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Molecular chain orientation in supercontracted and re-extended spider silk
International Journal of Biological Macromolecules 24 (1999) 203 – 210
Molecular chain orientation in supercontracted and re-extended spider silk D.T. Grubb a,*, Gending Ji a,b b
a Department of Materials Science, Cornell Uni6ersity, Ithaca NY 14853, USA Department of Polymer Science and Engineering, School of Chemistry and Chemical Engineering, Nanjing Uni6ersity, Nanjing, 210093, People’s Republic of China
Abstract The dragline silk from Nephila cla6ipes was studied by wide angle X-ray diffraction in its original state, after supercontraction to L/Lo =0.46, and during re-extension to its original length Lo. The fibers were carefully dried before each exposure. The molecular orientation in the crystalline regions is found to follow the simple predictions of affine deformation, indicating that the crystals act as inert rigid filler particles. The crystals retain considerable orientation after supercontraction, when non-crystalline orientation is weak. This shows that crystallization occurs after orientation as the fiber forms. The oriented amorphous material, treated as a phase of constant volume fraction, also follows affine deformation. These results do not contain any indication of a special structure in the protein fiber. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Dragline silk; Nephila cla6ipes; X-ray diffraction
1. Introduction Spider dragline silk has a unique combination of desirable mechanical properties. It has a low density, reasonably high strength and large elongation to break [1,2]. Together these give a specific toughness (energy stored before fracture per unit mass) which is comparable to the best synthetic material. This should not be surprising, as the dragline silk in nature acts both as the spider’s safety line and the structural support of its web. In both uses it absorbs kinetic energy of impacts. The molecular arrangement of proteins is in general exquisitely tuned to their purpose, so we might expect that specific subtle structures exist in dragline silk to produce the properties. If that is the case synthetic analogs that mimic only the overall properties of the silk proteins would not be able to attain the same mechanical properties.
* Corresponding author. Fax: +1-607-2552365. E-mail address: [email protected] (D.T. Grubb)
However, various methods of characterization have shown that the fibers have many structural features very similar to those of synthetic fibers. These features include fine fibrillar structures at a range of angles in the fiber [3,4], fine scale porosity [5] and a skin-core structure [4–7]. More highly organized fibrous structures have been observed in highly swollen dragline silk fibers on a scale too large to relate to other fibrosity [7]. X-ray diffraction shows that silk, like synthetic fibers (such as nylon or polyester) contains small crystals periodically arranged in stacks. The molecular chain axis in the crystals and the long axis of the stacks are both aligned along the fiber axis [8–10]. Both types of fibers are only partially crystalline; some of the material is isotropic and amorphous. The rest, the third phase, is variously described as ‘oriented amorphous’ or ‘oriented non-crystalline’. This phase could contain isolated b-sheets [11,12] or other structures [13] indicated by NMR and appear disordered to the larger-scale view of X-ray diffraction. Almost every structure in dragline silk can be found in synthetic materials. The structures may be quantita-
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tively different, but since the parameters describing them cannot reliably be associated with strength or toughness in synthetic fibers it is difficult to associate any particular differences with improved properties in dragline silk. Young’s modulus is often the only mechanical property that can clearly be associated with known structural parameters in synthetic fibers. Work and Morosoff discovered that many spider silks contract by about 50% when they are in contact with water, and called this supercontraction [14]. Contraction is not desirable for most practical applications, and many commercial synthetic fibers are heat-treated to prevent it. For the spider it results in a taut web after dewfall. The crystals in silk fibers are not dissolved by the water and remain in the contracted fiber with unchanged crystal structure [14]. Synthetic fibers which contract do so on heating or in solvent when the crystals begin to melt or dissolve, not in the presence of a swelling agent. Large degrees of contraction are associated with large amounts of molecular extension in the fiber [15]. Spider silk fibers are much less stiff when wet and contracted, but on re-stretching the mechanical properties are largely recovered [14,16,17]. Gosline [18] had already showed that mechanically the wet silk is a rubber. This specifically means that the elasticity of wet spider dragline silk is entropic in origin, caused by the random thermal motion of the disordered chains in the fiber. The crystals act as physical cross-links and as rigid filler particles in the rubber. Since the mechanical properties are largely recovered in re-stretched fibers, [17,18] the original mechanical properties can be obtained from a model of a stretched and filled rubber [19]. The essence of an entropic elastomer is that the amorphous chains follow random walks; this goes against the idea of specific protein structures. Fornes et al. [20] used birefringence to determine the changes in molecular orientation that occur on supercontraction. They found that the contracted fibers lost orientation as expected, but the simplest model prediction of affine deformation did not work. A formula derived from deformation of an isotropic array [21] was better. Birefringence is limited in that it cannot separate the orientation of different phases, it gives only an average orientation, and it requires the assumption that form birefringence is negligible. This may not be the case when intrinsic birefringence is low. X-ray diffraction can give a much more detailed view of orientation. Kratky first calculated the effects of affine deformation on diffraction in 1933 [22]. It is not impossible, but very difficult to detect local chain associations that might exist in disordered material using X-ray diffraction [23]. Instead the detailed molecular chain orientation as the fiber is deformed can be compared to predictions for a material behaving as a simple filled elastomer. A deviation would indicate otherwise unseen structural features in the partially
ordered material. In previous work [9] the molecular orientation of the crystalline phase was found to follow the simplest model of affine deformation on stretching the dry silk fiber, but the range of deformation before fracture in the X-ray beam is quite small. Loss of X-ray orientation in supercontracted fibers has been reported before [13,24] and numerical data was reported in 1997 [25]. It appeared at that time that the crystalline material continued to follow this affine deformation model over a much wider range of strains, while the oriented amorphous material did not, changing less than predicted. However, curve fitting for contracted fibers was very difficult in that experiment, and there appeared to be sudden changes in properties at short fiber lengths, L/Lo between 0.5 and 0.6. A primary purpose of the experiments reported here was to determine if these sudden changes were real.
