J. Mol. Biol. (1979) 135: 39-51


of the Elastic Constants of Collagen by Brillouin Light Scattering S. CUSACK AND A. MILLER

G’relrohle Outstation,

European Molecular Biology Laboratory c/o C.E.N.Q., L.M.A.. X5X, 38041 Grenoble Cedex, France

(Received 20 December 1978, and in revised form 1G .July 1979) The lligh-frequency elastic properties of rat-tail tendon collagen have been investigated by means of Brillouin (inelastic) light scattering. Longitudinally and transversely polarised elastic waves of frequency about l(F” Hz have been observed propagating at various angles to the fibre axis of stret’ched, partially dried tendon. Assuming t,hat the elastic properties of tendon are transversely isotropic, these measurements enable the five elastic constants for such a system to be determined. In particular the ratio of the Young’s modulus for st,rain parallel to the axis to that for strain perpendicular to the axis (E;,/E,) is found to be 1.43 and the ratio of the shear modulus to E,, is 0.28. In wet collagen only t,he longit)udinal branch has been observed and in t,his case the ratio E,,/E, increases t)o I .82. The absolute value for E,, in dry collagen is 11.9 GN nm2 reducing to 5.1 GN me2 in wet collagen. An interpretation of these results in t,erms of the expected vibrations of t)he collagen molecular assembly is given. Possible applications to the determination of the mechanical properties of collagen compositr materials such as bone are discussed as well as some measurements on silk and E- and /3-keratins, which are fibrous prot*eins of different molecular conformation t 0 collagen.

1. Introduction It is well known from modern material science that much closer tailoring of mechanical properties to function can be achieved by the use of composite materials, and it is clear from the composite structure of most biological materials (e.g. bone, cartilage, skin, insect cuticle) that this principle has been well recognised in nature (Wainwright et al., 1976). The theoretical prediction of the mechanical properties of composites is notoriously difficult, being dependent on detailed knowledge of the properties of the components and their interactions as well as their structural arrangement. Unfortunately such information is often unavailable and only qualitative explanations of observed properties can be given. Thus a quantitative theory of bone elasticity is still lacking, bone being a composite largely consisting of small crystallites of calcium apatite embedded in an organic matrix of collagen fibrils. Similarly, the relatively high Young’s modulus of silk fibres is usually attributed to the presence of crystalline regions in the silk fibroin structure possessing t,he fully extended p-sheet’ conformation, but silk again is a composite material with the sericin component, as well as the degree of crystallinity of the fibroin and the water content; all playing a role in determining macroscopic elasticity. 39 *r 1979 Academic Press Inc. (London) Ltd. 0022-2836/79/330039-13 $02.00/O





