Formation of Fibrin Gel in Fibrinogenâ Thrombin System: Static and

Biomacromolecules 2002, 3, 1013-1020

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Formation of Fibrin Gel in Fibrinogen-Thrombin System: Static and Dynamic Light Scattering Study Rio Kita,†,‡ Atsuo Takahashi,†,§,| and Makoto Kaibara† Supramolecular Science Laboratory, RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan, and Department of Physics, Faculty of Science, Science University of Tokyo, Shinjuku, Tokyo 162-0825, Japan

Kenji Kubota* Department of Biological and Chemical Engineering, Faculty of Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan Received April 2, 2002; Revised Manuscript Received May 27, 2002

The dynamics of thrombin-induced fibrin gel formation was investigated by means of static and dynamic light scattering. The decay time distribution function, obtained by the dynamic light scattering, clearly revealed a stepwise gelation process: the formation of fibrin and protofibril from fibrinogen followed by the lateral aggregation of protofibrils to form fibrin fibers and the formation of a three-dimensional network consisting of fibers. This conversion process was correlated with the angular dependence of the scattered light intensity (static light scattering). The correlation function of dynamic light scattering was analyzed in terms of solgel transition and gel structure. The correlation function showed a stretched exponential type behavior before the sol to gel transition point, and it showed a power law behavior at the gelation point. 1. Introduction The various physicochemical properties of gels are strongly correlated to the structure of cross-linking polymer chains and bridging sites, and the network structure is an essential factor in the characterization of the intrinsic properties of gels. The study of dynamic process of network formation (gelation) is, therefore, quite important for revealing the structure and properties of the gel, since the structure of a three-dimensional network is dependent on the kinetics of junction formation. A lot of studies have been conducted on various aspects of gelling systems of flexible polymers. However, the specific gel properties of rodlike polymers are not clear at present, although they would be expected to show many different features due to chain rigidity. The effect of chain rigidity on the dynamic mechanism of network formation is also of great interest. For example, poly(γbenzyl-L-glutamate) (PBLG) is a typical rodlike polymer which has been studied in terms of sol-gel transition and shows unique and complex behaviors.1 The observed gelation of PBLG is both concentration and temperature dependent because the gelation competes with phase separation. The interplay with the phase separation makes the detailed * To whom correspondence may be addressed. Fax: +81-277-30-1447. E-mail: [email protected]. † Supramolecular Science Laboratory, RIKEN (The Institute of Physical and Chemical Research). ‡ Present address: Max-Planck-Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany. § Department of Physics, Faculty of Science, Science University of Tokyo. | Present address: Surface Characterization Division, RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan.

analysis of gelation complex. Recently, Ferri et al. reported on a study of the gel structure of fibrinogen solution by use of small-angle light scattering techniques.2 They obtained various gel parameters which are characteristic to the fibrin network. For exapmle, the average diameter of lateral aggregation of fibrin fibers was determined to be 130 nm. The network structure was examined relating to the fractal dimension, and the angular dependence of the scattered light intensity was analyzed by special scattering functions. However the dynamical aspect of the gelling process of fibrinogen solution remains unclear. Fibrinogen is a rod-shaped protein with a molecular weight of 3.4 × 105 and plays essential roles in various pathological processes, including hemostasis, thrombosis, and adhesion and aggregation of platelets. Fibrin gel is the primary structural component of blood clots. The transformation of fibrinogen into fibrin gel is thought to involve several distinct steps. The first is the specific cleavage of small peptides, which are referred to as fibrinopeptides A and B, from the central domain of the fibrinogen molecule by the serine protease, thrombin. The cleaved fibrinogen is referred to as fibrin, which has binding sites at its central domain, and these binding sites interact with complementary sites on the end groups of two other fibrin monomers. The spontaneous association of fibrin molecules forms oligomers with halfstaggered overlapping. The resultant two-stranded protofibrils further aggregate laterally in the succeeding step to form fibers and a three-dimensional network.3 The dynamic process of the respective steps from fibrinogen to fibrin gel has been studied from the rheological standpoint4-9 and by use of the light scattering and turbidity methods.10-14 To

10.1021/bm025545v CCC: $22.00 © 2002 American Chemical Society Published on Web 07/03/2002

