Solid State 13C NMR Study of Collagen Molecular Dynamics in Hard and Soft Tissues*

The molecular dynamics of the collagen backbone in intact connective tissues has been elucidated using 13C line shape analysis. Since one-third of the amino acid residues in collagen are glycines, we have labeled: (a) reconstituted lathrytic (uncross-linked) chick calvaria collagen fibrils; (b) rat tail tendon (cross-linked); and (c) rat calvaria (cross-linked and mineralized) collagen with [l-'3C]glycine. The proton-enhanced and normal 90" - t proton-decoupled spectrum of each collagen sample shows an asymmetric chemical shift powder pattern for the glycine carbonyl carbon. The powder line width, A, (A = azz - ax%) at 22 *C for the uncross-linked reconstituted collagen fibril is 108 ppm, whereas the maximum value of A (140 ppm) is observed for the cross-linked and mineralized collagen fibrils in rat calvaria. The powder line widths for the cross-linked fibrils in tail tendons and demineralized calvaria are 124 and 120 ppm, respectively. However, since the same line shape and line width (145 ppm) are observed for all samples at -35 "C, the difference in A values observed at room temperature is attributed to differences in molecular mobility of collagen in various samples. The line shapes are analyzed using a dynamic model in which azimuthal orientation of the collagen backbone is assumed to fluctuate as a consequence of reo- rientation about the helix axis. The observed line shapes are sensitive to motions

The molecular dynamics of the collagen backbone in intact connective tissues has been elucidated using 13C line shape analysis. Since one-third of the amino acid residues in collagen are glycines, we have labeled: (a) reconstituted lathrytic (uncross-linked) chick calvaria collagen fibrils; (b) rat tail tendon (cross-linked); and (c) rat calvaria (cross-linked and mineralized) collagen with [l-'3C]glycine.
The proton-enhanced and normal 90"t protondecoupled spectrum of each collagen sample shows an asymmetric chemical shift powder pattern for the glycine carbonyl carbon. The powder line width, A, (A = azz -ax%) at 22 *C for the uncross-linked reconstituted collagen fibril is 108 ppm, whereas the maximum value of A (140 ppm) is observed for the cross-linked and mineralized collagen fibrils in rat calvaria. The powder line widths for the cross-linked fibrils in tail tendons and demineralized calvaria are 124 and 120 ppm, respectively. However, since the same line shape and line width (145 ppm) are observed for all samples at -35 "C, the difference in A values observed at room temperature is attributed to differences in molecular mobility of collagen in various samples.
The line shapes are analyzed using a dynamic model in which azimuthal orientation of the collagen backbone is assumed to fluctuate as a consequence of reorientation about the helix axis. The observed line shapes are sensitive to motions having correlation times less than s and the analysis provides the values of the root mean square fluctuation in azimuthal angle, Y~~~, due to such motions. It is found that Y~~~ equals 41", 33", and 14" for the uncross-linked, crosslinked, and mineralized collagens, respectively. These results provide the first information about the extent that cross-linking and mineralization restrict molecular motion in collagen.
Collagen is the major protein component of connective tissues. Its primary function is structural (1) with collagen fibrils imparting mechanical stability to tissues. Of the different typos of collagen, type I is found in tendon, skin, and bone (1,2). The type I collagen molecule consists of two a1 (1) chains and one a2 chain. These three chains wind around each other to form a triple helix (3), having a length of 3000 A and a diameter of 15 A. The sequence Gly-X-Y is repeated throughout each a-chain except for short nonhelical segments at the ends of the molecule. Because of steric interactions, * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. glycine residues occupy positions within the interior of the helix whereas the side chains of X and Y residues are on the surface (3). As a result of interactions among the side chains, collagen molecules associate to form fibrils (3). In the fibril, collagen molecules are staggered relative to one another by -670 A, and they are covalently cross-linked at their nonhelical ends (1,2). The resulting network of staggered crosslinked helical molecules produces high tensile strength fibers (1,2). The staggering of collagen molecules results in gap and overlap regions in the fibril ( Fig. 1) which may have special significance in bone (1,2,4). The major constituents of bone are mineral (hydroxyapatite) and the organic matrix, more than 90% of which is collagen (5). It has been hypothesized that mineral initially deposits in the gap region and then spreads to fill all of the available space in the fibril (4).
