Atomic Structural Models of Fibrin Oligomers

Summary

The space-filling fibrin network is a major part of clots and thrombi formed in blood. Fibrin polymerization starts when fibrinogen, a plasma protein, is proteolytically converted to fibrin, which self-assembles to form double-stranded protofibrils. When reaching a critical length, these intermediate species aggregate laterally to transform into fibers arranged into branched fibrin network. We combined multiscale modeling in silico with atomic force microscopy (AFM) imaging to reconstruct complete atomic models of double-stranded fibrin protofibrils with γ-γ crosslinking, A:a and B:b knob-hole bonds, and αC regions—all important structural determinants not resolved crystallographically. Structures of fibrin oligomers and protofibrils containing up to 19 monomers were successfully validated by quantitative comparison with high-resolution AFM images. We characterized the protofibril twisting, bending, kinking, and reversibility of A:a knob-hole bonds, and calculated hydrodynamic parameters of fibrin oligomers. Atomic structures of protofibrils provide a basis to understand mechanisms of early stages of fibrin polymerization.

Introduction

Fibrin is an end product of blood clotting that forms the scaffold of hemostatic clots and obstructive thrombi in blood vessels. Fibrin is also a major component of the extracellular matrix and is involved in a broad range of cellular processes, including cell adhesion, migration, proliferation and differentiation, wound healing, angiogenesis, and inflammation (Weisel and Litvinov, 2017Litvinov and Weisel, 2017). Fibrin is widely used as a versatile biomaterial in a variety of applications, such as hemostatic sealants, tissue engineering, as a delivery vehicle for cells, drugs, growth factors, and genes, and matrices for cell culturing (Janmey et al., 2009Radosevich et al., 1997). Because of the fundamental biological and medical importance, molecular mechanisms of fibrin formation as well as fibrin structure and properties continue to be major areas of research (Weisel and Litvinov, 2013Weisel and Litvinov, 2017Litvinov and Weisel, 2016).

Fibrin formation is initiated by the cleavage of fibrinopeptides A and B from the N termini of Aα and Bβ chains of fibrinogen, respectively, to produce fibrin monomer. The release of fibrinopeptides A exposes an N-terminal α-chain motif GPR, called knob “A”, which binds to constitutively exposed hole “a” in the γ nodule of another fibrin molecule (Everse et al., 1998Kostelansky et al., 2002), resulting in the formation of an A-a knob-hole non-covalent bond (Litvinov et al., 2005). Exposure of knobs “A” is necessary and sufficient to form fibrin through the interaction with holes “a.” The release of fibrinopeptides B exposes an N-terminal β-chain motif GHRP, called knob “B”, which is complementary to hole “b” located in the β nodule of another fibrin molecule.

Fibrin polymerization begins when two monomeric fibrin molecules interact in a half-staggered fashion through the A-a knob-hole interaction. The addition of a third molecule is accompanied by an end-to-end association where, in addition to the A-a knob-hole interactions, the globular D regions of two adjacent molecules form the D:D interface. The D:D interface provides a junction between the monomers in one of the two strands in a fibrin trimer. Furthermore, fibrin monomers add longitudinally via the inter-strand A-a knob-hole bond formation and intra-strand D-D interactions to form fibrin oligomers. This growth continues until the fibrin oligomers reach the critical length of protofibrils: oligomers made of ∼20–25 fibrin monomers. Fibrin protofibrils self-associate laterally to form twisted fibers of variable thickness. These branches form a three-dimensional fibrin network called a clot (Weisel and Litvinov, 2017).

The monomeric fibrin is essentially identical in structure and composition to fibrinogen except for small fibrinopeptides A and B, which are cleaved when fibrinogen is converted to fibrin, and αC domains, which are bound to the central nodule in fibrinogen but detached in fibrin (Medved et al., 2001). Therefore, fibrin oligomers and protofibrils can be reconstructed using resolved crystal structures of the human fibrinogen molecule and parts of fibrinogen and fibrin molecules, including the fibrinogen fragment D and the double-D fragment from crosslinked fibrin (see Table S1). Yet using the crystal structures of fibrinogen or fibrin [together denoted as fibrin(ogen)] is challenging. First, the crystallographic data available are incomplete. There are several flexible unstructured portions that are not resolved crystallographically yet are essential for fibrin formation, including residues 1–26 and 1–57 at the N-termini of the Aα and Bβ chains, respectively, and residues 201–610, 459–461, and 395–411 at the C-termini of the Aα, Bβ, and γ chains, respectively (Kollman et al., 2009). Second, a manifold of possible spatial arrangements of fibrin monomers when forming a protofibril makes in silico reconstruction of fibrin protofibril difficult. Third, the large system size requires using vast computational resources: a 0.5- to 0.6-μm-long protofibril made of 20 fibrin monomers contains ∼60,000 amino acids, which corresponds to ∼106 atoms.

