1782
Biomacromolecules 2008, 9, 1782–1786
Elasticity of Spider Silks Yi Liu,† Zhengzhong Shao,‡ and Fritz Vollrath*,† Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, United Kingdom, and Department of Macromolecular Science and The Key Laboratory of Molecular Engineering of Polymers of Ministry of Education, Fudan University, Shanghai 200433, People’s Republic of China Received December 23, 2007; Revised Manuscript Received February 17, 2008
The elasticity of spider MAA silks containing varying proline content was investigated and compared with that of silkworm (Bombyx mori) silk. For silks with similar breaking strain (suggesting similar molecular order), the elasticity appears to increase with increasing proline content. Particularly, across all spider silks, intra- and interspecies relationships are found between capacity to shrink (Csh) and strain recovery, while only the interspecies relationship is found between Csh and work recovery. Four factors, that is, molecular orientation, crystallinity, amino acid motif, and hydration, are discussed to explain the origin of silk’s elasticity. Our study corroborates the view that proline-containing motifs contribute to the elasticity of not only spider silks, but also other bioelastomers.
1. Introduction An elastic material is one at each material point of which the state of stress in the current configuration is determined solely by the state of deformation of this configuration relative to an arbitrary choice of reference configuration.1 This implies that the response of an elastic material during loading and unloading coincides. However, in the literature, the term “elastic” is ambiguous when describing a material.2 First, it means “resilient”, that is, able to deform reversibly without loss of energy. The second meaning ever used in literatures on silk is “stretchy”, that is, able to be deformed to a large strain with little force.2,3 For instance, a supercontracted spider major ampullate (MAA) silk is stretchy, but not resilient;4 collagen is not stretchy, but is resilient,5 while elastin is both stretchy and resilient.6 Apart from these two meanings, “elastic” also refers to “the ability of a material to resume its original shape after having been deformed by external force” (Oxford Dictionary). Therefore, in mechanical tests, three parameters can be used to describe a material’s elasticity: one is work recovery (WR), or resilience, which is the ratio between work input and work recovered in a cyclic test; the second is extensibility (b), or breaking strain in a tensile test; and the third is strain recovery (SR), or elastic recovery, which is the ratio between strain input and strain recovered in a cyclic test.7 In this paper, “elasticity” refers to resilience or ability to recover in shape. If necessary, the individual parameter, rather than the general term “elastic”, will be used to avoid ambiguity. An elastomer tends to return to the low-energy state. Vulcanized rubber is the most common elastomer, and its high resilience is driven by entropy maximization and comes from intermolecular cross-links. Those cross-links prevent molecular chains from irrecoverably sliding past one another.7 Some semicrystalline polymers, such as polypropylene (PP), polyoxymethylene (POM), poly(vinylidene fluoride) (PVDF), and polyethylene (PE), if appropriately processed, can form hard * To whom correspondence should be addressed. Telephone: +44 (0)1865 271216. Fax: +44 (0)1865 310447. E-mail: fritz.vollrath@ zoo.ox.ac.uk. † University of Oxford. ‡ Fudan University.
elastic materials.8 They enjoy high elastic recovery (90–97%) after large extension (50–100%).8 Their elastic properties were proposed to derive from the stacked crystalline lamellae that are aligned normal to the fiber or film extrusion direction. Those lamellae tend to return to their original unstrained configuration of lower energy during macroscopic deformation of the material.9 The elastic performance of such “as produced” fibers or films can generally be improved by annealing,8 which usually increases the molecular orientation,8 improves the perfection of crystals,9 and enhances crystalline content.10 Natural elastomers, such as elastin and resilin, have resilience as high as 90%.2 Their elasticity was thought to derive from hydrophobic forces and entropy-driven restoring forces.11 Successive β-turns made of proline-related motifs, for example, VPGVG and GPGXX, may provide the restoring forces.11–13 Native spider (Nephila edulis) MAA silk is reported to be of low resilience compared with other biomaterials,14 but it shows a good strain recovery, given enough time to relax between the first and the second load.15 Spider flagelliform silk, in the hydrated state, shows little hysteresis and good strain recovery up to a strain of 140%. Even dried over P2O5, it still possesses a strain recovery of about 70%, is to 15% of its original length.16 Silkworm silk, in contrast, is not good at resuming its shape and has a big hysteresis after being stretched.17,18 The difference in elasticity among these three silks probably comes from their different chemical make-ups. Indeed, in the MAA silk protein MaSp219–22 and the flagelliform silk protein Flag,21,23 a unique amino acid residual, proline when stretched abundantly present. However, it is almost absent in silkworm silk proteins.24,25 We showed in a previous study that MAA silk’s proline content is strongly linked with its initial modulus and Csh.26 Here we will explore the proline effects on a silk fiber’s elasticity.