Although much information about the three-dimensional structure and arrangement of collagen molecules in the fibril has come from x-ray diffraction and electron microscopic studies (4, 6, 7), these methods provide only a static view of the collagen molecule in the fibril. Recently, NMR studies have provided the first information about molecular dynamics in reconstituted (uncross-linked) type I collagen fibrils (8-11). These studies show that the peptide backbone of the collagen molecule undergoes restricted but rapid reorientation probably about its long axis (8,9). In addition, there is rapid side chain motion, indicating that the fibrillar structure is stabilized by multiple sets of interactions (10).
In the present communication, we report the first study of collagen peptide backbone dynamics in intact soft and hard tissues. The collagen peptide backbone is labeled in various tissues by injecting [l-'3C]glycine into rats, and the carbonyl line shapes observed in proton-decoupled 13C NMR spectra are analyzed to address the following question. How is the collagen peptide backbone mobility, observed in reconstituted fibrils, affected by ( a ) the presence of cross-linking in soft tissue and ( b ) the mineralization of collagen in bone?

MATERIALS AND METHODS
[ l-'3C]Glycine (90 atom % 13C) was purchased from Merck Isotopes (Canada) and characterized by elemental and amino acid analyses and by mass spectrometry.
Reconstituted collagen fibrils were labeled by means of chick calvaria tissue culture; the protein was characterized by using the method described in Ref. 9. The sample was equilibrated with 0.02 M Na,HPO, and packed into an NMR tube. Rat calvaria and tail tendon were labeled by injecting a 0.9% NaCl solution of [l-'3C]glycine (2.5 M ) subcutaneously above the calvarium in the following manner. Initially, we injected 30 pl of glycine solution into the 3-day-old rats for 5 days. Injection volume was increased to 50 pl for the next 7 days and finally 100 pl were injected from day 15 through day 20. The rats were killed on the 21st day. Calvaria were taken out and the periosteum was scraped off. The calvaria were then defatted, washed, cut in small pieces, equilibrated with 0.15 M NaC1, and finally packed into an NMR tube. Tendons were pulled out of the tail and washed with 1% Triton solution in 0.45 M NaCl. They were defatted, washed, equilibrated with 0.15 M NaC1, and then packed into an NMR tube. Control samples of tendon and calvaria were obtained in a similar manner except that unlabeled glycine was used for injection.

Collagen Molecular Dynamics in
The amino acid composition of collagen in calvaria and tail tendon was determined by analyses of protein hydrolysates using a Durrum automatic amino acid analyzer (9). Mineral content in 21-day-old rat calvaria was determined to be 55% from the difference in weight of the calvaria sample before and after burning it to ash by increasing the temperature in stages to 600 "C. This result indicates that mineralization is essentially complete in 21-day-old rat calvaria (12). The mineral was characterized as hydroxyapatite by elemental and x-ray diffraction analyses (12). Atomic absorption spectrophotometry (Perkin-Elmer 603) was used for determining Ca2+ content in mineral and the phosphate analysis was performed by using the method described in Ref. 13.
