Kinetics of formation of fibrin oligomers. I. Theory

The course of formation of fibrin oligomers is treated theoretically for the condition that self-assembly of fibrin monomers is rapid compared with the loss of A peptides by the enzymatic action of thrombin. The rate constant for removal of the second A peptide is taken to be larger than that for the first by an arbitrary factor q; the association of activated A sites with their complementary a sites is assumed to be random and independent of oligomer size. Two types of oligomers are considered: noncovalently bonded protofibrils formed by the staggered overlap of thrombin-activated monomers and covalently bonded linear oligomers formed by factor XIIIa-mediated end-to-end ligation of adjacent monomers within protofibrils. Oligomers of the first type, if ligated, are dissociated to oligomers of the second type by solubilization in SDS–urea. Theoretical curves are presented for x _w and x ′_w (weight-average degree of polymerization of staggered overlap and linear ligated oligomers, respectively) and for the weight fractions of monomer, dimer, and decamer of both ligated and unligated species as functions of y, the fraction of A peptide removed; and also for w_x and w′_x, the weight fractions of x-mer of the respective oligomer types, as a function of x at y = 0.5. With increasing q, the maximum w_x or w′_x that a low oligomer will reach during the reaction decreases and the size distribution is broadened toward larger oligomers. Comparison with experiment is made in a companion paper.     

Kinetics of formation of fibrin oligomers. III. Ligation kinetics concurrent with and subsequent to oligomer assembly

Human fibrinogen was treated with thrombin in the presence of fibrinoligase (Factor XIIIa) and calcium ion at pH 8.5, ionic strength 0.45, and the ensuing polymerization was interrupted at various time intervals (t) both before and after the clotting time (t_c) by solubilization with a solution of sodium dodecyl sulfate and urea. Aliquots of the solubilized protein were subjected to gel electrophoresis on polyacrylamide gels after disulfide reduction by dithiothreitol and on agarose gels without reduction. The degree of γ-γ ligation was determined from the former. The latter provided the size distribution of ligated end-to-end sequences produced by splitting the ligated staggered overlapped oligomers down the middle, for degrees of polymerization, x, from 1 to 10. Addition of fibrinoligase (in which the activating thrombin had been inhibited by p-nitrophenyl-p′-guanidinobenzoate, NPGB) to Kabi fibrinogen showed the presence of small amounts of ligatable oligomers. Addition of fibrinoligase to a polymerizing mixture in which the action of thrombin had been stopped before clotting by NPGB produced the same distribution of ligated end-to-end sequences that was obtained when fibrinoligase was originally present, at least for reaction times up to 0.7 of the clotting time. The kinetics of γ-γ ligation by fibrinoligase acting on a polymerized mixture stabilized by NPGB were followed. The reaction was first order in the concentration of ligatable γ-γ junctions and the initial velocity was proportional to the enzyme concentration. The time evolution of size distribution of ligated end-to-end sequences agreed with a theory based on random ligation of ligatable junctions.     

Gel formation by fibrin oligomers without addition of monomers

Soluble fibrin oligomers were formed by reacting fibrinogen with thrombin under fine clotting conditions where the action of thrombin is the rate-determining step for polymerization, and by inhibiting the reaction shortly before gelation. Oligomeric fibrin was separated from unreacted fibrinogen and small oligomers by gel permeation chromatography. Electron microscopy revealed that the largest soluble fibrin oligomers resemble the protofibrils present in fine clots, but are somewhat shorter and entirely lack the twisted, trifunctional junctions that contribute to the elastic properties of fine clots. When thrombin was added to the soluble fibrin oligomers, polymerization resumed and clots were formed at a more rapid rate than from fibrinogen at the same concentration and resulted in a less-opaque clot under coarse clotting conditions. The results confirm a prediction of a theory for the polymerization of fibrin and provide additional evidence that the final state of a coarse fibrin clot depends on the mobility of protofibrils during its formation.     

