Particle size and shape in a citrate extract of ichthyocol

Particle Size and Shape in a Citrate Extract of Ichthyocoll Paul M. Gallop2~2~ From

the Department

of Biology,

Massachusetts Massachusetts Received

April

Institute

of Technology,

Cambridge,

29, 1954

INTRODUCTION

Since the studies of Nageotte (15) it has been clear that collagenous tissue elements can be partially dispersed by acids and reconstituted into fibrous or gelatinous precipitat,es by the addition of salt or neutralization. Recently, interest in such systems has been revived by the work of Orekhovitch, Tustanovskii, Orekhovitch and Plotnikova (16) and of Orekhovitch (17), chiefly on citrate extractions of “procollagen” from mammalian skins, and by the electron optical investigations of Highberger, Gross and Schmitt (10, 11, 22) on the fibrous and segmental elements obtained by precipitation of similar material. Little is known as yet, however, about the sizesand shapes of the primary particles present in collagenous dispersions. Bresler, Finogenov, and Frenkel (4) reported observations of a rather homogeneous population of particles in citrate extracts of rat skin (procollagen). These particles were said to have weight 70,000 and dimensions 380 X 16.7 A., and Bear (2) has pointed out that a molecule of about this weight, though somewhat longer and thinner (640 X 12 A.), would account for the density and certain features of the x-ray diffractions of dry collagen. M’Ewen and Pratt (14), on the basis of light scattering on solutions of 1 Supported in part by a grant-in-aid for the study of connective tissue structure, under the supervision of Richard S. Bear, from the American Cancer Society upon recommendation of the Committee on Growth of the National Research Council. 2 Experimental material presented herein is drawn in part from a thesis submitted to the Graduate School of the Massachusetts Institute of Technology, September, 1953, in partial fulfillment of the requirements for the Ph.D. degree. 28 Present address: Dept. of Medicine, Long Island Jewish Hospital, New Hyde Park, N. Y. 486

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rat skin procollagen and rat tail tendon, could discover no particles of this description, but instead observed much longer particles with weights of 3-10 x 106. In this and the succeeding paper are presented results of an investigation which throws further light on the situation outlined above. This first’ account, describes methods of preparing and purifying an acid-soluble collageu (ichthyocol) from fish swim bladders, and gives a description of the protofibrillar particles present in an acid dispersion. The second paper deals with the conversion of this material to a homogenous gelatin. EXPERIMENTsL

Preparation

&b!2THODS

AND

of dcid-Extracted

hSULTS

Ichthyocol

The tunica externa of fresh carp swim bladder, used in this preparation, consists of a tough out,er lamellated section of collagenous fibers and elastic tissue R-hich merges into an inner, t,hicker section of finer collagenous fibers. These tunics arc separated from the inner muscular tissue and washed under running cold tap water. Material not intended for immediate use is stored at -20°C. Olle first removes appreciable amounts of soluble t,issur proteins and carbohydrates as follows: About 100 g. of wet tunic are placed in 400 ml. of cold 0.5 iIf sodium acetate, blended about 2 min. in a Waring blendor, and kept at 5°C. overnight with occasional shaking. The first sodium acetate extraction is centrifuged at 2000 r.p.m. at 5°C. for 1 hr. The remaining tissue paste is re-extracted in 400 ml. of cold 0.5 iV sodium acetate overnight. After another centrifugation, the remaining tissue paste is similarly washed with cold distilled water and re-collected. The sodium acetate extracts and washings probably contain collagenous components [see Harkness, Marko, Muir, and Neuberger (Q)], but these have not been further followed in the present study. The crude citrate extract is prepared by extracting the tissue paste 2648 hr. in 400 ml. of a cold pH 4.3 citrate buffer, which contains 0.1 iI1 citric acid and 0.1 fir sodium citrate. After centrifugation at 2000 r.p.m. at 5°C. for about 2 hr., the supernatant is filtered through coarse filter paper under suction. This filtrate is then spun at 50,000 X y at 5°C. in a Spinco preparative ultracentrifuge for 2 hr., which leaves a clear, highly viscous centrifugate. The ichthyocol is now collected b), dialysis of the extract, in the cold for 2418 hr. against a large volume of 0.02 IV dibasic sodium phosphat,e. Bfter about 8 hr., thick, rigid, needle-shaped fibrils appear in the dialysis bag. The solid is collected by rcntrifugation at low speed, washed with a large volume of cold distilled water, and stored at 5°C. in the wet condition. The yield is about 0.5% based on the initial wet weight of the tunic.