Since tissues such as tendon, bone. keratin and silk comprise the supporting framework for various organisms, study of the mechanical properties of these tissues is direct’ly relevant’ to understanding their biological function. With this in mind, Harley et al. (1977) made measurements of the elastic moduli of collagen fibres t)J t’he technique of Brillouin light scattering. As explained in more detail below this technique gives a direct’ measure of the velocity of propagation of high frequency (typically lOlo Hz) elastic wa’ves in the fibre from which elastic moduli can be derived using the relationship: modulus = dens&y x (velocity)2. Thus in common with ultrasonic methods, where frequencies of the order 106 Hz are employed. the elastic moduli so obtained correspond t,o a very high strain rate and are consequent I?; adiabatic moduli. In addition. the corresponding wavelength of the elastic waves being probed by Brillouin xcatt’ering is 300 to 400 nm. which. int,rrestingly, in t,tw case of collagen is close to the molecular length. In such cases, where there arch structures of comparable size to the wavelength. one must be careful in basing interpretation of the results on the assumption that the material behaves as a lineal elastic continuum. lndeed one of the interesting aspects of the t,echnique is that one is probing the material in a regime in which both intra- and inter-molecular forces art’ important. In Brillouin scattering experiments the scattered light is collected from a volume of linear dimension about 100 pm: again indicating the microscopic nature of the measuremenbs and their insensibility to macroscopic inhomogenieties in xtruct,ure. The results of Harley et nl. showed firsbly that t,he high-frequency microscopic; Young’s modulus of native collagen fibres (in the form of rat-bail tendon) is a,n order of magnitude greater than that obtained frorn t’he Hooke‘s law region of tht: stat,ic stress-strain curve; and secondly that’ drying of the fibrr markedly increased the modulus. An attempt was made to interpret) t,hese results in terms of the Young’s modulus of the rod-like collagen molecule itself and the possible effect of water in softening intra-molecular hydrogen bonds and increasing the mass per unit length of the molecule. Fmther considerations to be discussed lat’er have modified this picture and although it, remains possible t,hat the lower static Young’s modulus of collagen is a result of inhomogenieties of lower stiffness in the macroscopic tendon. viscoelastic effects may be introducing a marked frequency dependence into the mechanical properties of collagen. In this paper we present an extension of these original results to include measurements of the anisotropy of the elastic properties of collagen. These have been obtained by measuring the velocity of propagation of both longitudinally and transversely polarised elastic waves travelling at various angles to the fibre axis. Analysis of the results, on the assurnption that collagen is a transversely isohropic (i.e. cylindrically symmetrical) material as far as elastic properties are concerned, yields in t,he case of dry collagen the five independent elast,ic constants of such a system. For wet, collagen the results are less complete. These measurements are the first known of these quantities for collagen fihres and are important, in demonstrating t’hc application of Brillouin scattering to t’he study of biological materials and secondly, in providing a more complete pict’ure of collagen elasticity to be used in understanding the properties of collagen composite materials such as bone, cartilage and skin. In the next section the background t’o the experiments will he out#lined followed by a presentation of the results and their interpretation. In the Discussion. section (c) the application to bone elasticity will be discussed briefly as well as some new result,5 on other fibrous proteins possessing different chain conformations (section (d)).


2. Brillouin




Scattering and the Elasticity of Anisotropic


Brillouin scattering is the inelastic scatt’ering of light by thermally excited elastic waves propagating in a medium. First predicted by Leon Brillouin in 1922, the phenomenon has principally been applied to the study of liquids and inorganic crystals. Recently, however, work has begun on systems such as biopolymers (Harley et ul., 1977; Randall 81,Vaughan, 1979), liquid crystals (Le Pesant et al., 1978) and polymers (Peticolas, 1972) which are of direct or indirect interest t’o biologists. In a typical Brillouin experiment the velocity and polarisation of the elastic waves are determined as a funct,ion of direction of propagation. Assuming that the medium behaves as a linear elastic continuum the propagation of elastic waves is completely governed by the symmetric 6 x 6 matrix of elastic constants cij (1 < i, j < 6). This matrix is defined by means of the generalised Hooke’s law for anisotropic media which expresses the proportionality of the stress tensor t’o the strain tensor (Federov, 1968). The symmetry of the system constrains the number of independent elastic constants, there being a maximum of 21 (trigonal crystals) and a minimum of two (isotropic materials). We shall be particularly concerned with transversely isotropic materials, which include hexagonal crysta,ls as far as elasticity is concerned, i.e. those possessing one physically distinct direction (taken as the S-axis or Z-axis) with all perpendicular directions being equivalent. For such systems there are five elasGc constants denoted by cI1, c12, c13> ca3 and c44. The correspondence between these constants and the more familiar moduli of elastostIatics is useful in clarif.ying their meaning. Thus if one cuts a long rod of material such that) the rod axis is at’ an angle 0 to the axis of a transversely isotropic material and measures the Young’s modulus E(0) of the rod, it can be shown that 1 -=E(O)


cos40 E,;





E = (Cl1- h!NIc33(Cl1i c12)- 2&l , Q=c,,. I 2 CllC33



Here E,, and E, are the axial and transverse Young’s moduli, G is the shear modulus and g13 the major Poisson’s ratio. The fifth modulus (not appearing in this equation) is the second Poisson’s ratio 012

C 33 Cl2




= Cl1

2 Cl3 2' Cl3

Equation (1) has been used in the analysis of the elastic properties of bone (Reilly & Burstein, 1975). From the equation of motion of an elastic medium of density p it can be further shown that for a given direction of propagation there are in general three elastic wave modes, two of (quasi-)transverse polarisation (T, and T2) and one of (quasi-) longitudinal polarisation (L). The velocity w(O) of these waves is given in terms of the elastic constants by (Federov, 1968)






cl1 sin2 0 -+ cs3 cos2 19+ cqg


(4 = ;


