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The conversion of fibrinogen to fibrin. VII. Rigidity and stress relaxation of fibrin clots; effect of calcium
The Conversion of Fibrinogen to Fibrin. VII. Rigidity and Stress Relaxation of Fibrin Clots; Effect of Calcium1 John D. Ferry, Meredith Miller? and Sidney Shulman From
t.he Ijepadwlent
ef Chemistry,
IUniversity
Received
IJJ” Il’isconsin,
Jifcldison,
Ib*isconsin
June 13, 10.51
The most striking physical change accompanying the conversion of fibrinogen to fibrin is the development of rigidity. From measurements of this property and its dependence on temperature and other variables, conclusions can be drawn concerning the structure of the fibrin clot. In an earlier study (I), rigidities were reported for clots formed from human fibrinogen under different conditions of concentration and PH. These rigidities were measured by the method of transverse wave propagation (2,3), which provides values corresponding to mechanical deformations of very brief duration, of the order of a millisecond. The present investigation was undertaken primarily to study the effect of temperature on rigidity and also to compare dynamic or shorttime measurements with static measurements which can be extended for minutes or hours to determine whether stress relaxation occurs (4). Bovine rather than human fibrinogen was employed. It was found that, the mechanical properties, particularly as revealed in stress relaxation over long intervals, are markedly altered by the presence of calcium. An effect of calcium had already been detected in the tensile strength measurements of Wagreich (5) ; and the qualitative dissolution studies of Robbins (6), Laki and Lorand (7,8), and Mihalyi (9) indicate that’ when t#hrombin act’s in the preecnce of calcium together wit’h an unidcntified serum factor structural bonds are formed whose charact,er is different from those formed by thrombin alone. Our present studies of Fibrin and the Coagulatioll 1 This is paper Xo. 9 of a series on “The Fornlation of Blood” from the University of Wisconsin, supported in part hy research granb from the National Institutes of Health, Public Health Service. 2 Present address: Film Ihpartmmt,, R. f. tlu I’ont, de Scnmurs and Co., l~11ITaic1, -\‘. Y. 424
FIBRINOGEN
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support the conclusion that different bonds are formed, and suggest that they are additional t.0, rather than replacements of, the structural bonds formed by thrombin in the absence of calcium.
Uovine fraction I and thrombin were obtained from Armour and Company. Two preparat,ions of fraction I, C-757 and 120-18, which contained 7(r-730j0 clottable protein, were used without further purification in some experiments. Two types of refractionated fibrinogen were also employed: fraction I-2, prepared from 129-18 by alcohol fractionation as previously described (10); and fraction I-S, prepared from another .2rmour lot (128-63) by precipit,ation at 0” at ionic strength 0.08, following essential11 the method of Seegers (11). Fractions I-2 and I-S contained 89-91~~ and 855867c clottable protein, respectively. The mechanical properties of clots formed from fraction I, fraction I-2, and fraction I-S were qualitatively similar. Thrombin C-173B I’rom Armour and Company, containing 4.7 urrits/mg., was used for all esperimcnts except those with fraction I-S. For the latter, we employed a highly purified thrombin which was very kindly given us by Dr. W. H. Heegers. This material, which contained about 850 units/mg. on the basis of comparison with the Armour material, was diluted with 280 times its weight of crystallized bovine serum albumin (to minimize adsorption losses in solution) and stored as a frozen solution containing 60 units/ml. The assay of fibrinogen and the preparation of protein solutions were carried out as previously described (10,12). The concentration of sodium chloride was always 0.45 .lf, csxccpt. for fibrin clots formed at pH 6.2 in the absence of calcium; here the sodium chloritlc was 0.40 M and an additional ionic strength of 0.05 dl was contributed by ptiosphat P buffer. Stock solutions were clarified by filtration through Republic Seitz filter patls (previously washed with sodium citrate solution, to avoid introduction 01 traacs of calcium, and t,hcn with solvent). The systems described are calcium-free unless othrr\visc spcc~ifcd. (‘lots were always formed %VL sitrh by mixing fibrinogen and t~hrombin solutions and rompleting assembly of t,he apparatus well in advance of the moment of clotting. The clotting time for a solution containing 10 g. fibrinogen’l. was of the order of 5.0 min. at pH 6.2 and 3.5 min. at pH 7.0. Concentrations of clots are given as grams fibrin per lit,er (assuming complete conversion of fibrinogeri to fbrin). ignoring the prcsrncc of &her protein.
Measurements of wave propagation were ma& as previously described (1,2), in a cell with dimensions 2.5 X 5 X 6 cm. In this m&hod, transverse waves of small amplitude are generated by oscillatory motion of a thin plate in its own plane. The resulting strain double refraction gives a wavy pattern ~vhrn viewed with stroboscopic polarized light flashing with the same frequency as the vibration, passing through a double quartz wedge. The wavelength, A, and damping in&x. X,‘x,, (where x0 is the distance within which the wave amplit~ude falls off bv a f:tct,or of l/e) are obtained b? measurements on a photographic film. The wave rigidity, 6, is given by thr product A*& where Y is the frequencv and p the density.
426
J. D. FERRY,
M. MILLER
AND
S. SIIULMAN
Only fine, or transparent clots, prepared at pFI 7, wclre studied by t,his method, since transmission of light is essential. The behavior of the librin in x&vc propagation, as contrasted nit,h gelatin (2) and high polymer solut.ions (is), WM charactrrixed b> t,wo features: a high strain-optical coeffiickt, and tt low damping ind(~s. 1kc:ausc 01 the high strain-optical cocfficicnt, it. \vas n~essary t,o rchducarsthp amplitudr of mot,ion of the moving plate to an unusually low rscursion to obtain suit,ablc wave patterns. Anot,her consequence was distortion of the 13abint:t lincxs upon changing the temperature, due apparently to residual skrssrs acac*ompanying tjhc~rmal espansion or contraction of the gel as it was constrained in tho rectangular container. This did not seriously interfere with measurements for a cshange of 20”, however. Because of the low damping index, it was necessary to restrict, measurrmrnt,s to short wavelengths (<0.8 cm.) to avoid errors due to &lectior~ from th(a opposit,e end of the cell (14). Results are reported as the wave rigidity, G; since the damping is so slight, this is negligibly different, from G’, the real part, of t~he romplcs ~nodulus of rigidit,y (1.5). 1Ieasurcmcnts of st,atic* rigidity and of Aress relaratioll were made in a coaxial cylinder apparatus described elsewhertl (4). The outer cnylintlflr was rot,atetl through a small angle (Ed), and the inner csylinder, supported by a very stiff suspension, responded with a much smaller angle 0~. The average shear strain in the clot was about 1O0/0 or less. The ratio of stress to strain, whirh in the absence of stress relasation is the modulus of rigidity, was obtained from t,hr expression kQ~/h(Ba - 8s). where k is the torsion constant of thr, suspension and I) is :m apparatus constant involving the dimensions of the cylinders. Stress relaxation was measured by holding BA fixed and following t,he change in eR with time. Since BB was always much smaller than 0.4, the procedure corresponds to relaxation at essentially constant strain. In most, cases rcvcrse relaxations were also followed, according t,o t,he procedure described in detail for studies of grlat,in gels (4). Bot,h t,,vpicaal fhc clots, formed at pII 7.0, and typical coarse clot,s, formed at pIT 6.2, \vere investigated. As in the gelatin erperimcnts (4), the clot was always covered 1,~ mineral oil, and at, the end of each c~xperiment the syst,cnl was inspcctc~tl for conc(‘ntricity mtl at)srnccb of any obvious bn&rial action. RESCLTS
In each clot at several different the limits of 100 frequency within reported.