Properties

of 1Zcid-Extracted

Ichthyocol

In Figs. 1 and 2 are shown photographs of the precipitated needle-like structures as they appear under dark field and in the electron microscope. This material is similar to the “crystals” of procollagen described by Orekhovitch and his co-

488

FIG. 1. A dark of a citrate extract

PAUL

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GALLOP

field micrograph of ichthyocol against 0.02 M phosphate.

fibrils,

reconstituted

by dialysis

workers (16, 17). The electron micrograph was taken on a R.C.A. model EMU-2 electron microscope by Mrs. Genevieve Graf, who used unstained and unshadowed material. The structures have the typical banded appearance of collagen, showing the -640-A. macroperiod distinctly though somewhat variably (range 600-720 A., average 670 A.). For wide-angle x-ray investigations, the precipitated ichthyocol was packed in fine glass capillaries. In addition, films obtained by drying a distilled-water suspension on glass plates were packed together into specimens and irradiated parallel to the films for both wide-angle and small-angle diffraction studies. In Fig. 3, a typical wide-angle pattern is reproduced, which shows several of the principal

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FIG. 2. An electron micrograph of the fibrils on grids from a distilled-water suspension.

489

ICHTHYOCOL

in Fig.

1, unstained

and deposited

collagen spacings, in particular the rings at 2.86 and 11 A., with meridional and equatorial accentuation, respectively. The small-angle patterns yielded weak and diffuse indications of the 6th and 9th orders of the 640-A. spacing [for a discussion of the use of diffraction data in identifying collagens see Bear (2)]. The x-ray apparatus employed has been described elsewhere (1, 3). * If the ionic strength of solutions of this material is kept below 0.3, the solid will dissolve readily below pH 4.0 and can be kept in solution up to pH 5.2. Above pH 5.2 it precipitates and remains insoluble up to pH 11.3. Furthermore, dialysis of basic as well as acidic solutions of this material will result in reconstitution of fibrils having the normal collagen appearance in the electron microscope. The dry solid material is about 17.5% nitrogen according to Kjeldahl analysis. It contains a small but consistent amount of carbohydrate, as shown by the anthrone reaction. Acid solutions of the crystals were treated with anthrone reagent by the method of Koehler (12) and the optical densities at 625 rnp compared with

PACL

M.

GhI,LOP

FIG. 3. Wide-angle x-ray dilfractio I p’&t tern of films of reconstituted extracted ichthyocol, irradiated parallel to the film surfaces (Cu K, Ni filtered, specimen-to-film distance 5 cm.).

citrateradiation,

densities from glucose standards. For several concentrations of ichthyocol from different preparations t,he value of the carbohvdrate content is equivalent to 0.0054606 g. hexose/g. dry ichthyocol. The ultraviolet absorption spectrum obtained in l-cm. quartz cells in a Beckman mode1 DU spectrophotometer shows low absorption at wavelengths longer than 2500 A., the region where the aromatic amino acids tyrosine, tryptophan, and, to a lesser exte@, phenylalanine, absorb. The spectrum is in genera1 very similar to those of the purified collagens st,udied by Sizer (26), and by Loofbourow, Gould, and Sizer (13), as well as to the absorption of the electroplated ichthyocol of Sale (21). The concentration of solutions of ichthyocol was determined by a biuret procedure similar to that described by Gornall, Bardawill, and David (8).

Sedimentation If

the

acid-extracted

citrate at pH 3.7, a

material highly

and Viscosity

is redissolved viscous

solution

in acid, typically 0.15 M The viscosity was

results.

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0 0.01 0.02 0.010.04 005 006 0.070.08 0.09 0.10 0.11 FIG. 4. The concentration citrate-extracted ichthyocol

dependence of the reduced viscosity of solutions (at pH 3.7, 21.4”C. in 0.15 M citrate buffer).