2. Experimental Adult female Nephila cla6ipes spiders obtained from central Florida were silked to produce 1–2 mg samples [26]. The silk was collected at a constant 2 cm/s onto a piece of card taped around a rotating cylinder 1 inch in diameter, which takes about 1–2000 turns/mg. A dissecting microscope was used to view the silk and assure that no minor ampullate gland silk was included in the sample. For X-ray diffraction, fiber rings were removed from the card and held in a stretching frame mounted on a rotation stage. The silk was not gripped in clamps; instead the uncut ring was looped over plated steel hooks made from rod of diameter 0.06%%. The original gauge length was thus close to B/2%%. One hook is mounted on the frame, the other on a cross-head that can be driven by a motorized micrometer screw. Friction in the large number of turns prevented slippage on straining. Wide-angle X-ray diffraction (WAXD) was obtained at the Cornell High Energy Synchrotron Source (CHESS), beam line F1, using 0.0928 nm radiation. The F1 station provides a high-brightness beam converging to a focus with a flux of up to 5 ×1012 photons/s per mm2 [27]. A 0.2-mm diameter collimator limited the double-focused beam. The detector was a 2k× 2k CCD with a 80 × 80 mm sensitive area; pixels were binned to give a 1024×1024 image. In a previous experiment a high water content in contracted fibers made fitting the X-ray diffraction patterns much more difficult. To avoid this, two experimental procedures were used. In both a fiber ring was allowed to contract freely in DI water at room temperature. The cross-head was moved until the two hooks were very close together, with the silk loop hanging slackly between them. Water was added by pipette and the silk shrank into a wet blob. The hooks were separated until the folded silk again showed as a single
D.T. Grubb, G. Ji / International Journal of Biological Macromolecules 24 (1999) 203–210
loop. Excess water was removed with filter paper, and the hooks were separated cautiously until the two strands of silk that made up the loop were separate and just straightened. The fiber was then dried over desiccant for 10 min before taking an X-ray diffraction pattern. Previous experiments with a microbalance showed that the silk rings dried to constant weight in 2 – 5 min over the same desiccant. The silk samples that were used shrank to between 0.46 and 0.49 of their original length when prepared in this way. However, it is easy to leave a little slack and easy to stretch the silk with very little force, so some real variability may be suppressed. In one sequence, which gave the results reported in detail here, the fiber was re-wetted with DI water, extended by a small amount (between 2 and 4% of the original length) and re-dried as before. It was slowly re-extended in this way to near its original length, with an X-ray exposure at each length step. The data shown in Figs. 3–6 also includes some repeated exposures and some taken during a second relaxation of the same sample. Although these points increase the variance of the data, they cannot be separated statistically from the data taken during the initial re-extension. In a second sequence, the contracted and dried fiber was extended in similar steps but without further wetting and drying. There was no significant difference in the two sets of results. Crystal orientation was measured using the strong (200) and (120) equatorial reflections. Direct measurement of the (002) profile requires exact fiber orientation, and is more affected by the finite crystal size. Azimuthal scans of the (200) and (120) equatorial peaks were fitted as the sum of a constant background and two Gaussian curves, or as a single Pearson VII function. The data were analyzed using a combination of commercially available software. The raw data were first corrected for CCD background and distortion. The ‘air scatter’ background (data collected with no sample in place) was then subtracted, after correcting for the changing incident flux. Further analysis used sequential rather than ‘whole pattern’ fitting. That is, radial and circumferential scans were obtained from the corrected image files, using Matlab. The radial scans were intensity as a function of radius averaged over a small sector, typical 2–3° wide. Similarly the circumferential scans were averaged over a 5 pixel wide ring. The peaks were fitted with various analytical functions using nonlinear least-squares fitting routines in Genplot.
3. Results and discussion Fig. 1 shows the WAXD patterns of the spider silk. Fig. 1a is from the fiber in its original state, Fig. 1b is from the supercontracted and dried fiber, shrunk to
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0.46 of its original length. Fig. 1c is obtained when the fiber has been re-stretched to 0.65 of its original length. Looking at the inner peak on the equator, (200), there is a significant broadening on supercontraction, and the intermediate length fiber has an intermediate width of reflection. The picture is not so clear for the stronger (120) equatorial reflection, because the {201} reflections on the first layer line are at almost the same spacing as the (120) and overlap when the orientation is weak. As first reported by Work [14] the radial positions of the crystalline lattice peaks do not change on supercontraction, and there is no indication of a change in crystal size.
Fig. 1. Wide angle X-ray diffraction from the dragline silk of N. cla6ipes. (a) Original fiber bundle, L =Lo (b) Fibers supercontracted in water to L=0.46 Lo and then dried for 10 min. (c) Supercontracted fibers slowly extended while wet to L =0.65 Lo and then dried for 10 min.
