Dynamic Mechanical Properties of Elastin JOHN M. GOSLINE and CHRISTOPHER J. FRENCH, Department of Zoology, University of British Columbia, Vancouver, B.C., Canada, V 6 T 1 W5 Synopsis The dynamic mechanical properties of water-swollen elastin under physiological conditions have been investigated. When elastin is tested as a closed, fixed-volume system, mechanical data could be temperature shifted to produce master curves. Master curves for elastin hydrated a t 36OC (water content, 0.46 g water/g protein) and 55OC (water content, 0.41 g/g) were constructed, and in both cases elastin goes through a glass transition, with the glass transition temperatures of -46 and -2loC, respectively. Temperature shift data used to construct the master curves follow the WLF equation, and the glass transition appears to be characteristic of an amorphous, random-polymer network. For elastin tested as an open, variable-volume system free to change its swollen volume as temperature is changed, dynamic mechanical properties appear to be virtually independent of temperature. No glass transition is observed because elastin swelling increases with decreased temperature, and the increase in water content shifts elastin away from its glass transition. It is suggested that the hydrophobic character of elastin, which gives rise to the unusual swelling properties of elastin, evolved to provide a temperature-independent elastomer for the cold-blooded, lower vertebrates.

INTRODUCTION The long-range elasticity of vertebrate arteries can be attributed largely to the rubberlike protein elastin. A t its simplest, the elastin-based compliance of major arteries provides an elastic reservoir that helps to smooth the pulsatile blood flow from the heart. The actual role of elastic arteries is considerably more complex, as in most animals there is no simple elastic reservoir, but rather the arteries provide a series of elastic tubes that propagate pressure waves.1 Regardless of the exact fluid-dynamic role, the efficient storage of elastic energy by distensible arteries is a vital feature of the vertebrate circulatory system, and we expect that elastin provides an elastic component of sufficient resilience to meet these requirements, particularly in the range of frequencies that corresponds to the heart rate. Some preliminary dynamic measurements on purified elastin2 indicate that the resilience is high (ca. 85%) in this frequency range, and experiments with whole arteries3 indicate that the intact tissue is considerably less resilient than purified elastin at these frequencies. Thus the dynamic elastic properties of arteries are not limited by the properties of elastin. On the other hand, several workers have noted that under physiological conditions elastin is quite close to its glass t r a n ~ i t i o n , ~and , ~ ,thus ~ should become viscoelastic with increased frequency. This viscoelastic behavior Biopolymers, Vol. 18, 2091-2103 (1979) C 1979 John Wiley & Sons, Inc.

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may be of importance for the long-term fatigue of elastin in pathological conditions. For example, Roach6.7 has shown that vibrations a t sonic frequencies (i.e., 50-500 Hz) caused by turbulent blood flow in arteries cause the artery to dilate, and they suggest that this dilation is due to the dynamic fatigue of elastin. Although there are few data on dynamic fatigue (i.e., fatigue under cyclic loading) in rubberlike materials, the limited data that are available suggest that fatigue properties can be predicted from uniaxial extension tests or from tearing tests,&l0 and fortunately a reasonable amount is known about the ultimate properties of synthetic elastomers in these testing modes. In general it is possible to construct "master" failure envelopes to describe the ultimate properties of rubbers by employing WLF temperature shift factors for tests carried out a t different temperatures and strain r a t e ~ . * , ~ J For elastomers tested in the equilibrium or pseudoequilibrium region of their response curve, both stress a t failure, g b , and strain a t failure, c b , increase with increasing strain rate or decreasing temperature. However, for rubbers in their glass transition zone the pattern is changed, and in particular, Eb goes through a maximum and decreases with increased strain rate or decreased temperature.8-lO This deterioration of properties occurs just at the onset of the glass transition,'l and we suspect that dynamic fatigue in elastin may result if high-frequency vibrations drive elastin into its glass transition. Therefore, we have investigated the dynamic mechanical properties of elastin to establish the location of the glass transition in relation to physiological conditions.

