1206
DAVID F. WAUGH AND BETTY J. LIVINQSTONE
trometer Section for mass spectrographic analyses; to J. F. Shultz, B. Seligman, and the operators of the Catalyst Testing Section for the activity data; to W. Oppenheimer for chemical analyses of the catalysts; and to W. K. Hall, who duplicated the induction of some of the catalysts and made surface-area measurements. REFERENCES (1) ANDERSQN, R.’B., KRIZG,A., SELIGMAN, B., AND O’NEIL,W. E.: Ind. Eng. Chem. 89,
1548 (1947). (2) CLARK, E . L.,KALLENBERGER, R . H . , BROWNI,R . Y., AND PHILLIPB, J. R.: Chem. Eng. Progress 46, 651 (1949). (3) ELMORE, W . C . : Phys. Rev. 64, 309-10 (1938). (4) FISCHER, F., A N D TROPSCH, H . : Ges. Abhandl. Kenntnis Kohle 10,313 (1930). H.,AND LONGUET, MLLE.J . : Compt. rend. 208, 1729 (1939). (5) FORESTIER, (6) HOFER, L. J. E., COHN,E . M., A N D PEEBLES, w. c.:J.Am. Chem. SOC.71, 189 (1949). W . C., A N D DIETER,W . E . : J. Am. Chem. SOC. 68, 1953 (7) HOFER,L. J. E., PEEBLES, (1946). (6) KRIEG,A , , DUDASH, A,, AND ANDERSON, R . B . : Ind. Eng. Chem. 41, 1508 (1949). MLLE.J.:Thesis, University of Strasbourg, Series E, No. 72, 1943,p. 34. (9) LONGUET, W.O.,A N D HOLMES, J . : J. Am. Chem. SOC. 83, 149 (1941). (10) MILLIGAN, H . : “The Synthesis of Hydrocarbons from Carbon Monoxide and Hydrogen,’! (11) PICHLEH, U. S. Bureau of Mines Special Report, p. 76 (1947). (12) STORCH, H. H., ANDERSON, R. B . , HOFER,L . J. E., HAWK,C. O., ANDERSON, H. C., . ~ N DGOLUMBIC, K.:U. S. Bur. Mines Tech. Paper No. 709.
KINETICS OF T H E INTERACTION OF BOVINE FIBRINOGEN AND THROMBIN DAVID F. WAUGH
AND
BETTY J. LIVINGSTONE
Deparcment of Biology, Massachuserts Institute of Technology, Cambridge, ~?!fassachwetts Received July IS, 1960
The last steps in the clotting of blood or plasma (21) are the interaction of thrombin and fibrinogen and a subsequent association of the latter to form elongated fibrils of variable width. The rigidity of the resulting clot is probably due to the cross-linking of such fibrils (7). Of considerable interest are the mechanism by which fibrinogen modification takes place, the nature of the intermediate product, and the kinetics and bonds involved in fibrin formation. Heretofore studies of reaction kinetics agreed that fibrin formation appeared to follow pseudo-first-order kinetics (6, 11, 13). Available evidence indicates that no estensive structural alterations take place upon fibrinogen activation or fibrin formation (1, 12, 16, 24) and thus that fibrin, just aa fibrous insulin (29), represents linked corpuscular units. A technique has been developed by which the clotting reaction may be stopped quantitatively during its course and the resulting complex of nonclottable pro-
INTERACTION OF FIBRINOGEN AND THROMBIN
1207
tein, fibrinogen, and fibrin fractionated and analyzed. The authors have used this technique to study the kinetics of the waction with respect to thrombin concentration and fibrinogen concentration, keeping other variables constant. The evidence so obtained may be interpreted in terms of a constant descriptive of the reaction rate and a reversible combination of thrombin with fibrinogen and fibrin. It is hoped that other variables may be included as data become available. MATERIALS AND METHODS