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Fig. 2. Intensity of diffraction (arbitrary units) as a function of azimuthal angle, with zero at the equator (a) original fiber, at the radial position of the strong (120) equatorial reflection (b) original fiber, at the radial position of the inner (200) equatorial reflection (c) supercontracted fiber, at the radial position of the strong (120) equatorial reflection (d) supercontracted fiber, at the radial position of the inner (200) equatorial reflection In each case the central peak data is fitted to the sum of two Gaussian functions.
To obtain numerical data on orientation, azimuthal scans of the scattering at the radial position of the (200) and (120) peaks were obtained for all the diffraction patterns. Fig. 2 shows the extreme cases, the intensity as a function of angle R, measured from the equator, for the original silk sample and for the fully contracted fiber. The subsidiary peaks in the plot at the (120) position come from the {201} peaks. In Fig. 2a they can be easily separated and fitted, but when the peaks overlap, as in Fig. 2c, curve-fitting more complicated. Ambiguity is removed when the positions of the sub-
sidiary peak maxima are fixed at 9 37.7°, as found for the well-oriented fibers and in agreement with the calculated unit cell geometry. The fitting of the (200) peak, Fig. 2b and d is simpler, but the intensity is less. The central peak cannot be fitted with one Gaussian curve, but it can be well fitted with either one Pearson VII function or two Gaussian functions, one much wider than the other. While the fitting errors are less than9 5% for both functions, the two Gaussian fit is preferred. As previously described [9] both the (200) and (120) peaks have a comparatively small radial
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width on the equator, corresponding to a crystal size of a few nm. The wings of these peaks, 20° off the equator in the original fiber, are much broader radially, as wide as the amorphous peak is on the meridian. Thus the narrower Gaussian dominates at the equator, and corresponds to crystalline material (I120 or I200), while the broader Gaussian dominates at 20° off the equator and corresponds to oriented amorphous material (Iam). Unoriented amorphous material adds to the constant background level in azimuthal scans. The amount is found from the intensity of the amorphous halo on the meridian. Separation into two Gaussians is assumed to be also correct for the contracted fibers, although the contracted fiber data by itself would not suggest it (too much overlap of reflections). Fig. 3 shows how the full width at half maximum of the fitted functions varies with the sample length. At the (120) position, Fig. 3a, the Pearson VII width lies between the ‘crystalline’ Gaussian and the ‘oriented amorphous’ Gaussian. At the (200) position, Fig. 3b, the broad Gaussian is much broader, and the Pearson VII width is almost identical to the narrower Gaussian.
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This indicates that the sharp (200) peak, although weaker than the (120) peak, dominates the much weaker amorphous scatter at that radius. An amorphous material, even an oriented one, can only give one broad peak on the equator. Different values for the angular width of the oriented amorphous arc at different radial positions are obtained because a non-Gaussian spot will give the different apparent widths at different non-central sections. The radial position of the peak of the amorphous halo is much nearer to that of (120) so the width of Iam at that position is taken to represent the orientation of the oriented amorphous phase. In this case the mean angle between the molecular chains in the oriented amorphous component and the fiber axis, 8am, is given as B cos2 8am \ = 1− 2Bsin2 csm \ where
B sin cam \ = 2
&
(1)
p
Iam sin2 c cos c d c
0
&
p
(2)
Iam cos c d c
0
Iam is the intensity of the broader Gaussian curve found at the position of the strongest crystalline reflection. For the crystalline component both reflections must be taken into account, and assuming that the stronger is the (120), the angle between this plane and (200) in the crystal structure of silk means that the molecular chain orientation is given by B cos2 8cryst \ = 1−0.8B sin2 c200 \ − 1.2B sin2 c120 \
Fig. 3. Full width at half maximum for the fitting functions shown in Fig. 2, and for a single Pearson VII function fit to the data. (a) At the (120) position (b) At the (200) position. The width of the broader Gaussian is much greater at the (200) position.
(3)
where 8cryst is the angle between the molecular chains in the crystals and the fiber axis. B sin2 c200 \and B sin2 c120 \ are defined by analagous expressions to Eq. (2), with the intensity Iam replaced by I200 and I120, the intensities of the narrower Gaussian function at the position of the (200) and (120) reflections respectively [9]. This analysis gives a chain orientation of crystalline material in agreement with previous results, but the mean orientation angle of the amorphous material is surprisingly small, and does not vary much with fiber extension. The reason for this becomes clear when the relative areas of the two Gaussian curves are plotted as a function of fiber extension, in Fig. 4. The curve areas p0 Iam cos c d c and p0 I120 cos c d c are only useful in comparing one sample with another and do not give any absolute measure of content of one phase or the other. However, it appears from Fig. 4 that the relative amount of crystalline material is greater in the contracted fiber. This is not reasonable; crystal content is thought to be either unaffected by supercontraction, or
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Fig. 4. Relative areas under the two Gaussian functions that fit the central peak at the position of the (120) as a function of fiber length. The narrower (crystalline) peak becomes relatively stronger on contraction.
