The molecular weights, mass distribution, chain composition, and structure of soluble fibrin degradation products released from a fibrin clot perfused with plasmin.

We used a perfused clot system to study the degradation of cross-linked fibrin. Multiangle laser light scattering showed that plasmin-mediated cleavage caused the release of noncovalently associated fibrin degradation products (FDPs) with a weight-averaged molar mass (Mw) of approximately 6 x 10(6) g/mol. The Mw of FDPs is dependent on ionic strength, and the Mw observed at 0.15 M NaCl resulted from the self-association of FDPs having Mw of approximately 3.8 x 10(6) g/mol. Complete solubilization required the cleavage of approximately 25% of fragment D/fragment E connections, with 48% alpha-, 62% beta-, and 42% gamma-chains cleaved. These results showed that D-E cleavage cannot be explained by a random mechanism, implying cooperativity. Gel filtration and multiangle laser light scattering showed that FDPs range from 2.5 x 10(5) to 1 x 10(7) g/mol. In addition to fragment E, FDPs are composed of fragments ranging from 2 x 10(5) Da (D-dimer, or DD) to at least 2.3 x 10(6) Da (DX8D). FDP mass distribution is consistent with a model whereby FDPs bind to fibrin with affinities proportional to fragment mass. Root mean square radius analysis showed that small FDPs approximate rigid rods, but this relationship breaks down as FDPs size increases, suggesting that large FDPs possess significant flexibility.

Fibrinogen is the target protein of the coagulation cascade, and, following vascular injury, fibrin comprises the major protein component of the hemostatic plug. Fibrinogen is a 340-kDa soluble plasma protein consisting of three pairs of disulfidebonded ␣-, ␤-, and ␥-chains arranged as depicted in Fig. 1. The molecule consists of a central globular E region connected by coiled-coil regions to two identical globular D regions. In addition, two other structures comprising approximately the carboxyl-terminal two-thirds of the ␣-chains, designated ␣C regions, have been described (1,2). The E and D regions in each half-molecule are delineated by a pair of disulfide rings, which link chains ␣ to ␤, ␤ to ␥, and ␥ to ␣ (3). Numerous plasmin-and thrombin-sensitive bonds have been identified and are shown in Fig. 1 (4). Thrombin converts fibrinogen to fibrin by catalyzing the proteolytic removal of both fibrinopeptide A and fibrinopeptide B. These cleavages unmask two polymerization sites in the E region, forming soluble fibrin, to which one D region from each of two fibrin(ogen) molecules can bind (5). The soluble fibrin spontaneously polymerizes to form doublestranded protofibrils, with the fibrin monomers within each strand arranged end to end and the fibrin across strands arranged in a half-staggered overlap, as depicted by the combination of strands a and b in Fig. 2. The protofibrils may further associate laterally to produce fibers, which themselves may associate to form fiber bundles. Collectively, the protofibrils, fibers, and fiber bundles, variously branched, comprise the fibrin clot. As also indicated in Fig. 2, the ␥-chains of adjacent D regions within a strand of a protofibril are covalently crosslinked by isopeptide bonds, the formation of which is catalyzed by factor XIIIa (6,7). Thus, in cross-linked fibrin, the individual strands consist of polymers of covalently linked fibrin molecules. Factor XIIIa more slowly catalyzes isopeptide bond formation in the ␣C region between multiple ␣-chains within and presumably between protofibrils (8).
The solubilization of fibrin is the result of selected bond cleavages catalyzed by plasmin. The cleavage of fibrinogen and fibrin by plasmin has been extensively studied (4, 9 -24). Fragmentation of fibrinogen occurs upon cleavages within the ␣-chain to release the ␣C fragments, thereby producing fragment X (ϳ260 kDa; Fig. 1). Further cleavage of fragment X in the ␣-, ␤-, and ␥-chains between the two disulfide rings in one half of the molecule (see arrows in Fig. 1) produces fragment Y (ϳ160 kDa) and fragment D (ϳ100 kDa). Further cleavage of fragment Y produces a second fragment D and fragment E (ϳ60 kDa). The terminal fragments E and D approximately comprise the respective E and D regions of the parent fibrinogen molecule.
The current model for the solubilization of ␥-chain crosslinked fibrin is depicted in Fig. 2 (19,20). The release of soluble material requires cleavage of the ␣-, ␤-, and ␥-chains between the two disulfide rings in the region connecting the E and D regions of the fibrin monomers that are across from one another in the two strands of the protofibril. These are the same bonds that are cleaved in fibrinogen (25). Two sets of such cleavages must occur to obtain soluble products (Fig. 2). Numerous soluble products can be produced, the nature of which depends on the relative locations of the sets of cleavages. Examples are shown in Fig. 2. Cleavages depicted by 1 and 2, for example, yield the limit product of digestion of cross-linked fibrin, which is a species consisting of covalently cross-linked D regions from one strand (D-dimer (DD) 1 ) noncovalently associated with the E region from the other strand. This product is designated DD/E. Larger products are produced by sets of cleavages more distant than that which generates DD/E. Some examples are shown by sets 1 and 3, 1 and 4, and 1 and 5 in Fig.  2. Cleavages 1 and 3 produce two noncovalently associated DY fragments (DY/YD); cleavages 1 and 4 produce fragments DXD and YY associated noncovalently with one another (DXD/YY); and cleavages 1 and 5 produce two noncovalently associated DXY fragments (DXY/YXD). This pattern can be extended to include sets of cleavages more distant than those depicted in Fig. 2, but the upper limit for the distance and the corresponding limit size of soluble material is not known. In addition to the cleavages depicted in Fig. 2, cleavages within the connecting regions in each strand of each of the products (DY/YD, DXD/YY, and DXY/YXD) are possible, subject to the restraint that not all of the ␣-, ␤-, and ␥-chains of connecting regions across from one another on the two strands are cleaved, since this would produce two new noncovalently associated products.
Although the cleavage sites of fibrinogen and fibrin have been identified and the existence of products consistent with those depicted in Fig. 2 has been demonstrated upon digestion of fibrin, no quantitative analysis of the stoichiometry of release, chain composition, and size distribution of soluble products has been provided. Consequently, the studies described in this paper were carried out in order to identify and quantify the molecules released during the process of plasmin-catalyzed solubilization of cross-linked fibrin with respect to average molecular weight, molecular weight distribution, covalent structure, and ␣-, ␤-, and ␥-chain composition and their extents of cleavage. These were accomplished by collecting the materials solubilized from clots perfused with plasmin, inhibiting the plasmin in the eluted material to eliminate or at least minimize further degradation of soluble material, and analyzing the material by multiangle laser light scattering, size exclusion chromatography, and SDS-PAGE under both reducing and nonreducing conditions.

EXPERIMENTAL PROCEDURES
Protein Preparation-All human proteins were purified from citrated fresh frozen human plasma obtained from the Kingston General Hospital (Kingston, Canada). Human thrombin was prepared from purified human prothrombin (26) according to a modified procedure of Lundblad et al. (27). Prothrombin was dialyzed into a solution made up of 2 FIG. 1. The structure of fibrinogen. The arrangement of the six chains in the fibrinogen molecule is shown above. The disulfide bonds joining the chains are shown as lines, and the intrachain disulfides are shown as small boxes under each chain. The sites of glycosylation on the ␤and ␥-chains are indicated by the lollipop structures. Fibrinopeptides A and B are shown as black boxes on the ␣and ␤-chains, respectively. Plasmin cleavage sites are denoted by vertical lines in each chain, and the cleavages giving rise to the major structural fragments D and E are shown by the black arrows. The D, E, and ␣C regions are represented by the shading. The names, structures, and molecular weights of the fragments derived by plasmin cleavage are also shown. The depiction of the fibrinogen molecule shows the E region (small circle) flanked on either side by a D region (large circles) separated by the three-chain ␣-helical regions (straight lines), which contain the plasmin-sensitive sites. The ␣C regions are shown as curved lines protruding from the D regions, which self-associate near the E region. Cleavage of the ␣C regions by plasmin gives rise to fragment X; cleavage on one side of the molecule at the three plasmin-sensitive bonds yields one fragment Y and one fragment D. Further cleavage of fragment Y produces a second fragment D and fragment E.

FIG. 2. Fibrin formation and degradation.