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clarify the gelling process, kinetic analyses have also been carried out extensively.15-17 However, it is difficult to characterize the physicochemical properties of fibrin and/or protofibrils at the molecular level in the respective steps during the time course of gelation because the system is undergoing a reaction. Recently the role of fibrinopeptides A and B in terms of the relationships between the functions and structure of fibrin(ogen) have attracted much attention, and studies of biochemical aspects for fibrin(ogen) have been carried out.18-21 Therefore, studies of the gelling process at a molecular level are desired to confirm the mechanism of the fibrin gelation as well as the functions of fibrinopeptides A and B. Recently we have reported on the temporal evolution of dynamic light scattering by analysis of the decay time distribution function and found that the dynamic light scattering technique could be applied for the characterization of the dynamic process of fibrin gelation.22 The correlation function of the scattered light intensity, g(2)(t), defined as g(2)(t) ) 〈I(0)I(t)〉/〈I(0)〉2 includes the information on the density fluctuation and the topological structure of polymer components. Here, I(t) denotes the scattered light intensity and t the delay time. The scaling behavior of g(2)(t) against the delay time has been discussed in terms of dynamic aspects for the fractal dimension using a percolation model of gelling systems.23 Moreover, the decay time distribution function G(τ) derived by the Laplace inversion of the correlation function is related to the dynamic properties of the constituent chains and the constrained collective motions in the sol and gel states. Usually, studies of gel structure and gelation phenomena by means of light scattering have been carried out using various systems comprised of synthetic materials such as poly(methyl methacrylate),24 polyurethane25 and polysiloxane,26 polysaccharides such as cellulose derivatives27 and gellan gum,28 and globular proteins such as bovine serum albumin,29 and so on.30-32 There are only a few reports for gels composed of rod-shaped polymers as it is difficult to characterize their solution properties.33 In this paper, we investigated the dynamic process of fibrin gel formation by analyzing the temporal evolution of static and dynamic light scattering. The structure of the fibrin gel network was also examined by analyses of the correlation function and the decay time distribution function. Static light scattering was analyzed in terms of the formation of protofibrils. Sample solutions with different final concentrations of thrombin in the same fibrinogen concentration were used to produce suitable measurement conditions for static and dynamic light scattering. Low concentrations of thrombin were used, so that the gelation process should be sufficiently slow to enable the angular dependence measurement of scattered light intensity, and therfore it was possible to clearly describe the essential characteristics of network structure. 2. Materials and Methods Bovine fibrinogen (clottability 97%), from Sigma-Aldrich Co., was dissolved in a 0.15 M phosphate buffer solution at pH 7.4, which consists of Na2HPO4, KH2PO4, KCl, and NaCl. The solution was then dialyzed against the buffer

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solution for 24 h. The concentration of the fibrinogen solution was determined from the absorbance at 280 nm using a specific absorption coefficient (1.51 mL/mg cm).34 A final fibrinogen concentration of 0.22 g/100 mL was used for all the measurements. Purified bovine thrombin, obtained from Mochida Co., Japan, was also dissolved in the phosphate buffer solution. Just before the measurements, solutions of fibrinogen and thrombin were mixed and the time of mixing was denoted as the elapsed time te ) 0 in the time course of gelation. The final concentrations of thrombin were set to 0.02 and 0.00125 NIH units/mL.35 Hereafter, we designate the solutions of 0.02 NIH units/mL of thrombin in 0.22 g/100 mL of fibrinogen solution as sample A and of 0.00125 NIH units/mL thrombin in 0.22 g/100 mL of fibrinogen solution as sample B. Low concentrations of thrombin were used to ensure accurate measurements of the time evolution and to compare with each other in order to elucidate the concentration effect of thrombin. Dynamic light scattering measurements were carried out using a homemade spectrometer and an ALV-5000 multipletau digital correlator to obtain the correlation function g(2)(t) and the averaged scattered light intensity 〈I〉 simultaneously. Two light sources were used, a He-Ne laser with wavelength λ ) 632.8 nm and an Ar ion laser with λ ) 488.0 nm for samples A and B, respectively. Details of the apparatus have been described elsewhere.28,36,37 The measurements of g(2)(t) in the time course of gelation were carried out at a scattering angle θ ) 30° using homodyne detection, and the acquisition period of g(2)(t) was 90 s. We carried out static light scattering measurement, too, in the gelling process over the angular range of 30°-120°. For the light scattering measurements, the mixed solution of fibrinogen and thrombin was placed in a cylindrical cell with an optical path length of 6 mm by passing it through a membrane filter of 0.2 µm pore size immediately after the mixing. The sample preparation was carried out in a clean drybox in order to prevent contamination of impurities. The temperature of the sample cell was controlled at 37.00 ( 0.01 °C. The sample A was employed to measure the dynamic light scattering, but the static light scattering measurements could not be carried out because the reaction process was too fast to collect the angular dependence of scattered light intensity. Sample B was employed for both the static and dynamic light scattering as the use of sample B ensured a very slow progress of gelation due to very low thrombin concentration although the acquisition time to obtain the correlation functions was still fairly restricted. 3. Data Analysis Correlation functions of scattered light intensity g(2)(t) were analyzed by the inverse Laplace transformation program (constrained regularization program, CONTIN) developed by Provencher.38 g(2)(t) has the following form related to the normalized electric field correlation function, g(1)(t) as g(2)(t) - 1 ) b|g(1)(t)|2

(1)

where b is a machine constant relating to the coherence of detection. Generally, g(1)(t) is expressed by the distribution

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function G(τ) as a function of the characteristic decay time τ as g(1)(t) )

∫G(τ) exp(-t/τ) dτ ) ∫τG(τ) exp(-t/τ) d(ln τ)

(2)

where ∫G(τ) dτ ) 1. That is, g(1)(t) is the Laplace transformation of G(τ). τG(τ) corresponds to the scattered intensity of the mode having the characteristic decay time τ when the distribution is expressed against the logarithmic scale of decay time. At the gelation point, three-dimensional network structure develops up to the macroscopic scale and the density (concentration) fluctuation begins to have a self-similar nature. Therefore, the correlation function g(1)(t) has no characteristic time and shows a power law behavior, as has been observed in various gelling systems1,26,39-42 g(1)(t) ∼ t-φ