Materials Fibrinogen: Armour bovine Fraction I, Lot C739, prepared according to the methods of Cchn et al. (3) and containing approximately 65 per cent protein, of which 73 per cent was clottable. The nonprotein material was mainly sodium citrate. Of the total nitrogen, 0.G per cent was nonprotein nitrogen. Thrombin: Armour Lot P35, containing 21.2 N.I.H. units per milligram.' F m a l d e h y d e : Merck U.S.P. formaldehyde, containing 37 per cent formaldehyde and 10 per cent methanol. This material was diluted to20 per cent and used without further purification. Bufler solution: A phosphate buffer (2, 8) having a pH of 7.0 mas used. Where necessary the fibrinogen solutions were passed through a sintered-glass filter. The total added ionic strength was 0.15 (phosphate, 0.05; sodium chloride, 0.1). The final pH of the reaction mixtures was 6.85. The temperature was 22.7"C. Symbols: 6 = fibrinogen concentration expressed as milligrams of clottable nitrogen per milliliter; Th = thrombin in N.I.H. units per milliliter; $0 and Tho are the initial fibrinogen concentration and the total thrombin concentration. Methods I n several of the methods (see references in 17) used to follow the clotting reaction the clot is compacted mechanically and analyzed by dry weight or for nitrogen content, a difficult process where small aliquots are involved. The authors have preferred one which analyzes the supernatant after clot compaction. Effect of formaldehyde o n clotting and compaction: In previous work (31) it was found that formaldehyde decreases the clotting rate even when a11 components are mixed simultaneously. Under such conditions 1.8 per cent formaldehyde prevents clotting at least up to 0.36 mg. of clottable nitrogen per milliliter, the maximum value used, even a t 22.5 units of thrombin per milliliter. That clotting is blocked in partially clotted systems is shown by the fact that, with few exceptions, supernatants after clot compaction form no additional clot or material sedimentable at 35,000 g. As found previously for lower formaldehyde concentrations, 1.8 per cent formaldehyde does not block compaction as rapidly as it causes inhibition of clotting. Adsorption of thrombin: Clean glass vessels cause a disappearance of active 1 See the Minimum Requirements for Dried Thrombin, Second Revision, The Division of Biologics Control of the National Institute of Health, Bethesda, Maryland.
1208
DAVID F. WAUGH AND BETTY J. LIVINGSTONE
material, 1 unit of thrombin per milliliter losing 30 per cent of its activity in 30 a: thin layer of paraffin reduced the loss to about 5 per cent. Clean celluloid tubes gave losses of about 10 per cent in 30 or 60 min. and paraffining reduced these to less than 5 per cent. Essentially the same results were obtained with 0.1 unit per milliliter, the percentage losses in the paraflined vessels being somewhat larger (15 per cent in 1 hr.). Treatment with paraffin and silicone are comparable. Therefore all of the vessels may be capable of adsorbing considerable amounts of thrombin. In the reaction vessel, adsorption may be reduced by the presence of other proteins; gelation limits adsorption to diffusion of thrombin to the vessel walls. Experimentally a solution at 75 units of thrombin per milliliter is kept quiescent. It is diluted to appropriate strength and used within 120-180 sec. min. and 70 per cent in 1 hr. Coating with
.,...... 0
I
240
2%
2SO
WAVE LENGTH FRACTION-I =
0
270
280
290
.
300
Mp NON CLOTTABLE PROTEINS0
FIQ.1 . Ultraviolet absorption spectra of Fraction I and nonclottable protein: 0 , Fraction I ; 0 , nonclottable protein.