& ([(Cl1 -

c,,)sin2 19-I- (c4& -- C.JCOS~ 01” + 4(c,, + c44)2 sin” 0 cos2 0):

v& (0) = f


(‘11 T ‘la) sin2 19 +- c44 roh2 19 ) In the first equation the positive square root gives vJ0). The basis for t’he photoelastic interaction of light with high-frequency elastic braves is that the latter imply periodic fluctuations in the density and hence dielectric constant of the medium. The result is to modulate an incident electromagnetic wave and to introduce into the scattered radiation components of frequency us ---=WI 3: Q, where w1 is the incident’ light frequency and Q is the elastic wave frequency (Fabelinskii, 1968). Alternatively, this can be considered as the expression of the conservation of energy in a quantum scattering process in which an incident photon of energy fiw, either gains or loses energy as a result of destroying or creating a photon of energy fiQ. Furthermore conservation of momentum demands that, q = n (k, ~--k,), where kI, k, and q are the wave-vectors of the incident light, scat,tered light and elastic wave, and ‘12is the refractive index (here assumed to be isotropic) of the shift dw, =: medium. Since the elastic wave velocity or equals Q//ql, t,he Brillouin ws - wI is given by tk Aw, = &2uk,n sin - i 02 where OSis the scattering angle and k, := Zrr/h, h being the wavelength of the incident light in vucuo. A Brillouin spectrum thus consists of two satellite intensity maxima at, frequency (t,he Stokes line), xymmet,rically shifts of +Aw, (the anti-Stokes line) and -AU, placed either side of the often much stronger elastically scatt,ered component (thr: Rayleigh line). The high resolution required to observe t,he Brillouin doublet (wJAw, ~10~) is obtained by using a highly monochromatic laser source in conjunction with a triple-pass Fabry-Perot interferomet)er. This behaves as a narrow band frequency filter, bhe frequency passed depending on the separation of the mirrors of bhe interferometer. Piezo-electric scanning of one of the mirrors allows the frequency range of interest to be covered. It should be noted that t,lre properbies of the interferometer result in a, repetition of the Brillouin-Rayleigh triplet, alon g the frequency axis with a period equal to the so-called free specteral range of the inst,rument,. This explains t,hr appearance of the spectra in Figure 3. Measurement of Au, for various orientations of thp sample with respect to the light beams enables the anisotropy of the elastic wave velocity to be mapped out: and comparison with equations (3a) and (3b) leads to values of the elastic constant,s. Thc~ question of the polarisation of the elastic wave bring observed can bc resolved b> preselecting the polarisation of the incident and scatt’ered light. Thus in the case of H hexagonal crystal orientated so q is along the 3-axis, only the longitudinal mode appears in the VV spectrum (i.e. both incident and scat,tered light vertically polarised) and only the transverse mode T, appears in the VH spectrum (incident light) verticallqand scattered light horizontally polarised). For non-symmetry directions of “I, the results are less clear-cut, particularly in the case of birefringent materials such a* collagen where additional rotation of the polarisation plane may occur. (





3. Materials and Methods Tendons were excised from rat-tails of mature rats which had been stored deep-frozen. In the native state, simulated by immersion in a phosphate buffer (pH 7.2) with 0.15 MNaCl, the tendons appear as silky white t,hreads which are opaque and hence unsuitable for light scattering. On drying they become transparent and, depending on the degree of dehydration, can be rehydrated to the native opaque state or to a hydrated but transparent state. Brillouin scattering measurements were made on both air-dried samples (relative humidity about 50%) and rehydrated transparent samples. In each case the specimens were dried stretched (to remove the crimping) and pressed flat between glass slides to give relatively good optical surfaces for the passage of light. A scattering angle of 90” was used and the fibres were initially oriented at 45” to the incident and scattered light beams as shown in Fig. 1, wit,h the fibre axis in the scat,tering plane. In this symmet’rical configuration the scattering vector (i.e. the wave-vector of the elastic wave being



Scattered beam

ratotlan Direction scattermg

of vector

FIG. 1. Sample geometry for 90” Brillouin scattering. Tho specimen is held flat between glass slides and rotated about the axis shown to vary the angle between the scattering vector and t,hr fibre axis.