The per cent incorporation of I3C was determined to be 12% in the tissues and 50% in the reconstituted collagen by gas chromatography/ mass spectroscopy analyses of the N-acetylmethyl ester derivatives of the amino acids obtained after hydrolyzing the proteins with 6 N HC1 at 110 "C for 24 h (9). magnetic resonance spectra were obtained on a home-built solid state spectrometer employing a wide bore Oxford-250 superconducting magnet (5.9 Teslas) operating at 62.98 MHz for I3C. The probe Dewar contained a double-tuned solenoid coil accepting 5-mm sample tubes with a capacity of 125 pl. The spectrometer consisted of Novex transceivers and very high frequency translator, a MITEQ preamplifier, and a Nicolet 2090 digital oscilloscope interfaced to a NICdO computer. An ENI-3100-L ampiifier provided sufficient rfl power to achieve a 90" carbon pulse width of 5-6 ps. EN1 411-LA and Amtron amplifiers were used to achieve the high level proton-decoupling field (72B2/2r) of 40-50 kHz needed to remove the I3C/'H static dipolar coupling. The recovery time of the receiver after the rf pulse was 15 ps. The 1.4T spectrometer has been described (9).
The Hartmann-Hahn condition (-ylBl = -y2B2) is established by observing the proton-enhanced spectrum of an adamantane sample wet with 1.0 M NaC1. The power levels in the 'H and 13C channels were adjusted using precision attenuators at the input of the amplifiers, and the largest amplitude adamantane signal was taken as the best match attenuator levels. The same attenuator settings were used for the collagen sample because the amount of 1. adamantane sample was adjusted so that this sample and the collagen sample had virtually identical rf loss.
Free induction decays were collected using quadrature detection with a 100-kHz spectral window. An exponential filtering of 200 Hz was used to improve sensitivity. Constant sample temperature (within +lo) was attained by passing nitrogen gas through the probe Dewar. The gas temperature was regulated by a Varian temperature controiler. The sample temperature was measured before and after each experiment using a copper/Constantan thermocouple placed in the gas stream 1-2 mm above the NMR sample tube.
Spin-lattice relaxation times ( T I ) were measured using an inversion-recovery pulse sequence (180"t -90" -T ) , (17). TI values were calculated from the integrated intensities of the carbonyl resonance using a least squares fit of the data. NOE values were determined as follows. A spectrum was obtained with the protons saturated continuously but decoupled only during acquisition of free induction decay. The second spectrum was obtained by decoupling the protons during acquisition of free induction decay with the proton rf gated off otherwise. After normalizing the gated decoupled and continuously irradiated spectra to the same number of acquisitions, the former was multiplied by a scale factor and then subtracted from the continuously irradiated spectrum in the computer. The scale factor that yielded a nulled difference signal in the carbonyl region of the spectrum was taken as the NOE value (18). Within experimental error, we were unable to detect anisotropy in either TI or NOE values.

RESULTS
A 62.98-MHz natural abundance 13C spectrum of rat calvaria collagen is shown in Fig. 2a. Although this spectrum was obtained with proton dipolar decoupling, a well defined chemical shift powder pattern is not seen because of the poor resolution and the small signal to noise ratio obtained in natural abundance. In contrast, an axially asymmetric chemical shift powder pattern is clearly seen in the carbonyl region of the spectrum of rat calvaria collagen labeled with [1-13C] glycine (Fig. 2b). Well resolved chemical shift powder patterns are also seen in the spectra of demineralized calvaria and rat tail tendon collagen (Fig. 3). As is seen in the figure, the line shape observed for each sample using the 90" -t sequence is almost identical with the line shape obtained using Hartmann-Hahn matched cross-polarization. Principal values (azx, am, uzz) of the chemical shift tensors of the glycine carbonyl carbon are measured from these spectra and are listed in Table I At 22 "C, the residual powder line width of the glycine carbonyl carbon in rat calvaria collagen (140 ppm) is significantly larger than the line width of demineralized rat calvaria (120 ppm), rat tail tendon (124 ppm), and reconstituted chick calvaria collagen (108 ppm). In contrast, at -35 "C the same value of A (145 ppm) is measured from the spectra of all collagen samples (Fig. 4). This value of A is close to the static value of A measured for crystalline glycyl-glycine and polyglycine, 150 and 142 ppm, respectively. The small differences in A for collagen at -35 *C, glycyl-glycine, and polyglycine are probably a consequence of differences in sequence and conformation (19).