The production of ␥-chain cross-linked fibrin occurs as a result of the actions of thrombin and factor XIIIa in the presence of calcium ion. Thrombin removes fibrinopeptide A from fibrinogen, forming soluble fibrin. The fibrin monomers spontaneously polymerize, yielding a double-stranded protofibril. The monomers within each of the two strands (a and b) are arranged end-to-end, and each monomer in strand a is noncovalently associated (indicated by the triple lines) with two monomers in strand b in a half-staggered overlap, forming a protofibril. Thrombin also removes fibrinopeptide B from the fibrin monomers, which results in the lateral aggregation of the protofibrils into fibers. Factor XIIIa catalyzes isopeptide bond formation between the ␥-chains in the D regions of adjacent monomers within a strand, resulting in a cross-linked clot. The production of FDPs occurs as the result of plasmin-mediated cleavage of the ␣-, ␤-, and ␥-chains in at least four plasmin-sensitive regions. To produce FDPs, two sets of cleavages must occur (eg. 1 and 2, 3 and 5, and 1 and 5) such that in each set, the cleavages occur between reciprocally noncovalently associated D and E regions in two monomers as indicated by the diagonal lines 1-7. The size and structure of the noncovalently associated soluble material depends on the distance between the two sets of cleavages. The nomenclature and approximate molecular weights of the intact FDPs are indicated. The FDPs may contain additional cleavages and still retain their noncovalent structures, provided that at least one chain between reciprocally noncovalently associated D and E regions is not cleaved. volumes 0.02 M Tris, 0.15 M NaCl, pH 7.4 in 1 volume of water ( 2 ⁄3 TBS), and the concentration of prothrombin was adjusted to 0.1 mg/ml in 2 ⁄3 TBS. Prothrombin was activated to thrombin in the presence of 2 mM CaCl 2 , 10 M phosphatidylcholine/phosphatidylserine vesicles (75% phosphatidylcholine, 25% phosphatidylserine, made according to Barenholz (28)), 1.0 nM bovine factor Xa (29), and 1.0 nM bovine factor Va (29) with stirring at room temperature (ϳ22°C) for 30 min. The reaction was stopped by the addition of EDTA (5 mM final) and loaded onto a 2.5 ϫ 12-cm column of sulfopropyl-Sephadex C-50 (Amersham Pharmacia Biotech, Baie d'Urfé, Canada) pre-equilibrated in 2 ⁄3 TBS. The column was washed with 2 ⁄3 TBS until A 280 was Ͻ0.01 and was then washed with 0.1 M sodium phosphate, pH 6.5, until A 280 was Ͻ0.01. The thrombin was eluted using a linear gradient of sodium phosphate, pH 6.5 (0.1-0.3 M, 500 ml total), and the peak fractions were concentrated by precipitation with 80% ammonium sulfate at 4°C. The pellet obtained upon centrifugation (10,000 ϫ g, 20 min, 4°C) of the precipitated solution was taken up in a minimal volume of 50% glycerol and stored at Ϫ20°C.
Human Glu-plasminogen was isolated according to the procedure of Castellino and Powell (30) with the following changes: no Trasylol was used during the purification; the plasma was not slurried, but adsorbed under vacuum to lysine-Sepharose in a sintered glass funnel over a 15-min period; 0.05 M Tris, pH 8.0, was used to equilibrate the lysine-Sepharose and to wash the protein-bound resin under light vacuum in a sintered glass funnel; 0.05 M Tris, 0.02 M ⑀-aminocaproic acid was used to elute the plasminogen; and the plasminogen was concentrated with 80% ammonium sulfate, taken up in a minimal volume of 50% glycerol, and stored at Ϫ20°C.
Human plasmin was produced by a modification of the procedures of Bajzar et al. (31) and Robbins and Summaria (32). 20 mg of plasminogen was dissolved into 20 ml in 0.05 M Tris, 0.15 M NaCl, pH 8.0 (TBS) and then dialyzed three times in 2 liters of the same buffer for 1 h each. The solution was made 25% (v/v) in glycerol and 50 mM in ⑀-aminocaproic acid. The activation was initiated by the addition of urokinase (Calbiochem) to 50 units/ml and was carried out at 37°C. The progress of the reaction was monitored by the plasmin-catalyzed hydrolysis of S-2251 (Helena Laboratories, Beaumont, TX) at various times. When the level of plasmin appeared to plateau (ϳ120 min), a further 50 units/ml of urokinase was added, and the reaction was further monitored by S-2251 hydrolysis. A second plateau was reached at ϳ210 min, and the solution was loaded onto an 8-ml benzamidine-Sepharose (Sigma, Oakville, Canada) column equilibrated in TBS. The column was washed with TBS, and the plasmin was eluted from the column with TBS, 0.02 M benzamidine in 4-ml fractions. The plasmin-containing fractions were identified using the S-2251 assay and were concentrated by dialysis against 80% saturated ammonium sulfate at 4°C. The precipitated protein was centrifuged at 10,000 ϫ g for 30 min, and the pellet was dissolved in 2 ml of 50% glycerol and stored at Ϫ20°C. Active site titration using the p-nitrophenyl pЈ-guanidinobenzoate HCl method of Chase and Shaw (33) showed that the plasmin contained 100% active sites.
Factor XIII was purified by a modified procedure of Janus et al. (34). 250 ml of saturated ammonium sulfate, 1 mM EDTA was added to 1 liter of citrated, fresh frozen plasma on ice. The solution was allowed to sit for 1 h, and the precipitate was collected by centrifugation at 6000 ϫ g for 30 min at 8°C. The pellet was washed vigorously with 200 ml of 20% saturated ammonium sulfate, 1 mM EDTA and recentrifuged. The drained pellet was dissolved in 100 ml of 0.15 M KCl, 1 mM EDTA, pH 5.4. Saturated ammonium sulfate, 1 mM EDTA was added to 16% (v/v), and the sample was left at 22°C for 30 min followed by centrifugation at 6000 ϫ g for 30 min at 8°C. The pellet was dissolved in 100 ml of 0.05 M Tris, 0.2 M NaCl, 1 mM EDTA, pH 7.5, and heated to 56°C for 10 min in a water bath to denature/flocculate the fibrinogen, and the solution was clarified by centrifugation at 6000 ϫ g for 15 min at 8°C. The supernatant was made 36% in saturated ammonium sulfate, 1 mM EDTA, and after 30 min at 22°C it was centrifuged at 6000 ϫ g for 30 min at 8°C. The pellet was dissolved in 100 ml of 0.05 M Tris, 1 mM EDTA, pH 7.5, dialyzed three times in 2 liters at 22°C versus the same buffer and loaded onto a 50-ml DEAE-cellulose column equilibrated (22°C) in the same buffer. The column was washed with 100 ml of equilibration buffer, and the factor XIII was eluted from the column using a linear NaCl gradient from 0 to 0.2 M over 500 ml. The presence of factor XIII in the fractions was assessed by monitoring the fluorescence increase observed upon the factor XIIIa-mediated incorporation of dansyl cadaverine (Sigma) into fibrin clots. A 5-l aliquot from each fraction was added to the well of a fluorescence microtiter plate containing a separate 5-l aliquot of 600 nM human thrombin. The reaction was started by the addition of 200 l of 1.05 mg/ml fibrinogen, 105 M dansyl cadaverine, 2.1 mM CaCl 2 in 0.02 M HEPES, 0.15 M NaCl, pH 7.4 (HBS). The reactions were monitored every 2 min over 1 h at room temperature in a LS-50B fluorescence spectrophotometer (Perkin-Elmer, Montreal, Canada) using the plate reader accessory. The samples were excited at 360 nm, and the emission was monitored at 546 nm using a 530-nm emission filter. Both excitation and emission slits were set at 10 nm. Fractions containing factor XIII were pooled and concentrated by dialysis against ammonium sulfate at 36% (final) saturation. The precipitate was pelleted by centrifugation at 10,000 ϫ g for 15 min at 4°C and was dissolved in HBS, 1 mM EDTA, pH 7.4. The remaining fibrinogen was eliminated by repetitively (three times) heating the factor XIII to 56°C for 10 min, cooling on ice, and then centrifuging at 16,000 ϫ g at 22°C for 5 min to clarify. No difference in factor XIIIa activity was observed following the heating/cooling/centrifugation cycles. The purified factor XIII was dialyzed against HBS, 1 mM EDTA, pH 7.4, passed through a 0.22-m syringe filter, and stored at Ϫ70°C in small aliquots.