Determination of atomic structures of fibrin oligomers cannot be accomplished by X-ray crystallography and/or electron microscopy, owing to the unstable nature of these heterogeneous intermediate supramolecular assemblies and their characteristic elongated shape. Yet atomic-level information about these structures is necessary to elucidate the mechanisms of formation and properties of fibrin polymers, which provide the three-dimensional scaffold necessary to maintain the integrity and viscoelasticity of blood clots and thrombi. Here we employed multiscale modeling to computationally reconstitute the atomic structures of double-stranded fibrin oligomers of varying length. The atomic structural models were successfully validated using high-resolution atomic force microscopy (AFM) imaging of fibrin oligomers.

We employed the molecular dynamics (MD) simulations of atomic structural models (Brooks et al., 2009Zhmurov et al., 2012) and Cα-based self-organized polymer (SOP) models of fibrin(ogen) and its fragments (Hyeon et al., 2006), accelerated on graphics processing units (GPUs) (Zhmurov et al., 2010aZhmurov et al., 2010bZhmurov et al., 2011Alekseenko et al., 2016), to perform a step-by-step reconstruction of a complete atomic structure of a 19-monomer-long fibrin protofibril using the recently published structure of a short fibrin oligomer (Zhmurov et al., 2016). The protofibril structure has interesting properties, such as twisting, bending, and kinking, and the presence of free knobs “B” necessary for formation of additional intra- and inter-protofibril bonds. The models obtained enabled us to explore the dynamic structural transitions in fibrin protofibrils and to predict experimentally unavailable dynamic characteristics of fibrin oligomers and protofibrils, including density, radius of gyration, diffusion coefficient, and intrinsic viscosity.

Results

Stepwise Reconstruction of Fibrin Oligomers and Protofibril

As a building block, we used the structure of short double-stranded fibrin oligomer FO2/3 with two fibrin monomers in the first and three monomers in the second strands (Figure 1A). Using this structure, we performed stepwise elongation to create longer oligomers up to the length of a protofibril. The full-atomic model of FO2/3 was constructed computationally in our previous study (Zhmurov et al., 2016) using all 27 relevant crystal structures of fibrinogen and its fragments resolved to date (Table S1). The structure of FO2/3 showed good agreement with high-resolution AFM images (Zhmurov et al., 2016). In this work, we took the next step to elongate several-fold the known structure of FO2/3 in order to reconstruct longer fibrin oligomers FOm/n (m/n is the number of fibrin monomers in the first/second strand). This enabled us to recreate short fibrin oligomers from FO2/3 to FO5/6. A mere replication of the FO2/3 structure along the longitudinal axis has resulted in formation of elongated oligomers and protofibrils that do not show any twisting detected in experimental AFM and electron microscopy images (Weisel et al., 1987Medved et al., 1990Protopopova et al., 2015Huang et al., 2014). To overcome this problem, we designed an approach that uses two main crystal structures of the D:D junction. These structures correspond to the straight conformation (PDB: 1N86) of the D:D interface, used to recreate shorter fibrin oligomers, and the bent conformation (PDB: 1FZG) of the D:D interface, which we used to recreate longer oligomers (and a protofibril). To recreate twisted structures, we align two FO2/3constructs using the straight conformation of D-D junctions and then gradually switch to the bent conformation of the D:D junction (STAR Methods). This builds in the desired twist in the fibrin strands, in full agreement with AFM and electron microscopy experiments (Protopopova et al., 2015Weisel et al., 1987).