probed) is directed along the fibre axis and is of magnitude Q = d(2),&,, independent of the refractive index of the fibre which is not known accurat,ely. By rotating the specimen assembly about the axis in the scattering plane perpendicular to the scattering vector, as shown, the angle between the scattering vector and the fibre axis can be varied, while maintaining q constant. In this way the anisotropy of the elastic wave velocity can be measured. A single-mode argon--ion laser was used with wavelength 514.5 nm and the input laser power was typically 40 mW. A characteristic feature of light scattering from fibres is extremely intense elastic scattering both from static inhomogenieties in the material and from interfaces. Good sample preparation minimises this to an acceptable level and in the case of the wet tendon the presence of water between t,he slides provides some refractive index matching at t,ht) interfaces. However, particularly to observe the lower frequency transverse modes in dry collagen, it, has been found useful to interpose an iodine filter in the scattered beam, it being possible to tune the argon-ion 514.5 nm line to exactly coincide with a very strong absorption of iodine vapour (Devlin et al., 1971). Thus the elastically scattered component, of the spectrum is selectively attenuated by several orders of magnitude, although there is a drawback in that additional, weaker iodine absorption lines are present in the range of frequency of interest and can distort the shape of the Brillouin lines.





4. Results The variation in frequency of longitudinally and transversely polarised elastic waves, ~~(0) and w*(B), propagating at various values of 9 to the fibre axis in dry collagen are shown in Figure 2. As the absolute frequencies observed depend on t,he drying history of the specimen, results from different specimens have been correlated by plotting the normalised frequencies w(~)/c+ (0 = 0”). The absolute value of c+, (0 = 0’) varied from 9.78 to 10.24 GHz whereas the values for w(@/w~ (0 = 0”) show good agreement.


to flbre



FIG. 2. Elastic wave frequencies in collagen as a function of direction the fibre axis. Dry collagen: longitudinal branch (curve A) ; transverse collagen: longitudinal branch (curve R).

of propagation relative to branch (curve C). Native

The VV and VH spectra for 0 = 0” are shown in Figure 3. The free spectral range is 17.05 GHz and hence the Stokes and anti-Stokes lines of the longitudinal mode at 110.19 GHz are overlapped. The peak count-rate of the longitudinal mode in the VV spectrum was 350 cts/s and this was reduced by a factor of 30 in the VH spectrum. The transverse mode, with a frequency of 4.39 GHz gave a peak count-rate of 9 cts/s in the VH spectrum only. Use of the iodine filter confirmed the absence of the transverse mode in the VV spectrum. Although the longitudinal mode has been continually observed over the entire range of 0 values, the transverse mode has been only selectively observed at 0 = 0” and in the range 45” 10 170”. The latter measurements required use of the iodine filter. The transverse mode in this intermediate angular range, unlike that at 0 = 0”, is of comparable intensity to the longitudinal mode and both modes are present in the VV and the VH spectrum. Apparent continuity of the transverse branch confirms the identification of these modes. Figure 2 also shows the variation with 0 of the frequency of the longitudinally polarised elastic wave in wet, collagen. The absolute value of wL (0 = 0’) was found to vary from 6.96 to 7.50 GHz for different specimens, although in the case of wet collagen an additional factor in this variability is the drying effect of the focussed









Pm. 3. Brillouin spectra of dry collagen with the scattering vector parallel to the fibre axis. Top, VV spectrum with longitudinal mode (L) at 10.19 GHz. Note that the Stokes and anti-Stokes lines are overlapped. Bottom, VH spectrum with additional transverse mode (T) at 4.39 GHz. For intensities see text. Free spectral range 17.05 GHz.

laser beam on the sample. Even so, reasonably consistent values for wL(B)/wL (0 = 0”) were found for different samples. No transverse modes have unambiguously been observed in wet collagen yet.