(3)

then, g(2)(t) is expressed as a sum of a cooperative diffusional mode relating to the entangled (crossbridged) structure and a power law behavior, which was first reported by Martin et al.42,43 as g(2)(t) - 1 ∼ [A exp(-t/τf) + (1 - A)(1 + t/τ′)-φ]2 (4) Here, A is an amplitude factor of the relative scattered intensity, and τf and τ′ are the characteristic decay time of the fast (cooperative) mode and the lower cutoff time of the power law behavior, respectively. The exponent φ relates to the fractal dimension. On the other hand, g(2)(t) of the pregel solution is well described similarly by the stretched exponential form as

Figure 1. Time evolution for the scattered light intensity at θ ) 30° for the fibrinogen-thrombin system. (a) and (b) correspond to sample A (high concentration of thrombin) with λ ) 632.8 nm and sample B (low concentration of thrombin) with λ ) 488 nm, respectively.

being defined as q ) (4πns/λ) sin θ/2 with ns being the refractive index of the solution. In this expression the contribution of the concentration dependence is neglected. Since the Rayleigh ratio, Rθ, is proportional to the excess scattered light intensity I, the slope of the plot of I-1 vs sin θ/2 gives a weight-averaged mass per length ratio ∑Miwi/Li. The values of refractive index ns ) 1.334 and the increment of the index (dn/dc) ) 0.192 mL/mg were used.46

g(2)(t) - 1 ∼ {A exp(-t/τf) + (1 - A) exp[-(t /τs)β]}2 (5) Here, τs is the characteristic decay time of the slow stretched mode. Approaching the sol-gel transition point, the correlation function g(2)(t) varies from the stretched exponential form to the power-law one with β decreasing to zero and τs diverging.42,43 The technique of static light scattering is applied to determine the molecular parameters in dilute solutions. For highly cylindrical particles having length distribution (or molecular weight distribution), it is known that the mass per length ratio M/L is obtained by defining the scattering factor P(θ) ) (1/x) ∫ (1/z) sin(z) dz - [(1/x) sin(x)]2 ∼ π/2x 1/2x2 - ... at x . 1, where x ) (2πnsL/λ) sin θ/2 ) qL/2 with L being the length of the particle, according to Casassa44 and Holtzer.45 Then, the Rayleigh ratio Rθ is expressed as Kc/Rθ ) 1/∑MiwiPi(θ) ) (2/π2)(∑Miwi/Li2)/(∑Miwi/Li)2 + (q/π)/(∑Miwi/Li) + ... (6) where K is the optical constant, c the concentration of the sample solution, and Mi the molecular weight and wi the weight fraction of the ith solute species. q is the wave vector

4. Results and Discussion Entire Behavior of Gelation by Scattered Light Intensity. Parts a and b of Figure 1 show the scattered light intensity 〈I〉 at the scattering angle θ ) 30° as a function of the elapsed time te for samples A and B, respectively. 〈...〉 indicates the average over the acquisition time (ca. 1 min). The temporal growth of the scattered light intensity can be separated into three time regions: (1) initial lag and slow increase, (2) a rapid increase, and (3) a leveling-off behavior with oscillation. It is considered that these regions correspond to the gelation kinetics as (1) the cleavage of fibrinopeptides and the formation of protofibrils, (2) the lateral aggregation of protofibrils and the gelling process, and (3) the further growth of the gel network. These points are ascertained by the following results of static and dynamic light scattering. The fluctuating and oscillating behaviors of scattered light intensity were observed for te > 80 min (sample A) and te > 400 min (sample B). The results indicate the appearance of structural inhomogeneity of the gel components, which is characteristic of the nonergodic nature of the gelling system. In both systems the elapsed times for the appearance of a strong fluctuation are larger than the gelation times

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Figure 2. Casassa-Holtzer plots of the time evolution of static light scattering for sample B. Numbers in the figure mean the elapsed time (min). The dashed line has a slope corresponding to the case of (number of fibrinogen molecules)/(cross section) ) 2.

determined by the scaling behaviors and the coherence factor of g(2)(t) - 1, as described below. The difference between these two times would originate partly from the slow reaction rate, and this result seems to be a characteristic property of fibrin gelation. Time Evolution of Angular Dependence of Scattered Light Intensity. Figure 2 shows the results of the time evolution of static light scattering in an angular range of θ ) 30-120° by use of Casassa-Holtzer (C-H) plots for sample B. The numbers inside the figures indicate the elapsed time te (min), and the lines were drawn to guide the eyes. The scattered light intensity increased with increasing elapsed time te. This behavior corresponds to the fact that the molecular weight of fibrin components becomes larger, i.e., protofibril formation, fiber formation, and gelation. For te e 230 min, the slope of curves at high angles (sin θ/2 > 0.5) becomes larger gradually with time. The value of massto-length ratio M/L was calculated using eq 6 from the slope at high angle region, which must be essentially linear for 85 e te e 230 min. The obtained M/L was 1.2 × 1011 g/mol cm at te ) 230 min. This value gives the number of fibrinogen molecules per the cross section of protofibrils as 1.6, assuming that the fibrinogen molecule is a rigid-rod, with a molecular weight of 3.4 × 105 and the length of 45 nm. The result means that on average 1.6 fibrinogen molecules per cross section of protofibrils aggregate to form protofibrils. It should be noted that the obtained M/L value is the weight averaged value, according to eq 6. Since the protofibril has the double-stranded and staggered overlapping shape, the value of M/L for protofibril would be expected to be twice that of fibrinogen: in other words, (number of fibrinogen molecules)/(cross section) ) 2 for protofibrils. In fact, Casassa reported a value of 2 for protofibril solution44 and studies using electron microscopy are consistent with this observation.3,17 Therefore the protofibrils and fibrinogen molecules should coexist at te ) 230 min.