reduced. The relative amount of the narrower Gaussian is increasing because the area of the ‘oriented amorphous’ peak is decreasing. To confirm this, the curve area due to unoriented amorphous material was determined from meridional scans. The height of the amorphous peak on the meridian was measured at the radial position of the (120) peak of each pattern. Fig. 5 shows that when the unoriented material is taken into account, the apparent crystalline content remains reasonably constant. It can be seen from the curves in Fig. 2b and c that the oriented peak extends all the way to9 90°. The fitting method chosen tended to give constant background levels close to the minimum of the curve. With different initial values and allowing for very broad peaks to wrap around past 90°, it is possible to obtain equally good fits with broader peaks and lower constant background levels. To determine the true orientation of the ‘oriented amorphous’ material, we assume that it corresponds to a real third phase in the material, and that the amount of this phase is not affected by contraction. NMR strongly supports the view that a distinct third phase exists in the material [12]. Apparent changes are then due to some amorphous material being counted as unoriented in the contracted fiber, and counted as oriented in the extended fiber. A modified intensity for the oriented amorphous material I%am =Iam +A was used in Eq. (2). The constant A was chosen to make the
area. p0 I%am cos c d c a constant fraction (0.32) of the total area. The result is shown in Fig. 6, both as cos − 1( B cos2 8\ ) and as the orientation function f= 1/2 (3 cos2 8− 1). The lines through the data are calculated according to simple affine deformation. According to this, every microscopic object deforms in the same proportion as the macroscopic fiber and tan 8 is proportional to (L/Lo) − 3/2. The only fitting parameter is the value of 8 in the original fiber, at L/Lo =1. The fit is very good indeed for both components of the fiber. The oriented amorphous material approaches isotropy in the fully relaxed fiber. There are two problems with this analysis. It assumes that the entire angular width of the broad equatorial peak is due to orientation effects. But the width of a peak is due to both orientation and the intrinsic width of the peak caused by the finite size or imperfection of the diffracting objects. In the crystalline material, the diffracting objects are crystals and the crystal size along the molecular chain can be measured from the radial width of the (002) peak. It was found to be about 6 nm, (neglecting effects of imperfection) and the effect of this on the measured orientation was quite small, reducing 8 by about 1° [9]. But what is the size of the diffracting object along the chain direction for the non-crystalline material? This is difficult, because when the orientation is increased to near-perfect chain alignment the chain conformations must change, and the ‘amorphous’ character of the original material will be lost. The second
Fig. 5. Areas of the two Gaussian functions and of the amorphous halo, as fractions of the total area. The crystalline fraction is approximately constant with fiber length.
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209
ous change at the most contracted state [25]. Experiments made with extra care to fully dry the samples at each length do not show this discontinuous change, and fully follow the simple predictions of affine deformation. The orientation function of the crystals changes smoothly from 0.85 in the freely contracted state at L/Lo 0.46–0.98 at the original length of the fiber. The crystal orientation was not corrected for crystal size effects, but calculations have shown this is not very important, even for the small crystals that exist in spider silk [9]. The oriented non-crystalline material is not so easy to deal with. The distinction between oriented and unoriented material is clear in the original fiber, but quite unclear in the contracted samples. We have arbitrarily assigned a constant amount of each phase to be present in all samples, fixed at the amounts present in the original fiber. On this basis the chains in the oriented non-crystalline also follow affine deformation. The orientation function varies from 0.24 in the freely contracted fiber to 0.86 at L= Lo. Underestimation of the amount of disordered material to include in this phase may have made these values too high, while not correcting for size effects will have made them too low. These details aside, it seems that contraction of a rubbery matrix drives the fiber contraction and the crystals are carried along like inert filler particles.
Acknowledgements
Fig. 6. Molecular chain orientation in spider silk, in the crystals and in the oriented amorphous material, as a function of fiber length. The orientations is expressed as an equivalent angle in (a) and as the orientation function f in (b). The lines through the data are predictions of affine deformation.
problem is that this simple model of affine deformation should not be correct for a set of independent objects, originally distributed in random orientations. More correct models give a slower change of orientation with length [21,22]. Inclusion of some of the ‘unoriented’ material in the oriented phase might produce better agreement with these models.
4. Conclusions In a previous experiment on supercontracted spider silk the crystalline material was found to reorient according to affine deformation, except for a discontinu-
We thank Lynn Jelinski for her continued collaboration and support, Vikram Bala for setting up the experimental protocol and running at CHESS, and the invaluable CHESS and MACHESS support staff. We would also like to thank the National Science Foundation for financial support through MCB-9601018 and through access to CHESS.
References [1] Zemlin JC. Technical Report 69-29-CM (AD684333); US Army Natick Laboratories, Natick, MA, 1968. [2] Gosline JM, DeMont ME, Denny MW. Endeavour 1986;10:37. [3] Mahoney DV, Vezie DL, Eby RK, Adams WW, Kaplan D. In: Silk Polymers; Materials Science and Biotechnology ACS Symposium Ser. 544 ACS 1994:196 [4] Li SF, McGhie AJ, Tang SL. Biophys J 1994;66:1209. [5] Frische S, Maunsbach AB, Vollrath F. J Microsc 1998;189:64. [6] Work RW. Trans. Am. Micros. Soc 1984;103:113. [7] Vollrath F, Holtet T, Thøgersen HC, Frische S. Proc. R. Soc. Lond B 1996;263:147. [8] Warwicker JO. J. Mol. Biol 1960;2:350. [9] Grubb DT, Jelinski LW. Macromolecules 1997;30:2860. [10] Yang Z, Grubb DT, Jelinski LW. Macromolecules 1997;30:8254. [11] Simmons AH, Ray E, Jelinski LW. Macromolecules 1994;27:5235. [12] Simmons AH, Ray E, Jelinski LW. Science 1996;271:84. [13] Lewis RV. Acc. Chem. Res 1992;25:393.