OF DYKAMIC
RIGIDITY
MEASTTREMENTS
each t’emperature, the wave rigidity was measured at frequencies covering about a twofold range between and 1000 cycles/see . ; the results were independent’ of this range, and were averaged to give the values E$ect of Temperature
After formation of a clot at 25”, it was allowed to stand at that temperature for several hours to permit nearly complete development’ of rigidity, which increases for a long time after the moment of clotting (1). The rigidity was measured at 25”; then the temperature was lowered to 5” or 10” and maintained there for 2 hr., which was found
FIBlZINOGEN
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T-II
127
to be long enough to permit the rigidity to attain a new value charact’eristic of this temperature. A series of measurements was t’hen made at different temperatures, each preceded by about’ 2 hr. equilibration, ending at 25” to check the original measurement. The second measurrment at 25’ was usually slight,ly higher (3-15’:s) than the first, indicating some continued tea&on. In some c:ws the rigidity was mcasured at 30”, but Ihe clots could not, be taken to higher tcmpcraturcs than this without causing irreversible changes as shown by a marked drop in the rigidity at 25” measured afterward. The rigidity always increased with decreasing temperature but appeared to be reversible within the range studied. In Fig. 1, t,he logarit’hm of rigidity is plotted against the reciprocal absolute temperature for clots containing from 3.8 to 17.2 g. fibrin4 At, 9.5 g./l., the sequence of the different temperatures is indicated. Here the second measurement at 25” is 10% higher than the first, and appears to fit bet’ter with the data at other temperatures. The behavior at the ot’her concentrations was similar, and t,hc initial 25” points have thcreforc been omitted
2.5
I
3.2
1
3.3
I
3.4
3.5
I
3.6
3.7
1000/T
Fro. 1. Logarithm of bvavc rigidity plot&d against reciprocal of absolute temperature, for clots formed at. 25°C. from fraction I, l’repn. C-757, thrombin 0.95.unit/ml., pH 6.97-7.01, ionic strength 0.45. Fibrin concentrations as follows: 1, 17.2 g./l.; 2, 13.3 g./l.; 3, 10.9 g/l.; 4, 9.54 g./l.; 5, 6.70 g/l.; 6, 3.81 g./l. The small numbers along line 4 indicate t#he serial order of measurrments at different t,emperatures.
428
J.
D.
FERRY,
M.
MILLER
AND
S. SHULMAN
from the other plots. A series of straight lines is obtained whose slopes increase with concentration. The value of R d In c/d(l,/T) ranges from 2.8 to 5.6 kcal./mole. The change in rigidity of fibrin with temperature is thus similar to that of gelat,in in direction, but is far less in magnitude, and the rigidity does not, of course, vanish (corresponding to melting) at, any temperature which can be achieved without denaturation. Other preparations of fibrinogen gave clots whose rigidit’ies differed in magnitude somewhat from those shown in Fig. 1 but had a closely similar temperature rlependenco. In a few cases, clots were formed al 15” instead of 25”; the rigidities of such clots were higher at all temperatures by about 5054, but, again showed t,he same t#emperature dependence and reversibility. Eflect o.f Concentmtion The logarithm of rigidity at 25” is plotted against the logarithm fibrin concarntration in Fig. 2 for clots formed from two preparations
1
0.6
0.4 Log
Fibrm
0.8
I .o
Concentration
of of
1.2 I” c~ /I
FIG. 2. Logarithm of wave rigidity at 25°C. plotted against logarithm of concentration of fibrin, for clots formed at 25°C. from fraction I, Prepn. C-757 (line 1) and 129-18 (line 2). Thrombin 0.95 unit/ml., pH 6.Q7-7.01, ionic strength 0.45. Lines 1 and 2 are drawn with a slope of 2.3. Line 3 represents results on hmnan fibrin [Ref. (l)], pH 6.8, ionic strengt,h 0.30, thrombin 1 unit/ml.
fraction I. In each case the rigid&y is proportional to the 2.3 power of the concentration, though the values for the t’wo preparations differ by about 20yG. A plot for huma.n fibrin at a similar pH, from Ref. (I), is included for comparison; the values :IW considcrabIJ- higher, hilt Ihc slope is less, about’ 1.fi. So fundnmcntnl significance can be attached to t’he slope, however, since it varies wirith temperat.ure (as a corollar\- to the observation in Fig. I t’hat the tkmperature dependence \-arks with concentration). This beha\-ior tlilfers markedly i’rom that of gelatin gels, in which the rigidity is closely proportional t.o thrl square of t,hc concentration over a considerable range of tempwaturcs. Elffect of ~‘nlciu~rn Measurements were made on clots formed from fraction I-S both without calcium and in the presence of 0.01 A4 calcium chloride. These
3.4
I
3.5 1000/T
3.6
?
Fro. 3. Logarithm of wave rigidity of clots formed at 25°C. f'lo~n refractionatetl fibrinogen I-S with 0.01 M CaCl, (curve 1) and without (curve 2), plotted against reciprocal absolute temperature. Fibrin concentration 9.5 g./l., thrombin 0.95 unit,’ ml., pH 7.00 f 0.04, ionic strength (exclusive of CaClJ 0.45. Taggecl points refer to static measurements.
two clots were soluble and insolublr:, respectively, in 3.3 M urea; a concentration of 1O-3 M calcium sufficed to prevent, dissolut,ion of clots formed from this fraction, which evidently contained the serum factor of Laki and L&And (8). The data from one such comparison are shown in Fig. 3; a second experiment gave similar results. The rigidity of the insoluble clot showed less temperature dependence and was higher than t,hat of t,hc soluble clot by a factor of 1.5 at 5” and a factor of 1.9 at 2.5”. The 25’ points represent measurements about 12 hr. after clotting.