There is no apparent distortion of the glycyl carbonyl line shape in collagen due to l4N-I3C dipolar coupling. These spectra were taken at 5.9 T (62.98 MHz) and at this field the average contribution of the static heteronuclear (I4N-l3C) coupling to 13C line width was calculated to be 21.6 ppm using This result is strong evidence that 14N spin-lattice relaxation time (TI) is short enough at 22 "C to effectively decouple the peptide nitrogen from the glycine carbonyl carbon. Therefore, the contribution of I4N-l3C dipolar coupling to the I3C line   shapes, observed at 22 "C and 5.9 T, is negligible. This statement also applies to the 62.98-MHz spectra obtained at -35 "C since at this temperature the low field (1.4 T ) spectra show only minor broadening (10-15 ppm) due to 14N-13C dipolar coupling. Table I1 summarizes the TI and NOE values measured for the glycine carbonyl carbon in the collagen samples. These quantities are measured using the procedures described under "Materials and Methods."

DISCUSSION
Previous 13C and 'H NMR studies (8,9,11) have shown that the peptide backbone is flexible in fibrils of reconstituted chick calvaria collagen. Since it is known from x-ray and electron microscopic investigations that collagen fibrils are highly organized in the direction parallel to the molecular axis, it has been assumed that molecular motion is primarily a consequence of reorientation about the long axis of the molecule. Therefore, the molecule does not have a fixed azimuthal orientation but rather it rapidly samples a distribution, p ( y ) , of azimuthal angles, y. We define the root mean square fluctuation in azimuthal angle, yrms, as ( Y~. )~ = <y2> = LI P ( Y ) ( Yy d 2 d y (1) where yo is the mean value of y. If yrms 0.7 radian, we show in the Appendix that it is not necessary to specify p ( y ) explicitly since the NMR line shape depends only upon yrms. In the case of a two-site model in which azimuthal orientations y1 and y2 are equally populated, ylma = (yl -y2)/2. The previous NMR studies (9, 11) of lathrytic collagen showed that y1 -y2 = 30" which implies that yrms = 15" for the uncross-linked and unmineralized collagen fibrils.
The present study investigates the effect of cross-linking and mineralization on the peptide backbone motion in the collagen fibril. Of the four samples studied, the smallest value of A (108 ppm) is observed for the reconstituted lathrytic chick calvaria collagen fibrils which are neither cross-linked nor mineralized. In contrast, the largest value of A (140 ppm) is observed for the cross-linked and mineralized collagen fibrils in the rat calvaria. Intermediate size values of A (120-124 ppm) are observed for cross-linked collagen fibrils in rat tail tendon (not mineralized) and demineralized rat calvaria. Since all samples have the same line shapes and equal A values at -35 "C, we ascribe the difference in A values observed at room temperature to differences in molecular mobility in the various samples at 22 "C. Our problem is to determine yrm. for the various samples from an analysis of the observed NMR line shapes.
Values of yrms can be obtained by calculating the effect of motion on the line shape of the glycine carbonyl carbon. The detailed procedure for determining yrms is given in the Appendix. In brief this procedure is as follows. First, we assume that the orientation of the glycine peptide carbonyl chemical shift tensor is the same as that found for the model peptide glycylglycine.2 Second, we assume that the orientation of the glycyl molecular axis in collagen is the same as that in the collagen model peptide (Pro-Pro-Gly)lo (21). Third, the principal components of the static carbonyl chemical shift tensor are taken to be those we have measured for all collagen samples at -35 "C. Fourth, we use the above information to write the shift tensor in the coordinate system fixed in the triple helix for any value of the azimuthal angle, y. Fifth, if y assumes more than one value, as a consequence of rapid reorientation of the molecule, the averaged shift tensor is calculated and diagonalized as described in the Appendix. The resulting principal elements of the tensor yield the motionally averaged line shape which is compared with the experimental line shape. Small adjustments (~1 0 " ) are made in the orientation of carbonyl shift tensor to achieve the best agreement between calculated and observed line shapes.