2. Experimental Section 2.1. Sample Preparations. Adult females of Cyrtophora citricola, Latrodectus hesperus, Nephila edulis, Nephila senegalensis, Nuctenea sclopetaria, Argiope argentata, Argiope lobata, and Araneus diadematus were reared in the laboratory, fed on flies, and watered regularly. Single filaments of dragline silk were collected at four controlled speeds
10.1021/bm7014174 CCC: $40.75 2008 American Chemical Society Published on Web 06/05/2008
Elasticity of Spider Silks
Biomacromolecules, Vol. 9, No. 7, 2008
1783
Table 1. Correlations between Csh and Elastic Properties of MAA Silks from Representative Species properties
species
strain recovery
Cyrtophora citricola Nephila edulis Argiope lobata Araneus diadematus with similar breaking strainc with similar breaking strainc
work recovery
fitting equation SR SR SR SR SR SR
) ) ) ) ) )
0.285 + 2.679 × Csh 0.098 + 1.841 × Csh -0.203 + 2.050 × Csh -0.160 + 1.971 × Csh 0.493 + 0.655 × Csh 0.332 + 0.367 × Csh
a R2 is the square of correlation coefficient. b N indicates the number of data points. similar breaking strains (0.25 ( 0.02) in tensile tests.
Figure 1. Illustration of parameters involved in a cyclic test. f is the strain input; d is the permanent set; f - d is the strain recovered; the area A1 (shadow) represents the work lost (hysteresis); the area A2 (grids) represents the work recovered; and A1 + A2 represents the work input. The strain recovery (SR) can be calculated as SR ) [(f - d)/f] × 100%, and the work recovery (WR) can be calculated as WR ) [A2/(A1 + A2)] × 100%.
c
range of breaking strain
R2 a
Nb
0.180-0.579 0.181-0.664 0.192-0.460 0.182-0.498 0.219-0.279 0.219-0.279
0.856 0.932 0.700 0.840 0.916 0.817
29 37 37 18 34 34
The data are from MAA silks of all four species that showed
Figure 2. Stress–strain curves of Nephila edulis MAA silk: blue circles represent a cyclic test and red circles represent a following tensile test after a 2 min relaxation was allowed (note that the tensile curve lies on the reloading curve); the green solid line (superimposed by circles) represents a separate tensile test on a filament obtained in the same condition and from the same spider.