430
d. D. FERRP, M. MtI,I>ER AND S. SHTJLMAh-
Although without calcium the deveiopment of rigidity was substantially complete at t,his time, in the clots cont.aining calcium the rigidity was still slowly increasing. Marc pronounced effects of calcium are revealed in st.atic measuremen@ as described below. RESULTS OF STATIC RIGIDITY ASD STRESS RELAXATION ~VEASUREMENTS
Whereas the wave propagation method measures the rigidity within a time interval of a milliswond, the most rapid measurement possible in the static coaxial cylinder apparatus involves a time lapse of several seconds. In calcium-free, urea-soluble clots, the stress relaxes so quickly aft,er a strain is imposed t,hat no equilibrium rigidity measurement,s arc) possible. This surprising result indicates unespect,ed lability of a large proportion of the st’ruct8ural linkages. In urea-insoluble clots, the stress, while not constant,, relaxes slowly enough aft’cr imposition of strain so that it can be extrapolated to zero time to provide an instantaneous value for the rigidity; this agrees reasonably well with the dynamic value obtained from wave propagation, as illustrated by two point’s in Fig. 3. ?itress Kflazatiotz itb Calcizrm-Free ~‘dots .Ut,hough the stress relasat’ion following sudden strain of a calciumfree clot is too rapid to follow at first, the decay aft.er t.he first, felr minutes can be described by recording the ratio of shear stress to strain (which would give the instantaneous rigidity if it could be extrapolat,ed t,o zero time) as a function of time. This was done for clot’s formed from both fraction I and refractionated I-2 at pH 6.2 and 7, as well as from refract,ionated I-8 at pH 7, at various temperatures. In each experiment, t’he clot was formed at 25’ and allowed to stand at this temperat’ure for several hours. h strain was imposed and the stress was allowed to relax for about, 40 min., during which time it decayed to a small fraction of its init,ial value. This relaxation may be attribut,ed to dissociation of structural linkages. -4s in the case of gelatin (4), some of t,hese linkages must form again, or rearrange, corresponding to network strands in unstrained configurations; because when the strain was returned to its original position aft’er relaxat,ion, a reverse stress appeared, somewhat smaller in magnit~ude than t,he original stress and opposite in direction. The rclasation of the wvcrsc st,rcss was then followed, represent,ing dissociation of linkages formed during the period
FIRRINOGEK
TO
FIBRIN.
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VII
of the first relaxation. A pictorial represent’ation of this type of experiment is given in Fig. 1 of Ref. (4). After completion of relaxation and reverse relaxation at 25”, measurements n-ere made at’ several other
6
-
3
-0.5 Logartthm
of Time
I” Mmules
4. Stress relaxation of fibrin from rcl’ractionatcd fibrinogen I-2, pH 7.01, ionic FIG. strength 0.45, fibrin 9.5 g./l., thrombin 0.95 unit/ml. The numbers opposite curves denote serial order of m~asurrments at tcmpwxturri indicated.
temperatures, each preceded by equilibration for about 2 hr., and finnllJ again at 25”; the course of the last relaxation at 25” agreed reasonably well with the first. The ratio of shear stress t,o strain is plotted against the logarithm of time elapsed since imposition of strain in Figs. 4 and 5 for clots formed t 0 x
I
I ond 5 = 25 0” C 2 = IO S’C
0 Logarithm
of Time
I” Mmutes
FIG. 5. Stress relaxation of fibrin from refractionated fibrinogen I-2, pH 6.20, ionic strength 0.45, fibrin 9.5 g./l., thrombin 0.95 unit/ml. The numbers opposite curves denote serial order of measurements at temperatures indicated.
43’
J.
D.
FERRY,
M.
lMII,LEK
AND
S.
SHULMAN
from fraction I-2 at pH 7.01 and 6.20, respectively. The rate of relaxation increases rapidly wit’h temperature. Although the stressjstrain ratios are somewhat higher at, pH 6.20 bhan at 7.01, the course of the relaxation is similar in both cases, which is perhaps surprising in view of the marked difference in structure betSn-een these coarse and fine clots as revealed by opacity and syneresis (1) and electron microscopy (16). Relaxation curves for clots formed from fraction I and fraction I-X in the absence of calcium were similar. Representative curves for reverse stress relaxation at pH 6.20 are given in Fig. 6. Though the stresses are smaller, the course of relaxation closely resembles tha,t in Fig. 5, so the linkages formed during the initial
Logorllhm
of Tome I” Mtnufes
FIG. 6. Reverse stress relaxation of fibrin from refractionated fibrinogen I-2, pH 6.20, ionic strength 0.43, fibrin 0.5 R./I., t,hrombin 0.95 rurit~/ml. Tempw~tnres: 1, 10.8”C.; 2, 15.6”; 3, 20.3’; 4, 25.0”.
relaxation are evidently similar in character to those present initially. This fact, together with the reversible t,emperature dependence of both the dynamic rigidity and the stress relaxation, indicates t’hat at least some of the structural linkages are in a slow dynamic equilibrium, dissociating and rearranging with relaxation times (or half-t#imes) ranging from 10-l to lo3 sec.
Relaxation curves for a clot, formed from fra&on I-2 at pH 6.20 with 1OV M calcium and one formed from fraction I-S at ~1-16.98 with 10W2M calcium are shown in Fig. 7. These calcium concentrations are
FIBRISOGEK
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-133
about ten times t’he values required to prevent t&solution, in 3.5 X urea, of clots formed from these two preparations. The relaxation is far slower than without’ calcium, :rnd the stress decay;; by only about 20yCj in 400 min. Relaxation is depictBed at two temperatures for each clot, and the curve for the higher t,emperat)nre is slightly higher in each
o:
0
2 Logotllhm
of Time
VI Minutes
FIG. 7. Stress relaxation of fibrin containing calcium, at temperatures indicated. Open circles: refractionated fibrinogen I-2, pH 6.20, calcium 0.001 X. Filled circles: refractionated fibrinogen I-S, pH 6.98, calcium 0.01 M.
case. This is undoubtedly due to t,he fat% that the experiment was performed first at the lower temperature, and a slight increase in rigidit\ occurred during the long time required for following these slow relaxations. The presence of calcium, together with the serum factor of Laki and L&and whose presence must be inferred from the urea insolubility of these clots, affects the stress relaxation far more than does temperature or pH. In spite of this marked effect, clot,s formed with and without calcium in the amounts involved here are very similar in appearance and have almost identical clotting times.