Sheep anti-human factor XIII-Sepharose was prepared according to a modified procedure of Cuatrecasas (35). 10 ml of Sepharose CL-4B (Amersham Pharmacia Biotech, Baie d'Urfé, Canada) was washed with 250 ml of 2 M Na 2 CO 3 under light vacuum in a 25-ml sintered glass funnel. The resin was then activated by the addition of 3 ml of 1 g/ml CNBr in acetonitrile, and the slurry was stirred for 2 min. The CNBr/ acetonitrile was evacuated, and the resin was washed with 250 ml of 0.1 M NaHCO 3 , 0.5 M NaCl, pH 8.3, and taken to near dryness under vacuum. The resin cake was then added to 10 ml of 20 mg/ml sheep anti-human factor XIII total IgG (Affinity Biologicals, Hamilton, Canada) in 0.1 M NaHCO 3 , 0.5 M NaCl, pH 8.3, and the slurry was incubated overnight at room temperature with gentle rocking on an orbital shaker. The resin was stacked in a column and washed with 50 ml of 0.1 M NaHCO 3 , 0.5 M NaCl, pH 8.3, and the coupling efficiency, determined from the absorbance of the wash, was found to be 96%. The column was washed with 100 ml of 0.5 M Tris, 1.0 M NaCl, pH 8.0, to block any remaining reactive sites and then prepared for use by washing with 40 ml of Gentle Elution Buffer (Bio-Rad, Mississauga, Canada) followed by 100 ml of HBS. The column was stored in HBS, 0.02% NaN 3 at 4°C.
Human fibrinogen was purified according to a modified procedure of Straughn and Wagner (36). 80 ml of 1.0 M BaCl 2 was added with stirring to 1 liter of citrated, fresh frozen plasma over 5 min at 22°C. The solution was stirred at 22°C for 30 min and was then centrifuged at 6000 ϫ g for 30 min at 8°C. The supernatant was made 1 mM in diisopropylfluorophosphate and allowed to stand 10 min at 22°C. 4.0 M ␤-alanine, made up in 0.05 M trisodium citrate, 0.15 M NaCl, pH 6.5, was added to a final concentration of 1.0 M. After 30 min at 22°C, the solution was centrifuged at 6000 ϫ g for 30 min at 8°C. The supernatant was then made up to 2.0 M in ␤-alanine, stirred for 30 min at 22°C, and then centrifuged at 6000 ϫ g for 30 min at 8°C. The pellet was dissolved in the original plasma volume of 0.05 M trisodium citrate, 0.15 M NaCl, pH 6.5. The solution was made 2.0 M in ␤-alanine and centrifuged as before. The pellet was dissolved in ϳ 1 ⁄8 starting plasma volume of 0.05 M trisodium citrate, 0.15 M NaCl, pH 6.5. This was made 2% in PEG-8000 by the addition of 40% (w/v) PEG-8000 in water. The solution sat for 15 min at 22°C and then centrifuged at 10,000 ϫ g for 30 min at 4°C. The supernatant was made 5% in PEG-8000 and sat 15 min at 22°C before centrifugation at 10,000 ϫ g for 30 min at 4°C. The pellet was dissolved in 100 ml of 0.02 M HEPES, 1.0 M NaCl, pH 7.4, by rapid agitation on an orbital shaker table at 22°C. This was then dialyzed against 3 ϫ 4.0 liters of 0.02 M HEPES, 0.025 M NaCl, pH 7.4, at 22°C. The solution was passed over a 5-ml lysine-Sepharose column followed by a 10-ml anti-factor XIII-Sepharose column and finally loaded onto a 100-ml DEAE-cellulose column, all at 22°C. All columns were preequilibrated in 0.02 M HEPES, 0.025 M NaCl, pH 7.4, and were linked in tandem. The columns were washed with 50 ml of 0.02 M HEPES, 0.025 M NaCl, pH 7.4, and the DEAE-cellulose column was disconnected and was washed with a further 300 ml of equilibration buffer. Fibrinogen was eluted from the column with 0.02 M HEPES, 0.10 M NaCl, pH 7.4, and further fractionated to yield high molecular weight fibrinogen (containing intact ␣-chains) by precipitation with 19% ammonium sulfate as described previously (37). The purified fibrinogen was dialyzed extensively against HBS, passed through a 5-m syringe filter, and stored at Ϫ70°C at 5-10 mg/ml.
Clot Formation-A perfused clot system was used to produce fibrin degradation products (FDPs) for further analysis. The clot was formed in a disposable column (Econo-Pac, Bio-Rad) filled with the polyethylene disks supplied with the column as a solid support. The column was filled to the 10-ml mark, which yielded a 4.5-ml available volume for the clot. The column was washed extensively with degassed, 0.2-m-filtered HBS, 2 mM CaCl 2 , 0.01% Tween 80 prior to use. The clots were constructed as follows: an 8.0-ml solution containing 2.0 mg/ml fibrinogen, 2.0 mM CaCl 2 , 0.01% (w/v) Tween 80 in HBS was prepared in a 10-ml syringe, capped at the bottom. The solution was made 13 nM in plasmin, and the clotting was initiated by the addition of 92 l of 0.8 mg/ml factor XIIIa, 130 nM thrombin (90 l of 0.8 mg/ml factor XIII was activated to factor XIIIa by the addition of 2 l of 6 M thrombin followed by incubation at 37°C for 30 min). The solution was rapidly mixed and then passed through a prewetted 0.45-m syringe filter, filling the column (prefilled with degassed, 0.2 m filtered HBS, 2 mM CaCl 2 , 0.01% Tween 80) from the bottom using a four-way stopcock. The excess solution was removed from the top of the column, and the solution was allowed to clot and lyse minimally for 90 min at room temperature (22°C). The clotting time under these conditions is ϳ75 s. This procedure allowed for full polymerization of the fibrin, complete cross-linking of the ␥-chains, negligible cross-linking of the ␣-chains, removal of the ␣C regions, and negligible solubilization of the clot. The inclusion of plasmin in the clot was necessary to enable subsequent perfusion of fluid through the clot; clots formed in the absence of plasmin resist flow, resulting in channeling of the perfusate around the sides and not through the clot proper. Ten minutes after filling the column, the bottom of the column (under the bottom disk) was cleared of clotted fibrin by mechanical agitation and flushing with degassed, 0.2-m-filtered HBS, 2 mM CaCl 2 , 0.01% Tween 80 using a syringe fitted with a pipette tip.
Perfusion Experiments-Following the 90-min incubation, the plasmin and factor XIIIa were inhibited by perfusing 60 ml of 1 M valylphenylalanyl-lysyl chloromethylketone (VFKck; Calbiochem), 100 M iodoacetamide in degassed, 0.2-m-filtered HBS, 2 mM CaCl 2 , 0.001% Tween 80 at 0.5 ml/min. The inhibitors were then washed from the clot with 60 ml of degassed, 0.2-m-filtered HBS, 2 mM CaCl 2 , 0.001% Tween 80 at 0.5 ml/min. Following the wash, lysis was resumed by the perfusion of 0.05 nM plasmin in degassed, 0.2-m-filtered HBS, 2 mM CaCl 2 , 0.001% Tween 80 through the clot at 0.475 ml/min. During the wash and subsequent lysis, the eluate was mixed with 30 M VFKck in degassed, 0.2-m-filtered 0.1 mM HCl at the exit from the clot at 0.025 ml/min and then passed through a 0.45-m filter. The column, VFKck, and 0.45-m filter were connected by a four-way stopcock. The eluate was analyzed in tandem for absorbance at 280 nm and multiangle laser light scattering. Eluate fractions (10 ml) were collected. All steps were performed at 22°C. The inhibition of the initial plasmin followed by perfusion of 0.05 nM plasmin through the clot provided a simple system to produce large quantities of minimally degraded FDPs for further study. This system avoided the complexities that may be inherent in using a fibrin-dependent reaction to generate plasmin (eg. tissue plasminogen activator and plasminogen) when the fibrin is undergoing degradation.