5. Discussion (a) Elastic

constants of collagen

It is still an open question whether the symmetry of the lateral packing of collagen molecules (or possibly microfibrils) within fibrils is tetragonal or hexagonal (Miller, 1976). Neither is it clear whether the fibrils are single crystals or polycrystalline. Zn any case, as many fibrils of diameter 50 to 500 nm are bundled together in parallel array to make up a fibre, it is probably appropriate to assume that the latter is a transversely isotropic material and to interpret the Brillouin scattering results in terms of the five elastic constants appearing in equations (3a) and (3b). An additional requirement for this interpretation is that the elastic modes have a linear dispersion relat’ionship and this has been verified to within experimental error by making measurements at two different wavelengths, 514.5 nm and 488-O nm. One should expect to detect two transverse branches in collagen whereas evidence for only one has been established and this shows very little dispersion with angle 19. This situation can be approximated by setting cl2 N cI1 - 2c,,. By fitting the curves of Figure 2, the following elastic constants are then obtained.

These absolute values are only reproducible between different specimens for dr) collagen to *50/O and for wet collagen to +70/0, but the ratios between them are more accurate. Using equation (2) one can derive the following results for dry collagen : E,, = 1.1.9 GN


E’, =

8.3 GN rn2







ur2 = 0.26

In these results the relatively low value of 0.28 for the ratio G/E’,, for dry collagen and the increase in the anisotropy of elasticity as measured by (~a3/cll from 1.53 in dry to 1.95 in native collagen are of interest. The Young’s modulus E,, is about one-third lower than ca3 for dry collagen and. assuming this holds for native collagen as well (for which cl3 and cl2 are not known). we find the high frequency Young’s modulus of native collagen to be 5.1 GN m-2. (This differs from the value of 9.0 GN 111~’ quoted by Harley et al. (1977)? first,ly because of the correction for t,he difference between c,a3 and E!! and secondly because of the use here of the macroscopic density of native collagen 1.12 gjcma. rather than the value of 1.31 g/cm3 derived from t,he molecular weight and exclusion volume of the collagen molecule.) It is interesting t.o compare the hypersonic elastic moduli and velocit’y of sound of wet collagen a#s obtained by Brillouin scabtering with corresponding measurements at, lower frequencies. Torn d al. (1975) obtained a value of 1.0 GN m-2 for the macroscopic Young’s modulus of rat-hi1 tondon at a strain rate of 6% per minute. The hypersonic modulus is thus about five Cmes higher than 6his quasi-static measurement. Goss & O’Brien (1979) have recently made ultrasonic velocity measurements on mouse-tail tendon collagen using a scanning laser acoustic microscope operating at 100 MHz. These authors obtain a velocity of 1.73 km s-l although the direction of propagation that this refers t’o is not specified. However. it would appear from the geometry of t’he acoustic microscope that the propagation direction is about 10” from the perpendicular to the fibre axis. The Brillouin measurements reported above have demonstrated marked anisotropy in the hypersonic velocity of colla,gen with speeds of 2.64 km s- ’ parallel t’o the 6bre axis and 1.89 km SKI perpendicular to the axis. The latt,er figure is more likely tjo be the one with which the ultrasonic measurements should be compared. This discussion suggests that the elastic properties of collagen are frequency dependent’, i.e. that collagen is dispersive. Harley et a,l. pointed out that this difference between the high frequency/microscopic and stat,ic/macroxcopic Young’s modulus may reflect the presence of inhomogenieties in the macroscopic tendon (e.g. resulting from the finite length of the collagen fibrils) which can relatively easily take up strain,





but, are on a scale to which the Brillouin measurements are insensitive. An alternative suggestion is that Brillouin scattering is measuring the Young’s modulus of individual collagen fib&, whereas tendon is a composite consisting of fibrils embedded in a soft’er polysaccharide gel with a consequently lower macroscopic Young’s modulus. However, the packing fraction of fibrils in the tendon is probably at least O-65 (Parry & Craig. 1978) which is not low enough to account for the reduction if one assumes that bhr law of mixtures (i.e. modulus of composite = volume fraction of fibrils x moduhrs of fibrils + volume fraction of matrix x modulus of matrix; see Wainwright r,t al.. 1976, p. 144) applies to the Young’s modulus of the composite. However, it is possible that the increase in stiffness of collagen with frequency is a genuine viscoelastic effect arising through the disappearance of certain molecular relaxation mechanisms when the period of excitation becomes smaller than the appropriate relaxation time. Such viscoelastic effects can be understood in a phenomenological way by adding a damping term proport’ional t’o the rate of strain to t,he equation of motion of an elastic medium (see; for instance, Vachcr & Boyer, 1975), alt’hough it is often difficult to give an exact molecular interpretation of the relaxation processes involved. However, the presence of considerable water in the collagen fibrils suggests a possible hydrodynamic mechanism for the high-frequency viscous damping of t,he motion of the collagen molecules. Clearly more complete data on the velocity and attentuation of sound in the frequency range from lo6 to lOlo Hz are needed before further progress can be made on this aspect of the problem. (b) Low frepuency