3. Results and Discussion (1, 6, 20, and 200 mm/s), as described elsewhere, to prepare samples containing various “molecular order”.27 The silkworm silk was reeled at four controlled speeds (4, 13, 20, and 24 mm/s) from immobilized silkworms (Bombyx mori) in the same manner as for spiders. The collected silkworm silk was degummed with a traditional aqueous solution standard wash of 1% sodium hydrogen carbonate before testing.28 2.2. Cyclic Test. The silk was carefully transferred with dividers from the spool to a custom-built microscale mechanical testing machine for measurements.15,29 A single thread (12 mm in length) was mounted to the hooks of the testing machine with cyanoacrylate adhesive and tested at the straining speed of 50% per minute under ambient room conditions of 22–25 °C and 35–50% r.h. Each fiber was stretched to a strain of 0.17 for the first loading and then relaxed to its original length. The same procedure was employed for the second loading. After two loads, some fibers were stretched to rupture, and the breaking strain was recorded. The single thread adjacent to the one used for the cyclic test was supercontracted in water to measure the shrinkage, as described elsewhere,15 and this value was taken as Csh of the cyclically tested thread. Fiber diameters were measured with SEM (JEOL JSM-5510) and used to calculate engineering stress. 2.3. Test Statistics. Cyrtophora citricola (which produces prolinepoor silk), Nephila edulis (which produces proline-moderate silk), Argiope lobata, and Araneus diadematus (which produce proline-rich silks) are selected as four representative species. As such, silks from each of these four species cover a wide range of “order”, as indicated by their breaking strains (see Table 1). Silks from additional species, on the other hand, may contain a similar degree of “order” (with a breaking strain of 0.25 ( 0.04) and their presence fills the gaps in the distribution of proline content.26 They are Latrodectus hesperus (six cyclic tests), Nephila senegalensis (three cyclic tests), Nuctenea sclopetaria (three cyclic tests), Argiope argentata (six cyclic tests), and silkworm silk (Bombyx mori, six cyclic tests). 2.4. Parameters. The parameters relevant to a cyclic test are illustrated in Figure 1.
3.1. Typical Cyclic Curves of Animal Silks. Figure 2 illustrates a typical cyclic curve of Nephila edulis MAA silk. No time was allowed between unloading and reloading. The silk fiber showed a permanent set of 0.07. It should be noted that the “permanent set” here can actually be removed after the silk is “healed” in water, or perhaps be reduced if a long time is allowed for the silk to recover between loads.15 However, the term “permanent set” is still habitually used in this paper. After the cyclic test, the fiber was rested for 2 min and stretched again up to rupture, with a stress developing from the strain of 0.07 and a similar stress–strain curve as the reloading curve in the cyclic test. Comparing them with the normal tensile test (monotonic loading) on the fiber of the same spider, we found that the cyclic loading did not alter the overall shape of an MAA silk’s stress–strain curve. This behavior could be compared to the Mullins effect known to occur in elastomers.30 Figure 3a compares the hysteresis behaviors of native Nephila edulis MAA silks of different Csh, with a cyclic curve of supercontracted silk shown for reference. As Csh decreases, a silk is less able to return to its original length after loading-unloading. The supercontracted silk shows the greatest permanent set (0.13) and the lowest strain recovery (24%). On the other hand, due to the lower initial and secant moduli, a silk of low Csh shows smaller hysteresis compared with that of high Csh. Apparently, the supercontracted silk consumes the least energy during a cyclic loading. Of particular interest is the difference between species (Figure 3b). With a similar breaking strain, spider MAA silks of different species show similar mechanical behavior patterns, except for stiffness,26 yet they recover to different degrees after cyclic loading. This interspecies difference may well be attributed to the different proline contents. Araneus silk (proline % ) 14.3) and Argiope silk (proline % ) 10.4) enjoy the smallest permanent sets (0.03) and, therefore, the best strain recovery
1784
Biomacromolecules, Vol. 9, No. 7, 2008
Figure 3. Typical stress–strain curves of cyclic test on (a) native Nephila edulis MAA silks with different Csh (deep blue circle, Csh ) 0.189; green circle, Csh ) 0.273; red circle, 0.359) and supercontracted silk (light blue circle); (b) spider MAA silks from different species (containing different proline contents) and silkworm silk with a similar breaking strain of 0.24 ( 0.02, as distinguished in different colours: grey squares, Cyrtophora citricola (proline % ) 0.6); black squares, Nephila edulis (proline % ) 4.2); purple squares, Argiope lobata (proline % ) 10.4); blue squares, Araneus diadematus (proline % ) 14.3); and yellow squares, Bombyx mori (proline % ) 0). The data of proline content of spider MAA silks are taken from ref 26 and that of Bombyx mori is taken from refs 48, 49. The triangles along the x-axes indicate the permanent sets of samples.