I n the final technique used, 20-ml. lusteroid tubes, coated with paraffin, contain fibrinogen solution which is brought to temperature and clotted by addition of thrombin. A sample is terminated by agitating with a plunger consisting of a stainless-steel shaft on the end of which is a rounded plastic head having a 0.5-mm. annular clearance with the tube. The first disturbance, ca. 4 sec., compacts the clot, after which sufficient 20 per cent formaldehyde is distributed to give a final concentration of 1.8 per cent. The clot is removed by centrifugation for 2 min. at 400 g. Analysis of supernatants: The optical density of the supernatant was determined a t 2800 A. in a cell 0.998 cm. long. From the total was subtracted that due to the nonclottable protein. Figure 1 shows the absorption curve ( 0 ) for Fraction I containing 0.112 mg. of clottable nitrogen per milliliter, and the absorption curve ( 0 ) for the nonclottable protein obtained by clotting a solution of Fraction I a t 60 = 0.373 mg. of clottable nitrogen per milliliter. Both curves have maxima near 2800 A.
INTERACTION OF FIBRINOQEN AND THROMBIN
1209
I n figure 2, linear relationships between optical density and nitrogen content are shown for total Fraction I (curve 1) and nonclottable protein (curve 2). Curve 3, obtained from curves 1 and 2, indicates the optical density of fibrinogen. Nitrogen values were obtained by micro-Kjeldahl d y s i s . The presence of 1.8 per cent formaldehyde increases optical densities uniformly by about 3 per cent.
MG N / M L
FIG.2. Optical density a t 2800 1.t ' s . nitrogen content forFraction1 (curve I), nonclottable protein (curve 2), and that calculated for fibrinogen (curve 3).
FIG.3. A typical reaction curve. 90 = 0.18 ml. of clottable nitrogen per milliliter; Tho 0.045 unit of thrombin per milliliter (curve 1). Curve2 represents the same reaction run in the presence of 1.54 per cent purified gum acacia. =
EXPERIMENTAL
Typical reaction curve
Curve 1 of figure 3 shows a typical reaction curve obtained by clotting a solution of Fraction I, &o = 0.18 mg. of clottable nitrogen per milliliter, with 0.045 unit of thrombin per milliliter. 0 represents the fraction of total clottable nitrogen remaining in the supernatant at time t . A pseudo-first-order reaction was assumed in plotting figure 3. From 0 to 2.5 min. insufficient fibrin is present to give a compactable clot and In l/e is at zero. Between 2.5 and 5.5 min. In l / O follows a smooth curve joining the abcissa and a linear portion behond 5.5 min., the extrapolation of which passes through the origin. The difference between corresponding ,points on the nonlinear portion and the linear extrapolation is felt to
1210
DAVID F. WAUGH AXD BETTY J. LIVINGSTONE
represent the accumulation of intermediate and noncompactable fibrin. Linearity is established when sufficient compactable fibrin is present to keep the concentrations of these components at negligible values. Curve 2 of figure 3 supports this interpretation. Here is shown a similar, and typical, reaction at 60 = 0.176 in the presence of 1.54 per cent purified gum acacia. Linear plots of different rate are obtained, but that in the presence of acacia has a much shorter nonlinear portion. It is evident that acacia has promoted compaction, suppressing residual intermediate and noncompactable fibrin. The clarity of the supernatants indicates that formaldehyde stops not only intermediate formation but the further linkage of intermediate and small fibrin particles. According t o Seegers and Smith (25), the presence of acacia increases the activity of thrombin to an extent greater than can be accounted for by the difference in slopes seen in figure 3. It is likely that the shorter clotting times observed are due in large part to the enhancing of compaction. (Reaction rate and clotting time will be treated elsewhere.)
0
w
40
eo
00
MINUTES
FIG.4. Linear portions of reaction curves for 4 0 = 0.185 mg. of clottable nitrogen per milliliter. Thrombin concentrations in units per milliliter were: curve 1, 0.454; curve 2. 0.227; curve 3, 0.091; curve 4,0.068; curve 5, 0.045; curve 6, 0.023; curve 7, 0.018; curves 8 and 9,0.009. Temperature, 22.7"C.
Since extrapolations of the linear portions of all reactions pass through the origin, these are considered to represent the formation of activated fibrinogen or an intermediate. Similar reactions run from the same stock solutions are highly reproducible, while some variability is observed from one experiment to the next. The variability increases as the aliquot of thrombin weighed out decreases, suggesting that small amounts of thrombin of equal weight differ slightly in total activity.