of

measured at 21.4”C. in capillary viscometers with flow times of about 60 sec. with water at 20°C. The intrinsic viscosity of 13.2 was obtained by plotting q,,/c versus concentration and extrapolating to infinite dilution, as is shown in Fig. 4. NO attempt was made to study the gradient dependence of the intrinsic viscosity. Ultracentrifugation in a Spinco model E analytical ultracentrifuge revealed a sharp, nondiffusing peak (Fig. 5) as one might expect, judging from the high intrinsic viscosity. Runs were done in a temperature range of 21-25”C., and in the course of each individual run the temperature rose about one degree every 2 hr. The average temperature between the first and last sedimentation photographs is used in the calculations. The sedimentation constant was obtained and corrected to water at 20°C. in the usual manner. A plot of sso versus concentration (Fig. 6) presents an unusual behavior, similar to results reported on methylcellulose by Signer and Liechti (23) [seealso Signer (24)]. Nothing quantitative can be inferred from this concentration dependence, but qualitatively it appears that the two relatively flat regions represent, respectively, the sedimentation of the individual threadlike particles at low concentrations (<0.08 %) and the sedimentation of interacting threads at higher concentration (> 0.14 %). The intermediate region, where strong concentration dependenceis apparent, can be considered as a transition region. The extrapolated sedimentation constant has a value of 2.85 svedberg units. However, at concentrations lower than those accessible experimentally in an ultracentrifuge employing schlieren optics, it is possible that further concentration effects exist.

492

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FIQ. 5. Typical sedimentation diagram of a 0.158% solution of citrate-extracted ichthyoool, 67 min. after the rotor reached a full speed of 60,000 r.p.m. (at pH 3.7, at 21.8”C., in 0.15 M citrate buffer).

1.0 -

‘.‘o

(Lo?. II

0.01

II 0x6

COIICEmRmO* WlOOrnl I 11 oc4 010 O.IP 0,.

11 016

0.18

2 am

FM. 6. The concentration dependence of the corrected sedimentation constants of citrate-extracted ichthyocol solutions (at pH 3.7 in 0.15 M citrate buffer).

An estimate of the concentration range at which the particles are at least mechanically independent can be obtained as follows: If the effective length of the particle is R(root mean square separation of chain ends) the swept out volume per gram, V, , is given by Eq. (1)

iv? (4)” va= M = 3.15 x

1o23$

The reciprocal of Va , multiplied by 100, will give the concentration in

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493

g./lOO ml., Ci , at which mechanical independence is expected. An estimate of R3/M can be obtained from the intrinsic viscosity by using the Flory-Fox relation (6a), given in Eq. (2):

Here Cp is a universal constant, equal to about 2.1 X 10zl. Taking [q] as 13, R3/M is 6.2 X 1O-21 and V, is 19.5 X lo2 cc. Then Ci is equal to 0.051% and is in the concentration range where the sedimentation data have been extrapolated to obtain the value at infinite dilution. An estimate of M/L, the particle mass per angstrom of contour length, can be obtained from the sedimentation constant by using the equation of Burgers [Eq. (3), see Svedberg and Pedersen (27)]:

M

87r 3 tNsOzo

27 = (1 - Vp)(ln

C-r0

(L/d)

+ 0.19)

Here 7 is the viscosity of water at 20”, p the density of water at 20°C d the particle diameter, and B the partial specific volume of the ichthyocol, which is assumed to be 0.705, a value obtained with a gelatin derived from ichthyocol as described in the following paper. An estimate of L/d need not be too acurate since it appears in Eq. (3) as a logarithm. The Simha equation (25) relates the viscosity increment (Y = [q]lOO/P) to the axial ratio of the particle. Tables of this relationship are given by Cohn and Edsall (5). Since the particle is probably not completely extended, but may be in part randomly coiled, the use of the Simha equation to estimate axial ratio may be questioned, although the equation of Burgers is still valid because the sedimentation properties are strongly determined by the cross section of the threads. From the intrinsic viscosity of 13.2 the viscosity increment uncorrected for hydration is 1880 and the axial ratio is about 190. The M/L value derived from Eq. (3), with 2.85 used as the extrapolated sedimentation constant, is about 88 avograms3 per angstrom. If the axial ratio is taken as 500, the value of M/L is 76 avograms/A., which demonstrates the relatively small dependence of the M/L value upon the axial ratio. 8 The term avogram has been approved by the Committee on the Nomenclature of Physical Chemistry of the Division of Physical and Inorganic Chemistry of the American Chemical Society [see Chem. and Eng. News %,I841 (1950)], as “a quantity of matter which is one gram divided by Avogadro’s number.”