(82%), as opposed to Cyrtophora silk (proline % ) 0.6) that shows the greatest permanent set (0.07) and the lowest strain recovery (59%), while Nephila silk (proline % ) 4.2) has a moderate strain recovery (66%). The cyclic curve of Bombyx mori silk (proline ) 0%) is included in Figure 3b for comparison. And this silk is indeed rather poor at recovering after being stretched: with a permanent set of 0.11 and a strain recovery of 35%, it is even “worse” than Cyrtophora silk. 3.2. Comparison of Elasticity between Animal Silks. The correlations between strain recovery, work recovery, and Csh are plotted in Figure 4 for silks from different species. For each of the four representative species (Cyrtophora citricola, Nephila edulis, Argiope lobata, and Araneus diadematus), there is a positive linear correlation between Csh and strain recovery, as summarized in Table 1. Nearly identical fitting curves were found for Araneus and Argiope silks. Moreover, a linear relationship between Csh and strain recovery exists across these four species for fibers with similar extensibility. This interspecific relationship also applies to MAA silks from other spider species (Figure 4a) while silkworm silk, however, is somewhat far off it. Work recovery does not show a clear intraspecific dependence on Csh, though Nephila edulis MAA silk seems to have a better work recovery at high Csh (attempted fitting returns an R2 of 0.336 and a P value of 0.0002). Nevertheless, for MAA silks with similar extensibility, work recovery is still positively correlated with Csh across species. Within each species, hysteresis increases with Csh (Figure 5), but no clear correlation can be established across species.
Liu et al.
Figure 4. Intraspecific and interspecific relationships between (a) strain recovery and (b) work recovery and Csh. Hollow symbols represent data points from the four representative species: Cyrtophora citricola (diamond), Nephila edulis (square), Argiope lobata (circle), and Araneus diadematus (triangle). Solid squares represent data points from various species with a similar breaking strain of 0.25 ( 0.03 and each species is indicated with a distinct color as follows: grey squares, Cyrtophora citricola (proline % ) 0.6); red squares, Latrodectus hesperus (proline % ) 1.9); black squares, Nephila edulis (proline % ) 4.2); brown squares, Nephila senegalensis (proline % ) 5.7); green squares, Nuctenea sclopetaria (proline % ) 8.8); light green squares, Argiope argentata (proline % ) 9.3); purple squares, Argiope lobata (proline % ) 10.4); blue squares, Araneus diadematus (proline % ) 14.3); and yellow squares, Bombyx mori (proline ) 0).49 The data on proline of spider MAA silks content are taken from ref 26 and that of Bombyx mori is taken from refs 48 and 49. Dashed lines in (a) represent the intraspecies fitting curves between strain recovery and Csh for the four representative species; solid pink lines in (a) and (b) represent the interspecies fitting curves between strain recovery, work recovery, and Csh for the four representative species with a similar breaking strain.
Crystals, acting as cross-links,3 prevent the molecular chains from irrecoverably sliding past one another and, therefore, should improve a fiber’s elastic recovery.7 However, Bombyx mori silk, with a crystallinity of 50–65%,31,32 shows a much lower elastic recovery than most spider MAA silks for which a crystallinity of 12% was proposed.33 This suggests that other factors, whose effects override that of crystallinity, contribute to elastic recovery, as discussed in the following paragraphs. Csh is an important parameter that indicates the molecular orientation/order in MAA silk from one species.27,34–36 MAA silks from the four representative species all demonstrate increasing strain recovery, respectively, with increasing Csh. This suggests that molecular orientation/order benefits elasticity. Indeed, molecular chains in a highly oriented silk are pretensioned, therefore strongly tending to return to a low energy level, while this tendency is weaker for a less oriented silk. An extreme is the supercontracted silk: with molecular chains being disoriented, it shows the least ability to recover (Figure 3a).
Elasticity of Spider Silks
Figure 5. Intraspecific and interspecific relationships between hysteresis and Csh. Hollow symbols represent data points from the four representative species: Cyrtophora citricola (diamond), Nephila edulis (square), Argiope lobata (circle), and Araneus diadematus (triangle). The data of proline content of spider MAA silks are taken from ref 26 and that of Bombyx mori is taken from refs 48 and 49. Solid squares represent data points from various species with a similar breaking strain of 0.25 ( 0.03, and each species is indicated with a distinct color, as described in the legend of Figure 4.