Reaction kinetics Two examinations have been made. The fibrinogen cohcentration has been held constant (+o = 0.185 mg. of clottable nitrogen per milliliter) and that of the thrombin varied over a fifty-fold range. The solid lines of figure 4 represent the linear portions of the reactions; the dotted lines extapolations. In figure 5 the slopes of the lines are plotted as ordinates versus Tho, giving the linear relationship, In A = 1 . 9 0 ~ h t 0
( 1)
INTERACTION OF FIBRINOGEN AND THROMBIN
1211
The reactions of figure 6 illustrate a set in which the thrombin is constant at 0.0454 unit per milliliter and $0 is varied over a tenfold range. Were equation 1 to describe the reaction completely, the slopes should be independent of $o. Tables 1 and 2 list data according to the sequence in which the experiments were performed.
INITIAL THROMBIN U./ML.
FIG.5 . Plot of slopes of curves of figure 4 us. initial thrombin concentration
1 0
10
20
30
MINUTES
FIG.6. Linear portions of the reaccion curves for Tho = 0.0154 unit of thrombin permilliliter. The fibrinogen concentrations were, in milligrams of clottable nitrogen per milliliter: curve 1, 0.036; curve 2, 0.075; curve 3, 0.088; curve 4, 0.11; curve 5, 0.182; curve 6 , 0355. Temperature, 22.i°C.
Consideration of the nonclottable protein The data of figures 4 and 6 indicate combination of thrombin with another component in the system. Since clottable and nonclottable components are present in a constant proportion in the experiments thus far, either could be responsible. The nonclottable protein present during a reaction has been increased by adding clot supernatant to fresh fibrinogen to give approximately 1.5 and 3 times the usual value. Supernatant mas obtained from Fraction I at +o = 0.714 mg. of clottable
1212
DAVID F. WAUQH AND B E m Y J. LIVINQSTONE
nitrogen per milliliter after clotting for 18 hr. with 0.054 unit of thrombin per milliliter. Ultraviolet absorption indicated the expected 0.264 mg. of nonclottable nitrogen per milliliter after clot compaction. No residual fibrinogen could be detected in the supernatants on adding additional thrombin. When supernatant was added to fresh fibrinogen no clot formed within 3 hr., a small amount appearing after 18 hr. Supernatant, Fraction I a t 0.383 mg. of clottable nitrogen per milliliter, and thrombin were mixed to give reaction solutions containing & = 0.176 mg. of clottable nitrogen, 0.125 mg. of nonclottable nitrogen, and 0.0454 unit of thrombin per milliliter and a second solution identical except for the nonTABLE 1 Slopes of linear portions of reaction curves obtained by plotting In bo/+ versw time in minutes 40 values are in milligrams of clottable nitrogen per milliliter; Tho = 0,0454 unit per milliliter
*'
REACTION CURVE SLOPE
~
REACTION CURVE SLOPE
.~
0.187 0.185 0.188 0.180
0.086 0.083 0.094 0.091
0.108 0.102 0.108 0.85
0.176 0.176 0.176 0.172
0.173 0.173 0.173 0.172
I
'
0.098 0.094 0.104 0.094
0.097 0.105 0.095 0.094
0.168 0.170 0.176
TABLE 2 Slopes of linear portions of reaction curves obtained by plotting In +o/+ versus time i n minutes 40 values are in milligrams of clottable nitrogen per milliliter; Tho = 0.0454 unit per milliliter
0.036 0.075 0,110
1
REACTION CURVE SLOPE
%
-
,
~
,
0.257 0.172 0.121
0.355
::::
1
'
~
REACTION CURVE SLOPE
_ _ 0.051 0.260 0.201
'
I _ ~ 0.100 0.068 0 335
~
REACTION
CW;El;3PE
_ 0.166 0.055
_
_
'
''
0.088 0.185 0.36
BEACTION CURVE SLOPE
_
~
~ ~ 0.155 0 091 0.052