Identification of fibrin oligomers in sonicated fibrin clots

Clots of bovine fibrin, with both coarse and fine structure, and ligated to different extents by fibrinoligase, have been broken up by ultrasonic agitation and the sonicates have been examined by ultracentrifugal sedimentation. Sonication is followed by gross aggregation of the fragments unless guanidine hydrochloride is introduced (order of 1 M). In that case, sonicates of gamma-ligated fine clots contain two species whose sedimentation coefficients correspond to fibrin monomer and an oligomer with twice the monomer cross-section area and at least 20 monomer units, presumably with the structure of lateral dimerization with staggered overlapping. If the gamma ligation is incomplete, shorter oligomers are identified. The monomer and oligomer with degree of polymerization greater than 20 appear also in sonicates of coarse clots, but in smaller amounts, the principal product consisting of larger aggregates. The implications of these results with respect to metastability of the fine clot and the pattern of polymerization are discussed.     

Structural transformations of fibrin oligomers

The morphology of equilibrium of soluble fibrin oligomers at different stages of assembly was studied. Results of Rauleigh's light scattering, analytical ultracentrifugation and viscosimetry show that fibrin-polymers throughout the entire homology range present rigid, rod-like structures dispersed by weight and dimensions. It was shown, that along with the traditional double-stranded chain protofibrills, where the monomer molecules are connected "end-to-center", there is an alternative variant, which is a result of single-stranded chain dimerization, where the monomers are formed up in an "end-to-end" fashion. Identity of physicochemical features of fibrin oligomers obtained by means of different enzyme activation of fibrinogen indicates that E1 and E2 sites interact with the complementary D1 and D2 sites only at the stage of protofibrill formation. It is suggested that the lateral aggregation is initiated by other sites that exist in fibrinogen and fibrin-monomer molecules in an accessible state. Thermodynamic reasons for the cooperative ability of protofibrill aggregation processes and gel-formation are discussed.     

Kinetics of rouleau formation. II. Reversible reactions.

Red blood cells aggregate face-to-face to form long, cylindrical, straight chains and sometimes branched structures called rouleaux. Here we extend a kinetic model developed by R. W. Samsel and A. S. Perelson (1982, Biophys. J. 37:493-514) to include both the formation and dissociation of rouleaux. We examine thermodynamic constraints on the rate constants of the model imposed by the principle of detailed balance. Incorporation of reverse reactions allows us to compute mean sizes of rouleaux and straight chain segments within rouleaux, as functions of time and at equilibrium. Using the Flory - Stockmayer method from polymer chemistry, we obtain a closed-form solution for the size distribution of straight chain segments within rouleaux at any point in the evolution of the reaction. The predictions of our theory compare favorably with data collected by D. Kernick , A.W.L. Jay , S. Rowlands , and L. Skibo (1973, Can. J. Physiol. Pharmacol. 51:690-699) on the kinetics of rouleau formation. When rouleaux grow large, they may contain rings or loops and take on the appearance of a network. We demonstrate the importance of including the kinetics of ring closure in the development of realistic models of rouleaux formation.     