This is consistent with what has been reported for hard-elastic polymers.10 Moreover, hydrogen bonds play an important role in silks, though they are generally absent in hard-elastic polymers. Higher molecular alignment would more likely lead to inter- and intramolecular hydrogen bonds. Those hydrogen bonds can be viewed as weak cross-links that add to a fiber’s stiffness3 and to some degree reduce the molecular flow when a fiber is deformed, contributing to the elastic recovery. Csh quantitatively links with proline contents in MAA silks from different species if the effect of molecular order is removed by tuning the silk to similar breaking strains.26,35,36 Thus, the interspecific variability in strain and work recovery may actually be explained by the difference in proline content. Indeed, the proline content in MAA silks increases in the following order: Cyrtophora citricola, Latrodectus hesperus, Nephila edulis, Nephila senegalensis, Nuctenea sclopetaria, Argiope lobata, Argiope argentata, and Araneus diadematus.26 This order is consistent with the MAA silk’s ability of strain/work recovery. Recently, proline’s contribution to elasticity has been discussed in the work of Rauscher et al. on a wide range of bioelastomers and amyloids. They suggested rigid proline decreases the hydrogen-bonded self-interactions; thus, the polypeptide chains can readily extend under strain and, after unloading, the chain entropy, as well as hydrophobic packing, leads to elastic recoiling.37 For spider MAA silk, proline may function within the form of GPGXX motif, because almost all proline residuals reside in it.19,38 This motif is virtually absent in Bombyx mori silk,24,25 which also shows the least strain/work recovery. In contrast, flagelliform silk, with a proline content over 20%,39 has a large number of GPGXX motifs and is good at strain/work recovery.21,23 This silk was suggested to possess few crystals and a low degree of orientation.14,40 The vast majority of amino acid links in its polypeptide chains, not bound up in highly oriented and inextensible crystals, would be free to participate in the extension of the material14 but still be able to recover due to the coiling of continuous GPGXX motifs.41 Hence, it is much more stretchy and more resilient compared to MAA silks, if being stretched to the same strain.16 Although its elasticity is maximized by an aqueous coating, after being dried with P2O5, a good strain/work recovery still persists.16 The GPGXX motifs in MaSp2 and Flag were hypothesized to form β-turns that
Biomacromolecules, Vol. 9, No. 7, 2008
1785
accumulate into β-spirals.41 Those β-spirals can act like springs that tend to coil when being stretched, as described by the librational entropy mechanism, and, therefore, add elasticity to materials.42,43 A fiber of higher proline content would be potentially more sensitive to moisture in an environment of certain humidity, because proline has been shown to account for an MAA silk’s capacity to shrink.26 This speculation, again, fits with the work of Rauscher et al. They proposed that proline and glycine modulate a polypeptide’s propensity for hydration and that proline is the primary determinant.37 Indeed, Araneus diadematus MAA silk, with the highest proline content (14.3%) among the silks we studied,26 showed the strongest hygroscopy: mounted on our microtensile tester, only this silk tended to contract at an r.h. of 50%, where an increasing tension force was detected. This should be compared to a much higher humidity threshold (r.h. ) 70%) for Argiope trifasciata MAA silk.44 Based on this fact, the hydrophilicity of flagelliform silk may also be attributed to, at least partially, abundant GPGXX motifs,23,45 apart from its hygroscopic coating materials, including carbohydrates.46,47 The reformed hydrogen bonds after a fiber has been deformed was suggested to lock molecules into place and therefore to enhance permanent set.15 A wet environment interrupts inter/ intramolecular hydrogen bonding of a fiber and introduces restoring hydrophobic forces.11,15 Hence, hydration benefits a fiber’s elasticity. For instance, when plasticized by water, both either spider MAA silk and flagelliform silk are able to fully recover to their original length after cyclic loading.15,16 Prolinerich silks (e.g., Araneus diadematus and Argiope lobata) are more likely to be permeated by moisture. Given the same testing environment, they would benefit more from hydration than proline-moderate (e.g., Nephila edulis) and proline-poor (e.g., Cyrtophora citricola) silks would, thus enjoying better elasticity.