clottable nitrogen, which w&s 0.186 mg. per milliliter, Appropriate controls a t 40 = 0.176, 0.065 mg. of nonclottable nitrogen, and 0.454 unit of thrombin per milliliter were run at the same time. The runs containing 1.5 and 3 times the usual nonclottable nitrogen produced lines whose slopes differed by less than 5 per cent from the control runs, which mere consistent in turn with figures 4 and 6. If nonclottable protein were responsible, the slopes should have been decreased by factors of 1.4 and 2.5, respectively. The above results also indicate that accelerating or inhibiting substances have been removed during fractionation. DISCUSSION
From the preceding, the variation in rate with 40 is to be attributed to an association of thrombin with fibrinogen or fibrinogen and fibrin. At least four
INTERACTION OF FIBRINOGEN AND THROMBIN
1213
mechanisms are possible: Type 1, active complex formation alone; Type 2, active complex formation with fibrinogen followed by inactive combination with fibrin; Type 3, active complex formation and inactive combination with fibrinogen and inactive combination with fibrin; and Type 4, inactive combination with fibrinogen and fibrin. The reaction curves exhibit certain important characteristics: reaction rates vary directly with the total thrombin concentration but as a more complicated function of the fibrinogen concentration. With the exception of initial portions all curves are linear when In +o/+ is plotted us. time up to values of In +o/+ = 3.0 or more, at which point the experimental error is usually significant. Extrapolations of all reaction curves pass through the origin. In the presence of acacia the rate is somewhat increased, but a linear plot of In +o/+us. time is obtained. From the molecular weights of fibrinogen (10, 19) and thrombin (26) and the activity of the latter (22), a solution containing the maximum thrombin and minimum fibrinogen used contains about 120 fibrinogen molecules per thrombin molecule. A general equilibrium constant for all combinations may be taken as
where + will be expressed in milligrams of clottable nitrogen per milliliter and Th in N.I.H. units per milliliter. For a more detailed discussion of the manner in which the following equations are derived and certain of their properties see Wilson (32) and Neurath and Schwert (18). The general approach may be illustrated by examining active complex formation alone (Type l ) . According to Michaelis and Menten (15), Th+ represents an active complex whose concentration governs the rate of the reaction. Equation 2 leads to:
where le1 is a rate constant measuring the decomposition of Th+ into enzyme and activated fibrinogen and K , is an equilibrium constant. The initial rate of a reaction is
where S is the slope of the linear reaction curve. Following Lineweaver and Burke (14), equation 3 may be inverted to give:
A plot of R-I us. + *: should give a straight line. The points of figure 7 are from table 2 , the cross being an average of table 1. The method of least squares and both tables were used to calculate the line shown, which has a slope of 2.32 and intercept of 45.7 f 0.5. From a plot of R-' us. 6-0' appropriate rate and equilibrium constants may be chosen for all mecha-
1214
DAVID
b. WAUGH
AND BE-
J. LIVINQSMNE
nisms which will account for the variation in initial rate with +o. Slopes and inter-
cepts are recorded in columns 2 and 3 of table 3.
“4
c
FIG.7. Plot of reciprocal of R = text.