Size Exclusion Chromatography-Protein-containing fractions from the perfusion experiment were pooled, adjusted to 0.5 M NaCl, concentrated by ultrafiltration at 22°C under N 2 to ϳ10 ml in a stirred cell using a YM-100 membrane (Amicon, Oakville, Canada), passed through a 5-m syringe filter, and then finally concentrated at 37°C to ϳ750 l by centrifugal concentration (Ultrafree-15; Amicon). The concentrated sample was centrifuged at 16,000 ϫ g for 10 min at 22°C, degassed briefly (ϳ2 min) under vacuum in a Speed Vac ® Plus (Savant, Farmingdale, NY), and then loaded into a 500-l sample loop. The sample was injected onto a 110 ϫ 1.5-cm Sephacryl S-1000 column (Pharmacia) equilibrated in degassed, 0.2-m-filtered 0.02 M HEPES, 0.5 M NaCl, 0.001% Tween 80, pH 7.4, and the chromatography was carried out at 0.5 ml/min using a P-500 pump (Pharmacia). The eluate was passed in tandem through an absorbance detector and a multiangle laser light scattering detector, and fractions (3.5 ml) were collected. The gel filtration experiments were performed at 22°C. The weight-averaged molar mass (M w ) and the root mean square radius (RMSr) of eluted material were calculated at any given point by regression analysis of the Debye plot according to the method of Zimm (38), which involves a plot of (K* ϫ c)/R versus sin 2 (/2), where K* is an optical constant, c is the weight concentration of the sample in g/ml, R is the Rayleigh ratio at a given angle (the ratio of the intensity of the light scattered by the solution (in excess over the solvent alone) to the intensity of the incident laser light), and is the angle of scattering. For a detailed treatment of multiangle laser light scattering theory and principles, see Wyatt (38). The molar mass is found from the regression of the Debye plot, where M w ϭ R /(K* ϫ c) at ϭ 0 (i.e. sin 2 (/2) ϭ 0). The RMSr is determined from the slope of the Debye plot at sin 2 (/2) ϭ 0, where RMSr ϭ ((3 m 2 M w )/(16 2 )) 0.5 , where m is the slope, is the wavelength of light, and M w is molar mass. The M w and RMSr were calculated by the Astra program using the following parameters: ⑀ 280 nm fibrin degradation products ϭ ⑀ 280 nm fragment X ϭ 1.66 ml/mg/cm (21); refractive index gradient for protein (␦n/␦c) ϭ 0.192 ml/g (39,40); refractive index for solvent (HBS/2 mM CaCl 2 /0.001% Tween 80) ϭ 1.3333; A 2 (second virial coefficient) ϭ 0. The DAWN-DSP instrument was fitted with a K5 flow cell and a He-Ne laser (632.8 nm) and was calibrated with 0.02-nm-filtered toluene, and the detectors were normalized for the experiments on the monomer peak of bovine serum albumin (ϳ98% monomeric bovine serum albumin; Sigma) gel filtered on Sephacryl S-1000 in degassed, 0.2-m-filtered 0.02 M HEPES, 0.5 M NaCl, 0.001% Tween 80 as per the manufacturer's instructions. The differences in the refractive indexes of the different buffer systems used was assumed to be negligible.

Molar Mass and Root Mean
Electrophoresis-Fractions collected over the course of the perfusion and gel filtration were analyzed by SDS-PAGE. Selected fractions were pooled, concentrated to ϳ500 l by centrifugal concentration (Ultrafree-15, Amicon), and subjected to SDS-PAGE under nonreducing and reducing conditions. Samples from the concentrated fractions were analyzed by SDS-PAGE under nonreducing conditions in 2.5-5.0% gradient gels (140 ϫ 110 ϫ 1.5 mm) using the system described by Neville (41). Due to their fragile nature, the gels were carefully floated off the glass plates into water. The gels were stained overnight with a dilute Coomassie Blue R-250 stain (0.0016% Coomassie Blue R-250 in 7.5% EtOH, 5% HOAc, adapted from Zehr et al. (42)) and then destained briefly (ϳ2 h) with 18% MeOH, 9% HOAc. The gels were incubated with 15% MeOH, 3% glycerol for 4 h and then dried overnight using Bio Gel Wrap (Biodesign, Carmel, NY). Samples were also analyzed by SDS-PAGE under reducing conditions in 12% gels (140 ϫ 110 ϫ 1.5 mm) using the Tris-Tricine system described by Schagger and von Jagow (43). Gels were fixed for 1 h in 50% MeOH, 10% EtOH; stained overnight in a dilute Serva Blue G (0.0016% Serva Blue G in 10% HOAc, adapted from Zehr et al. (42)); and then destained briefly (ϳ2 h) with 18% MeOH, 9% HOAc. The gels were then dried as described above. The dried gels were digitally scanned, and densitometry was performed using the Pho-toPaint program from Corel.

Analysis of Material
Released from a Perfused Clot-4.5 ml of 2.0 mg/ml fibrinogen was clotted with thrombin in the presence of factor XIIIa, plasmin, and Ca 2ϩ in a column filled with polyethylene disks. Factor XIIIa was included at a level sufficient to provide quantitative cross-linking of the ␥-chains. Plasmin was included at a level sufficient to initiate fibrinolysis. The clot was perfused with iodoacetamide and VFKck to inhibit factor XIIIa and plasmin, respectively. This initial exposure to plasmin typically caused the solubilization of about 20 -25% of the mass of the clot. This material was composed almost exclusively of ␣-chain fragments, as deduced by SDS-PAGE (Fig. 5, Wash). The inhibitors were then washed from the clot with buffer, and the perfusion was continued with a very low level of plasmin (0.05 nM). A stream of VFKck was added to the eluate as it left the bottom of the column to inhibit the plasmin, and the combined stream was passed through a 0.45-m filter, an absorbance monitor, and a multiangle laser light scattering detector arranged in tandem, and fractions were collected. The relationship between the concentration (g/ml) of material released during the perfusion, and the volume perfused is shown in Fig. 3A. The linear relationship shows that the rate of fibrinolysis is directly proportional to the amount of plasmin perfused. This is consistent with the input plasmin accumulating in a superficial layer (44) resulting in a top-down lysis of the clot. In this experiment, perfusion with plasmin was initiated at 50 ml. Typically, Ͼ95% of the input fibrin was recovered during the experiment. The R values from selected detectors at different angles from the multiangle laser light scattering instrument are shown in Fig. 3B. The fact that R increased with decreasing detector angle implies the existence of large soluble molecules in the perfusate (38).
Knowledge of the concentration and R allowed the determination of M w at any given volume. M w was found from the inverse of the y intercept of the second order fit of the Debye plot, using the method of Zimm (see "Experimental Procedures"). An example is shown in Fig. 3C, obtained at 170.7 ml of perfusion, and shows the M w of the material in the eluate to be 5.6 ϫ 10 6 g/mol. Determinations of M w were performed at ϳ65-l increments throughout the perfusion experiment, and a plot of M w versus perfusion volume is shown in Fig. 3D, with the concentration profile from Fig. 3A shown for clarity. Initially, starting at about 90 ml, material was released with a M w of ϳ3 ϫ 10 6 g/mol. The value of M w steadily increased to 5.6 ϫ 10 6 g/mol at 140 ml, after which the value slowly increased to ϳ6 ϫ 10 6 g/mol at 300 ml. The data of Fig. 3 clearly show that molecules released during the solubilization of fibrin by plasmin are of very high molecular weight, the observed M w being approximately 20 -25 times the mass of the DD/E complex, the terminal product of fibrin digestion by plasmin (19).
The Effect of NaCl on the Apparent Mass of FDPs-In order to determine the extent to which the observed M w of the particles was influenced by relatively weak ionic interactions, the material eluted between 140 and 180 ml was pooled, and the M w was determined at increasing ionic strength. The measurements were made by passing the sample through the absorbance and scattering detectors using a syringe driver, collecting the sample at the end, increasing the ionic strength of the sample by the addition of an aliquot of 4.0 M NaCl, and then redetermining M w . The relationship between M w and ionic strength is shown in Fig. 4. At 0.15 M NaCl, the M w of the pooled fractions was found to be 5.8 ϫ 10 6 g/mol. As the ionic strength was increased, the M w decreased until a plateau value of ϳ3.8 ϫ 10 6 g/mol was reached at 0.50 M NaCl. These results suggest that at physiological ionic strength (0.15 M NaCl) the released material consists of fragments with a M w of ϳ4 ϫ 10 6 g/mol that are resistant to dissociation by NaCl but that associate with one another by relatively weak ionic interactions to yield complexes with higher a M w . This interpretation is consistent with the observations of Carr and Gabriel (45) and Baradet et. al. (46), who showed that lateral association of fibrin protofibrils within a fibrin clot to form thicker fibers is promoted at low ionic strength and inhibited at high ionic strength.