4. Conclusion We studied loading-unloading curves of spider MAA silks from a variety of species and compared them with that of silkworm silk (Bombyx mori). Within a certain species, Csh, which denotes shrinkage in water and suggests the molecular orientation/order, is found to determine a fiber’s elasticity. This is consistent with the elastic behavior of hard-elastic polymers. Across species, fibers with similar extensibility show different elasticity that correlate with a fiber’s proline content and Csh. We hypothesize that proline may affect a silk fiber’s elasticity in two respects: (1) in the form of GPGXX motif, it makes successive β-turns that provide springy structures;42 (2) it increases the exposure of molecular chains to moisture, therefore inducing the restoring of hydrophobic forces and disfavoring the reformation of hydrogen bonds.11 Acknowledgment. Y.L. thanks the UK-NERC/Hutchison Whampoa for a Dorothy Hodgkin doctoral studentship. Z.S. thanks the National Natural Science Foundation of China (NSFC 20434010) and the Programme for Changjiang Scholars and Innovative Research Team in the Fudan University. F.V. thanks the European Commission and the US-AFOSR. F.V. and Z.S. are grateful to the Royal Society of London for an exchange grant. Finally, we thank C. Dicko, C. Holland, D. Porter, A. Sponner, Y. M. Liu. and C. Zentile for comments and suggestions on the research and manuscript.
References and Notes (1) Ogden, R. W. Non-linear Elastic Deformation; Ellis Horwood: Chichester, 1984.
1786
Biomacromolecules, Vol. 9, No. 7, 2008
(2) Gosline, J.; Lillie, M.; Carrington, E.; Guerette, P.; Ortlepp, C.; Savage, K. Philos. Trans. R. Soc. London, Ser. B 2002, 357, 121–132. (3) Termonia, Y. Macromolecules 1994, 27, 7378–7381. (4) Shao, Z. Z.; Vollrath, F.; Yang, Y.; Thogersen, H. C. Macromolecules 2003, 36, 1157–1161. (5) Pollock, C. M.; Shadwick, R. E. Am. J. Physiol. 1994, 266, R1016– 1021. (6) Aaron, B. B.; Gosline, J. M. Biopolymers 1981, 20, 1247–1260. (7) Warner, S. B. Tensile properties. In Fiber Science; Stenquist, B., Ed.; Prentice Hall: Englewood Cliffs, NJ, 1995; p 138. (8) Park, I. K.; Noether, H. D. Colloid Polym. Sci. 1975, 253, 824–839. (9) Noether, H. D.; Whitney, W. Colloid Polym. Sci. 1973, 251, 991– 1005. (10) Du, C. H.; Zhu, B. K.; Xu, Y. Y. Macromol. Mater. Eng. 2005, 290, 786–791. (11) Wasserman, Z. R.; Salemme, F. R. Biopolymers 1990, 29, 1613–1631. (12) Kim, W.; Conticello, V. P. Polym. ReV. 2007, 47, 93–119. (13) Yao, J. M.; Asakura, T. J. Biochem. 2003, 133, 147–154. (14) Denny, M. J. Exp. Biol. 1976, 65, 483–506. (15) Shao, Z.; Vollrath, F. Polymer 1999, 40, 1799–1806. (16) Vollrath, F.; Edmonds, D. T. Nature 1989, 340, 305–307. (17) Perez-Rigueiro, J.; Viney, C.; Llorca, J.; Elices, M. J. Appl. Polym. Sci. 1998, 70, 2439–2447. (18) Sirichaisit, J.; Brookes, V. L.; Young, R. J.; Vollrath, F. Biomacromolecules 2003, 4, 387–394. (19) Hinman, M. B.; Lewis, R. V. J. Biol. Chem. 1992, 267, 19320–19324. (20) Lawrence, B. A.; Vierra, C. A.; Moore, A. M. F. Biomacromolecules 2004, 5, 689–695. (21) Gatesy, J.; Hayashi, C.; Motriuk, D.; Woods, J.; Lewis, R. Science 2001, 291, 2603–2605. (22) Guerette, P. A.; Ginzinger, D. G.; Weber, B. H. F.; Gosline, J. M. Science 1996, 272, 112–115. (23) Hayashi, C. Y.; Lewis, R. V. J. Mol. Biol. 1998, 275, 773–784. (24) Mita, K.; Ichimura, S.; James, T. C. J. Mol. EVol. 1994, 38, 583–592. (25) Zhou, C. Z.; Confalonieri, F.; Medina, N.; Zivanovic, Y.; Esnault, C.; Yang, T.; Jacquet, M.; Janin, J.; Duguet, M.; Perasso, R.; Li, Z. G. Nucleic Acids Res. 2000, 28, 2413–2419. (26) Liu, Y.; Sponner, A.; Porter, D.; Vollrath, F. Biomacromolecules 2008, 9, 116–121. (27) Liu, Y.; Shao, Z.; Vollrath, F. Nat. Mater. 2005, 4, 901–905.