494

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Light Scattering Solutions prepared by dissolving wet reconstituted material in 0.02 M citrate at pH 2.5, with 0.2% NaCl added to increase the ionic strength, were centrifuged at 5°C. in the Spinco preparative ultracentrifuge at about 50,000 X g for 5 hr. Precautions were taken in filling t,he scattering cells to obtain optically clean solutions. The light-scattering photometer was constructed by the author and is in general similar to apparatus in common use. A lP21 photomultiplier, powered by a carefully regulated power supply (1000 f 1.0 v.), was mounted to rotate from 0” to 150” about a cylindrical scattering cell 3 cm. in diameter, with flat polished entrance and exit, windows, set in a thermostatically regulated jacket at, 25°C. Fluctuations in the intensity of the mercury source were compensated for by varying the photomultiplier gain with a phototube monitor connected across two dynodes of the photomultiplier in a manner described by Hadow, Sheffer, and Hyde (8a). The magnitudes of the scattering at various angles were converted to Re values by comparison with the 90” scattering from a quartz block standard with Tyndall effect (7), which had been calibrated against Ludox (colloidal silica) by a method similar to that described by Oster (18). The refractive-index increment, (n - nJ/c, was measured in a &ice-Speiser differential refractometer at 25°C. and was found to be 0.192 for the 4358-A. mercury line. A Zimm plot (28), Fig. 7, was made in the customary manner from data for protein concentrations (c) ranging from 0.00105 to 0.000684 g./ml., by plotting Kc/R@ versus sin2 (e/2) + 1000~. Here K is a constant given by (2fni/NX4) [(n - n~)/c]~, where X is the wavelength of the light employed, N is Avogadro’s number, and no is the refractive index of the solvent. From the value of (Kc/R,),,0 , the reciprocal of the e-+0 molecular weight is obtained. In this case the result was a weight-average molecular weight of 1.67 f 0.17 X 106. The Kc/R0 versus sin2 (e/2) curve at zero concentration can be normalized to a plot of l/P8 (the reciprocal of the particle-scattering factor) against sin* (e/2) by multiplication of Kc/R@ by M. The l/PO versus v curve [Fig. 8; v is equal to three times the limiting slope of the l/PO-sin (e/2) curve multiplied by sin2 (e/2)] for the ichthyocol solutions is intermediate between the theoretical rigid rod (X = 0) and random coil (Z = m) curves with the same limiting slope. The general shape of the curve suggested that one might employ the

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ICHTHYOCOL

treatment of Peterlin (20), although the state of polydispersity of the solutions is unknown. In this treatment it is possible to compare experimental scattering factors for coils of varying flexibilities, measured by a stiffness parameter 2. From the theoretical stiffness parameter which best fits the experimental data and the limiting slope of the l/PO-sin2 (e/2) curve, factors such as the contour length, L, and the effective length, R (root-mean-square separation of chain ends) can be calculated. Figure 8 indicates that a value of 20 for the stiffness parameter 2 will give a good fit of the data. From the limiting slope of 13.3 (Fig. 7) and the best value of x, the contour length was found to be 13,400 A. and the effective length was 4,100 A. The chains, therefore, have a degree of folding of 0.309, as compared to 1.000 for the rigid rod and 0.081 for the random coil. The data are summarized in Table I. The value of M/L obtained was about 120 avograms/A.

FIG. 7. Zimm plot of light scattering by citrate-extracted in 0.02 M citric acid, 0.2yc NaCI, at 25°C.

ichthyocol

dissolved

496

PAUL RECIPROCAL

M.

GALLOP X-0

PARTICLE

12 SCATTERING

PMTOR

FOR OlwENwT

VAuJE8

L~‘V P@ O? x

IO /

5

k 6

4 0 ~EXPERIMENTAL FROM LNIU

PLOY

POINTS

ON ICHTHYOCOL

2

4

5

IO

15

20

2s

30

V-7

8. Peterlin analysis of the reciprocal particle-scattering factor for citrateextracted ichthyocol. The experimental points are taken from the Zimm plot. The values of z correspond to different chain-stiffness parameters, x = 0 for the rigid rod, and x = m for the completely flexible coil. FIQ.