SDS-PAGE Analysis of Intact FDPs-In order to disrupt all noncovalent associations in the eluted molecules and thereby disclose the molecular weight distribution of covalent species in the eluate, SDS-PAGE under nonreducing conditions was perwith polyethylene disks and allowed to incubate for 90 min. The crosslinking and lysis reactions were stopped by perfusing the clot with 60 ml of buffer containing the factor XIIIa inhibitor iodoacetamide and the plasmin inhibitor VFKck. The clot was then washed with 60 ml of buffer, and lysis was resumed by perfusing the clot with 0.05 nM plasmin at 0.475 ml/min. The eluate from the clot was mixed with VFKck to quench the plasmin and was then passed through a spectrophotometer and a multiangle laser light scattering detector arranged in tandem. The profile in A shows the concentration of eluting materials versus the volume of perfusate. Plasmin was added to the perfusate at The M w of the sample is equal to the inverse of (K* ϫ c)/R at sin 2 (/2) ϭ 0 (i.e. ϭ 0) and was determined from a second order fit through the points. The plot was generated at 170.7 ml and shows the sample M w to be 5.6 ϫ 10 6 g/mol. D plots the M w of the material eluting during the perfusion experiment, as well as the concentration profile from A (dotted line), and shows how the observed M w varied over the course of lysis. FIG. 3. Perfusion of a fibrin clot with plasmin. A clot was formed in the presence of factor XIIIa, plasmin, and Ca 2ϩ in a column filled

Analysis of Fibrin Degradation
formed. In addition, in order to determine the extent to which ␣-, ␤-, and ␥-chains had been cleaved in the eluted materials, SDS-PAGE was performed under reducing conditions. The results of nonreducing SDS-PAGE are shown in Fig. 5A. The lanes correspond to the material solubilized during the initial incubation with plasmin (Wash) or the material solubilized during the perfusion with plasmin. The fractions collected during the perfusion with plasmin show that the same fragments are present at all stages of the perfusion. The fragments observed, in addition to fragment E, ranged in escalating molecular weight from DD to DX 8 D, which consists of two D regions connected by eight covalently linked X fragments. The identity of the products was assessed on the basis of molecular weights, according to the model of Francis and Marder (19). The pattern of products is characterized as a series of triplets. The first triplet consists of DD, DY, and YY. The second consists of these fragments with an intervening X fragment (DXD, DXY, and YXY). The pattern continues with 2, 3, 4, 5, 6, and 7 intervening X fragments. The last distinct fragment consists of DX 8 D, although more slowly migrating Coomassie Blue staining material suggests the existence of even larger fragments. These fragments confirm the existence of very high molecular weight soluble materials. The fragment DX 8 D has a molar mass of about 2.3 ϫ 10 6 g/mol. Since the fragment represents, at the least, a single strand of a protofibril, SDS-PAGE demonstrated that noncovalently associated fragments with a molar mass of at least 4.4 ϫ 10 6 g/mol (DX 8 D/YX 7 Y) are released from the perfused clot.
The soluble material was also analyzed by SDS-PAGE under reducing conditions. The results are presented in Fig. 5B. A "triplet" of cross-linked ␥-chains was present, which corresponded to intact ␥ dimers (␥-␥), a ␥ dimer with one ␥-chain cleaved (␥-␥ c ), and a ␥ dimer with both ␥-chains cleaved (␥ c -␥ c ). The ␥-␥ c was present as a closely spaced doublet, while the ␥ c -␥ c was present as a closely spaced triplet, with the higher molecular weight species predominating. This implies that cleavage of the ␥-chain in fibrin occurs at both Lys 62 -Ala 63 and Lys 85 -Ser 86 , with the Lys 62 -Ala 63 cleavage being preferred. The products resulting from these cleavages, Tyr 1 -Lys 85 and Tyr 1 -Lys 62 , are identified as ␥Љ and ␥ٞ, respectively. The ␤-chain appeared as four species, corresponding to intact Gly 15 -Gln 461 (␤), ␤ cleaved at Arg 42 -Ala 43 (␤Ј), ␤ cleaved at Lys 133 -Asp 134 (␤Љ), and the small ␤ fragment Gly 15 -Lys 133 (␤ٞ). Three fragments from the ␣-chain were present. The fragment labeled ␣ 25 probably represents Gly 17 -Lys 219 (Lys 219 deduced from prior N-terminal amino acid sequence analysis of an ␣ fragment starting at Ser 220 ). The other ␣ fragments result from cleavage at Arg 104 -Asp 105 , producing Asp 105 -Lys 219 (␣Ј) and Gly 17 -Arg 104 (␣Љ). The assignment of the fragments to their corresponding sequences was based on sequence analysis (␣ 25 , ␤, and ␤Љ) and the expected migration of the peptides present in fragments D and E (␣Ј, ␣Љ, ␤Ј, ␤ٞ, ␥, ␥ c , ␥Љ, and ␥ٞ) known to be produced by plasmin cleavage as described previously (4).
Densitometry was performed to quantify the ratio of the intact to cleaved chains, where intact refers to ␣-, ␤-, and ␥-chain forms that have not been cleaved at the plasmin-sensitive sites between the disulfide rings. The intact forms are calculated by ␣ (␣ 25 ), ␤ (␤ ϩ ␤Ј), and ␥ (␥-␥ ϩ 1 ⁄2 ␥-␥ c ), and the cleaved forms are calculated by ␣ (␣Ј ϩ ␣Љ), ␤ (␤Љ ϩ ␤ٞ), and ␥ ( 1 ⁄2 ␥-␥ c ϩ ␥ c -␥ c ϩ ␥Љ ϩ ␥ٞ). The results of chain cleavage obtained over the course of the perfusion experiment are shown in Fig. 5C. The results showed that 48% of ␣-chains, 62% of ␤-chains, and 42% of ␥-chains were cleaved in all fractions collected over the course of perfusion. In addition, densitometry was performed on the nonreduced gels in an effort to quantify the fractional cleavage of all three-chain segments linking each D region to the central E region in the fibrin monomers. The results, shown in Fig. 5C, demonstrate that 25% of all D-E triple-stranded connections were cleaved at all points of the perfusion.
The densitometry results from the nonreduced and reduced SDS-PAGE gels taken together indicate that plasmin catalyzes degradation of fibrin to produce soluble FDPs through very discrete and limited proteolysis and that complete solubilization requires cleavage of only a minority (ϳ25%) of all available D-E connections. The limited cleavage observed is consistent with the presence of high molecular weight species seen in the nonreduced gels as well as the results from the laser light scattering analysis.

Determination of the Molar Mass Range of FDPs by Gel Filtration and Multiangle Laser Light Scattering-
The analyses of solubilized materials by both SDS-PAGE and multiangle laser light scattering indicated the presence of high molecular weight soluble species. These analyses, however, did not provide a measure of the degree of dispersion or distribution of sizes of the noncovalently associated products. Thus, the solubilized materials were pooled, concentrated, and subjected to size exclusion chromatography with on-line analysis by multiangle laser light scattering and absorbance measurements. Results are presented in Fig. 6. The concentration of protein in the eluate appeared as a single broad peak. The light scattering profiles from detectors at angles ranging from 26 to 163°also exhibited single peaks, with the peak maxima both decreased and displaced toward higher elution volumes with increasing angle. In addition, all scattering intensity peaks were shifted toward lower elution volumes in relation to the mass peak. That the positions of the peaks are not coincident indicates heterogeneity of the sample with respect to the molecular weights of its components (38). From these data, the weightaveraged molecular weight was calculated as a function of elution volume. The results are shown by the filled diamonds in Fig. 6. The chromatography was performed in 0.5 M NaCl to eliminate the weak nonionic interactions occurring between the products at 0.15 M NaCl, as inferred from the data shown in Fig. 4. A continuum of molar masses was observed, beginning with material having M w of ϳ1 ϫ 10 7 g/mol and progressing to a minimum of about 2.5 ϫ 10 5 g/mol, the size of the DD/E complex. These results confirm that plasmin-catalyzed fibrinolysis produces many products with different molecular FIG. 4. The effect of ionic strength on the weight-averaged molar mass of material solubilized from a perfused clot. The material solubilized between 140 and 180 ml from the perfusion experiment (Fig. 3) was collected, and the M w was determined. The NaCl concentration of the pooled material was then successively increased from 0.15 to 0.75 M, and the M w was determined at each different NaCl concentration. The material had a M w of 5.5 ϫ 10 6 g/mol at physiological NaCl (0.15 M), which decreased to a plateau of 3.8 ϫ 10 6 g/mol at 0.50 M NaCl. The figure shows that fibrinolysis produces degraded fibrin polymers of high molecular weight that weakly self-associate in a NaClsensitive manner.
weights ranging over almost 2 orders of magnitude.