MATERIALS AND METHODS Elastin samples were prepared from the ligamentum nuchae obtained from freshly killed, mature beef cattle. The tissue was purified by repeated autoclaving in distilled water, and samples were held under sterile conditions in water until they were used.12 Test specimens of about 1.5 cm long were mounted in brass cups as described pre~ious1y.l~ Dynamic mechanical measurements were carried out on a forced-vibration testing apparatus constructed in our laboratory (Fig. 1). Samples were deformed in tension by an electromagnetic vibrator (Ling Dynamic Systems, model 203) driven by the function generator of a SE Labs, SM272DP-transfer function analyzer through an audio power amplifier. Sample displacement was measured with a compliant strain gauge transducer attached to the moving element of the vibrator. Force was measured with a stiff (maximum deflection, lop4cm) semiconductor strain gauge transducer that had a resonant frequency of about 4500 Hz. Force and displacement amplitude and the phase shift d between force and displacement were measured with the transfer function analyzer. The elastin sample and the force transducer were immersed in a thermostatically controlled water bath (&O.l"C). Samples were prestrained by about 15%and vibrated at a nominal amplitude of 0.2 mm peak to peak.

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VIBRATOR DISPL.

FUNCTION GENERATOR

_---------

FORCE

/-CORRELATOR

t Fig. 1. Diagram of the dynamic testing apparatus used in this study. T h e sample is deformed in tension by an electromagnetic vibrator. The vibrator is driven by the sine generator of a transfer function analyzer, and displacement and force are measured directly by strain gauge transducers. Force and displacement amplitude and the phase shift between force and displacement are measured by the transfer function analyzer.

Thus the experiments were carried out a t peak-to-peak strains of the order of 0.01. Measurements were made in a series starting a t the lowest frequency, working upwards to about 200 Hz. However, several measurements a t lower frequencies were taken a t the end of a series to ensure that there had been no change in properties during the test period. Our measurements were limited to frequencies below about 200 Hz because the test frame showed several resonances a t 250 Hz and above. Elastin samples were tested either as open, variable-volume systems by maintaining them in swelling equilibrium with a solvent or as closed, fixed-volume systems by sealing the sample under mineral oil. In order to obtain a sample that could be tested as a closed system, it was necessary to remove all free water from the numerous spaces in the fibrous material. This was done by hydrating the sample under vacuum over water a t constant temperature. Ideally one would like to hydrate the sample over pure water, but under these conditions water vapor condenses on surfaces in the desiccator, and it is impossible to keep free water from condensing on the sample. Therefore, the samples were hydrated for approximately 7 days over 0.05M NaCl (relative humidity 99.8%). The small gradient provided by this dilute solution kept water from condensing on the sample and allowed us to obtain samples without any free water. The amount of bound water lost from the sample is extremely small and probably has no major effect on the mechanical properties reported here.

RESULTS Figure 2(a) shows the results of dynamic measurements on elastin in swelling equilibrium with distilled water a t 36°C. These results are consistent with the hypothesis that elastin is a crosslinked network near to its glass transition r e g i ~ n . ” ~Although ,~ the storage modulus (E’) remains essentially constant at about 2 X 106 nmP2over the entire frequency range,

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-1

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(a) (b) Fig. 2. Dynamic mechanical properties of an elastin sample tested as an open system in swelling equilibrium with water a t 36 and 2.5”C. E’ is the storage modulus, E“ is the loss modulus, and tan d is the damping (E”/E’).

the loss modulus ( E ” ) ,and therefore tan d (where d is the phase shift between force and displacement, tan d = E”IE’), increases with increasing frequency. It appears that elastin is just entering its glass transition a t frequencies above those that we can attain with our apparatus. Since resonances in our apparatus precluded direct measurement of mechanical properties above 200 Hz, we attempted to use the time-temperature superposition principle to make indirect measurements a t frequencies above 200 Hz.14 According to this principle, one can shift the time scale by altering temperature. A temperature increase will increase the rate of molecular motion and thus allow one to “observe” properties a t longer times (i.e., a t lower frequencies), or conversely a temperature decrease will slow molecular motion and allow one to observe properties at higher frequencies. This equivalence of time and temperature has been found to apply to a wide range of amorphous polymeric systems.14 However, when we lowered temperatures for elastin in swelling equilibrium with water, we found, quite unexpectedly, that elastin does not show any tendency to enter its glass transition. In fact, elastin appears farther from its glass transition at 25°C than it does at 36°C [Fig. 2(b)]. Does this mean that under physiological conditions elastin is not near its glass transition? Probably not, because the temperature range studied here is just the range in which elastin shows a dramatic, temperaturedependent increase in ~wel1ing.l~Figure 3 shows the volume of waterswollen elastin over the temperature range 0-65°C. The swollen volume is expressed on an arbitrary scale that sets a value of 1.00 at 3OoC,and the figures given after the arrows indicate the calculated water content (in grams water per gram dry elastin) for elastin at 2.5, 36, and 55°C. Note that in decreasing the temperature from 36 to 2.5”C, the water content increases by 65%,and this increase in water content probably explains our inability to find the glass transition by lowering temperature. Water is an important plasticizing agent for e l a ~ t i n ,and ~ , ~the increased water content will lower the glass transition temperature ( t g ) . I t appears that the increase in water content lowers t, by just the amount that decreased