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The dashed line was added between 230 and 270 min in Figure 2 in order to show the slope which corresponds to (number of fibrinogen molecules)/(cross section) ) 2. In our experimental conditions, the data acquisition time to obtain the scattered light intensity in the whole angular range is not short enough (ca. 10 min), and the measurements at a fine time interval were difficult. Although the time corresponding to the completion of protofibril formation cannot be observed, the protofibril formation is accomplished between 230 and 270 min because of the gradual increase of the slope and the change of curvature as can be seen in Figure 2. The downward deviation at small scattering angles for te e 230 is due to the existence of fibrin aggregation, i.e., protofibril formation, and the aggregation size becomes larger with the elapsed time. This result corresponds to the fact that protofibril formation occurred to a limited extent, even at 5 min. Furthermore this time region corresponds to the lag time region of 〈I〉 in Figure 1b. The curvature changes to an upward curvature at te ) 270 min and shows a drastic change between 270 and 330 min. The time of the drastic curvature change includes the gelation time at 286 min, which was determined by the correlation function g(2)(t) as described in the next section. These results obtained by the static light scattering indicate that the staggered aggregation of fibrins to form protofibrils is accomplished at least until 270 min, and then the lateral aggregation to form the fibrin fibers proceeds until the gelation time (286 min). In the case of a fibrin gel, a qualitative variation of the shape of scattering function can be attributed to gelation. Recently, Bernocco et al. reported the time evolution of static light scattering by use of a multiple detection apparatus for a fibrinogen-thrombin solution.46 They showed that the method is valid for examining fibrin aggregation in the early stages by means of a detailed analysis of scattering functions. Their results showed the dynamics of protofibril formation and its size quantitatively. Later, they reported on the kinetics of fibrin gelation by small angle light scattering.2 Since the thrombin concentration differs substantially from the present study and also a large difference of proceeding time exists, it is difficult to compare with our result of the gelation kinetics quantitatively. However, the gel structures are discussed between their static light scattering and our dynamic light scattering results as described below. Sol to Gel Transition Elucidated by Correlation Function. The characteristics for the sol to gel transition obtained so far by the light scattering methods can be summarized as follows: (1) power law behavior in g(2)(t) (as the limit of decrease in β and increase in τs of stretched exponential behavior), (2) appearance of a long time tail in τG(τ), (3) beginning of the decrease in coherence factor in g(2)(t) (nonergodicity), and (4) rapid increase in scattered light intensity and its oscillating behavior. (1) to (3) are related to the dynamic light scattering measurements and indicate the utility of the dynamic light scattering method for the study of sol to gel transition phenomena.26,47 It is important to examine whether these characteristics are valid for the present system.


Figure 3. Double-logarithmic plots of the correlation function g(2)(t) - 1 as a function of the delay time t for sample B at θ ) 30° with λ ) 488 nm. Figures were divided at the time te ) 286 min. Solid curves were calculated using the stretched exponential (eq 5) for te e 260 min and the power law (eq 4) for te ) 286 min.

Figure 3 shows the typical double logarithmic plots of correlation functions g(2)(t) - 1 as a function of delay time t for sample B. Here, the amplitude of g(2)(t) - 1 depends on the instrumental coherence factor and shows the same value in the incipient elapsed time (sol state). Then the initial amplitude of g(2)(t) - 1 was normalized to the unity using its data at te ) 25 min in order to clarify the diminishing behavior in time evolution of the coherence factor. Also, the figure is divided at te ) 286 min to show the data points more clearly. The existence of the characteristic decay time of the slow mode τs means that the relaxation time of a growing cluster is finite; i.e., the system is in the sol state. However, g(2)(t) begins to show a long time tail in the range of the long delay time with a gradual decrease of b in eq 1 at te > 260 min. In fact a least-squares fit to the stretched exponential formula (eq 5) shows a good agreement for te e 260 min but shows systematic deviations for te g 286 min. The power law relation (eq 4) can be fitted well for te g 286 min, and g(2)(t) is described adequately by the power law relation especially in the long delay time region. The solid curves show the resultant fitting curves. The first term on the right-hand side in eqs 4 and 5 was not necessary in the fitting procedure before te ) 237 min, which is corresponding to the results of τG(τ) as shown in Figure 5. The decay at te ) 286 min became independent of the time scale; i.e., the clusters which are composed of fibrin fibers obtain a self-similar structure on a large scale compared with the molecular size. The sol to gel transition point is defined as the point where at least one of the clusters of the cross-linking polymer grows up to the macroscopic size. That is, the behavior at te ) 286 min can be denoted that the formation of the fibrin gel is completed until this time. The initial amplitude of g(2)(t), coherence factor, is an indicator