The results of the calculation are shown in Table 111, which lists the values of yrm. obtained for collagen in different samples. Comparison of Tables I and 111 shows that our model not only gives the correct value of the experimental line widths (A) in every case, but also predicts the observed principal elements of the shift tensor as well. The calculated spectra using these principal elements are in excellent agreement with the experimental spectra as shown in Fig. 5.    Table I11 show that reorientation is slightly more restricted in cross-linked fibrils (yrms = 33") than in reconstituted (uncross-linked) fibrils (yrm8 = 41"). However, in mineralized collagen fibrils the reorientation is significantly more restricted, yrms = 14". Before discussing the implications of these results, we will comment upon the accuracy of the ym. values listed in Table 111. We will also compare the yrms value calculated in the present study for the reconstituted collagen fibrils with that obtained previously from 13C relaxation studies (8,9).
As noted earlier, we have assumed that the orientation of the glycyl peptide carbonyl shift tensor and the orientation of the glycyl molecular axis can be obtained from data on model compounds. In fact, small differences in orientation Collagen Molecular Dynamics in Tissues between the model compounds and the collagen molecule are expected because of differences in crystal packing, molecular conformation, and amino acid sequence. We find that if the values of the Euler angles (see Appendix) are varied by +30" in our calculation it is still possible to reproduce the observed line widths (although not usually the line shapes) but the yrms values obtained differ from those in Table 111 by as much as 20%. Significantly, for a given variation in Euler angles, yrms values calculated for all collagen samples experience nearly the same fractional change. In a related calculation, we obtain yrms values, each greater by "5" than those listed in Table  111, if a static line width of 150 ppm (as found for glycylglycine) rather than 145 ppm is assumed.
The uncertainty in the calculated values of yrms may partly explain the discrepancy between yrma observed for the reconstituted collagen fibrils from 13C relaxation data (yrms = 15") (8,9) and the value obtained from line shape analysis (yrm. = 41"). However, a plausible physical argument also explains the fact that the value of yrms obtained from the line shape analysis is substantially larger than the yrmS value obtained from spin-lattice relaxation data. The spin-lattice relaxation time is determined by motions on the time scale of IO-@ s. In contrast, any motion on the time scale of less than s induces motional narrowing of line shape. Since large amplitude motions would be expected to encounter more steric hindrance than small amplitude motions, only the latter take place on the fast (TI) time scale. Therefore a Tl measurement will be sensitive only to the fast small amplitude motions whereas the line shape will be sensitive to larger amplitude slower motions as well.
We have attempted to determine the amplitude of the rapid motions in the intact labeled collagen samples by analyzing the measured spin-lattice relaxation times listed in Table 11. As expected, the TI values increase as one goes from the reconstituted collagen to the mineralized collagen samples and are about 1 order of magnitude larger than the natural abundance aliphatic Tl values (not listed). Unfortunately, the carbonyl carbon Tl values are so large that the longitudinal relaxation may be affected by 13C-'3C spin-diffusion (22). Therefore, we have not attempted a quantitative analysis of the data in Table 11. We are instead measuring spin-lattice relaxation times of collagen labeled with [2-'3C]glycine. Since in this case the labeled carbon is directly bonded to two protons, the Tl values are much shorter than those reported in Table 11. Hence, spin-diffusion should not complicate analysis of the data and quantitative estimates of yrms, obtained from relaxation data, should be available shortly.