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[14] [15] [16] [17]
Work RW, Morosoff N. Text. Res J 1982;52:349. Grubb DT. J Mater Sci Lett 1984;3:499. Work RW. J Exp Biol 1985;118:379. Shoa, Z.; Vollrath, F. In: Proceedings of the 10th International Conference on deformation Yield and Fracture of Polymers, 1997:262. [18] Gosline JM, Denny MW, DeMont ME. Nature 1982;309:551. [19] Gosline JM, Pollak CC, Guerette PA, Cheng A, DeMont ME, Denny MW. in: Silk Polymers; Materials Science and Biotechnology ACS Symposium Ser. 544 ACS 1994;328. [20] Fornes RE, Work RW; Morosoff N. J. Polym Sci: Polym. Phys. Edn. 1983;21:1163
.
[21] Wilchinksy ZW. Polymer 1964;5:271. [22] Kratky O. Kolloid Z 1933;64:213. [23] Murthy NS, Minor H, Benarczyk C, Krimm S. Macromolecules 1993;26:1712. [24] Parkhe AD, Seeley SK, Gardner K, Thompson L, Lewis RV. J Mol Recogn 1997;10:1. [25] Grubb DT, Jackrel D, Jelinski LW, Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1997;38:73. [26] Work RW, Emerson PD. J Arachnol 1982;10:1. [27] For more details, see http://www.chess.cornell.edu/Facility/F1 – station.html
Molecular chain orientation in supercontracted and re-extended spider silk D.T. Grubb a,*, Gending Ji a,b b
a Department of Materials Science, Cornell Uni6ersity, Ithaca NY 14853, USA Department of Polymer Science and Engineering, School of Chemistry and Chemical Engineering, Nanjing Uni6ersity, Nanjing, 210093, People’s Republic of China
Abstract The dragline silk from Nephila cla6ipes was studied by wide angle X-ray diffraction in its original state, after supercontraction to L/Lo =0.46, and during re-extension to its original length Lo. The fibers were carefully dried before each exposure. The molecular orientation in the crystalline regions is found to follow the simple predictions of affine deformation, indicating that the crystals act as inert rigid filler particles. The crystals retain considerable orientation after supercontraction, when non-crystalline orientation is weak. This shows that crystallization occurs after orientation as the fiber forms. The oriented amorphous material, treated as a phase of constant volume fraction, also follows affine deformation. These results do not contain any indication of a special structure in the protein fiber. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Dragline silk; Nephila cla6ipes; X-ray diffraction
1. Introduction Spider dragline silk has a unique combination of desirable mechanical properties. It has a low density, reasonably high strength and large elongation to break [1,2]. Together these give a specific toughness (energy stored before fracture per unit mass) which is comparable to the best synthetic material. This should not be surprising, as the dragline silk in nature acts both as the spider’s safety line and the structural support of its web. In both uses it absorbs kinetic energy of impacts. The molecular arrangement of proteins is in general exquisitely tuned to their purpose, so we might expect that specific subtle structures exist in dragline silk to produce the properties. If that is the case synthetic analogs that mimic only the overall properties of the silk proteins would not be able to attain the same mechanical properties.
* Corresponding author. Fax: +1-607-2552365. E-mail address: [email protected] (D.T. Grubb)
However, various methods of characterization have shown that the fibers have many structural features very similar to those of synthetic fibers. These features include fine fibrillar structures at a range of angles in the fiber [3,4], fine scale porosity [5] and a skin-core structure [4–7]. More highly organized fibrous structures have been observed in highly swollen dragline silk fibers on a scale too large to relate to other fibrosity [7]. X-ray diffraction shows that silk, like synthetic fibers (such as nylon or polyester) contains small crystals periodically arranged in stacks. The molecular chain axis in the crystals and the long axis of the stacks are both aligned along the fiber axis [8–10]. Both types of fibers are only partially crystalline; some of the material is isotropic and amorphous. The rest, the third phase, is variously described as ‘oriented amorphous’ or ‘oriented non-crystalline’. This phase could contain isolated b-sheets [11,12] or other structures [13] indicated by NMR and appear disordered to the larger-scale view of X-ray diffraction. Almost every structure in dragline silk can be found in synthetic materials. The structures may be quantita-
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tively different, but since the parameters describing them cannot reliably be associated with strength or toughness in synthetic fibers it is difficult to associate any particular differences with improved properties in dragline silk. Young’s modulus is often the only mechanical property that can clearly be associated with known structural parameters in synthetic fibers. Work and Morosoff discovered that many spider silks contract by about 50% when they are in contact with water, and called this supercontraction [14]. Contraction is not desirable for most practical applications, and many commercial synthetic fibers are heat-treated to prevent it. For the spider it results in a taut web after dewfall. The crystals in silk fibers are not dissolved by the water and remain in the contracted fiber with unchanged crystal structure [14]. Synthetic fibers which contract do so on heating or in solvent when the crystals begin to melt or dissolve, not in the presence of a swelling agent. Large degrees of contraction are associated with large amounts of molecular extension in the fiber [15]. Spider silk fibers are much less stiff when wet and contracted, but on re-stretching the mechanical properties are largely recovered [14,16,17]. Gosline [18] had already showed that mechanically the wet silk is a rubber. This specifically means that the elasticity of wet spider dragline silk is entropic in origin, caused by the random thermal motion of the disordered chains in the fiber. The crystals act as physical cross-links and as rigid filler particles in the rubber. Since the mechanical properties are largely recovered in re-stretched fibers, [17,18] the original mechanical properties can be obtained from a model of a stretched and filled rubber [19]. The essence of an entropic elastomer is that the amorphous chains follow random walks; this goes against the idea of specific protein structures. Fornes et al. [20] used birefringence to determine the changes in molecular orientation that occur on supercontraction. They found that the contracted fibers lost orientation as expected, but the simplest model prediction of affine deformation did not work. A formula derived from deformation of an isotropic array [21] was better. Birefringence is limited in that it cannot separate the orientation of different phases, it gives only an average orientation, and it requires the assumption that form birefringence is negligible. This may not be the case when intrinsic birefringence is low. X-ray diffraction can give a much more detailed view of orientation. Kratky first calculated the effects of affine deformation on diffraction in 1933 [22]. It is not impossible, but very difficult to detect local chain associations that might exist in disordered material using X-ray diffraction [23]. Instead the detailed molecular chain orientation as the fiber is deformed can be compared to predictions for a material behaving as a simple filled elastomer. A deviation would indicate otherwise unseen structural features in the partially
ordered material. In previous work [9] the molecular orientation of the crystalline phase was found to follow the simplest model of affine deformation on stretching the dry silk fiber, but the range of deformation before fracture in the X-ray beam is quite small. Loss of X-ray orientation in supercontracted fibers has been reported before [13,24] and numerical data was reported in 1997 [25]. It appeared at that time that the crystalline material continued to follow this affine deformation model over a much wider range of strains, while the oriented amorphous material did not, changing less than predicted. However, curve fitting for contracted fibers was very difficult in that experiment, and there appeared to be sudden changes in properties at short fiber lengths, L/Lo between 0.5 and 0.6. A primary purpose of the experiments reported here was to determine if these sudden changes were real.