The rigidit,y measures the resistance to elastdc deformat)ion of t,he network structure of which fibrin is known to be composed (16). Calculations for human fibrin have shown t,hat t,his rigidity is too high to be attributed to rubberlike elasticity mechanisms (l), and the same arguments are applicable to bovine fbrin. The rigidity presumabl) involves the inherent stiffness of the network strands, but the det,ailed mechanism is not understood.
434
.J.
D.
FERRY,
M.
MILLER
AND
S.
SHULMAN
The hypothesis has been advanced (1,17) that the network is bound together with primary chemical bonds. The more recent demonstrat,ion that fibrin can be dissolved in urea to yield fragment,s very similar to the original fibrinogen in size and shape (18,19) does not necessarily invalidate this hypothesis, although it severely restrict’s the types of chemical bonds that might be involved. Our present mechanical mcasurements, however, indicate that some (though probably by no means all) of the bonds constituting the network in calcium-free clots arc relatively weak secondary bonds. This conclusion is supported by thcl reversible decrease in rigidity with increasing temperature, t)hc rapid stress relaxation and its marked dependence on temperature, and the reverse stress, indicating newly formed bonds which relax in turn much like those they have replaced. It would be attractive to identify these weak and easily rearranged bonds with secondary associations among the long linear fibrils which are seen in the electron microscope. Such associations would not depend on the action of thromhin, which can hardly be involved in t’he formation of t,he new bonds that are revealed by our reverse stresses. On t,he other hand, the bonds within the fibrils themselves, which unite the fibrinogen residues t,ogether, and for which thrombin is directly responsible, may well be of a stronger character. In the presence of calcium and serum factor, the network is joined by bonds of a far more permanent nature. The comparison in Fig. 3 indicates that these bonds are additional to the associations formed in t,ha absence of calcium. But from the very slow relaxat’ion shown in Fig. 7 it appears that even the weak associations are considerably strengthened in the presence of calcium, and their relaxation times greatly increased, while it is probable that a substantial fraction of the network structure undergoes no rearrangement at all within a period of several hours. The observations of Lhr&nd (8) suggest that the additional bonds may be disulfide links. Further measurements of mechanical properties should prove valuable in elucidating the role of calcium and serum factor in modifying the structure of fibrin clots, and they will be continued when more information is available concerning the isolation and characterization of the serum factor. ~~CKNOWLEDQMENTS
FIBRINOGEN
TO FIBRIN.
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of the Iiniversity of Wisconsin from funds supplied by the LVisconsin Alumni Research Foundation; and by a grant, from Eli Lilly and Company, for which WC are most grateful. R’c are indebted t,o 1Ir. n’arrcn I<:. Evans and Mr. George E. Heckler fol help wit,h some of the experiments.
1. Dynamic rigidity has been measured by the method of wave propagation in bovine fibrin clots at pH 7.0 at’ various fibrin concentrations and temperatures, and in the abstnce and presence of small amounts of calcium. Static rigidity and stress relasa,tion have been measured at, pH 6.2 and 7.0 at various temperatures with and without calcium. 2. The dynamic rigidity without calcium decreases reversibly with increasing temperature between 5” and 3O”C., and at 23” is proportional to the 2.3 power of the fibrin concentratOion. The addition of small amounts of calcium (in the presence of the serum factor of Laki and L&&d, as deduced from insolubility in 3.5 M urea) increases t,he rigidity somewhat’ and diminishes the temperature dependence. 3. In the presence of calcium, t(he dynamic rigidity (corresponding to measurement within a millisecond) agrees wit8h the stat’ic rigidity (corresponding to measurement within several seconds). In the absenw of calcium, the static rigidity cannot be determined because of rapid stress relaxation. 4. The rate of relaxation of stress in clot’s formed without calcium increases rapidly with increasing t#emperature; when the strain is returned to zero after relaxation, a reverse stress appears which in turn relaxes. 5. The rate of relaxation of st,ress in clots formed with calcium is extremely small. 6. The results indicate that in clots formed without calcium some of the linkages which compose the network are weak associations which can easily rearrange. In clots formed in the presence of calcium (and serum factor), the network strands are joined by bonds of a far more permanent nature. REFERENCES I. FERRY, J. D., ANU MORRISON, I'. R., .I. An,. Cl~cw. SW. 69, 388 (1!)47). 2. FERRY, .J. D., Rev. Sci. Znstru~wzts 12, 79 (1941). 3. FERRY, J. D., AND ELDRIDGE, J. E., J. Phy/s. & Colloid Chenl. 53, 184 (1949). 4. MILLER, X1., FERRY, J. D., SCHREMP, F. TV., .~ND ELDRIDGE, .J. E., J. Phys. K: Colloid Chem. 55 (in press). 5. WAGREICH, H., AND TARLOV, I. M., Arch. Hiochem. 7, 345 (1945). 6. ROBBINS, I<. C., iirn. .T. Ph~lsiol. 142, 581 (1944).
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12. 13. l-1. t.i. 16. 17. 18. I!).
D.
F”ERRY,
M.
MILLER
AND
8.
SHULMAN
K., AND L~R~ND, I,., Science 108, 280 (1948). L~R~ND, L., Nature 166, 694 (1950). RIIH~YI, E., Acta Chem. &and. 4, 344 (1950). SHULMAN, S., AND FERRY, J. D., J. Phgs. d%Colloid Chern. 55, 135 (1951). WARE, A. G., GUEST, RI. M., AND SEEGERS, W. II., Arch. Biockem. 13, 231 (1947). FERRY, J. D., BND SHIJLMAN, S., J. Am. Chem. Sot. 71, 3198 (1949). SAWYER, W. Il., AND FERRY, J. D., .I. Am. Chem. Sot. 72, 5030 (1950). ADIXR, F. T., SAWYER, IV. M., .4m FERRY, ,J. D., J. Applied 1%/s. 20, 1036 (1949). b%RRy, .I. I)., S:A\I'YEH, \v. &I., ANI) ASHWORTH, J. N., b. PO&W kki. 2, 5% (1947). PORTER, I<., AND I~AWX, (2. v. Z., J. Ezptl. Med. 86, 285 (1947). FERRY, .I. D., Advanws in Protein Chem. 4, 1 (1948). STXINEK, R. F., AXI) LAKI, K., J. Am. Chem. Sot. 73, 882 (1951). ~+ULMAS, s., EHR~,KH, I’., ANI) T~F:KRY, .J. D., ,I. .4m. Chem. A%%.73, 1388 (1951).