Figure 4. Elapsed time dependence of β and τs of the stretched exponential fitting to the correlation function (eq 5). (a) and (b) correspond to samples A and B, respectively. The shaded regions indicate the time region of gelation.

of the ergodic nature of the sample. When some frozen inhomegeneity exists resulting from cluster formation on a very large scale, this amplitude should decrease dramatically.48 As shown in Figure 3, the initial amplitude is unchanged for te e 260 min, indicating that the system remains in the sol state. The suppression at te ) 286 min means gelation of the system occurred. These results indicate that the gelation time is considered to be between 260 and 286 min for sample B. On the other hand, the gelation time of sample A was elucidated in the same manner to be between 60 and 65 min. The obtained fitting parameters of the exponent β and the characteristic decay time τs in eq 5 are shown in parts a and b of Figure 4 for samples A and B, respectively. Τhe shaded regions indicate the gelation time as determined by the crossover behavior of the correlation function g(2)(t). At very near the gelation point, the correlation function shows very slow decaying behavior and it becomes difficult to determine τs and β due to the restriction of acquisition period of the correlation function. However, the decay time τs and the exponent β show a divergence and diminishing tendencies as they approach the gelation point. These characteristics are consistent with the view that the system is in the pregel (sol) state, because τs should diverge and β should decrease to 0 at the gelation point. It should be noted that the τf and τs in the stretched exponential formulation (eq 5) cannot be distinguished by the fitting procedure in the sol state for te ) 60 min (sample A) and for te e 220 min (sample B) due to the very low magnitude of the coefficient A and the fact that the decay time distribution does not show well the separation of the two modes. Insights into Gelation Kinetics from Inverse Laplace Transformation. The lateral aggregation of protofibrils has been investigated by a number of workers, and the functions

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Figure 5. Time evolution of the decay time distribution function τG(τ) for sample B.

of fibrinopeptides A and B have been investigated using enzymes and various buffer conditions. Among them, a light scattering study using the cumulant expansion method was carried out in order to elucidate the diffusion coefficient and the polydispersity effect due to the decay time distribution.14,49,50 In the lateral aggregation process, the cumulant method showed that the polydispersity index of the solution becomes larger. However, this method could not give detailed information concerning the decay time distribution in the lateral aggregation (i.e., not the staggered but the lateral aggregation). In this section, we attempt the distribution function τG(τ) determined by CONTIN to study the gelation kinetics, as it could illuminate the steps of protofibril formation, lateral aggregation, and gelation phenomena. Figure 5 shows the time proceeding for τG(τ) of sample B. The entire behavior of τG(τ) for samples A and B were essentially the same except for the elapsed time. For 0 < te e 220 min, where the time region corresponds to the protofibril formation as discussed in the above sections, the peak of τG(τ) of the fast mode varies from the fastest relaxation (3 × 10-1-100 ms) with a sharp single peak to another slower relaxation peak (100-101 ms). The protofibril formation from the fibrin monomer and/or oligomer is clearly distinguished by the appearance of intergradations (crossover) between the two modes. The behaviors of τG(τ) for those initial time regions of te e 220 min correspond to the view that the molecular weight of the polymer becomes larger with an increase in elapsed time; that is, fibrin oligomers become larger and the formation of protofibrils proceeds. The decay time corresponding to the translational diffusion of rigid rods of 450 nm in length and 9 nm in diameter12 as a model of protofibril is calculated to be about 2.4 ms (for sample B measured at λ ) 488 nm) and is in good agreement with the decay time at te ) 220 min, although the decay time distribution does not necessarily correspond to the molecular weight distribution because of the finite concentration. At the fibrinogen concentration used here, the solution is a dilute one without protofibril formation, but the solution