2. Experimental Adult female Nephila cla6ipes spiders obtained from central Florida were silked to produce 1–2 mg samples [26]. The silk was collected at a constant 2 cm/s onto a piece of card taped around a rotating cylinder 1 inch in diameter, which takes about 1–2000 turns/mg. A dissecting microscope was used to view the silk and assure that no minor ampullate gland silk was included in the sample. For X-ray diffraction, fiber rings were removed from the card and held in a stretching frame mounted on a rotation stage. The silk was not gripped in clamps; instead the uncut ring was looped over plated steel hooks made from rod of diameter 0.06%%. The original gauge length was thus close to B/2%%. One hook is mounted on the frame, the other on a cross-head that can be driven by a motorized micrometer screw. Friction in the large number of turns prevented slippage on straining. Wide-angle X-ray diffraction (WAXD) was obtained at the Cornell High Energy Synchrotron Source (CHESS), beam line F1, using 0.0928 nm radiation. The F1 station provides a high-brightness beam converging to a focus with a flux of up to 5 ×1012 photons/s per mm2 [27]. A 0.2-mm diameter collimator limited the double-focused beam. The detector was a 2k× 2k CCD with a 80 × 80 mm sensitive area; pixels were binned to give a 1024×1024 image. In a previous experiment a high water content in contracted fibers made fitting the X-ray diffraction patterns much more difficult. To avoid this, two experimental procedures were used. In both a fiber ring was allowed to contract freely in DI water at room temperature. The cross-head was moved until the two hooks were very close together, with the silk loop hanging slackly between them. Water was added by pipette and the silk shrank into a wet blob. The hooks were separated until the folded silk again showed as a single
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loop. Excess water was removed with filter paper, and the hooks were separated cautiously until the two strands of silk that made up the loop were separate and just straightened. The fiber was then dried over desiccant for 10 min before taking an X-ray diffraction pattern. Previous experiments with a microbalance showed that the silk rings dried to constant weight in 2 – 5 min over the same desiccant. The silk samples that were used shrank to between 0.46 and 0.49 of their original length when prepared in this way. However, it is easy to leave a little slack and easy to stretch the silk with very little force, so some real variability may be suppressed. In one sequence, which gave the results reported in detail here, the fiber was re-wetted with DI water, extended by a small amount (between 2 and 4% of the original length) and re-dried as before. It was slowly re-extended in this way to near its original length, with an X-ray exposure at each length step. The data shown in Figs. 3–6 also includes some repeated exposures and some taken during a second relaxation of the same sample. Although these points increase the variance of the data, they cannot be separated statistically from the data taken during the initial re-extension. In a second sequence, the contracted and dried fiber was extended in similar steps but without further wetting and drying. There was no significant difference in the two sets of results. Crystal orientation was measured using the strong (200) and (120) equatorial reflections. Direct measurement of the (002) profile requires exact fiber orientation, and is more affected by the finite crystal size. Azimuthal scans of the (200) and (120) equatorial peaks were fitted as the sum of a constant background and two Gaussian curves, or as a single Pearson VII function. The data were analyzed using a combination of commercially available software. The raw data were first corrected for CCD background and distortion. The ‘air scatter’ background (data collected with no sample in place) was then subtracted, after correcting for the changing incident flux. Further analysis used sequential rather than ‘whole pattern’ fitting. That is, radial and circumferential scans were obtained from the corrected image files, using Matlab. The radial scans were intensity as a function of radius averaged over a small sector, typical 2–3° wide. Similarly the circumferential scans were averaged over a 5 pixel wide ring. The peaks were fitted with various analytical functions using nonlinear least-squares fitting routines in Genplot.