7. LAKI,
8. 9. 10. 11.
J.
t.he Ijepadwlent
ef Chemistry,
IUniversity
Received
IJJ” Il’isconsin,
Jifcldison,
Ib*isconsin
June 13, 10.51
The most striking physical change accompanying the conversion of fibrinogen to fibrin is the development of rigidity. From measurements of this property and its dependence on temperature and other variables, conclusions can be drawn concerning the structure of the fibrin clot. In an earlier study (I), rigidities were reported for clots formed from human fibrinogen under different conditions of concentration and PH. These rigidities were measured by the method of transverse wave propagation (2,3), which provides values corresponding to mechanical deformations of very brief duration, of the order of a millisecond. The present investigation was undertaken primarily to study the effect of temperature on rigidity and also to compare dynamic or shorttime measurements with static measurements which can be extended for minutes or hours to determine whether stress relaxation occurs (4). Bovine rather than human fibrinogen was employed. It was found that, the mechanical properties, particularly as revealed in stress relaxation over long intervals, are markedly altered by the presence of calcium. An effect of calcium had already been detected in the tensile strength measurements of Wagreich (5) ; and the qualitative dissolution studies of Robbins (6), Laki and Lorand (7,8), and Mihalyi (9) indicate that’ when t#hrombin act’s in the preecnce of calcium together wit’h an unidcntified serum factor structural bonds are formed whose charact,er is different from those formed by thrombin alone. Our present studies of Fibrin and the Coagulatioll 1 This is paper Xo. 9 of a series on “The Fornlation of Blood” from the University of Wisconsin, supported in part hy research granb from the National Institutes of Health, Public Health Service. 2 Present address: Film Ihpartmmt,, R. f. tlu I’ont, de Scnmurs and Co., l~11ITaic1, -\‘. Y. 424
FIBRINOGEN
TO
FIBRIN.
VII
425
support the conclusion that different bonds are formed, and suggest that they are additional t.0, rather than replacements of, the structural bonds formed by thrombin in the absence of calcium.
Uovine fraction I and thrombin were obtained from Armour and Company. Two preparat,ions of fraction I, C-757 and 120-18, which contained 7(r-730j0 clottable protein, were used without further purification in some experiments. Two types of refractionated fibrinogen were also employed: fraction I-2, prepared from 129-18 by alcohol fractionation as previously described (10); and fraction I-S, prepared from another .2rmour lot (128-63) by precipit,ation at 0” at ionic strength 0.08, following essential11 the method of Seegers (11). Fractions I-2 and I-S contained 89-91~~ and 855867c clottable protein, respectively. The mechanical properties of clots formed from fraction I, fraction I-2, and fraction I-S were qualitatively similar. Thrombin C-173B I’rom Armour and Company, containing 4.7 urrits/mg., was used for all esperimcnts except those with fraction I-S. For the latter, we employed a highly purified thrombin which was very kindly given us by Dr. W. H. Heegers. This material, which contained about 850 units/mg. on the basis of comparison with the Armour material, was diluted with 280 times its weight of crystallized bovine serum albumin (to minimize adsorption losses in solution) and stored as a frozen solution containing 60 units/ml. The assay of fibrinogen and the preparation of protein solutions were carried out as previously described (10,12). The concentration of sodium chloride was always 0.45 .lf, csxccpt. for fibrin clots formed at pH 6.2 in the absence of calcium; here the sodium chloritlc was 0.40 M and an additional ionic strength of 0.05 dl was contributed by ptiosphat P buffer. Stock solutions were clarified by filtration through Republic Seitz filter patls (previously washed with sodium citrate solution, to avoid introduction 01 traacs of calcium, and t,hcn with solvent). The systems described are calcium-free unless othrr\visc spcc~ifcd. (‘lots were always formed %VL sitrh by mixing fibrinogen and t~hrombin solutions and rompleting assembly of t,he apparatus well in advance of the moment of clotting. The clotting time for a solution containing 10 g. fibrinogen’l. was of the order of 5.0 min. at pH 6.2 and 3.5 min. at pH 7.0. Concentrations of clots are given as grams fibrin per lit,er (assuming complete conversion of fibrinogeri to fbrin). ignoring the prcsrncc of &her protein.
Measurements of wave propagation were ma& as previously described (1,2), in a cell with dimensions 2.5 X 5 X 6 cm. In this m&hod, transverse waves of small amplitude are generated by oscillatory motion of a thin plate in its own plane. The resulting strain double refraction gives a wavy pattern ~vhrn viewed with stroboscopic polarized light flashing with the same frequency as the vibration, passing through a double quartz wedge. The wavelength, A, and damping in&x. X,‘x,, (where x0 is the distance within which the wave amplit~ude falls off bv a f:tct,or of l/e) are obtained b? measurements on a photographic film. The wave rigidity, 6, is given by thr product A*& where Y is the frequencv and p the density.
426
J. D. FERRY,
M. MILLER
AND
S. SIIULMAN
Only fine, or transparent clots, prepared at pFI 7, wclre studied by t,his method, since transmission of light is essential. The behavior of the librin in x&vc propagation, as contrasted nit,h gelatin (2) and high polymer solut.ions (is), WM charactrrixed b> t,wo features: a high strain-optical coeffiickt, and tt low damping ind(~s. 1kc:ausc 01 the high strain-optical cocfficicnt, it. \vas n~essary t,o rchducarsthp amplitudr of mot,ion of the moving plate to an unusually low rscursion to obtain suit,ablc wave patterns. Anot,her consequence was distortion of the 13abint:t lincxs upon changing the temperature, due apparently to residual skrssrs acac*ompanying tjhc~rmal espansion or contraction of the gel as it was constrained in tho rectangular container. This did not seriously interfere with measurements for a cshange of 20”, however. Because of the low damping index, it was necessary to restrict, measurrmrnt,s to short wavelengths (<0.8 cm.) to avoid errors due to &lectior~ from th(a opposit,e end of the cell (14). Results are reported as the wave rigidity, G; since the damping is so slight, this is negligibly different, from G’, the real part, of t~he romplcs ~nodulus of rigidit,y (1.5). 1Ieasurcmcnts of st,atic* rigidity and of Aress relaratioll were made in a coaxial cylinder apparatus described elsewhertl (4). The outer cnylintlflr was rot,atetl through a small angle (Ed), and the inner csylinder, supported by a very stiff suspension, responded with a much smaller angle 0~. The average shear strain in the clot was about 1O0/0 or less. The ratio of stress to strain, whirh in the absence of stress relasation is the modulus of rigidity, was obtained from t,hr expression kQ~/h(Ba - 8s). where k is the torsion constant of thr, suspension and I) is :m apparatus constant involving the dimensions of the cylinders. Stress relaxation was measured by holding BA fixed and following t,he change in eR with time. Since BB was always much smaller than 0.4, the procedure corresponds to relaxation at essentially constant strain. In most, cases rcvcrse relaxations were also followed, according t,o t,he procedure described in detail for studies of grlat,in gels (4). Bot,h t,,vpicaal fhc clots, formed at pII 7.0, and typical coarse clot,s, formed at pIT 6.2, \vere investigated. As in the gelatin erperimcnts (4), the clot was always covered 1,~ mineral oil, and at, the end of each c~xperiment the syst,cnl was inspcctc~tl for conc(‘ntricity mtl at)srnccb of any obvious bn&rial action. RESCLTS
In each clot at several different the limits of 100 frequency within reported.