SDS-PAGE Analysis of FDPs of Differing Molar Masses-
Fractions from the gel filtration experiment were subjected to SDS-PAGE analysis as shown in Fig. 7. Under nonreducing conditions, Fig. 7A, the materials of different masses can be seen to be composed of the same fundamental structural units (i.e. DD, DY, YY, etc.), suggesting that no unique cleavages are required to create products with the mass range observed. Indeed, the only differences observed between fractions were that the materials of higher M w contained larger covalently associated fragments, and the proportion of smaller fragments increased as the M w of the FDPs decreased. Interestingly, the fractions above M w of ϳ2.5 ϫ 10 6 g/mol were essentially indistinguishable by SDS-PAGE, illustrating the value of the data obtained from light scattering. Fig. 7B shows the same frac- conditions by SDS-PAGE. The labels under the lanes correspond to the material collected from either the initial wash following the 90-min incubation or during defined lysis intervals (eg. 0 -5 ϭ material from 0 to 5% lysis) and represent different stages of the perfusion experiment from beginning to end. Following the initial wash, the material solubilized at all points of the perfusion consisted of fragment E as well as covalently linked polymers of fragments D, Y, and X as shown in A. The overall pattern is that of a series of triplets, read from bottom to top, consisting of DX n D, DX n Y, and YX n Y, where n ϭ 0 to at least 8. The largest discernible band, corresponding to fragment DX 8 D, has a molecular mass of 2.3 ϫ 10 6 Da implying the existence of noncovalently associated species of at least 4.4 ϫ 10 6 Da in the eluate. The chain composition of the fragments from the perfusion was analyzed under reducing conditions as shown in B. At all points of lysis, the degraded fibrin polymers were composed of intact ␥ dimers (␥-␥), ␥ dimers with one ␥-chain cleaved (␥-␥ c ), or ␥ dimers with both ␥-chains cleaved (␥ c -␥ c ), as well as lower molecular weight ␥ products (␥Љ and ␥ٞ); "intact" ␤-chains (␤ and ␤Ј) or cleaved ␤-chains (␤Љ and ␤ٞ); and "intact" ␣-chain of 25 kDa (␣ 25 ) or cleaved ␣-chain (␣Ј and ␣Љ). C shows the results of scanning densitometry performed on the nonreduced and reduced gels. The results from the reduced gel show that the same amount of ␣-(ϳ48%), ␤-(ϳ62%), and ␥-(ϳ42%) chains are cleaved at all points of the perfusion. In addition, the results from the nonreduced gel show that the same fraction (ϳ 25%) of D-E triple-stranded connections are cleaved at all points of perfusion.
FIG. 6. Molecular weight distribution of the fibrin degradation products. The material collected from a perfusion experiment was pooled, made 0.5 M in NaCl, concentrated by ultrafiltration, and subjected to gel filtration on a Sephacryl S-1000 column. The eluate was passed through a spectrophotometer and a laser light scattering detector linked in tandem, and the resulting concentration ([FDP]), R , and M w profiles are shown. The concentration profile showed that the sample eluted as a single broad peak with a small shoulder on the trailing edge. The Rayleigh ratios initially show a strong angular dependence, which decreases during the profile, being almost coincident at the end. This is typical of samples that are heterogeneous with respect to molecular weight. The molar mass profiles showed that the sample consisted of a heterogeneous mixture of material ranging in molar mass from ϳ1 ϫ 10 7 g/mol (ϳ40 degraded fibrin monomers) to ϳ2.5 ϫ 10 5 g/mol (DD/E). tions analyzed by SDS-PAGE under reducing conditions. The figure shows that FDPs of differing masses are all formed through the same sets of cleavages, the ratio of cleaved chains to intact chains increasing with decreasing FDP size. Again, FDPs above M w of ϳ2.5 ϫ 10 6 g/mol were essentially indistinguishable by SDS-PAGE. Fig. 7C shows the results of densitometric analysis of the two gels. The extent of cleavage of all three chains was found to increase with decreasing FDP mass. The extent of cleavage for each chain rapidly decreased with increasing FDP mass, reaching plateau levels of 45% for ␣, 60% for ␤, and 40% for ␥. The proportion of D-E connections cleaved was found to have the same relationship with increased cleavage corresponding to decreased FDP mass. The larger fragments contained 20% cleaved D-E regions.
These results and the results obtained prior to gel filtration have implications in the mechanism of chain cleavage during fibrinolysis. If chain cleavage were completely random, then the proportion of D-E regions cleaved would be directly proportional to the extents of cleavage of the individual chains: D-E cleaved ϭ ␣ cleaved ϫ ␤ cleaved ϫ ␥ cleaved . This relationship was not observed for any of the different FDP masses or for the total pool of FDPs. In all cases, the proportion of D-E cleaved is significantly higher than can be explained by a random cleavage mechanism. From this we conclude that cleavage of the three chains does not occur independently of the cleavage state of neighboring chains. Cleavage of one chain at a D-E site would create a new carboxyl-terminal lysine or arginine, and these structures might, by attracting plasmin, cooperatively influence subsequent cleavage of the remaining chains at the same D-E site. The spatial proximity of neighboring chains may also play a role in the apparent cooperativity observed.
The Distribution of FDP Molar Mass during the Course of Fibrinolysis-A measure of the distribution of FDP molar mass in the protein eluted from a perfused clot is shown in Fig. 8, where the cumulative mass fraction is plotted against M w . The filled circles in Fig. 8 represent data taken from the gel filtration profile of Fig. 6. The data show, for example, that 50% of the eluted protein had M w of Յ2.5 ϫ 10 6 g/mol, and 80% of the eluted protein had a M w of Յ5.0 ϫ 10 6 g/mol. Likewise, 5% of the material had a M w of Ն7.5 ϫ 10 6 g/mol. These results clearly show that the products released from a perfused clot consist of a heterogeneous population with a large range of molecular weights. Furthermore, these results demonstrate that the "small" products DD/E, DY/YD, DXD/YY, and DXY/ correspond to the concentrated sample prior to gel filtration (Load) or the weight-averaged molar mass ( ϫ 10 Ϫ6 g/mol) of the pooled fractions following gel filtration. The labeling of the bands is the same as in Fig.  5. Nonreduced gel analysis (A) showed that the noncovalently associated degraded fibrin polymers separated by gel filtration differ by the presence of larger covalent species in the fractions with higher molar mass (i.e. a fraction with a higher molar mass contains all covalent fragments of a fraction with a lower molar mass). Furthermore, the fractions become essentially indistinguishable above a molar mass of 2.5 ϫ 10 6 g/mol, the only differences being in the relative amounts of the lower molecular weight bands. Reduced gel analysis (B) showed that all fractions contained the same ␣-, ␤-, and ␥-chain fragments, but the extents of cleavage varied according to molar mass of the fraction; fractions with a lower molar mass contained more of the cleaved products. C shows the relationship between molar mass and ␣-, ␤-, and ␥-chain cleavage from densitometric analysis of the reduced gel as well as the relationship between molar mass and the extent of cleavage of the triple-stranded D-E connecting regions as determined from the nonreduced gel. These data show that, regardless of their size, all fibrin degradation products are produced by the same series of limited and discrete cleavages. The data imply that fibrin degradation products of a particular mass consist, prior to denaturation, of covalent fragments with sizes ranging from fragment E and fragment D-D up to a fragment with one-half the mass of the fibrin degradation product. This largest covalent fragment would comprise one intact strand of the doublestranded fibrin degradation product. The solid lines in Fig. 8 represent efforts to account theoretically for the observed FDP molar mass distribution. Thus, fragment release was modeled according to Francis and Marder (19,20), wherein a protofibril consists of two noncovalently associated strands of fibrin monomers, which are composed of plasmin-sensitive nodes. The structure of the protofibril and the constituent plasmin-sensitive nodes may be represented by Scheme 1.