3. Results and discussion Fig. 1 shows the WAXD patterns of the spider silk. Fig. 1a is from the fiber in its original state, Fig. 1b is from the supercontracted and dried fiber, shrunk to
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0.46 of its original length. Fig. 1c is obtained when the fiber has been re-stretched to 0.65 of its original length. Looking at the inner peak on the equator, (200), there is a significant broadening on supercontraction, and the intermediate length fiber has an intermediate width of reflection. The picture is not so clear for the stronger (120) equatorial reflection, because the {201} reflections on the first layer line are at almost the same spacing as the (120) and overlap when the orientation is weak. As first reported by Work [14] the radial positions of the crystalline lattice peaks do not change on supercontraction, and there is no indication of a change in crystal size.
Fig. 1. Wide angle X-ray diffraction from the dragline silk of N. cla6ipes. (a) Original fiber bundle, L =Lo (b) Fibers supercontracted in water to L=0.46 Lo and then dried for 10 min. (c) Supercontracted fibers slowly extended while wet to L =0.65 Lo and then dried for 10 min.
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Fig. 2. Intensity of diffraction (arbitrary units) as a function of azimuthal angle, with zero at the equator (a) original fiber, at the radial position of the strong (120) equatorial reflection (b) original fiber, at the radial position of the inner (200) equatorial reflection (c) supercontracted fiber, at the radial position of the strong (120) equatorial reflection (d) supercontracted fiber, at the radial position of the inner (200) equatorial reflection In each case the central peak data is fitted to the sum of two Gaussian functions.
To obtain numerical data on orientation, azimuthal scans of the scattering at the radial position of the (200) and (120) peaks were obtained for all the diffraction patterns. Fig. 2 shows the extreme cases, the intensity as a function of angle R, measured from the equator, for the original silk sample and for the fully contracted fiber. The subsidiary peaks in the plot at the (120) position come from the {201} peaks. In Fig. 2a they can be easily separated and fitted, but when the peaks overlap, as in Fig. 2c, curve-fitting more complicated. Ambiguity is removed when the positions of the sub-
sidiary peak maxima are fixed at 9 37.7°, as found for the well-oriented fibers and in agreement with the calculated unit cell geometry. The fitting of the (200) peak, Fig. 2b and d is simpler, but the intensity is less. The central peak cannot be fitted with one Gaussian curve, but it can be well fitted with either one Pearson VII function or two Gaussian functions, one much wider than the other. While the fitting errors are less than9 5% for both functions, the two Gaussian fit is preferred. As previously described [9] both the (200) and (120) peaks have a comparatively small radial
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width on the equator, corresponding to a crystal size of a few nm. The wings of these peaks, 20° off the equator in the original fiber, are much broader radially, as wide as the amorphous peak is on the meridian. Thus the narrower Gaussian dominates at the equator, and corresponds to crystalline material (I120 or I200), while the broader Gaussian dominates at 20° off the equator and corresponds to oriented amorphous material (Iam). Unoriented amorphous material adds to the constant background level in azimuthal scans. The amount is found from the intensity of the amorphous halo on the meridian. Separation into two Gaussians is assumed to be also correct for the contracted fibers, although the contracted fiber data by itself would not suggest it (too much overlap of reflections). Fig. 3 shows how the full width at half maximum of the fitted functions varies with the sample length. At the (120) position, Fig. 3a, the Pearson VII width lies between the ‘crystalline’ Gaussian and the ‘oriented amorphous’ Gaussian. At the (200) position, Fig. 3b, the broad Gaussian is much broader, and the Pearson VII width is almost identical to the narrower Gaussian.
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This indicates that the sharp (200) peak, although weaker than the (120) peak, dominates the much weaker amorphous scatter at that radius. An amorphous material, even an oriented one, can only give one broad peak on the equator. Different values for the angular width of the oriented amorphous arc at different radial positions are obtained because a non-Gaussian spot will give the different apparent widths at different non-central sections. The radial position of the peak of the amorphous halo is much nearer to that of (120) so the width of Iam at that position is taken to represent the orientation of the oriented amorphous phase. In this case the mean angle between the molecular chains in the oriented amorphous component and the fiber axis, 8am, is given as B cos2 8am \ = 1− 2Bsin2 csm \ where
B sin cam \ = 2
&
(1)
p
Iam sin2 c cos c d c
0
&
p
(2)
Iam cos c d c
0
Iam is the intensity of the broader Gaussian curve found at the position of the strongest crystalline reflection. For the crystalline component both reflections must be taken into account, and assuming that the stronger is the (120), the angle between this plane and (200) in the crystal structure of silk means that the molecular chain orientation is given by B cos2 8cryst \ = 1−0.8B sin2 c200 \ − 1.2B sin2 c120 \
Fig. 3. Full width at half maximum for the fitting functions shown in Fig. 2, and for a single Pearson VII function fit to the data. (a) At the (120) position (b) At the (200) position. The width of the broader Gaussian is much greater at the (200) position.
(3)
where 8cryst is the angle between the molecular chains in the crystals and the fiber axis. B sin2 c200 \and B sin2 c120 \ are defined by analagous expressions to Eq. (2), with the intensity Iam replaced by I200 and I120, the intensities of the narrower Gaussian function at the position of the (200) and (120) reflections respectively [9]. This analysis gives a chain orientation of crystalline material in agreement with previous results, but the mean orientation angle of the amorphous material is surprisingly small, and does not vary much with fiber extension. The reason for this becomes clear when the relative areas of the two Gaussian curves are plotted as a function of fiber extension, in Fig. 4. The curve areas p0 Iam cos c d c and p0 I120 cos c d c are only useful in comparing one sample with another and do not give any absolute measure of content of one phase or the other. However, it appears from Fig. 4 that the relative amount of crystalline material is greater in the contracted fiber. This is not reasonable; crystal content is thought to be either unaffected by supercontraction, or
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Fig. 4. Relative areas under the two Gaussian functions that fit the central peak at the position of the (120) as a function of fiber length. The narrower (crystalline) peak becomes relatively stronger on contraction.