Optical Activity The optical activity of the acid-extracted ichthyocol in the pH 3.7 citrate buffer was measured by Miss Carolyn Cohen in a Schmidt and Haensch polarimeter at temperatures below 25°C. Thermostatically controlled cells 2 dm. in length were used with unfiltered sodium light. The optical activity (c&, was -350” f 30”, and no apparent concentration dependence could be detected from 0.2 to 0.7 %. This value has also been obtained on solutions of calf hide procollagen and is higher than the

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TABLE Light-Scattering

Data

on Acid-Extracted

497

ICHTHYOCOL

I Ichthyocol

from

Zimm

Plot

and

Pete&n

Treatment (In

0.02 M citric

acid,

Molecular weight (M) Limiting ‘slope (tan y) Stiffness parameter (2) Contour length (L) Effective length (R) Mass per unit length (M/L) Degree of folding (R/L)

0.2%

NaCl,

at W’C.)

1.67 f 0.17 x 108 13.33 20 13,400 A. 4,100 A. -120 avograms/A. 0.309

rotations (cu. - 110”) obtained with solutions of gelatins of various origins in their sol state. Further discussion of the optical activity of ichthyocol and ichthyocol gelatin is presented in the succeeding paper. DISCUSSION

The acid-soluble ichthyocol herein studied represents a small fraction (about 0.5 %) of the total tissue from which it was extracted. The results obtained cannot, therefore, be taken as typical of the entire collagenous component. Nevertheless, the extracted material is capable of being dispersed and reconstituted into fibrillar elements with structure very similar to that of normal native fibrils of collagen, as is shown by the electron-optical and x-ray diffraction examinations. The present light-scattering studies confirm the observations of M’Ewen and Pratt (14) that acid dispersions of extracted collagens contain long filamentous particles. The sedimentation studies described above also supply direct evidence for this fact. Two important characteristics of the filamentous elements appear from examination of the quantitative figures supplied by the physical-chemical investigations in the light of other facts known about collagen: (a) The various values reported here for M/L lie in the range 80-120 avograms per angstrom, which means roughly one amino acid residue per angstrom of particle (contour) length. One residue can extend, along a contour axis, 3.67 A. at most [see Corey and Donohue (6)], probably somewhat less on the average in collagen because of the presence of an appreciable proportion of pyrrolidine residues. It follows that the aciddispersed particles contain at most about three separate polypeptide chains in lateral aggregation [cf. the 3-chain helix of Pauling and Corey (19)]. In thinness these filamentous particles would be of the order of

498

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diameter (12 A.) described for “protofibrils” of dry collagen by Bear (2). The latter author placed about one residue along one angstrom of protofibrillar length and connected all residues serially, to picture the protofibril as a single, regularly coiled, polypeptide chain capable of severalfold extension. (b) In length the acid-dispersed particles are about twenty times the macroperiod (600-700 A.) seen in fibrils electron optically or by means of small-angle x-ray diffraction. According to the M/L values for the dispersed protofibrillar particles, a segment of length equal to the macroperiod would contain 50,000-80,000 avograms. While Bresler et al. (4) had reported that acid dispersions of their rat skin hide procollagen contained independent particles of 70,000 weight, this has now failed confirmation in two laboratories. Gelatin particles of this size can ‘be isolated from the acid extract upon heating, however, as is shown in the next paper. The results of the physical-chemical studies at the present stage suggest that the behavior of the simple collagenous extracts in neutral and acid environments are partially understandable in terms of the simple equilibrium : fibrils e protofibrillar

particles

Appropriate acid solutions displace the equilibrium toward the right, possibly by charging basic groups, discharging acidic ones, and breaking up some hydrogen-bond links, all of which would promote disintegration of interprotofibrillar unions. Conversely, neutralization or increase in ionic strength permits the protofibrils to reaggregate along their lengths into fibrils, i.e., causes displacement of the equilibrium to the left. Native fib& are not as easily converted completely to protofibrils as are the reconstituted ones. Reasons for this are not hard to imagine: very few intrafibrillar, interprotofibrillar linkages, consisting either of rare primary valence combinations between side chains or of entanglements involving small proportions of other chemical substances [polymeric carbohydrates, mucoproteins, etc.; cf. Highberger, Gross, and Schmitt (11, 22)] might easily restrain some native protofibrils from readily separating from a fibrillar structure. While evaluation of the validity of such possibilities awaits further study, and may produce results of importance to an understanding of the biological organization of connective tissues, it would seem that the simpler extractable fractions can be useful in investigating many of the primary chemical and physical aspects of the structure of collagen-like fibrils.

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SUMMARY

Viscosity, sedimentation, and light-scattering data indicate that an acid-soluble component of carp swim bladder (ichthyocol), capable of reconstitution into typical collagen-like fibrils, disperses as long thin filaments (protofibrils) of weight one to two million, containing about one amino acid residue per angstrom of contour length. REFERENCES 1. 2. 3. 4.