of collagen

.In their discussion Harley et al. (1977) suggested that’ Brillouin scattering was measuring the effective modulus of the triple-helical collagen molecule, i.e. was probing the intra-helical forces rather than the inter-molecular forces involved in the relative movement of molecules. They tried to explain the hydration effect as due to a rigid loading of the peptide chains but a reduction in the strength of the intra-helical hydrogen-bond force constant was invoked as well. On the basis of a simple model of the collagen crystal we would now like to analyse this picture further to see wha’t kind of low-frequency vibrations are to be expected. In axial projection collagen fibrils consist of rodlike molecules of length L about 300 nm and Young’s modulus E, coupled together by forces arising from electrostatic and hydrophobic interactions and covalent cross-links. Assuming E is relatively high, the vibrational spectrum of such a system will consist of an acoustic branch with linear dispersion at low frequencies and velocit’y of sound largely reflecting the weak coupling, i.e. at low frequencies the collagen molecules vibrate as rigid rods. In addition there will be a series of higher frequency optical branches showing little dispersion, each derived from t’he coupling of the internal modes of the stiff rods. which vibrate at a fundamental frequency of d(E/p)/2 L. Such accordion modes and their harmonics have been observed in polymethylene chains of length up to 94 carbon atoms by Raman scatt,ering and have led to a value of E for the fully extended hydrocarbon chain of 358 GN me2 (Schaufele & Shimanouchi, 1967). So far these modes have not been observed in collagen or indeed other biopolymers although estimates have been made for the Young’s modulus of the x-helix which, however, are strongly dependent on the choice of hydrogen-bond force constant (Peticolas, 1972). This discussion, together with the fact that one is observing acoustic modes. suggests that the Brillouin measurements are largely probing inter-molecular forces.





Furthermore the dependence on hydrat’ion is more easily explicable by the solventdependent nature of these forces and changes in inter-molecular packing on drying, rather than by changes in the stability of the triple-helix, whose structure as det,ermined by high-angle X-ray diffraction appears t’o be insensitive t’o hydration. To confirm this picture it would be highly desirable to observe t’he accordion modes of the collagen molecules by looking at, the low-frequency Raman spectrum. dlso H study of the effect of adding more cross-links on the anisotropy of the elastic properties would be interesting. The ratio of the Young’s modulus of native collagen (p, := 1.12 g/ems) to that’ at, 0% relative humidity (pd = 1.40 g/cm3) is 0.36 using the velocities of sound given by Harley et al. (1977). Interestingly this is very close to t,he reduction in t,he volume fraction V of collagen in tendon if one assumes this is given b> jl = e!d

= 0.3.


Thus it seems that the effect of hydration can be explained phenomenologically by. saying tendon is a composite of collagen and a softer water gel of negligible modulus which obeys the law of mixtures. Clearly this approach could be extended to intermediate hydrations if reliable measurements of density as a function of relative humidity were available. (c) Applications

to the elasticity

of bone

One of the purposes of studying the microscopic elastic properties of collagen is t.o utilise the results in trying to understand the mechanical proper&s of collagencomposite materials. Of particular interest is bone, in which crystallites of hydroxyapatite are embedded in an organic matrix consisting largely of collagen. Ideally one would like to combine knowledge of the elastic properties of the components together with a model of the microscopic structure of bone to explain its observed elastic properties. A qualitative theory to do just this was proposed by Currey (1969), being specifically designed to explain the sharp increase in Young’s modulus of bone with only a modest increase in mineral content. The model idealises the structure of boric to consist of parallel cylinders of apatite embedded in a matrix of collagen and requires such parameters as the dimensions, volume fract’ion and Young’s modulus of the crystallites and the Young’s and shear modulus of the matrix. Brillouin scattering has given the first experimental value for the shear modulus of colla’gen, and the low value of G/E,, is much as anticipated by Currey. The model also gives specific predictions for the anisotropy of the Young’s modulus of bone assuming complete orientation of the apatite cylinders with the collagen fibres. The Currey model is on1.v applicable to oriented bone such as fish bone (see below), ot’her types of bone requiring more sophisticated theories of composite materials as, for instance, developed b,v Hashin & Rosen (1964). Experiments have begun on trout rib-bone to investigate hone elasticity 1)~ Brillouin scattering. Fish bone has been chosen as it is transparent and shows reasonably high orientation of the collagen fibrils as indicated by low-angle X-ray diffraction. Furthermore, Carlstrijm $ Glas (1959) showed that in fish hone the apatite crystallites are in the form of long rods of average diameter 40 t’o 45 A and average length 600 to 700 A, as pictured in the Currey model. Preliminary results prove the feasibility of