reduced. The relative amount of the narrower Gaussian is increasing because the area of the ‘oriented amorphous’ peak is decreasing. To confirm this, the curve area due to unoriented amorphous material was determined from meridional scans. The height of the amorphous peak on the meridian was measured at the radial position of the (120) peak of each pattern. Fig. 5 shows that when the unoriented material is taken into account, the apparent crystalline content remains reasonably constant. It can be seen from the curves in Fig. 2b and c that the oriented peak extends all the way to9 90°. The fitting method chosen tended to give constant background levels close to the minimum of the curve. With different initial values and allowing for very broad peaks to wrap around past 90°, it is possible to obtain equally good fits with broader peaks and lower constant background levels. To determine the true orientation of the ‘oriented amorphous’ material, we assume that it corresponds to a real third phase in the material, and that the amount of this phase is not affected by contraction. NMR strongly supports the view that a distinct third phase exists in the material [12]. Apparent changes are then due to some amorphous material being counted as unoriented in the contracted fiber, and counted as oriented in the extended fiber. A modified intensity for the oriented amorphous material I%am =Iam +A was used in Eq. (2). The constant A was chosen to make the
area. p0 I%am cos c d c a constant fraction (0.32) of the total area. The result is shown in Fig. 6, both as cos − 1( B cos2 8\ ) and as the orientation function f= 1/2 (3 cos2 8− 1). The lines through the data are calculated according to simple affine deformation. According to this, every microscopic object deforms in the same proportion as the macroscopic fiber and tan 8 is proportional to (L/Lo) − 3/2. The only fitting parameter is the value of 8 in the original fiber, at L/Lo =1. The fit is very good indeed for both components of the fiber. The oriented amorphous material approaches isotropy in the fully relaxed fiber. There are two problems with this analysis. It assumes that the entire angular width of the broad equatorial peak is due to orientation effects. But the width of a peak is due to both orientation and the intrinsic width of the peak caused by the finite size or imperfection of the diffracting objects. In the crystalline material, the diffracting objects are crystals and the crystal size along the molecular chain can be measured from the radial width of the (002) peak. It was found to be about 6 nm, (neglecting effects of imperfection) and the effect of this on the measured orientation was quite small, reducing 8 by about 1° [9]. But what is the size of the diffracting object along the chain direction for the non-crystalline material? This is difficult, because when the orientation is increased to near-perfect chain alignment the chain conformations must change, and the ‘amorphous’ character of the original material will be lost. The second
Fig. 5. Areas of the two Gaussian functions and of the amorphous halo, as fractions of the total area. The crystalline fraction is approximately constant with fiber length.
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ous change at the most contracted state [25]. Experiments made with extra care to fully dry the samples at each length do not show this discontinuous change, and fully follow the simple predictions of affine deformation. The orientation function of the crystals changes smoothly from 0.85 in the freely contracted state at L/Lo 0.46–0.98 at the original length of the fiber. The crystal orientation was not corrected for crystal size effects, but calculations have shown this is not very important, even for the small crystals that exist in spider silk [9]. The oriented non-crystalline material is not so easy to deal with. The distinction between oriented and unoriented material is clear in the original fiber, but quite unclear in the contracted samples. We have arbitrarily assigned a constant amount of each phase to be present in all samples, fixed at the amounts present in the original fiber. On this basis the chains in the oriented non-crystalline also follow affine deformation. The orientation function varies from 0.24 in the freely contracted fiber to 0.86 at L= Lo. Underestimation of the amount of disordered material to include in this phase may have made these values too high, while not correcting for size effects will have made them too low. These details aside, it seems that contraction of a rubbery matrix drives the fiber contraction and the crystals are carried along like inert filler particles.
Acknowledgements
Fig. 6. Molecular chain orientation in spider silk, in the crystals and in the oriented amorphous material, as a function of fiber length. The orientations is expressed as an equivalent angle in (a) and as the orientation function f in (b). The lines through the data are predictions of affine deformation.
problem is that this simple model of affine deformation should not be correct for a set of independent objects, originally distributed in random orientations. More correct models give a slower change of orientation with length [21,22]. Inclusion of some of the ‘unoriented’ material in the oriented phase might produce better agreement with these models.
4. Conclusions In a previous experiment on supercontracted spider silk the crystalline material was found to reorient according to affine deformation, except for a discontinu-
We thank Lynn Jelinski for her continued collaboration and support, Vikram Bala for setting up the experimental protocol and running at CHESS, and the invaluable CHESS and MACHESS support staff. We would also like to thank the National Science Foundation for financial support through MCB-9601018 and through access to CHESS.
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[21] Wilchinksy ZW. Polymer 1964;5:271. [22] Kratky O. Kolloid Z 1933;64:213. [23] Murthy NS, Minor H, Benarczyk C, Krimm S. Macromolecules 1993;26:1712. [24] Parkhe AD, Seeley SK, Gardner K, Thompson L, Lewis RV. J Mol Recogn 1997;10:1. [25] Grubb DT, Jackrel D, Jelinski LW, Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1997;38:73. [26] Work RW, Emerson PD. J Arachnol 1982;10:1. [27] For more details, see http://www.chess.cornell.edu/Facility/F1 – station.html