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becomes semidilute when sufficient formation of protofibrils occurs, judging from the criterion of cL3 for the rodlike polymer solutions. Here, c and L correspond to the concentration and the rod length, respectively. Therefore substantial entanglements among protofibrils are generated at an elapsed time of te ) 220 min, and the cooperative diffusional motion due to entanglements would appear. At te ) 237 min, another peak at τ ) 3 × 102-103 appeared and the magnitude of the peak of protofibril decreased. This elapsed time corresponds to the region of the curvature change of C-H plot in Figure 2 and that corresponds to protofibril formation. These results indicate that the fiber formation (lateral aggregation of protofibrils) occurs after sufficient protofibril formation. This stepwise progression from protofibrils to fibers was observed similarly for both sample A and sample B. This fact is consistent with the computer modeling of fibrin polymerization reported by Weisel and Nagaswami and with the conversion mechanism of a half-staggered aggregation.17 The peak at the longest relaxation time shifts toward a slower relaxation time side for 237 e te e 286 min. This suggests that lateral aggregation to form fiber occurs and that the network formation proceeds by fiber growth due to the lateral aggregation of protofibrils. At te ) 286 min, τG(τ) showed the slowest relaxation mode, and the time corresponded to the gelation time determined by the crossover behavior of g(2)(t). The slowest peak of τG(τ) should originate from the gelling clusters. The relationship of 〈τ〉 (corresponds to the average hydrodynamic radius) against the scattered intensity 〈I〉 was examined as shown in parts a and b of Figure 6 for samples A and B, respectively. The 〈τ〉 increases in a nearly linear fashion with 〈I〉 until te ) 50 min and te ) 237 min for samples A and B, respectively, and deviates upward from the linear relation at te ) 55 min and te ) 240 min (open circles). Here, 〈τ〉 is evaluated for the overall τG(τ) as shown in Figure 5. If the long τ tail regions (τ > 10 ms) for te ) 55 min (data not shown for sample A) and for te ) 240 and 243 min for sample B in Figure 5 were omitted, 〈τ〉 deviates in a downward direction, which is shown by the closed circles in parts a and b of Figure 6, respectively. Moreover, the peaks of τG(τ) at around τ ) 100-101 ms region do not change between te ) 220 and 286 min in Figure 5. The increase in the characteristic decay time is nearly proportional to the scattered light intensity. This result indicates that the lengthy (axial) growth of rodlike polymer proceeds, because τ ∼ L/ln(L/d) with L and d being the rod length and diameter, respectively, or more exactly τ ∼ 1/D ) (3πηL/kBT)/ [ln(L/d) + γ(L/d)] with γ being the function, where the denominator is weakly dependent on L/d, and the scattered intensity is almost proportional to L. Therefore, the time regions of te e 50 min for sample A and of te e 237 min for sample B essentially correspond to the step of the conversion of fibrinogen to fibrin by the removal of fibrinopeptides and the formation of protofibril (axial growth by staggered aggregation). In physiological conditions, it has been reported that the removal of fibrinopeptide A from the central domain of the fibrinogen molecule occurs faster than that of fibrinopeptide


Figure 6. Double logarithmic plots of the average decay time 〈τ〉 against the scattered light intensity 〈I〉 in the early elapsed time (te < 60 min and te < 243 min for samples A and B, respectively). (a) and (b) correspond to samples A and B, respectively. Closed circle indicates that 〈τ〉 is calculated only from the fastest mode (τ < 10 ms) of τG(τ) as can been seen in Figure 5. The slope of the solid line is unity.

B. Therefore we conclude that the removal of fibrinopeptide A serves as a direct trigger for the spontaneous aggregation of fibrin monomers to form half-staggered two-stranded protofibrils and the removal of fibrinopeptide B which follows more slowly than that of fibrinopeptide A is necessary to enhance the lateral aggregation of protofibrils to form fibers. However, the role of fibrinopeptide B still remains controversial, because studies by use of some enzymes in various buffer conditions show a variety of observations (see refs 3 and 17 and references therein). Although the lateral aggregation of protofibrils is strongly dependent on thrombin concentration, our experimental results for fibrin gel formation in a stepwise manner suggest that the specific cleavage of fibrinopeptides A and B does not occur simultaneously and that the cleavage of fibrinopeptide B occurs after protofibril formation. The formation of protofibrils might cause some steric changes and promote the cleavage of fibrinopeptide B. This speculation is consistent with the mechanism of the fibrin assembly proposed by Medved et al.;18,19 that is, the conformational change of the end groups of fibrinogen molecules resulted from the protofibril formation due to the cleavage of fibrinopeptide A may be involved in the regulation of the lateral aggregation of protofibrils. Structural Characteristic by Fractal Dimensions. Martin et al. first reported fractal dimensions of gels deduced from the correlation function g2(t) of dynamic light scattering.42,43 They revealed that the g(2)(t) showed a power law behavior and the fractal dimension of a gel network was determined based on Muthukumar’s theory. On


the other hand, we recently accomplished a real space observation of the three-dimension network structure of the fibrin gel in a hydrated state by means of confocal laser scanning microscopy.51 A three-dimensional box-counting analyses of the network structure gave the mass fractal dimensions as 1.42 ( 0.01 and 1.51 ( 0.01 for the same condition with this study of samples A and B, respectively. Although the Muthukumar’s theory is formulated for the Rouse chain,52,53 we tentatively attempted to analyze the correlation function for the fibrin gel composed of rigid rods according to Martin’s treatment.42,43 At the sol to gel transition point, the exponents of power law behavior of g2(t) were obtained as φ ) 0.093 ( 0.004 (te ) 65 min) and as φ ) 0.16 ( 0.01 (te ) 286 min) using eq 3 for samples A and B, respectively. Then, the fractal dimensions were calculated as Df ) 1.42 ( 0.01 (sample A) and Df ) 1.53 ( 0.01 (sample B), where the Df is formulated as 1 - φ ) d(d + 2 - 2Df)/2(d + 2 - Df), with d being the dimension and with screening the excluded volume effect. Ferri et al.2,54 reported that the mass fractal dimension for a fibrinogen-thrombin system was 1.2 and further analysis gave 1.3 by the angular dependence of scattered light intensity in the small q region. According to their results, the power law relation of the angular dependence of scattered light intensity, from which the fractal dimension was evaluated, is valid at the fairly small q region (q < 105 cm-1). The present results (1.42 and 1.53) obtained by using Muthukumar’s theory are in agreement with their values. Their experimental conditions of the thrombin concentration were much higher than that of our sample, and the temperature was 25 °C, although the fibrinogen concentration is almost the same. In fact, a higher concentration of thrombin causes a lower value of fractal dimension as indicated by the results of samples A and B. In other words, a slower gelation process might lead to a denser network. Although the meaning of a similar value of (or, equivalence of) static fractal dimension (mass fractal) and the dynamic fractal dimension Df is not yet definite, the resultant values suggest that the structural image of a fibrin gel is largely inhomogeneous by means of axial growth of fibrin fiber. Percolation theory predicts Df ) 5/2 for the percolating cluster and Df ) 2 for the solution in the reaction bath, which is substantially larger than the present values. Winter et al. reported rheological measurements as a function of frequency and observed the power law behavior of elastic moduli for a polyurethane system.55,56 Antonietti et al. reported that the exponent depends on the chain length between the crosslinkages.57 These facts indicate that the fractal dimension of the gelling system is not universal in agreement with other works1,24-26,28,30,42,58,59 but depends on the stoichiometry, the excluded volume effect, network structure, chain rigidity, and so on. As a conclusion in this section, we tentatively analyzed the structural characteristics of the fibrin gel in terms of the fractal dimension deduced from the dynamic light scattering. However, it needs to be considered further in order to clarify the fractal dimension as some controversial problems still remain with this analogy.