CONCLUSION
The results presented in Table I11 show that fluctuations in azimuthal orientation (as measured by y,,,) are smaller in cross-linked tendon and demineralized calvaria collagen fibers than in reconstituted collagen fibers. In addition, yrms is slightly larger for the demineralized calvaria collagen fibers than for the tail tendon fibers. X-ray fiber diffraction studies (23) show that average equatorial diffraction maxima are 16, 15.3, and 15 A, respectively, for reconstituted, demineralized bone and tendon collagen fibers. It therefore appears that ylms is correlated with the intermolecular separation of collagen molecules in the fibers that are not mineralized. Finally, we note that ylms for mineralized calvaria collagen is much less than that for the demineralized calvaria. Evidently, the presence of mineral is the source of the small value of yrms observed for collagen fibers in the intact rat calvaria.
The preliminary relaxation data in Table I1 suggest that rapid small amplitude fluctuations in azimuthal orientation persist in calvaria collagen. Currently, relaxation times of [2- "C]glycine-labeled collagen are being measured in various tissues in order to characterize these motions in detail. The motions of specifically labeled individual side chains are also being studied. These investigations, when complete, should provide a basis for a better understanding of the interactions between mineral and collagen in bone.

APPENDIX
The chemical shift powder line shape is completely determined by the principal elements of the chemical shift tensor, uxx, uw, and uzr (24-26). In the presence of rapid reorientation, the chemical shift tensor is averaged and the principal elements of the averaged shift tensor determine the motionally averaged line shape (26). We describe here in detail our calculation of the peptide carbonyl line shape averaged by reorientation about the helix axis in collagen. We further show that the motionally averaged line shape is completely determined by the root mean square fluctuation in azimuthal angle when this quantity is small.
The principal components of the peptide carbonyl shift tensor are obtained from the low temperature spectra of the collagen samples. The shift tensor, uH, in the triple helix axis system (as defined for (Pro-Pro-Gly)lo in Ref. 21) is given by where u p is the shift tensor in the PAS and R is the threedimensional rotation matrix (26) that transforms Cartesian tensor components from the PAS to the helix axis system and is given by -sin a sin y +cos a sin y -sin a cos y +cos a cos y R = "cos a cos 6 sin y -sin a cos sin y sin sin y where a , @, and y are the Euler angles, and rotations through these angles bring the PAS into coincidence with the helix axis system (26) (Fig. 6). The elements of the R matrix are calculated in a straightforward manner since the orientation of the shift tensor PAS has been determined in the molecular frame of the glycyl residue' and orientation of the glycyl molecular frame in the helix axis system is provided by the crystal structure of (Pro-Pro-Gly),, (21). Once evaluated, elements of the R matrix yield the values of the Euler angles, D = (a, @, y), that transform the PAS to the helix system and we find that D = The Euler angles (p, 180"y ) are the REFERENCES polar angles (0, $) that define the orientation of Zp in the helix axis system. Examination of Fig. 6 shows that reorientation about the helix (2,) axis causes the angle y to vary. If the fluctuations in y are rapid, then the averaged chemical shift tensor, i?H, is calculated as (26) UH = s P(IY)UHdY

(AI)
where p ( y ) d y is the probability that the PAS has azimuthal orientation in the range between y and y + dy. We diagonalize GH to obtain the principal values of the motionally averaged shift tensor and these in turn yield the motionally averaged powder pattern.
It appears from Equation A 1 that the averaged powder line shape depends upon the detailed form of p ( y ) . However, for small amplitude fluctuations, C H depends only upon the root mean square fluctuation in y. This is readily shown by expanding UH in Taylor series about yo, the mean value of y. So to a first approximation, (TH, depends upon <y2>. It should be noted that ifp(y) is an even function, e.g. if both the sites are equally populated in a two-site jump model, <y"> = 0, where n = 1, 3, 5, . . .

We have tested Equation A5
by calculating the motionally averaged line shapes using 2-, 4-, and 8-site jump models with c y 2 > fixed. We find that if Y~,,,. < 40", the calculated averaged shift tensor elements change by less than 1 ppm as the number of sites changes from two to eight. We also find that the best agreement between calculated and observed line shapes occurs when /3 = 133.5" rather than the 123.5" as calculated from the model compound data.