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Fig. 3. The temperature-dependent swelling of elastin in water and two mixed solvents [20%ethanol (EtOH) and 25% dimethylsulfoxide (DMSO)]. The volume scale is an arbitrary one, established by assigning a value of 1.00 a t 30°C in water. The values shown after the arrows give the water content (g water/g protein) a t 2.5,36, and 55°C. The volume changes were measured as described previously (Ref. 15).

temperature shifts the time scale towards shorter times, and interestingly this results in a material whose mechanical properties are largely independent of temperature over quite a wide temperature range. We will return to this aspect of elastin's properties in the Discussion. We have used two techniques to eliminate these temperature-dependent swelling effects so that we could use temperature shift data to investigate the glass transition of elastin: (I)mixed solvent systems for which d Vldt = 0 and (2) hydration of elastin in the vapor phase and testing as a closed system under mineral oil. Two mixed solvents were used, 20% ethanol and 25% dimethylsulfoxide. For both solvents the swollen volume of elastin is largely independent of temperature between 0 and 65°C (Fig. 3, broken lines), and in both cases elastin does indeed enter its glass transition when the temperature is lowered. However, the swollen volume of elastin in these solvents is not absolutely constant, and these solvents do not evenly faintly resemble the solvent conditions in a living animal. Therefore, the data obtained for elastin hydrated in the vapor phase and tested as a closed system under mineral oil are presented as a reasonable approximation of normal physiological conditions. (Elastin in vivo is bathed by a dilute aqueous salt solution, but we find no significant change in properties in dilute NaCl solutions.) As with the mixed solvent systems, elastin tested as a closed system shows the properties expected for an amorphous polymer network entering its glass transition. Figure 4 shows storage and loss modulus data for a single sample hydrated in the vapor phase at 36°C (water content, 0.46 g/g) and tested under mineral oil at temperatures between 36 and -15°C. Figure 5 shows the

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N(!I)7 3

56 -

8 2

&g; E'

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c7

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Fig. 5. Master curve for elastin hydrated a t 36"C, constructed from the data in Fig. 4. The inset curve shows the temperature shift data used to construct the master curve.

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are able t o observe most of the transition from the low-modulus rubbery state to the high-modulus glassy state. Again, Fig. 6 shows the individual storage and loss modulus curves for a single sample tested at seven temperatures between 55 and -4"C, and Fig. 7 shows the master curve constructed from this data. The master curve has been temperature shifted to a reference temperature of 36"C, so it shows the dynamic mechanical behavior that we would expect for an elastin sample with a water content of 0.41 g/g, tested a t a temperature of 36°C over the frequency range indicated. In both Figs. 5 and 7 the inset curve shows the temperature shift data used to construct the master curves, plotted in Arrhenius form as log at against llt. at is the temperature shift factor.14 The temperature shifting was carried out by simultaneously shifting both E' and E" curves to obtain the best overlap of data. In all cases the overlap between any two adjacent temperatures in the series was a t least two decades of frequency, and the curves could be quite accurately superimposed in this overlap region. Thus the simultaneous shifting of both E' and E" curves seems to provide a good criterion for the time axis (horizontal) shift. In most cases it was also necessary to include a very small shift along the modulus (vertical) axis to obtain good fit. However, such vertical shifting is to be expected,14 and no attempt was made to analyze this vertical shift. One important criterion for the temperature shifting of mechanical data for glass-forming, amorphous polymers is the empirical relationship commonly referred to as the WLF equation,*4,16 log at = -C?(t - to)/C!

u

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Fig. 6. Dynamic mechanical properties of elastin tested as a closed system. Elastin was hydrated a t 55OC (water content, 0.41 g/g) and tested under mineral oil a t the temperatures indicated.

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LOG FREQ.