The production of a soluble fragment results from cleavage (q) at two sets of complementary nodes (with or without intervening cleavages) as illustrated by Scheme 2.
The probability of producing a fragment of any size (with the removal of soluble fragments as they are made, as in a perfused system) is equal to the probability of randomly cleaving any two complementary sites given the cleavage of two other complementary sites. This is the same as the probability of two cleavage events happening at any given distance (e.g. 3, 3Ј) from the first set of cleavages (Scheme 3).
Assuming that all sites are equally accessible, they would be cleaved with equal probabilities. All sequences of cleavage are thus equally probable (e.g. 1, 5Ј, 3Ј, 4Ј, 3 ϭ 3, 5Ј, 4Ј, 1, 3Ј ϭ 4Ј, 1, 5Ј, 3, 3Ј, etc.), and therefore the probability that two complementary sites are cleaved in any sequence of cleavages is the same for all sets of complementary sites. The result is that, in any system of random cleavage with fragment removal, all fragment sizes are made in equal stoichiometry. The solid curve labeled ⌬G 0 ϭ 0 in Fig. 8 is the expected cumulative mass curve based on the above statistical considerations. This curve clearly diverges from the observed relationship. These theoretical results were based on the assumption that fragments produced during lysis have no affinity for the remaining fibrin. Therefore, the model was modified to include the assumption that FDPs interact with residual fibrin with affinities that are directly proportional to the size of the fragment (i.e. the number of interaction sites on a fragment is directly proportional to fragment length, and thus larger fragments would have stronger affinities for the clot).
The binding energy for the interaction of a fragment containing a single site with the fibrin lattice (⌬G 0 single site ) is related to the equilibrium constant for the binding interaction (K single site), the gas constant (R), and temperature (T) by the following equation. Since binding energies are additive, the binding energy for a fragment with j sites is j ϫ ⌬G 0 single site , and the relationship to the equilibrium constant, K j , is as follows, and therefore Since ⌬G 0 single site , R, and T are all constants, the equation may be rewritten as follows, The equilibrium constant is, by definition, as follows,  8. The mass distribution of fibrin degradation products of varying molar mass. The plot shows the fraction of the total mass of the sample that is contained in a molar mass range. The data (q), taken from the gel filtration experiment of Fig. 6, show, for example, that 50% of the mass was contained in fragments of molecular mass less than or equal to 2.5 ϫ 10 6 g/mol, and 75% of the mass was in fragments of 4.2 ϫ 10 6 g/mol or less. Similarly, 10% of the mass was in fragments with molar mass greater than or equal to 6.7 ϫ 10 6 g/mol, and 2% was in fragments 7.9 ϫ 10 6 g/mol or greater. The solid lines represent the expected cumulative mass fraction curves derived from a model where there is binding of the degraded fibrin polymers to the residual clot. In the model, the random action of plasmin produces fibrin degradation products of all sizes in equal stoichiometry (see "Results"). The number of binding sites, j, each with binding energy ⌬G 0 , on a degraded fibrin polymer, is directly proportional to polymer length (mass). The strength of the binding is therefore proportional to exp(length) ϭ exp(j ϫ ⌬G 0 ). The binding interaction results in two phases of degraded fibrin polymers in equilibrium: solution phase (free) polymers and clot bound (bound) polymers. Only those polymers in the free phase can elute from the clot. As the relative binding energy per interaction, ⌬G 0 , increases from 0, the fragments bind more tightly to the clot, and the exponential relationship between length and binding strength results in a shifting of the curves to the left. The indicated relative ⌬G 0 values range from 0, where there is no binding, to 1 and represent the binding energy, in arbitrary units, for a single site on a polymer. The data are consistent with a model whereby smaller fragments bind with lower affinity than larger fragments and therefore elute in a greater molar amounts.
In the case where K j Ͼ Ͼ [ᏸ], there is no binding of the fibrin degradation products to the clot (f j ϭ 1), and all products produced elute in equal stoichiometry. In the case where the concentration of free lattice sites appreciably exceeds the value of K j , the relationship approximates to Equation 8.
Substitution from Equation 4 yields the following, Eq. 9) and the ratio of free fragments with j sites, relative to that with a single site is simply as follows.
Ϫ͑jϪ1͒⅐⌬G 0 single site R⅐T (Eq. 10) The lines in Fig. 8 show the expected cumulative mass fraction versus molecular weight curves resulting from increasing the relative single site binding energy, ⌬G 0 , and therefore the affinity of the fibrin degradation products for the clot.
The curves are derived by plotting the cumulative mass fraction function versus the molecular weight of the fragments. The value of the cumulative mass fraction function, C, at the molecular weight of a fragment with j sites, C j , is found from the following, where m r is the mass of a fragment with r sites, and f r is the fraction of fragments with r sites that are free, relative to the fraction of fragments with one site that are free (Equation 10). For the purpose of the model, the number of sites was based on the mass of the fragment, and only those fragments with a mass less than or equal to 1.0 ϫ 10 7 were considered, since fragments larger than this account for less than 0.1% of the total mass observed experimentally. While the definition of a site and the actual numbers of binding sites per fragment were arbitrarily assigned, a rigorous definition was not essential, since the fit of the model relied on the product of the binding energy, ⌬G 0 single site , and the number of sites, j, as shown in Equation 10 (increasing the number of binding sites/unit mass results in a decrease in the binding energy/site, and the same fit is generated). Fig. 8 shows that to a good approximation, the data are consistent with a mechanism whereby the affinity of fibrin degradation products for the clot is proportional to the size of the fragment. Larger fragments have a stronger affinity and are therefore not released as readily as smaller fragments, resulting in a cumulative mass fraction curve that is weighted toward smaller fragments. We conclude from this that FDPs associate with residual fibrin with binding energies that are directly proportional to the size of the FDP.
Root Mean Square Radius Determinations Indicate Significant Flexibility of FDPs-The RMSr of the material eluted from the gel filtration experiment was determined. The RMSr was found from the slope of a first-order fit of the Debye plot, using the method of Zimm (see "Experimental Procedures"). Fig. 9 shows the observed relationship between RMSr and M w (q) as well a rectangular hyperbolic fit through the points. The observed RMSr was 12 nm at M w ϭ 5 ϫ 10 5 g/mol, the mass of fragment DY/YD. This fragment should be as long as a fibrinogen molecule (47 nm (47, 48), 46 nm (49)), and indeed the RMSr approximates that of fibrinogen when treated as a rigid rod with a length (L) of 47 nm (RMSr ϭ ((L 2 /12) 0.5 ϭ 13.6 nm). An indication of the shape and flexibility of the FDPs was found from a plot of the slope of log(RMSr) versus log(M w ). The value of the slope of such a plot should be 1.0 for ideal rigid rods, 0.5 for an ideal random coil, and 0.33 for a perfect sphere. The value also depends on the flexibility and branching of the molecule (branched or flexible rods will have lower values than rigid rods), as well as intramolecular forces that (de)stabilize compact conformations. Fig. 9 shows how the point-to-point slopes of the log(RMSr) versus log(M w ) varied with M w . The plot shows that at low M w the FDPs behave as rigid rods, but as the M w increases, this relationship no longer holds. We interpret these results as an indication of the flexibility of the FDPs; increased fragment size yields increased fragment flexibility, resulting in significant deviations from the ideal rigid rod structure. These results indicate that large FDPs (greater than 1.5 ϫ 10 6 g/mol) possess significant flexibility. While the double-stranded protofibril structure of fibrin should not easily lend itself to high degrees of branching, the possibility that the observed results may be due to branching of FDPs cannot be excluded.

DISCUSSION
The model describing plasmin-mediated fibrin degradation proposed by Francis and Marder was constructed based on native and SDS-PAGE-derived structures of soluble fibrin degradation products (19,20) and the products released from a particulate clot upon washing a plasmin-treated suspension of ground, lyophilized fibrin with SDS (18). While this model adequately describes the required cleavage events that lead to the formation of the noncovalently associated soluble material FIG. 9. The dependence of the root mean square radius of degraded fibrin polymers on their molar mass. The plot shows the measured RMSr of the degraded fibrin polymers (q) (obtained from the slope of the first-order fit of the Debye plot, using the method of Zimm; see "Experimental Procedures" and Fig. 3) plotted against their M w values. The data are taken from the gel filtration experiment of Fig. 6. The data were fit to a rectangular hyperbola, and the resulting curve was used to construct a plot of log(RMSr) versus log(M w ). The point-topoint slopes from the log(RMSr) versus log(M w ) plot are indicative of the shape of the polymer and are shown here plotted against the molar mass of the degraded fibrin polymers. The figure shows that at low molar masses, the degraded fibrin polymers approximate a rigid rod (slope ϭ 1). As the molar mass increases, the slope decreases, indicating that the polymers attain increased flexibility with increased mass (length).
observed, no analysis of the stoichiometry of release, size distribution of materials, and chain composition of the soluble products has been described.