Frequency shift FIG. 4. Brillouin mnge 35.90 GHz.








of wet fish bone with longitudinal

mode at 10.10 GHz. Free spectral

the experiments and Figure 4 shows the Brillouin spectrum for wet trout rib-bone with the scattering vector directed along the local axis of the bone. The value deduced for the velocity of longitudinal elastic waves along the bone axis is 3.7 km s-l. The density of the bone was found bo be 1.9 g/cm3 giving a value for ca3 of 25.6 GN m 2. This compares with a value for c33 of 32.5 Gh’ mm2 obtained by Yoon & Katz (1976) by ultrasonic measurements at 5 MHz on dried human cortical bone of density 1.858 g/cm3. The axial Young’s modulus is expected to be less than ca3 and therefore well within the range of values usually quoted for bone as derived from stress-strain curves. Interestingly the Brillouin technique does not appear to be giving anomalously high values for the Young’s modulus as in the case of pure collagen. This may imply significant changes in the viscoelastic properties of collagen when reinforced with apatite. Experiments to measure the other elastic moduli of fish bone are continuing.

(d) Other jibrous proteins It has long been recognised that fibrous proteins are composed of varying arrangements of long molecules with only three main types of conformation. The triplehelical conformation of collagen exists in the widely occurring connective tissue of metazoic animals ; the M conformation occurs in muscle proteins, keratin and fibrinogen and the fl conformation in silks and feather. It is of interest to measure Brillouin scattering from the a and /3 conformations in order to compare them with that from t,he collagenous tissues used in the studies described above. Harley et al. (1977) measured the Brillouin scattering from the “catch” muscle of mussels because of its structural similarity to the fibrils of collagen. In catch muscles the paramyosin molecules are rod-shaped and fully a-helical. A paramyosin molecule is of length 1500 A and is composed of two a-helical chains wound round each other to form a two-&and rope. In the thick myofilaments of catch muscle these molecules are



staggered with respect to each other Measurements of Brillouin scattering & Vaughan (1978). Table 1 shows a summary of the on fibrous proteins. The velocity of the elastic modulus (cS3) has been


results OS our Brillouin scattering measurements sound is for propagation along the fibre axis and calculated assutning a,n average density of 14 1

scattering results for various j2mus Molecular conformation


Bombyx rnori silk (dry,


in a manner similar to that of collagen molecules. from cc-keratin have been reported by Randall






A%xial velocity of sound (km s-l) /3sheet

yroteim Elastic

modulus (GN rnm2)



lOOq/, triple-hclts



cc-Keratin cc-helix



fi-Keratin 28”,, p structure

3.7 1


a-Keratin r-helix






in oil) Collagen


Horsehair? Feather oil)

in oil)

(dry) rachis

Porcupine in oil)





Molluscan catch muscle$ (12% rel. humidity) t Randall 1 Harley

& Vaughan el al. (1977).



l’aramyosin supercoiled a-helix (1979).

g/cm3 for dry protein. The highest elastic modulus is that of silk in w-hich the molecules are in the fully extended /I-conformation. Feather keratin consists of a modified /3 structure embedded in an amorphous matrix (Fraser et aZ.. 1971) and the elastic. modulus is greatly reduced compared with that of silk. The lowest elastic modulus is that of the fully x-helical catch muscle. a-Keratin consists of coiled z-helices embedded in an amorphous matrix and has a higher elastic modulus than that of catch muscle. Thus the matrix appears to stiffen a-keratin. but soften j?-keratin. l!he increasing elastic moduli from an a-helical structure through collagen to j3 structure appears to correlate with the degree of extension of the polypeptide backbone of the molecules in these conformations. The a-helix is a relatively flat coil, the p structure is fully extended and the collagen triple-helix is intermediate. While t’his correlation ir interesting it should be remembered that the proportion of protein in the stated conformation can be quite low and the composite nature of t,he keratins and silk needs to be t,aken more fully into account. Furthermore, as discussed in bhe case of collagen, we believe that intermolecular forces play a particularly important role in the elastic properties probed by Brillouin scattering.