- dgo/dt us. the reciprocal of 90.For details see the
TABLE 3 Columns 2 and 3 give slopes and interccpts of the lines obtained by plotting (initial rate)-’ versus The reaction types are given in the first column. Columns 4 and 5 list the corresponding values of A and B t o be used in equation 5. K., Ks, and K; are equilibrium constants for active complex formation, inactive combination of thrombin with fibrinogen, and inactive combination of thrombin with activated fibrinogen and fibrin. kl, kt, ks, and k, are rate constants. SLOPE -2.32
TYPE
RnEaCxFT
1.. . . . . . . . KJklTho
l/kiTho
2 . . . . . . . . . KJktTho
l/kzTho
-
45.7
3 . . . . . . . . . KJkrTho
4 . . . . . . . . . l/k,Tha
1/K &Tho
I
The linearity o j the reaction curves The difTerenCial rate equations for all types may be integrated and arranged in the form: ln
9
+
ii (+o
- 6)
= ~t
(5)
Table 3 (columns 4 and 5) lists the constants corresponding to A and B , in which K., Ka, and Ki are equilibrium constants for active complex formation, inactive combination of thrombin with fibrinogen, and inactive combination of thrombin with activated fibrinogen and fibrin. The reaction velocity is related to the concentration of active complex through the rate constants kl, k t , and ka in Types 1, 2, and 3. In Type 4 the free thrombin concentration is assumed to
INTERACTION OF FIBRINOGEN AND THROMBIN
1215
govern the reaction velocity according to the bimolecular equation:
The integrated equations should describe the course of the reaction. T y p e I : According to table3, k. = 0.051 and klTho = 0.022. A is therefore 19.7 and B is 9.5Tho (since Tho = 0.0454). A reaction for $18 = 0.18 mg. of clottable nitrogen per milliliter and Tho = 0.0454 unit of thrombin per milliliter, proceeding according to equation 5 but plotted as In +o/+ us. t, is shown in curve 2 of figure 8, to be compared with the experimental curve 1. The observed deviation eliminates active complex formation alone.
Types 9,3, and 4: Deviations from linearity ;h plotting In
1 eo = In - us. time $ e
will increase with increasing A , whose value is determined by the equilibrium con-
-1
/'
*
YI*utCS
-
FIG.8. Comparison of the experimental curve for +e = 0.18 mg. of clottable nitrogen per milliliter and Tho 0.045 unit of thrombin per milliliter (curve 1) with that calculated for active complex formation alone, Type 1 (curve 2). Curve 3, calculated from equation 5, Type 2, suggests that the value of A in equation 5 is small compared to In +o/#.
stants involved. Permissible values of A maybe obtained by examining equation 5 for Type 2. Residual thrombin (see belaw) suggests a maximum of Ki = 0.071. Table3 yields K . = 0.051 andklTho = 0.022.A reaction for do= 0.18 and Tho = 0.0454, proceeding according to equation 5, Type 2, with the above constants but plotted as h l/e U8. t, is shown aa curve 3 of figure 8. The deviations from the experimental curve 1 and the linearity of all experimental curve8 (figures 4 and 6) suggest that the value of A(+o - 4) is small compared to In +o/$; thus, that 1
+1
1
(Type 2), - - w - (Type 3), or Kb = Ki (-4). OnsubstituK e Kb Ki tion of constants derived from table 3 and noting that the experiments were performed a t Tho = 0.0454, Types 2, 3, and 4 become:
'K.
= Ki
In 40 - = 0.472Tho (7) 4 0.051 40 The total fibrinogen concentration used in obtaining the rate CUNB of figures 3 and 4 and equation 1 was 0.185 mg. of clottable nitrogen per milliliter. Sub-
+
1216
DAVID E. WAUGH AND BETTY J. LIVINGSTONE
stituted into equation 7 this yields 2.04Thot, to be compared with 1.9OThd of equation 1, which was based on early dilution series. The reaction +o = 0.07 and Tho = 0.022, a combination not represented so far, was examined. The measured slope was 0.086; the calculated slope 0.088. Equation 7 is therefore generally applicable. The constants given in equation 7 differ slightly from those previously reported (30). The reactions behave essentially as bimolecular reactions (equation 6) in which the thrombin concentration is determined by: ,