OF DYKAMIC
RIGIDITY
MEASTTREMENTS
each t’emperature, the wave rigidity was measured at frequencies covering about a twofold range between and 1000 cycles/see . ; the results were independent’ of this range, and were averaged to give the values E$ect of Temperature
After formation of a clot at 25”, it was allowed to stand at that temperature for several hours to permit nearly complete development’ of rigidity, which increases for a long time after the moment of clotting (1). The rigidity was measured at 25”; then the temperature was lowered to 5” or 10” and maintained there for 2 hr., which was found
FIBlZINOGEN
TO
FIBRIP;.
T-II
127
to be long enough to permit the rigidity to attain a new value charact’eristic of this temperature. A series of measurements was t’hen made at different temperatures, each preceded by about’ 2 hr. equilibration, ending at 25” to check the original measurement. The second measurrment at 25’ was usually slight,ly higher (3-15’:s) than the first, indicating some continued tea&on. In some c:ws the rigidity was mcasured at 30”, but Ihe clots could not, be taken to higher tcmpcraturcs than this without causing irreversible changes as shown by a marked drop in the rigidity at 25” measured afterward. The rigidity always increased with decreasing temperature but appeared to be reversible within the range studied. In Fig. 1, t,he logarit’hm of rigidity is plotted against the reciprocal absolute temperature for clots containing from 3.8 to 17.2 g. fibrin4 At, 9.5 g./l., the sequence of the different temperatures is indicated. Here the second measurement at 25” is 10% higher than the first, and appears to fit bet’ter with the data at other temperatures. The behavior at the ot’her concentrations was similar, and t,hc initial 25” points have thcreforc been omitted
2.5
I
3.2
1
3.3
I
3.4
3.5
I
3.6
3.7
1000/T
Fro. 1. Logarithm of bvavc rigidity plot&d against reciprocal of absolute temperature, for clots formed at. 25°C. from fraction I, l’repn. C-757, thrombin 0.95.unit/ml., pH 6.97-7.01, ionic strength 0.45. Fibrin concentrations as follows: 1, 17.2 g./l.; 2, 13.3 g./l.; 3, 10.9 g/l.; 4, 9.54 g./l.; 5, 6.70 g/l.; 6, 3.81 g./l. The small numbers along line 4 indicate t#he serial order of measurrments at different t,emperatures.
428
J.
D.
FERRY,
M.
MILLER
AND
S. SHULMAN
from the other plots. A series of straight lines is obtained whose slopes increase with concentration. The value of R d In c/d(l,/T) ranges from 2.8 to 5.6 kcal./mole. The change in rigidity of fibrin with temperature is thus similar to that of gelat,in in direction, but is far less in magnitude, and the rigidity does not, of course, vanish (corresponding to melting) at, any temperature which can be achieved without denaturation. Other preparations of fibrinogen gave clots whose rigidit’ies differed in magnitude somewhat from those shown in Fig. 1 but had a closely similar temperature rlependenco. In a few cases, clots were formed al 15” instead of 25”; the rigidities of such clots were higher at all temperatures by about 5054, but, again showed t,he same t#emperature dependence and reversibility. Eflect o.f Concentmtion The logarithm of rigidity at 25” is plotted against the logarithm fibrin concarntration in Fig. 2 for clots formed from two preparations
1
0.6
0.4 Log
Fibrm
0.8
I .o
Concentration
of of
1.2 I” c~ /I
FIG. 2. Logarithm of wave rigidity at 25°C. plotted against logarithm of concentration of fibrin, for clots formed at 25°C. from fraction I, Prepn. C-757 (line 1) and 129-18 (line 2). Thrombin 0.95 unit/ml., pH 6.Q7-7.01, ionic strength 0.45. Lines 1 and 2 are drawn with a slope of 2.3. Line 3 represents results on hmnan fibrin [Ref. (l)], pH 6.8, ionic strengt,h 0.30, thrombin 1 unit/ml.
fraction I. In each case the rigid&y is proportional to the 2.3 power of the concentration, though the values for the t’wo preparations differ by about 20yG. A plot for huma.n fibrin at a similar pH, from Ref. (I), is included for comparison; the values :IW considcrabIJ- higher, hilt Ihc slope is less, about’ 1.fi. So fundnmcntnl significance can be attached to t’he slope, however, since it varies wirith temperat.ure (as a corollar\- to the observation in Fig. I t’hat the tkmperature dependence \-arks with concentration). This beha\-ior tlilfers markedly i’rom that of gelatin gels, in which the rigidity is closely proportional t.o thrl square of t,hc concentration over a considerable range of tempwaturcs. Elffect of ~‘nlciu~rn Measurements were made on clots formed from fraction I-S both without calcium and in the presence of 0.01 A4 calcium chloride. These
3.4
I
3.5 1000/T
3.6
?
Fro. 3. Logarithm of wave rigidity of clots formed at 25°C. f'lo~n refractionatetl fibrinogen I-S with 0.01 M CaCl, (curve 1) and without (curve 2), plotted against reciprocal absolute temperature. Fibrin concentration 9.5 g./l., thrombin 0.95 unit,’ ml., pH 7.00 f 0.04, ionic strength (exclusive of CaClJ 0.45. Taggecl points refer to static measurements.
two clots were soluble and insolublr:, respectively, in 3.3 M urea; a concentration of 1O-3 M calcium sufficed to prevent, dissolut,ion of clots formed from this fraction, which evidently contained the serum factor of Laki and L&And (8). The data from one such comparison are shown in Fig. 3; a second experiment gave similar results. The rigidity of the insoluble clot showed less temperature dependence and was higher than t,hat of t,hc soluble clot by a factor of 1.5 at 5” and a factor of 1.9 at 2.5”. The 25’ points represent measurements about 12 hr. after clotting.