Hz

Fig. 7. Master curve for elastin hydrated a t 55"C, constructed from the data in Fig. 6. The reference temperature, t o , for this master curve is 36°C. The inset curve shows the temperature shift data that were used to construct the master curve.

where at is the temperature shift factor, t o the reference temperature of the master curve, t the temperature of each individual experiment, and Cy and C!j' are empirical constants that apply at the reference temperature to. This relationship has been shown to be generally applicable to an extremely broad range of amorphous polymers, and it is commonly taken as a universal description of the glass transition. We find that the temperature shift data for elastin can also be described by this relationship, and the empirical constants for t o = 36°C are given in Table I. Although we were not able to observe the low-temperature thermal expansion of our samples and thus determine their glass transition temperatures ( t g ) we , attempted to use the WLF equation to calculate t, from our TABLE I Empirically Derived Constants for the WLF Equation Calculated for Hydrated Elastin" Hydration Temperature ("C)

Water Content (gk)

G

C!

t, ("C)

36 55

0.46 0.41

5.09 6.17

109.1 117.2

-46 -21

a The glass transition temperature t, was calculated using Eq. (2) and the "universal" WLF constants, as explained in the text.

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temperature shift data. The slope of an Arrhenius-type plot of log at versus l / t yields a temperature-dependent activation energy (AH,,,) for the viscoelastic relaxation process of the glass transition. Then, using a modified form of the WLF equation that includes the activation energy term [Eq. (2)],14we calculated tg by taking the empirical constants Cf and C$ a t the glass transition temperature to be equal to their "universal" values, 17.5 and 51.6, respectively. The results are given in the last column of Table I:

DISCUSSION It has been recognized for some time that elastin goes through a dramatic shift in mechanical properties with decreased temperature, and this shift in properties has been identified as a glass transition on the basis of this mechanical behavior4 and on the basis of differential scanning ~alorimetry.~ Our study provides the first detailed analysis of the glass transition of elastin under temperature and solvent conditions closely resembling those in living animals. We find, in agreement with other^,^.'^ that the glass transition of elastin is very similar to transitions observed for a wide range of amorphous polymeric systems. The excellent agreement of our data with the WLF equation strongly supports this conclusion. Although the calculated values of the glass transition temperature (t,) are based on assumed values for the WLF constants, the t, values are in reasonable agreement with measured t, values for hydrated elastin samples.5 Although the measured values, obtained by differential scanning calorimetry, are all substantially higher than the values calculated in the present study, the measurements were made on samples with quite low water contents. A t the highest water content used, 0.31 g water/g protein, the t, was about 1O"C, and linear extrapolation of these data to water contents of 0.41 g/g and 0.46 g/g suggests that the t, should be about -15 and -26"C, respectively. The t, could not be measured directly a t these higher water contents by scanning calorimetry because the loosely bound water in the elastin freezes a t temperatures where the glass transition is expected. The comparison between the samples hydrated a t 36 and 55°C (Table I) confirms the conclusion of others4p5 that the glass transition is very sensitive to water content. In particular, our data suggest that under physiological conditions the loss of only 10%of the bound water raises the glass transition temperature by about 20°C. Since elastin properties are extremely sensitive to water content in the physiological state, we suspect that any process that displaces even a small amount of the loosely bound water from the elastin network could substantially increase the rate of dynamic fatigue. This aspect of elastin rheology clearly warrants further study.