1020


Conclusion The dynamic process of the conversion of fibrinogen to fibrin and of the formation of fibrin gel induced by thrombin was studied by means of static and dynamic light scattering, and the results obtained by these two methods were in agreement with each other. The respective components of fibrinogen, protofibril, fiber, and fibrin gel cluster during the transformation steps from fibrinogen to fibrin gel were clearly detected. It should be pointed out that the formation of a fibrin gel proceeds in a stepwise manner: fibrin to protofibril via axial aggregation, and protofibril to fiber and gel via lateral aggregation. Present results suggest that the important difference in the functional properties of the cleavage of fibrinopeptides A and B might be involved in the course of fibrin gel formation. The structure of the fibrin gel was also elucidated by the analysis of the power law behavior of the correlation function. The fractal dimension of the network structure was tentatively determined as about 1.5 in the present experimental conditions, as deduced from the power law exponent using the Muthukumar equation. The present results suggest that fibrin gel network consists of loose rigid fibrin fibers (lateral aggregates of protofibrils) and inhomogeneous cross-linking. Acknowledgment. We are indebted to Dr. Yoshiharu Toyama of Gunma University for helpful discussion and to Mr. Masayuki Kutani of Toyo Seiki Seisaku-Sho Ltd. for his kind help. K.K. thanks the Grant-in-Aid for Scientific Research (C) from the Ministry of Education, Culture, Sports, Science and Technology and Japan Society for the Promotion of Science. References and Notes (1) Tipton, D. L.; Russo, P. S. Macromolecules 1996, 29, 7402-7411. Russo, P. S.; Baylis, M.; Bu, Z.; Stryjewski, W.; Doucet, G.; Temyanko, E.; Tipton, D. J. Chem. Phys. 1999, 67, 1746-1752. (2) Ferri, F.; Greco, M.; Arcovito, G.; Andreasi Bassi, F.; De Spirito, M.; Paganini, E.; Rocco, M. Phys. ReV. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2001, 60, 031401. (3) Weisel, J. W. Biophys. J. 1986, 50, 1079-1093. (4) Ferry, J. D.; Morrison, P. R. J. Am. Chem. Soc. 1947, 69, 388-399. (5) Kaibara, M.; Fukada, E. Biorheology 1971, 8, 139-147. (6) Kirkpatrick, J. P.; McIntire, L. V. J. Rheol. 1979, 23, 769-787. (7) Kaibara, M. Polym. Gels Networks 1994, 2, 1-28. (8) Ryan, E. A.; Mockros, L. F.; Weisel, J. W.; Lorand, L. Biophys. J. 1999, 77, 2813-2826. (9) Nemoto, N.; Nestler, F.; Schrag, J. L.; Ferry, J. D. Biopolymers 1977, 16, 1957-1969. (10) Donnelly, T. H.; Laskowski, M.; Notley, N.; Scheraga, H. A. Arch. Biochem. Biophys. 1955, 56, 369-387. (11) Hantgan R. R.; Hermans, J. J. Biol. Chem. 1979, 254, 11272-11281. (12) Palmer, G. R.; Fritz, O. G. Biopolymers 1979, 18, 1659-1672. (13) Carr, M. E.; Hermans, J. Macromolecules 1978, 11, 46-50. (14) Wiltzius, P.; Dietler, G.; Kanzig, W.; Haberli, A.; Straub, P. W. Biopolymers 1982, 21, 2205-2223. (15) Kaibara, M. Biorheology 1973, 10, 61-73. (16) Kaibara, M.; Fukada, E. Biochim. Biophys. Acta 1977, 499, 352361. (17) Weisel, W. J.; Nagaswami, C. Biophys. J. 1992, 63, 111-128. (18) Yakovlev, S.; Litvinovich, S.; Loukinov, D.; Medved, L. Biochemistry 2000, 39, 15721-15729.