430
d. D. FERRP, M. MtI,I>ER AND S. SHTJLMAh-
Although without calcium the deveiopment of rigidity was substantially complete at t,his time, in the clots cont.aining calcium the rigidity was still slowly increasing. Marc pronounced effects of calcium are revealed in st.atic measuremen@ as described below. RESULTS OF STATIC RIGIDITY ASD STRESS RELAXATION ~VEASUREMENTS
Whereas the wave propagation method measures the rigidity within a time interval of a milliswond, the most rapid measurement possible in the static coaxial cylinder apparatus involves a time lapse of several seconds. In calcium-free, urea-soluble clots, the stress relaxes so quickly aft,er a strain is imposed t,hat no equilibrium rigidity measurement,s arc) possible. This surprising result indicates unespect,ed lability of a large proportion of the st’ruct8ural linkages. In urea-insoluble clots, the stress, while not constant,, relaxes slowly enough aft’cr imposition of strain so that it can be extrapolated to zero time to provide an instantaneous value for the rigidity; this agrees reasonably well with the dynamic value obtained from wave propagation, as illustrated by two point’s in Fig. 3. ?itress Kflazatiotz itb Calcizrm-Free ~‘dots .Ut,hough the stress relasat’ion following sudden strain of a calciumfree clot is too rapid to follow at first, the decay aft.er t.he first, felr minutes can be described by recording the ratio of shear stress to strain (which would give the instantaneous rigidity if it could be extrapolat,ed t,o zero time) as a function of time. This was done for clot’s formed from both fraction I and refractionated I-2 at pH 6.2 and 7, as well as from refract,ionated I-8 at pH 7, at various temperatures. In each experiment, t’he clot was formed at 25’ and allowed to stand at this temperat’ure for several hours. h strain was imposed and the stress was allowed to relax for about, 40 min., during which time it decayed to a small fraction of its init,ial value. This relaxation may be attribut,ed to dissociation of structural linkages. -4s in the case of gelatin (4), some of t,hese linkages must form again, or rearrange, corresponding to network strands in unstrained configurations; because when the strain was returned to its original position aft’er relaxat,ion, a reverse stress appeared, somewhat smaller in magnit~ude than t,he original stress and opposite in direction. The rclasation of the wvcrsc st,rcss was then followed, represent,ing dissociation of linkages formed during the period
FIRRINOGEK
TO
FIBRIN.
431
VII
of the first relaxation. A pictorial represent’ation of this type of experiment is given in Fig. 1 of Ref. (4). After completion of relaxation and reverse relaxation at 25”, measurements n-ere made at’ several other
6
-
3
-0.5 Logartthm
of Time
I” Mmules
4. Stress relaxation of fibrin from rcl’ractionatcd fibrinogen I-2, pH 7.01, ionic FIG. strength 0.45, fibrin 9.5 g./l., thrombin 0.95 unit/ml. The numbers opposite curves denote serial order of m~asurrments at tcmpwxturri indicated.
temperatures, each preceded by equilibration for about 2 hr., and finnllJ again at 25”; the course of the last relaxation at 25” agreed reasonably well with the first. The ratio of shear stress t,o strain is plotted against the logarithm of time elapsed since imposition of strain in Figs. 4 and 5 for clots formed t 0 x
I
I ond 5 = 25 0” C 2 = IO S’C
0 Logarithm
of Time
I” Mmutes
FIG. 5. Stress relaxation of fibrin from refractionated fibrinogen I-2, pH 6.20, ionic strength 0.45, fibrin 9.5 g./l., thrombin 0.95 unit/ml. The numbers opposite curves denote serial order of measurements at temperatures indicated.
43’
J.
D.
FERRY,
M.
lMII,LEK
AND
S.
SHULMAN
from fraction I-2 at pH 7.01 and 6.20, respectively. The rate of relaxation increases rapidly wit’h temperature. Although the stressjstrain ratios are somewhat higher at, pH 6.20 bhan at 7.01, the course of the relaxation is similar in both cases, which is perhaps surprising in view of the marked difference in structure betSn-een these coarse and fine clots as revealed by opacity and syneresis (1) and electron microscopy (16). Relaxation curves for clots formed from fraction I and fraction I-X in the absence of calcium were similar. Representative curves for reverse stress relaxation at pH 6.20 are given in Fig. 6. Though the stresses are smaller, the course of relaxation closely resembles tha,t in Fig. 5, so the linkages formed during the initial
Logorllhm
of Tome I” Mtnufes
FIG. 6. Reverse stress relaxation of fibrin from refractionated fibrinogen I-2, pH 6.20, ionic strength 0.43, fibrin 0.5 R./I., t,hrombin 0.95 rurit~/ml. Tempw~tnres: 1, 10.8”C.; 2, 15.6”; 3, 20.3’; 4, 25.0”.
relaxation are evidently similar in character to those present initially. This fact, together with the reversible t,emperature dependence of both the dynamic rigidity and the stress relaxation, indicates t’hat at least some of the structural linkages are in a slow dynamic equilibrium, dissociating and rearranging with relaxation times (or half-t#imes) ranging from 10-l to lo3 sec.
Relaxation curves for a clot, formed from fra&on I-2 at pH 6.20 with 1OV M calcium and one formed from fraction I-S at ~1-16.98 with 10W2M calcium are shown in Fig. 7. These calcium concentrations are
FIBRISOGEK
TO
FIIIRIK.
VII
-133
about ten times t’he values required to prevent t&solution, in 3.5 X urea, of clots formed from these two preparations. The relaxation is far slower than without’ calcium, :rnd the stress decay;; by only about 20yCj in 400 min. Relaxation is depictBed at two temperatures for each clot, and the curve for the higher t,emperat)nre is slightly higher in each
o:
0
2 Logotllhm
of Time
VI Minutes
FIG. 7. Stress relaxation of fibrin containing calcium, at temperatures indicated. Open circles: refractionated fibrinogen I-2, pH 6.20, calcium 0.001 X. Filled circles: refractionated fibrinogen I-S, pH 6.98, calcium 0.01 M.
case. This is undoubtedly due to t,he fat% that the experiment was performed first at the lower temperature, and a slight increase in rigidit\ occurred during the long time required for following these slow relaxations. The presence of calcium, together with the serum factor of Laki and L&and whose presence must be inferred from the urea insolubility of these clots, affects the stress relaxation far more than does temperature or pH. In spite of this marked effect, clot,s formed with and without calcium in the amounts involved here are very similar in appearance and have almost identical clotting times.