Soluble fibrin consists of fibrin oligomers of heterogeneous distribution

Soluble fibrin is observed in patients with intravascular coagulation and represents an intermediary product of conversion of fibrin monomers into a fibrin clot whereby the presence of fibrinogen may suppress fibrin clot formation. The interactions between fibrin and fibrinogen and the occurrence of fibrin oligomers in soluble fibrin were studied by sucrose density ultracentrifugation. Different concentrations of soluble fibrin, prepared by mixing 125I-fibrin (24 nM - 1.5 microM) with a constant concentration of 131I-fibrinogen (6 microM) were analyzed at 37 degrees C in stable linear sucrose density gradients containing a uniform concentration of unlabelled fibrinogen (6 microM) and calcium ions in order to mimic the physiological situation. At any fibrin concentration, 125I-fibrin sedimented faster than 131I-fibrinogen through 5-30% (w/v) sucrose gradients. Sedimentation rates of fibrin increased from 9 S to 23 S depending on the initial fibrin concentration. The relative amount of residual fibrin monomer not incorporated into oligomers was calculated from the sedimentation profiles. At any fibrin concentration, the portion of free monomer was always more than twofold higher for batroxobin-generated (desAA-) fibrin than for thrombin-generated (desAABB-) fibrin. Apparent association constants for desAABB-fibrin were 3-10 times higher than those for desAA-fibrin indicating a stronger interaction between monomers of the former type of fibrin. In the presence of excess fibrinogen the predominant species in soluble desAA-fibrin were monomers and dimers, whereas dimers, trimers and higher-molecular-mass oligomers were present in soluble desAABB-fibrin. Strong interactions between both types of fibrin were demonstrated from their cosedimentation, whereby the size of these copolymers were shown to be governed by the oligomer size of the desAABB-fibrin type. These results provide evidence for the occurrence of differently sized oligomers of fibrin in soluble fibrin and for the concept of a cooperative polymerization process between both types of fibrin devoid of any stable complexes between fibrin and fibrinogen.     

Interaction of fibrinogen-binding tetrapeptides with fibrin oligomers and fine fibrin clots

The polymerization of fibrin, at pH 8.5 and ionic strength 0.45, and under conditions where the action of thrombin on fibrinogen was the rate-determining step, was interrupted by inactivating thrombin with p-nitrophenyl-p′-guanidinobenzoate (NPGB). Addition of the tetrapeptide Gly-Pro-Arg-Pro (GPRP) partially dissociated the fibrin oligomers as shown by subsequent ligation with Factor XIIIa and calcium ion followed by denaturation and gel electrophoresis; polyacrylamide gel electrophoresis with reduction showed a decrease in the proportion of γ-γ ligation compared with controls untreated by GPRP, and agarose gel electrophoresis showed a shift in the distribution of oligomer sizes. The dissociation was accomplished within 15 min and its extent was consistent with establishment of an equilibrium in which two molecules of GPRP react to sever an oligomer. When GPRP was introduced into fine unligated fibrin clots by diffusion, there was some dissociation as shown by differences in the degree of γ-γ ligation after treatment by Factor XIIIa; but the action of GPRP was much slower and less complete than on soluble oligomers. However, even a small amount of dissociation affected the mechanical properties of fine clots profoundly. The shear modulus (measured 25 s after application of stress) decreased progressively with increasing concentration of GPRP introduced by diffusion. The rate of shear creep under constant stress and the proportion of irrecoverable deformation also increased enormously. If the steadystate creep rate is interpreted in terms of an effective viscosity, the latter is decreased by up to three orders of magnitude by the presence of GPRP. In terms of transient network theories of viscoelasticity, the average lifetime of a network strand is greatly diminished. However, the total density of strands remains constant during creep and creep recovery as shown by constancy of the differential modulus or compliance. Removal of GPRP by diffusion only partially restores the original shear modulus and creep behavior of the original clot. Some limited data on the effect of the tetrapeptide Gly-His-Arg-Pro are also reported.     

Self-assembly of soluble unlinked and cross-linked fibrin oligomers

Self-assembly of soluble unlinked and cross-linked fibrin oligomers formed from desA-fibrin monomer under the influence of factor XIIIa was studied in the presence of non-denaturing urea concentrations. By methods of elastic and dynamic light scattering combined with analytical ultracentrifugation, desA-fibrin oligomers formed in both the presence and absence of the factor XIIIa were shown to be ensembles consisting of soluble rod-like double-stranded protofibrils with diverse weight and size. Unlinked and cross-linked soluble double-stranded protofibrils can reach the length of 350–450 nm. The structure of soluble covalently-linked protofibrils is stabilized by isopeptide γ-dimers. Electrophoretic data indicate a complete absence of isopeptide bonds between α-chains of desA-fibrin molecules. The molecular mechanism of formation of soluble rod-like fibrin structures and specific features of its covalent stabilization under the influence of factor XIIIa are discussed.     