A step-by-step reconstruction of short fibrin oligomers (FOm/n) is illustrated in Figure 1B (elongation step with the straight conformation of D:D interface). Reconstruction of longer fibrin oligomers and protofibril (FP9/10) is illustrated in Figure 1C (a procedure to introduce a twist; bent conformation of D:D interface; see also STAR Methods for more details). In step A of the twisting procedure, coarse-graining of FO2/3 is performed (diamonds in Figure 1B) and Langevin simulations of the Cα-based representation of FO2/3 is carried out to switch from the straight to the bent configuration of the D:D interfaces. In step B of the twisting procedure, the obtained conformation of FO2/3 is back-mapped and energy-minimized using the all-atom solvent-accessible surface area model of implicit solvation. Next, we perform the elongation procedure. The atomic model of FO2/3 with knobs “A” and “B” is replicated to reconstruct fibrin oligomers (FOn/m) of the desired length. In the last structure-addition step, the αC regions are incorporated into each fibrin monomer, and the covalent γ-γ crosslinks between residues γ398 and γ406 of abutted fibrin monomers are introduced (Rosenfeld et al., 2015). The final structures of double-stranded fibrin polymers from the structure-addition step (Table 1) were energy-minimized to exclude possible steric clashes.

Table 1Molecular Parameters of Fibrin Monomer, Oligomers FOn/m, and Protofibril FP9/10Calculated Based on the Atomic Models Reconstructed In Silico with and without the αC Regions: Molar Mass (M), Radius of Gyration (Rg), Diffusion Coefficient (D), Density (ρ), and Intrinsic Viscosity (η)
Constructs M(G/mol) Rg(nm) D (cm2/s) ρ(g/cm3) η(cm3/g)
Fibrin(ogen) monomers
Truncated des-αC fibrin monomer 246,395 12.5 ± 2.0 (2.5 ± 0.3) × 10−7 1.361 24 ± 9
Full-length fibrin monomer 332,418 12.7 ± 1.3 (1.9 ± 0.2) × 10−7 1.328 38 ± 19
Double-stranded fibrin oligomers/protofibril without the αC regions
FO1/2 739,185 12.5 ± 2.0 (1.4 ± 0.1) × 10−7 1.350 42 ± 12
FO3/4 1,724,765 19.6 ± 2.1 (8.1 ± 0.4) × 10−8 1.352 114 ± 18
FO5/6 2,710,345 41.6 ± 2.2 (6.0 ± 0.3) × 10−8 1.346 209 ± 29
FO7/8 3,695,925 67.5 ± 2.1 (4.79 ± 0.08) × 10−8 1.344 344 ± 19
FP9/10 4,681,505 117.1 ± 2.0 (4.0 ± 0.1) × 10−8 1.342 483 ± 42
Double-stranded fibrin oligomers/protofibril with the αC regions
FO1/2 997,254 20.1 ± 1.9 (1.14 ± 0.04) × 10−7 1.326 50 ± 7
FO3/4 2,326,926 41.8 ± 2.4 (6.8 ± 0.2) × 10−8 1.325 113 ± 17
FO5/6 3,656,598 67.5 ± 2.0 (5.1 ± 0.1) × 10−8 1.325 204 ± 12
FO7/8 4,986,270 93.0 ± 1.7 (4.15 ± 0.07) × 10−8 1.324 309 ± 14
FP9/10 6,315,942 116.8 ± 1.9 (3.4 ± 0.2) × 10−8 1.324 450 ± 27

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The values of RgDρ, and η are for 20°C.

Atomic Structures and AFM Images of Fibrin Oligomers and Protofibrils

To compare in silico structures with AFM images, we employed the computational Monte Carlo procedure, which overlaps the positions of the centers of mass of D and E regions in the atomic structural model and in AFM images (see STAR Methodsand Figure 2B). To quantify the agreement between AFM images and atomic models, we monitored the dynamics of total root-mean-square deviation (RMSD) in Monte Carlo runs. The trajectories in Figure 2C show a great reduction in RMSD values to 0.9–2 nm depending on the oligomer length.

We first recreated atomic models of short fibrin oligomers by applying the elongation procedure (Figure 1B) to the initial structure of FO2/3, to reconstruct the structures up to nine monomers long (FO4/5Figure 2A). We correlated these structures with their high-resolution AFM images for short oligomers containing up to nine fibrin monomers (FO4/5Table 1). In AFM imaging, short fibrin oligomers appear as elongated constructs with regularly spaced heart-shaped nodules and two adjacent nodules facing in opposite directions (Figure 2). Each of these nodules corresponds to a single D-E-D trinodular unit. The derived atomic structures and AFM images for short fibrin oligomers are compared in Figures 2B and 2D, which show good agreement between the structures obtained experimentally and computationally. Next, we turned to reconstruction of longer oligomers (FO5/6 and longer) up to a protofibril FP9/10. We elongated oligomer FO4/5 with FO2/3 using the elongation procedure described in the STAR Methods (Figure 1B). The structures obtained in silico did not compare well with their corresponding AFM images (Figures 2E and 3F ), which could be due to protofibril twisting not present in the modeled structures. Quantitatively, this is reflected in higher values of RMSD for longer structures (0.9–1.0 nm for short oligomer FO3/3 versus 1.8–2.0 nm for long oligomer FO6/7; see Figure 2C). Next, we elongated short oligomers up to the length of a fibrin protofibril FP9/10 (Figure 3A and Table 1). At this length scale, the structure of FP9/10 obtained with the straight conformation of D:D interface did not capture the helical twist observed in AFM images (Figures 2E, 2F, and 3D). Using the structure of FP9/10obtained computationally, we calculated the helical radius and helical pitch, which came to 650 nm and 3,300 nm, respectively. This is a straight structure on the protofibril length scale of ∼500 nm.