Kita et al. (19) Yakovlev, S.; Makogonenko, E.; Kurochkina, N.; Nieuwnhuizen, W.; Ingham, K.; Medved, L. Biochemistry 2000, 39, 15730-15741. (20) Everse, J. S.; Spraggon, G.; Veerapandian, L.; Doolittle, F. R. Biochemistry 1999, 38, 2941-2946. (21) Rooney, M. E.; Mullin, L. J.; Lord, T. S. Biochemistry 1998, 37, 13704-13709. (22) Kita, R.; Kaibara, M.; Kubota, K. Trans. MRS-J. 2001, 26, 573576. (23) Stauffer, D.; Coniglio, A.; Adam, M. AdV. Polym. Sci. 1982, 44, 103-158. (24) Fang, L.; Brown, W.; Konak, C. Macromolecules 1991, 24, 68396842. (25) Adam, M.; Delsanti, M.; Durand, D. Macromolecules 1985, 18, 2285-2290. (26) Norisuye, T.; Inoue, M.; Shibayama, M.; Tamaki, R.; Chujo, Y. Macromolecules 2000, 33, 900-905. (27) Kita, R.; Kaku, T.; Kubota, K.; Dobashi, T. Phys. Lett. A 1999, 259, 302-307. (28) Okamoto, T.; Kubota, K. Carbohydr. Polym. 1996, 30, 149-153. (29) Valstar, A.; Vasilescu, M.; Vigouroux, C.; Stilbs, P.; Almgren, M. Langmuir 2001, 17, 3208-3215. (30) Cohen Addad, J. P., Ed. Physical properties of polymer gels; John Wiley & Sons Ltd.: New York, 1996. (31) Ikeda, S.; Foegeding, A. E.; Hagowara, T. Langmuir 1999, 15, 85848589. (32) Nishinari, K.; Zhang, S.; Ikeda, S. Curr. Opin. Colloid Interface Sci. 2000, 5, 195-201. (33) Wegner, G. Acta Mater. 2000, 48, 253-262. (34) Mihalyi, E. Biochemistry 1968, 7, 208-223. (35) Biggs, R., Ed. Human Blood Coagulation, Haemostasis and Thrombosis, 2nd ed.; Blackwell Scientific Publications: Philadelphia, PA, 1976; p 722. (36) Kubota, K.; Urabe, H.; Tominaga, Y.; Fujime, S. Macromolecules 1984, 17, 2096-2104. (37) Kita, R.; Kubota, K.; Dobashi, T. Phys. ReV. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1998, 58, 793-800. (38) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 213-227. (39) Onuki, A. J. Non-Cryst. Solids 1994, 172-174, 1151-1157. (40) Coviello, T.; Burchard, W.; Geissler, E.; Maier, D. Macromolecules 1997, 30, 2008-2015. (41) Tsianou, M.; Kjoniksen, A.-L.; Thuresson, K.; Nystrom, B. Macromolecules 1999, 32, 2974-2982. (42) Martin, J. E.; Wilcoxon, J. P. Phys. ReV. Lett. 1988, 61, 373-376. (43) Martin, J. E.; Wilcoxon, J.; Odinek, J. Phys. ReV. A: At., Mol., Opt. Phys. 1991, 43, 858-872. (44) Casassa, E. F. J. Chem. Phys. 1955, 23, 596-597. (45) Holtzer, A. J. Polym. Sci. 1955, 17, 432-434. (46) Bernocco, S.; Ferri, F.; Profumo, A.; Cuniberti, C.; Rocco, M. Biophys. J. 2000, 79, 561-583. (47) Norisuye, T.; Shibayama, M.; Tamaki, R.; Chujo, Y. Macromolecules 1999, 32, 1528-1533. (48) Pusey, P. N.; van Megen, W. J. Chem. Phys. 1984, 80, 3513-3520. (49) Palmer, G. R.; Fritz, O. G.; Hallett, F. R. Biopolymers 1979, 18, 1647-1658. (50) Arcovito, G..; Bassi, A. A.; Spirito, M.; Stasio, E. D.; Sabetta, M. Biophys. Chem. 1997, 67, 287-292. (51) Takahashi, A.; Kita, R.; Shinozaki, T.; Kubota, K.; Kaibara, M. Submitted. (52) Muthukumar, M. J. Chem. Phys. 1985, 83, 3161-3168. (53) Muthukumar, M. Macromolecules 1989, 22, 4656-4658. (54) Spirito, M.; Arcovito, G.; Bassi, F. A.; Rocco, M.; Paganini, E.; Greco, M.; Ferri, F. Il MuoVo Cimento 1998, 20, 2409-2417. (55) Winter, H. H.; Morganelli, P.; Chambon, F. Macromolecules 1988, 21, 532-535. (56) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367-382. (57) Antonietti, M.; Folsch, K. J.; Sillescu, H.; Pakula, T. Macromolecules 1989, 22, 2812-2817. (58) Wang, C. H.; Fisher, E. W. J. Chem. Phys. 1985, 82, 632-638. (59) Meir, G.; Hagenah, J.-U.; Wang, C. H.; Fytas, G.; Fisher, E. W. Polymer 1987, 28, 1640-1644.

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