Previous work has identified very large FDPs in patients with chronic subdural hematoma (50) on the basis of electrophoretic mobility as well as demonstrated the existence of large molecular weight (ϳ2 ϫ 10 6 ) fibrin degradation products in patients who have disseminated intravascular coagulation (51).
The present study was undertaken to further investigate fibrin degradation in terms of product size, composition, and distribution with the aim of incorporating these results into an expanded model of plasmin-mediated fibrinolysis. The use of a perfused clot system coupled to multiangle laser light scattering has allowed for the determination of the M w of fibrinolytic products as they elute from the clot, under native conditions and in real time, as well as enabling the analysis of minimally degraded fibrin degradation products by gel filtration-coupled multiangle laser light scattering and by SDS-PAGE.
The results from the perfusion experiments indicated that at physiologic ionic strength, fibrin degradation products are primarily composed of very large polymers (greater than 1 ϫ 10 6 g/mol), which weakly self-associate. The observed decrease in M w from ϳ6 ϫ 10 6 at 0.15 M NaCl to a plateau of ϳ4 ϫ 10 6 at 0.5 M NaCl may be attributed to the shielding of weak ionic interactions existing between the fibrin degradation products. While unordered aggregation of the polymers cannot be ruled out, the results suggest that degraded fibrin polymers retain at least some of the sites required for lateral association, consistent with previous findings regarding the effect of ionic strength on the thickness of fibrin clots; increased ionic strength promotes the formation of thin fibers, presumably by inhibiting the lateral association of double-stranded protofibrils into thick fibers (45,46). The results suggest that fibrin degradation products produced in vivo may circulate as large, weakly associated complexes; such complexes would not be detectable using conventional analyses such as SDS-PAGE and enzymelinked immunosorbent assay. Additionally, this report demonstrates that traditional SDS-PAGE is unable to provide accurate determinations of the size of FDPs, since FDPs larger than 2.5 ϫ 10 6 g/mol are essentially indistinguishable by SDS-PAGE under both reducing and nonreducing conditions.
Multiangle laser light scattering analysis of the fragments separated by gel filtration showed that the fibrin degradation products generated through the action of plasmin in a perfused system comprise a broad distribution of molecular weights. The upper limit observed for M w (ϳ1 ϫ 10 7 g/mol) following gel filtration indicated that fragments containing as many as 40 DD/E complexes are released from a perfused clot. The mass distribution of FDPs was investigated and showed that 50% of the mass was accounted for by fragments with M w of Յ2.5 ϫ 10 6 g/mol. The remaining 50% was distributed among fragments with M w Յ ϳ1 ϫ 10 7 g/mol such that 45% of the total mass was contained in fragments with M w of Ն2.5 ϫ 10 6 and Յ7.5 ϫ 10 6 g/mol. The remaining 5% of the total mass was contained in fragments having M w of Ն7.5 ϫ 10 6 g/mol.
Analysis of the cumulative mass distribution according to two different models describing fragment release showed that FDPs are not released in equal stoichiometry, as would be predicted if the FDPs had no affinity for the fibrin clot. Instead, the data approximate a model whereby FDPs possess affinities for the residual clot proportional to the size of the fragment. Consequently, the cumulative mass fraction curve is shifted toward smaller fragments. That this type of interaction may occur is supported by two other observations from these experiments. First, the isolated fragments obtained from a peak fraction during the perfusion were found to self-associate in a manner that could be inhibited by increased NaCl concentrations. It is reasonable to conclude that the interactions leading to the self-association would also occur between the fragments and the residual clot. Second, when plasmin was reapplied to the clot (following the wash), the M w of the FDPs increased from an initial value of 3 ϫ 10 6 to 6 ϫ 10 6 g/mol over the first 60 ml (2 h) of fragment release. If the fragments did not bind to the clot, we would have expected that the M w of the eluting fragments would be the same at all points of the perfusion, but this was not observed. This effect cannot be explained as a function of FDP concentration, since the subsequent M w plateau occurred while the concentration of FDPs continued to increase. We interpret the results as follows: as the fragments are produced, they equilibrate with the clot according to their affinity, which is proportional to their size. Thus, a fraction of each different fragment size is free in the solution phase, and a fraction is bound to the clot; only those fragments in the solution phase will flow through the clot with the perfusate. The larger the fragment, the tighter the binding and, therefore, the more time required for elution from the clot. The observed M w increased over time as the fragments with higher affinity began eluting. The steady increase in M w reflects the differences in the time required for fragments of different sizes to elute.
The cumulative molecular weight profile may be further skewed toward smaller fragments, compared with the case in which no binding occurs, since binding of fragments to the clot would tend to result in larger fragments being exposed to plasmin for a greater period of time, resulting in the cleavage of larger fragments into smaller fragments. Preliminary computer modeling has shown that a similar cumulative molecular weight profile is generated when additional proteolytic attack of the fragments is accounted for and that the fit generated requires lower binding energies of the fragments than a model where no additional cleavage of the fragments occurs.
Analysis of the root mean square radius of the fibrin degradation products provided insight into the shape and flexibility of the fibrin degradation products. The fragments separated during gel filtration were shown to have RMSr values ranging from ϳ12 nm at M w ϭ 5 ϫ 10 5 g/mol to ϳ85 nm at M w ϭ 8.0 ϫ 10 6 g/mol. The relationship between the observed M w and the RMSr was fit to a rectangular hyperbola, and the slope of the curve of log(RMSr) versus log(M w ) was plotted against M w . Assuming a rigid rod model for the structure of the fibrin degradation products, the slope of the plot was expected to be 1.0 at all M w , since increases in both the RMSr and the M w for a rigid rod are directly proportional to fragment length. As seen in the plot, the relationship approaches the theoretical value of 1.0 for a rigid rod at lower M w but deviates from this relationship progressively as the M w increases.
The flexibility of fibrin degradation products may arise from three related sources. First, fibrinogen and fibrin protofibrils have been shown to possess intrinsic flexibility (52), and it is reasonable to conclude that fibrin degradation products will also possess intrinsic flexibility. The amount of flexibility (movement) of a fibrin degradation product, relative to the long axis of the protofibril, is related to its length such that longer protofibrils possess greater flexibility. Secondly, flexibility may result from the cleavage of monomers at the plasmin-sensitive sites between the disulfide rings. The data from SDS-PAGE under nonreducing conditions indicated that ϳ25% of the D-E connecting regions of fibrin monomers were cleaved at all three chains, and the data from SDS-PAGE performed under reducing conditions indicated that a further ϳ20% were cleaved at two of the three chains. Assuming a random distribution for cleavage sites, all fragments produced would have ϳ25% of all internal D-E connecting regions cleaved. At the points of complete D-E cleavage, the double-stranded protofibrils would assume the flexibility of a single strand, freed from the restricted movement imposed by reciprocal binding to a second strand. Additionally, at sites where one monomer has been completely cleaved and the adjacent, reciprocal site has had two of the three chains cleaved, the degradation product would assume the flexibility of a single, extended polypeptide. Finally, a third source of flexibility is that the D/E interface of noncovalently associated monomers may have some movement/rotation with respect to the long axis of the strand containing the fragment E monomer. While movement of this kind occurring in a doublestranded product may be limited, and while free rotation of the D/E interface seems unlikely, complete cleavage of one strand of the protofibril, as discussed above, would enable the maximum allowable rotation of the D/E interface.
The work described in this paper shows that fibrinolysis is a complex process leading to the formation of a range of FDPs of varying masses and flexibilities that associate both with the clot and with themselves. An analysis of fragment release and chain structure of FDPs indicates that fibrinolysis occurs through limited and discrete cleavage, such cleavage not being completely random, producing structures that cannot be adequately discriminated on SDS-PAGE gels. Future work aimed at defining a model of plasmin-catalyzed fibrinolysis should be reconcilable with the aspects of fragment production and release that have been described here.