Liu et al. (28) Monti, P.; Freddi, G.; Bertoluzza, A.; Kasai, N.; Tsukada, M. J. Raman Spectrosc. 1998, 29, 297–304. (29) Vollrath, F.; Madsen, B.; Shao, Z. Proc. R. Soc. London, Ser. B 2001, 268, 2339–2346. (30) Dorfmann, A.; Ogden, R. W. Int. J. Solids Struct. 2004, 41, 1855– 1878. (31) Hu, X.; Kaplan, D.; Cebe, P. Macromolecules 2006, 39, 6161–6170. (32) Bhat, N. V.; Nadiger, G. S. J. Appl. Polym. Sci. 1980, 25, 921–932. (33) Grubb, D. T.; Jelinski, L. W. Macromolecules 1997, 30, 2860–2867. (34) Du, N.; Liu, X. Y.; Narayanan, J.; Li, L. A.; Lim, M. L. M.; Li, D. Q. Biophy. J. 2006, 91, 4528–4535. (35) Porter, D.; Vollrath, F.; Shao, Z. Eur. Phys. J. E 2005, 16, 199–206. (36) Vollrath, F.; Porter, D. Appl. Phys. A: Mater. Sci. Process. 2006, 82, 205–212. (37) Rauscher, S.; Baud, S.; Miao, M.; Keeley, F.; Pomes, R. Structure 2006, 14, 1667–1676. (38) Xu, M.; Lewis, R. V. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 7120– 7124. (39) Gosline, J. M.; DeMont, M. E.; Denny, M. W. EndeaVour 1986, 10, 31–43. (40) Bonthrone, K. M.; Vollrath, F.; Hunter, B. K.; Sanders, J. K. M. Proc. R. Soc. London, Ser. B 1992, 248, 141–144. (41) Hayashi, C. Y.; Shipley, N. H.; Lewis, R. V. Int. J. Biol. Macromol. 1999, 24, 271–275. (42) Becker, N.; Oroudjev, E.; Mutz, S.; Cleveland, J. P.; Hansma, P. K.; Hayashi, C. Y.; Makarov, D. E.; Hansma, H. G. Nat. Mater. 2003, 2, 278–283. (43) Urry, D. W. J. Protein Chem. 1988, 7, 1–34. (44) Guinea, G. V.; Elices, M.; Perez-Rigueiro, J.; Plaza, G. Polymer 2003, 44, 5785–5788. (45) Lewis, R. V. Chem. ReV. 2006, 106, 3762–3774. (46) Tillinghast, E.; Kavangah, E.; Kolbjornsen, P. J. Morphol. 1981, 169, 141–148. (47) Vollrath, F.; Fairbrother, W. J.; Williams, R. J. P.; Tillinghast, E. K.; Bernstein, D. T.; Gallagher, K. S.; Townley, M. A. Nature 1990, 345, 526–528. (48) Lucas, F.; Shaw, J. T. B.; Smith, S. G. J. Mol. Biol. 1960, 2, 339– 349. (49) Ito, H.; Muraoka, Y. Text. Res. J. 1995, 65, 755–759.
BM7014174