BEAR, R. S., J. Am. Chem. Sot. 64, 727 (1942). BEAR, R. S., Advances in Protein Chem. 7. 69 (1952). BOLDUAN, 0. E. A., AND BEAR, p. S., J. Appl. Phys. 20, 983 (1949). BRESLER, S. E., FINOGENOV, P. A., AND FRENKEL, S. Y., Doklady Akad. Nauk S.S.S.R. 78, 555 (1950). 5. COHN, E. J., AND EDSALL, J. T., “Proteins, Amino Acids and Peptides.” Rheinhold Pub. Corp., New York, 1943. 6. COREY, R. B., AND DONOHUE, J., J. Am. Chem. Sot. 73, 2899 (1950). 6a. FLORY, P. J., AND Fox, T. G., JR., J. Am. Chem. Sot. 73,1904 (1951). 7. GALLOP, P. M., AND SIZER, I. W., Rev. Sci. I&r. 24, 399 (1953). 8. GORNALL, G. A., BARDAWILL, C. J., AND DAVID, M. M., Can. J. Research B27, 791 (1949). 8a. HADOW, H. J., SHEFFER, H., AND HYDE, J. C., Can. J. Research B27, 791 (1949). 9. HARKNESS, R. D., MARBO, A. M., MUIR, H. M., AND NEUBERGER, A., “The Nature and Structure of Collagen” (J. T. Randall, ed.). Academic Press, New York, 1953. 10. HIGHBERGER, J. H., GROSS, J., AND SCHMITT, F. O., J. Am. Chem. Sot. 72, 3321 (1950). 11. HIGHBERGER, J. H., GROSS, J., AND SCHMITT, F. O., Proc. Natl. Acad. Sci. U.S. 37, 286 (1951). 12. KOEHLER, L. N., Anal. Chem. 24, 1576 (1952). 13. LOOFBOUROW, J. R., GOULD, B. S., AND SIZER, I. W., Arch. Biochem. 22, 406 (1949). 14. M’EwEN, M. B., AND PRATT, M. I., “The Nature and Structure of Collagen” (J. T. Randall, ed.). Academic Press, New York, 1953. 15. NAGEOTTE, J., Compt. rend. 184, 115 (1927); Compt. rend. sot. biol. 96, 172, 464, 838, 1268 (1927); 97, 559 (1927); 98, 15 (1928); 104, 156 (1930); 113, 841, 1398, 1401 (1933); Ann. anat. pathol. et anat. normale mbd.-chir. 8, 1 (1931). 16. OREHHOVITCH, B. N., TUSTANOVSKII, A. A., OREKHOVITCH, K. D., AND PLOTNIKOVA, N. E., Biokhimiya 13,55 (1948); Doklady Akad. Nauk S.S.S.R. 60, 837 (1948). 17. OREKHOVITCH, B. N., Intern. Congr. Biochem. Communs. 2nd Congr. Paris, 1962; Acad. Sci. U.S.S.R., Moskow, 106 (1952). 18. OSTER, G., J. Polymer Sci. 9, 525 (1952). 19. PAIJLING, L., AND COREY, R. B., Proc. Natl. Acad. Sci. U. S. 37, 272 (1951). 20. PETERLIN, A., J. Polymer Sci. 10,426 (1953). 21. SALO, T. P., Arch. Biochem. 28, 68 (1950).

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25. 26. 27.

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GALLOP

F. O., GROSS, J., AND HIOHBERQER, J. H., Proc. Natl. Acad. Sci. U.S. 39,459 (1953). SIGNER, R., AND LIECHTI, J., Helv. Chim. Acta 21, 530 (1938). SIGNER, R., in “The Ultracentrifuge” (Svedberg, T., and Pedersen, K. O., eds.), part IV, B-2. Clarendon Press, Oxford, 1940. SIMHA, R., J. Phys. Chem. 44, 25 (1940). SIZER, I. W., J. Am. Leather Chemists’ Assoc. 47, 634 (1952). SVEDBERG, T. AND PEDERSEN, K. O., “The Ultracentrifuge.” Clarendon Press, Oxford, 1940. ZIMM, B. H., J. Chem. Phys. l&l099 (1948).

22. SCHMITT, 23. 24.

M.