Formation of soluble fibrin oligomers in purified systems and in plasma.

The kinetic parameters for release of fibrinopeptide A (FPA) from human fibrinogen by thrombin are: Km = 2.3 X 10(-6)M and Vmax. = 1.1 X 10(-10)mol of FPA/s per unit of thrombin; for fibrin formation, Km is similar to that for FPA release, but, the conditions of the present study, Vmax. was approximately half of that for FPA release. The formation of fibrin polymer before the sol-gel transition was studied by gel-permeation chromatography combined with effluent analysis for fibrinogen antigen and residual FPA. Polymer formation in purified fibrinogen incubated with thrombin proceeded as a bimolecular association of exposed sites in a manner predicted by probability calculations and assuming random FPA cleavage. Each oligomer consisted of n molecules of fibrin monomer and two fibrinogen molecules, each of the latter lacking one FPA molecule, i.e. each oligomer, regardless of molecular size, retains two FPA molecules. The addition of 5 mM-CaCl2 to the reaction mixture changed the rate of polymer formation, so that dimer was no longer the prevalent oligomer; in the presence of Ca2+, the trimer was the oligomer in highest concentration. The polymers formed in the presence of calcium were similar in composition to those without, i.e. 2 mol of FPA/mol of oligomer. EDTA-treated plasma samples incubated for short periods of time, 30s or less, with thrombin ranging in concentration up to 1 N.I.H. unit/ml did not form clots during the 10-15 min period of observation until they were applied to the column, though a large proportion of the available FPA was cleaved (maximum 45%). The soluble polymers in plasma were mostly of the high-Mr variety (tetramer and greater); these high-Mr polymers contained less than 2 mol of FPA/mol of polymer, whereas dimer and trimer in plasma were similar to those in the purified systems, i.e. 2 mol of FPA/mol.     

Kinetics of fibrin clot lysis

The principles relating the lysis times of fibrin clots to their contents of fibrin, plasminogen and plasminogen-activator were investigated. Mathematical considerations suggested that the square of the lysis time should correlate linearly with the fibrin content, and inversely with the activator and the plasminogen contents of the system. Experimental studies, during which these parameters were independently varied, showed that the predicted relationships were valid for concentrations that gave clot-lysis times in the range normally used for studies of fibrinolysis.     

The kinetic significance of cell size : II. Size distributions of resting and proliferating cells during interphase

This second part in a two part report describes the kinetic, cell size and nuclear size characteristics of S phase cells and cells with greatly protracted generation times (‘resting’ cells) in a cell line of human lymphoid cells. The median cell and nuclear sizes of S phase cells were greater than the corresponding median sizes observed in the whole population. Resting cells (operationally defined as unlabelled cells after 5 days of continuous labelling with [³H]TdR) have cell and nuclear size distributions overlapping with the cell and nuclear size distributions of the whole population. These resting cells are kinetically characterized by means of the observed labelling index vs time data during continuous labelling. The implication of these results are discussed.     

Polymorphism of fibrin equilibrium oligomers in the presence of fragment D

The methods of viscosimetry, the Rayleigh light-scattering and analytical ultracentrifugation were applied to study the physicochemical mechanism of the effect of fragment D on the structure of fibrin equilibrium oligomers. Using the values of intrinsic viscosity, weight average molecular masses and mass/length ratio it was shown that when producing an antipolymerization effect the fragment D retains the three-dimensional organization of fibrin polymers, i.e. rigid rod-like single- and double-stranded protofibrillas. The paper has proved that along with the traditional mechanism of inhibiting self-assembly of of the double-stranded structure due to the competition of fragment D with fibrin monomer for central domain E there is an alternative attributed to its attachment to a peripheral region of the fibrin monomer. The second mechanism is the only one which occurs in the region of single-stranded pseudoprotofibrillas existence. The role of alpha C-domains in protein-protein interactions is also discussed.