a black double spiral. The observed one was not per- fectly black, presumably because of departure from linear propagation, or to effects arising from material outside the plane of sharp focus of the objective. 1 Robinson, Trans. Faraday Sac., 1956, 52, 571. 2 Friedel, Ann. Physique, 1922, 18, 273. 3 Doty, Bradbury and Holtzer, J. Amer. Chem. SOC., 1956,78,947. 4 Moffitt and Yang, Proc. Nat. Acad. Sci., 1956, 42, 596. 5 Oseen, Trans. Faraday SOC., 1933, 29, 883. 6 Maugin, Bull. SOC. Franc. Min., 191 1, 34, 6, 71. 7 de Vries, Acta Cryst., 1951, 4, 219. 8 Robinson and Ward, Nature, 1957, 180, 1183. 9 Bernal and Fankuchen, J. Gen. Physiul., 1941, 25, 11 1, 120, 147. 10 Yang and Doty, J. Amer. Chem. SOC., 1957, 79, 761. 11 Downie, Elliott, Hanby and Malcolm, Proc. Roy. SOC. A , 1957, 242, 325. 12 Bamford, Hanby and Happey, Pruc. Roy. SOC. A, 1951,205,30. 13 Pauling, Corey and Branson, Proc. Nat. Acad. Sci., 1951, 37,205.