where K = 0.051. In all probability the actual mechanism corresponds to Type 3 but, because the interacting molecules are large and few in number, the average life of the complex is small compared to the diffusion time between fruitful collisions. According to the theories of Michaelis and Menten (15) and Van Slyke (27), linear relationships between rate and substrate and enzyme concentration would then be expected. K,' would be negligible compared to KC' (table 3). Fibrinogen (and fibrin) remove thrombin by combining so that the fibrinogen is not activated, but the thrombin is prevented from activating other fibrinogen molecules. The fact that acacia accelerates the reaction without affecting its linearity eliminates Type 2 and also suggests that inhibition alone may be mainly involved. Current investigations are being undertaken with a mechanism of Type 3 in mind. In any case, the thrombin remaining in solution at the end of a reaction should be in accord with equation 8. That fibrin combines with thrombin has been demonstrated (4, 17, 21, 23) and that thrombin can be recovered quantitatively is also known (21). After gentle compaction terminal supernatant has been recovered from the reaction +o = 0.187 mg. of clottable nitrogen per milliliter and 0.205 unit of thrombin per milliliter at 22.7"C. Aliquots of,6 ml. of supernatant were added to 2-ml. portions of fibrinogen sufficient to give +o = 0.194. The measured slopes of two reaction curves were near 0.10. According to equation 7 the total thrombin for the second reaction was 0.05, the residual thrombin of the first then being 0.067 unit per milliliter. The conditions for the first reaction and equation 8 predict a residual thrombin of 0.044. The discrepancy between these values can be accounted for by the dissociation of 14 per cent of the thrombin combined with the clot, probably during compaction.
Multiple activation Endwise bonding (9) and minor physical changes on the part of fibrinogen (1, 12,24) have generally been assumed to characterize fibrin formation. Possibly the fibrinogen molecule retains its size and rodlike structure (5, 9, 10, 19) but requires two critical contacts with thrombin, essentially at each end, to produce +' and +", the latter forming fibrin. The assumptions that the reactions are equivalent, pseudo-first order, and irreversible, according to Walker (28) and Rakowski (20), lead to
INTERACTION OF FIBRINOGEN AND THROMBIN
1217
where kc includes a rate constant and the free thrombin concentration. A reaction proceeding according to equation 9, but plotted rn though a single pseudo-firstorder reaction were involved, is reasonably linear beyond In &,/+ = 0.8. An extrapolation of the linear portion intersects the time axis a t 0.28 of the value for In &/c$ = 2.0. Since all extrapolations of experimental curves pass through the origin, multiple activation of the above type seems improbable. Were the fibrinogen molecule to retain its main physical properties, as suggested also by the action of urea on fibrinogen and fibrin ( l G ) , a single activation means that bonding groups are liberated at considerable distances from the interaction locus. SUMMARY
The interaction of fibrinogen and thrombin, over the ranges 0.036-0.36 mg. of clottable nitrogen per milliliter and 0.009-0.45 N.I.H. unit of thrombin per milliliter, has been examined at pH (3.85, added ionic strength 0.15, and 22.7"C. Supernatant protein concentrations, 2fter clot compaction, were determined by ultraviolet absorption at X = 2800 A. When plotted as though a pseudo-first-order reaction were involved, the typical reaction curve has an initial nonlinear portion and a linear portion the extrapolation of which passes through the origin. The nonlinear portion is due to the presence of intermediate and noncompactable fibrin and is suppressed by the addition of gum acacia. Konclottable protein does not affect the course of the reaction. The linear portions of all reactions studied conform to the equation: 90 0.472Tb = 9 0.051 40
In-
+
where 40 and Tho are the initial fibrinogen and thrombin concentrations. Of the four possible mechanisms considered, it seems most probable that the average life of any assumed active complex is short compared to the time elapsing between fruitful collisions. The observed variation in rate with fibrinogen concentration is attributed to an equal and reversible inactive combination of thrombin with fibrinogen and fibrin, according to the equation
where 4 and Th are expressed in the units given a t the start. The possibility that each fibrinogen molecule requires two critical contacts with thrombin, presumably endwise, is excluded on the basis of the reaction curves. This suggests that a single fibrinogen-thrombin interaction may liberate bonding groups at some distance from the site of contact. The authors are indebted to the Chemical Research and Development De-
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DAVID F. WAUGH AND BETTY J. LIVINGBTONE
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