The rigidit,y measures the resistance to elastdc deformat)ion of t,he network structure of which fibrin is known to be composed (16). Calculations for human fibrin have shown t,hat t,his rigidity is too high to be attributed to rubberlike elasticity mechanisms (l), and the same arguments are applicable to bovine fbrin. The rigidity presumabl) involves the inherent stiffness of the network strands, but the det,ailed mechanism is not understood.
434
.J.
D.
FERRY,
M.
MILLER
AND
S.
SHULMAN
The hypothesis has been advanced (1,17) that the network is bound together with primary chemical bonds. The more recent demonstrat,ion that fibrin can be dissolved in urea to yield fragment,s very similar to the original fibrinogen in size and shape (18,19) does not necessarily invalidate this hypothesis, although it severely restrict’s the types of chemical bonds that might be involved. Our present mechanical mcasurements, however, indicate that some (though probably by no means all) of the bonds constituting the network in calcium-free clots arc relatively weak secondary bonds. This conclusion is supported by thcl reversible decrease in rigidity with increasing temperature, t)hc rapid stress relaxation and its marked dependence on temperature, and the reverse stress, indicating newly formed bonds which relax in turn much like those they have replaced. It would be attractive to identify these weak and easily rearranged bonds with secondary associations among the long linear fibrils which are seen in the electron microscope. Such associations would not depend on the action of thromhin, which can hardly be involved in t’he formation of t,he new bonds that are revealed by our reverse stresses. On t,he other hand, the bonds within the fibrils themselves, which unite the fibrinogen residues t,ogether, and for which thrombin is directly responsible, may well be of a stronger character. In the presence of calcium and serum factor, the network is joined by bonds of a far more permanent nature. The comparison in Fig. 3 indicates that these bonds are additional to the associations formed in t,ha absence of calcium. But from the very slow relaxat’ion shown in Fig. 7 it appears that even the weak associations are considerably strengthened in the presence of calcium, and their relaxation times greatly increased, while it is probable that a substantial fraction of the network structure undergoes no rearrangement at all within a period of several hours. The observations of Lhr&nd (8) suggest that the additional bonds may be disulfide links. Further measurements of mechanical properties should prove valuable in elucidating the role of calcium and serum factor in modifying the structure of fibrin clots, and they will be continued when more information is available concerning the isolation and characterization of the serum factor. ~~CKNOWLEDQMENTS
FIBRINOGEN
TO FIBRIN.
VII
435
of the Iiniversity of Wisconsin from funds supplied by the LVisconsin Alumni Research Foundation; and by a grant, from Eli Lilly and Company, for which WC are most grateful. R’c are indebted t,o 1Ir. n’arrcn I<:. Evans and Mr. George E. Heckler fol help wit,h some of the experiments.
1. Dynamic rigidity has been measured by the method of wave propagation in bovine fibrin clots at pH 7.0 at’ various fibrin concentrations and temperatures, and in the abstnce and presence of small amounts of calcium. Static rigidity and stress relasa,tion have been measured at, pH 6.2 and 7.0 at various temperatures with and without calcium. 2. The dynamic rigidity without calcium decreases reversibly with increasing temperature between 5” and 3O”C., and at 23” is proportional to the 2.3 power of the fibrin concentratOion. The addition of small amounts of calcium (in the presence of the serum factor of Laki and L&&d, as deduced from insolubility in 3.5 M urea) increases t,he rigidity somewhat’ and diminishes the temperature dependence. 3. In the presence of calcium, t(he dynamic rigidity (corresponding to measurement within a millisecond) agrees wit8h the stat’ic rigidity (corresponding to measurement within several seconds). In the absenw of calcium, the static rigidity cannot be determined because of rapid stress relaxation. 4. The rate of relaxation of stress in clot’s formed without calcium increases rapidly with increasing t#emperature; when the strain is returned to zero after relaxation, a reverse stress appears which in turn relaxes. 5. The rate of relaxation of st,ress in clots formed with calcium is extremely small. 6. The results indicate that in clots formed without calcium some of the linkages which compose the network are weak associations which can easily rearrange. In clots formed in the presence of calcium (and serum factor), the network strands are joined by bonds of a far more permanent nature. REFERENCES I. FERRY, J. D., ANU MORRISON, I'. R., .I. An,. Cl~cw. SW. 69, 388 (1!)47). 2. FERRY, .J. D., Rev. Sci. Znstru~wzts 12, 79 (1941). 3. FERRY, J. D., AND ELDRIDGE, J. E., J. Phy/s. & Colloid Chenl. 53, 184 (1949). 4. MILLER, X1., FERRY, J. D., SCHREMP, F. TV., .~ND ELDRIDGE, .J. E., J. Phys. K: Colloid Chem. 55 (in press). 5. WAGREICH, H., AND TARLOV, I. M., Arch. Hiochem. 7, 345 (1945). 6. ROBBINS, I<. C., iirn. .T. Ph~lsiol. 142, 581 (1944).
436
12. 13. l-1. t.i. 16. 17. 18. I!).
D.
F”ERRY,
M.
MILLER
AND
8.
SHULMAN
K., AND L~R~ND, I,., Science 108, 280 (1948). L~R~ND, L., Nature 166, 694 (1950). RIIH~YI, E., Acta Chem. &and. 4, 344 (1950). SHULMAN, S., AND FERRY, J. D., J. Phgs. d%Colloid Chern. 55, 135 (1951). WARE, A. G., GUEST, RI. M., AND SEEGERS, W. II., Arch. Biockem. 13, 231 (1947). FERRY, J. D., BND SHIJLMAN, S., J. Am. Chem. Sot. 71, 3198 (1949). SAWYER, W. Il., AND FERRY, J. D., .I. Am. Chem. Sot. 72, 5030 (1950). ADIXR, F. T., SAWYER, IV. M., .4m FERRY, ,J. D., J. Applied 1%/s. 20, 1036 (1949). b%RRy, .I. I)., S:A\I'YEH, \v. &I., ANI) ASHWORTH, J. N., b. PO&W kki. 2, 5% (1947). PORTER, I<., AND I~AWX, (2. v. Z., J. Ezptl. Med. 86, 285 (1947). FERRY, .I. D., Advanws in Protein Chem. 4, 1 (1948). STXINEK, R. F., AXI) LAKI, K., J. Am. Chem. Sot. 73, 882 (1951). ~+ULMAS, s., EHR~,KH, I’., ANI) T~F:KRY, .J. D., ,I. .4m. Chem. A%%.73, 1388 (1951).
7. LAKI,
8. 9. 10. 11.
J.