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I t has been suggested17that the absorption of water during the extension of elastin may have a significant effect on the dynamic mechanical properties. If this is true, we should see a difference in properties between elastin tested in swelling equilibrium with water as a n open system and elastin tested under mineral oil as a closed system. Figures 2(a) and 5 provide the data necessary for this comparison. Although we have made no great effort to compare these two conditions in detail, there are no obvious differences. tan d appears to be slightly higher for the sample tested in oil, suggesting that t, for the closed system is somewhat higher than the equivalent open system. For example, a t 100 Hz, tan d = 0.09 for the open system and 0.11 for the closed system. However, these small differences may just be due to the removal of a small amount of the bound water in the preparation of the sample for testing as a closed system (see Materials and Methods). We suspect that there is no significant difference in properties between these two testing conditions. The presence of the glass transition has been used as evidence for a n isotropic, random-network structure for elastin,5Js in contrast to the anisotropic, fibrillar models proposed by o t h e r ~ . ~Since ~ - ~the ~ glass transition of elastin is typical of all amorphous polymers, it seems likely th a t the random-network model provides a reasonable description of elastin. Further, since the glass transition is due to a dramatic shift in chain mobility from virtually unrestrained random coils to fixed, glasslike structures, we can exclude elastin models based on fixed-helical structure^.'^ However, more recent descriptions of fibrillar model^^^-^^ suggest th a t limited mobility is a feature of the elastin network, but unfortunately there are no quantitative estimates of the mobility in these models. Since mobility is a feature of water-swollen e l a ~ t i n , 2 4 -it~is ~ likely that any fibrillar or anisotropic structure represents transient and short-range features of the elastin network, and that the random-network model provides the best description of the properties observed a t the macroscopic level. However, the fibrillar model may be useful in understanding features of elastin fibrillogenesis a t the microscopic level.21 T he mechanical data for elastin tested as a n open, variable volume system, however, may provide some interesting information about elastin network structure. Although increased swelling with decreased temperature largely balances the tendency of decreased temperature to shift elastin into its glass transition, there are measurable changes in dynamic properties. These changes have been summarized in Fig. 8, where damping (tan d ) a t low frequency (1 Hz) and high frequency (100 Hz) is plotted as a function of temperature. Interestingly, the damping a t low frequency appears to rise continuously with decreasing temperature, while damping a t high frequency increases to a maximum a t about 30°C and then decreases again. These observations can be explained as follows. T h e swelling changes are quite small above about 30°C and are very large below this temperature (Fig. 3). Therefore, the plasticizing effect of swelling should be most important below about 30°C. On the other hand, thermal energy

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Fig. 8. The effect of temperature on damping (tan d ) of elastin tested as an open, variable-volume system in swelling equilibrium with water. Solid circles give damping a t 100 Hz; open circles give damping a t 1 Hz. The data have been pooled from experiments with three different samples.

( h T )decreases uniformly with decreasing temperature. The 100-Hz peak in damping arises because the decrease in thermal energy is more important than the swelling increase a t temperatures above and less important below 30°C. The absence of a peak in the low-frequency properties presumably arises because swelling effects are less important a t the lower frequencies, and the properties are dominated by the continuously decreasing thermal energy. In general, high-frequency deformation of a rubbery material is limited by small-scale, segmental mobility, while low-frequency properties reflect larger scale movements, perhaps a t the level of entire polymer chains. Although the frequency range in Fig. 8 is small, the dramatic difference in properties suggest that, in this range of swelling and temperature, smallscale features of the elastin network are more sensitive to hydration level than are large-scale features. As the dramatic increase in swelling with decreased temperature is due almost entirely to the weakening of hydrophobic interactions,I5 we conclude that hydrophobic regions (i.e., transient regions of reduced water content formed by the clumping of nonpolar groups) represent small-scale features of the elastin network. Further, these are regions of reduced mobility that give rise to the 100-Hz damping peak. This conclusion is in agreement with the observations of Ellis and Packer,26who used nmr to study the proton relaxation behavior of DzOswollen elastin. They were able to identify three components of differing mobility. One of these components with reduced mobility, which they

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attributed to clusters of nonpolar groups, showed a temperature profile very similar t o the 100-Hz damping curve in Fig. 8. I t is impossible to predict the exact scale of these regions, other than to say that they are of the order of a random segment and smaller than an entire random chain. In fact, they may represent P-turns of the fibrillar model.23 Finally, a comparison of elastin tested as an open system with elastin tested as a closed system (Fig. 9) suggests a possible explanation for the previously, elastin extreme hydrophobic character of e l a ~ t i n . ~ JAs ~ Jnoted ~ swelling can be attributed to hydrophobic interactions, and these swelling changes create a material whose mechanical properties are nearly temperature independent. This temperature independence is probably not important to higher vertebrates that maintain constant body temperature, but elastin evolved in the fishes and is found in other lower ~ e r t e b r a t e s , ~ 7 where it must function in arteries to efficiently store elastic energy a t temperatures as low as -2°C. The comparison in Fig. 9 shows the importance of the hydrophobic-based swelling changes graphically. Damping is virtually identical a t temperatures above 35"C, but below this temperature damping for the closed system increases very quickly because the material is entering its glass transition. We suggest, therefore, that the

TEMP.

"G

Fig. 9. Comparison of damping for elastin tested as a closed, fixed-volume system (solid lines) and as an open, variable-volumesystem (broken lines). The open-system lines are taken directly from Fig. 8 and plotted on a different tan d scale. The closed-system data were taken from experiments with five different samples, including two where volume was held constant by swelling in mixed solvents (20% ethanol and 25% dimethylsulfoxide). For tan d less than 0.1, it is possible to calculate a measure of elastic efficiency or resilience from dynamic properties, as R = exp(-2 a tan d ) . For tan d = 0.1, R = 50% (i.e., one-half of the energy put into deforming the sample is recoverable and the other half is dissipated as heat). The elastic efficiency of the closed system drops to very low values as temperature drops below about 35°C.