6. Summary By means of Brillouin light scattering the high-frequency elastic properties of tendon collagen have been investigated. Assuming a transversely isotropic model the five elastic constants have been determined for dry collagen. The shear modulus is





found to be relatively low and there is considerable anisot’ropy in the Young’s modulus for strains at different angles to the fibre axis. On rehydration the tendon becomes markedly less stiff and the anisotropy in the Young’s modulus increases. A quantative explanation of these observations in terms of the int,er-and intra-molecular forces in collagen and the role of water in the molecular structure is still needed. It, has been suggested that these results should be useful in understanding the elastic properties of the collagen-composite material bone. The authors gratefully acknowledge the help of Dr Richard Harley in setting up the apparatus and the continued close interest of Dr J. W. White. One of us (S. C.) thanks the European Molecular Biology Organisation for the award of a fellowship during the course of this work. REFERENCES CarlstrGm, D. & Glas, J. E. (1959). Biochim. Biophys. Acta, 35, 46-53. Currey, J. D. (1969). J. Biomechanics, 2, 477-480. Devlin, G. E., Davis, J. L., Chase, L. & Geschwind, S. (1971). Ap$. Phys. Letters, 19, 138-141. Fabelinskii, I. L. (1968). In &/IoZecuZar Scattering of Light, Plenum Press, New York. Fcbdorov, F. I. (1968). In Theory of Elastic waves 1:n.Crystals, Plenum Press, New York. Fraser, R. D. B., Mac Rae, T. P., Parry, D. A. D. 8: Suzuki, E. (1971). Polymer, 12, 35-56. Goss, S. A. & O’Brien, W. D., Jr (1979). J. Acomt. Xoc. Am 65 (2), 507-511. (London), 267, 285.-287. Harley, R., James, D., Miller, A. & White, J. W. (1977). Nature Hashin, Z. & Rosen, B. W. (1964). J. Appl. Mechanics, 31E, 223.-232. Le Pesant. *l.-P.. Powers, L. & Per&an, P. S. ( 1978). Proc. .Vat. Acad. 8ci., B.,q.A. 75, 1792.-1795. Miller. A. (1976). In Biochewaistry of Collagen, pp. 85-136, Plenum, New York. Parry, D. A. D. & Craig, A. S. (1978). Biopolyrners, 17, 843-855. Peticolas, W. L. (1972). Advan. Polymer Sci. 9, 285-333. Randall, J. T. & Vaughan, J. M. (1979). Phil. Trans. Roy. Sot., ser. A, 293, 133-140. Reilly, D. T. & Burstein, A. H. (1975). J. Biomechanics, 8, 393-405. Schaufele, R. F. & Shimanouchi, T. (1967). J. Chem. Phys. 47, 3605-3610. Tarp. 8.. Arridge, R. G. C., Armeniades, C. D. & Baer, E. (1975). In Structure of Fibrous Biopolymers, Colston papers no. 26, (Atkins. E. D. T. $ Keller, 4., eds), pp. 197 -221. Butterworths, London. Vachcr, R. & Boyer, L. (1975). J. Acoust. Sot. Am. 58, 385.-391. Wainwright, S. -4., Riggs, W. D., Currey, J. D. & Gosline, J. M. (1976). In Mechanical Desig?r 1:n Organisms, Arnold, London. Yoxl, II. S. & Katz, J. L. (1976). J. Biomechanica, 9, 459-464.

Determination of the elastic constants of collagen by Brillouin light scattering.

J. Mol. Biol. (1979) 135: 39-51 Determination of the Elastic Constants of Collagen by Brillouin Light Scattering S. CUSACK AND A. MILLER G’relrohle...
997KB Sizes 0 Downloads 0 Views