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hydrophobic character of elastin arose in the evolution of this rubberlike protein as a design feature to produce a temperature-independent material. This research was supported by grants from the British Columbia Heart Foundation and the Canadian National Research Council to J.M.G.

References 1. Bergel, D. H. & Schultz, D. L. (1971) Prog. Riophys. Mol. Biol. 22, 1-36. 2. Gosline, J. M. (1976) Int. Reu. Connect. Tissue Res. 7,211-249. 3. Bergel, D. H. (1961) J . Physiol. (Lond.) 156,458-469. 4. Gotte, L., Mammi, M. & Pezzin, G. (1968) in Symposium on Fibrous Proteins, Crewther, W. G., Ed., Butterworths, Sydney, pp. 236-245. 5. Kakivaya, S. R. & Hoeve, C. A. J . (1975) Proc. Natl. Acad. Sci. U S A 72,3505-3507. 6. Roach, M. R. (1963) Circ. Res. 13,537-551. 7. Roach, M. R. (1972) in Cardiovascular Fluid Dynamics, Vol. 2, Bergel, D. H., Ed., Academic, London, pp. 111-139. 8. Mocanin, J. & Landel, R. F. (1971) in Riomaterials, Beament, A. L., Jr., Ed., University of Washington Press, Seattle, pp. 235-247. 9. Landel, R. F. & Fedors, R. F. (1973) in Deformation and Fracture of High Polymers, Kausch, H. H., Hassell, J. A. & Jaffee, R. I., Eds., Plenum, New York, pp. 131-148. 10. Fedors, R. F. & Landel, R. F. (1975) J . Polym. Sci., Polym. Phys. Ed. 13,419-429. 11. Fedors, R. F. & Landel, R. F. (1964) in Fracture Processes i n Polymeric Solids, Rosen, B., Ed., Interscience, New York, pp. 361-485. 12. Gosline, J. M., Yew, F. F. & Weis-Fogh, T. (1975) Riopolymers 14,1811-1826. 13. Gosline, J. M. (1978) Riopolymers 17,677-695. 14. Ferry, J . D. (1970) Viscoelastic Properties of Polymers, WiIey, New York. 15. Gosline, J. M. (1978) Biopolymers 17,697-707. 16. Williams, M. L., Landel, R. F. & Ferry, J . D. (1955) J . A m . Chem. Soc. 77, 37013704. 17. Dorrington, K., Grut, W. & McCrum, N. G. (1975) Nature 255,476-478. 18. Hoeve, C. A. J . & Flory, P. J. (1974) Biopolymers 13,677-686. 19. Gray, W. R., Sandberg, L. B. & Foster, J . A. (1973) Nature 246,461-466. 20. Serafini-Fracassini, A., Field, J . M., Spina, M., Stephens, W. G. S. & Delf, B. (1976) J . Mol. Riol. 100,73-84. 21. Urry, D. W. & Long, M. M. (1976) in Elastin and Elastic Tissue, Sandberg, L. B., Gray, W. R. & Franzblau, C., Eds., Plenum, New York, pp. 685-714. 22. Urry, D. W., Okamoto, K., Harris, R. D., Hendrix, C. F. & Long, M. M. (1976) Biochemistry 15,4083-4089. 23. Urry, D. W. & TJong, M. M. (1976) Crit. Reu. Riochem. 4.1-45. 24. Torchia, D. A. & Piez, K. A. (1973) J. Mot. Biot. 76,419-424. 25. Lyerla, J . R., Jr. & Torchia, D. A. (1975) Biochemistry 14,5175-5183. 26. Ellis, G. E. & Packer, K. J. (1976) Riopolymers 15,813-832. 27. Sage, E. H. & Gray, W. R. (1977) in Elastin and Elastic Tissue, Sandberg, L. B., Gray, W. R. & Farnzblau, C., Eds., Plenum, New York, pp. 291-312.

Received August 28,1978 Accepted March 12,1979

Dynamic mechanical properties of elastin.

Dynamic Mechanical Properties of Elastin JOHN M. GOSLINE and CHRISTOPHER J. FRENCH, Department of Zoology, University of British Columbia, Vancouver,...
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