To build in a twist in fibrin oligomers and protofibrils, we first applied the twisting procedure (Figure 1C) and then the elongation procedure (Figure 1B). The equilibrium structure obtained shows that the transition from the straight to the bent double-D conformation with the twisting procedure results in an overall shape change of FP9/10 from the parallel double-stranded (Figure 3A) to the twisted (double-stranded) helical form (Figure 3B). Transient structures of FP9/10 populated in the course D:D interface remodeling are displayed in Figure S2 (see Video S1). As the protofibril FP9/10 twists, the helical radius and helical pitch decreases, respectively, from 650 nm to 5 nm and from 3,300 nm to 400 nm (see Figure S2 and Video S1), as a result of dynamic remodeling of all D:E:D interfaces reinforcing the protofibril’s structure. The comparison of atomic structures and AFM images of longer fibrin oligomers showed better agreement (Figure 3D). Note that the average values for RMSD are slightly lower for twisted structures (1.2 ± 0.3 nm; sample size = 30) compared with straight oligomers (1.4 ± 0.4 nm; sample size = 30).

Complete Structure of a Fibrin Protofibril with the αC Regions

The C-terminal part of fibrinogen’s Aα chain, called the αC region (residues Aα221–610), consists of the proline-rich unstructured αC connector (Aα221–390) and the relatively compact αC domain (Aα391–610) (Tsurupa et al., 2009). The αC region is missing in all the crystal structures of fibrinogen and its fragments resolved to date. The structure of bovine fibrinogen’s αC domain was partially resolved by nuclear magnetic resonance (Burton et al., 2007), yet the structure of human fibrinogen’s αC domain is not known (Tsurupa et al., 2009). We recreated this structure using sequence homology between the human and bovine fibrin(ogen) with the Modeller software suite (Webb and Šali, 2017). Structure snapshots of the αC domain randomly selected from independent MD runs showed a double β hairpin stabilized by the S-S bond. The αC-domains can be separated into the N-terminal and C-terminal subdomains as suggested earlier (Tsurupa et al., 2009Tsurupa et al., 2012). Since αC connectors are not resolved by the X-ray crystallography, they do not possess stable secondary or tertiary structure. Therefore, the incorporation of αC connectors in a random coil conformation does not lead to any structural artifacts. In a structure-addition procedure (Figure 1D), we incorporated the missing C-terminal portions of the α connector in a random conformation to arrive at the complete atomic structure of a fibrin protofibril FP9/10 (Figure 3C).

We compared the full-atomic structure of FP9/10 containing αC regions with the AFM images (Figure 3). The protofibril’s shape and positions of the αC regions in the atomic model and AFM images of FP9/10 agreed well. The αC regions were predominantly perpendicular to the protofibril axis. Although the αC regions were occasionally interconnected, they were mostly single. Not all αC regions were seen in AFM images (assuming two αC regions per monomer), and we identified on average 1.6 αC regions per monomer. Some of the αC regions might have been proteolytically truncated in the fibrinogen purified from plasma or have been adsorbed at positions not clearly visible on the surface (e.g., under the protofibril backbone).

Conformational Dynamics of the Fibrin Protofibril Chain

From experimental AFM images, the average contour length of fibrin protofibrils is 213 ± 101 nm and the average end-to-end distance is 197 ± 86 nm (n = 30). This gives an average end-to-end to contour length ratio of 0.94 ± 0.09 (n = 30), which shows that protofibrils are bent. Since our in silico structures were recreated based on the X-ray data, they lack this conformational flexibility. To explore dynamic transitions in the protofibril structure, we performed MD simulations using the obtained structure of FP9/10 (see STAR Methods and Video S2), which revealed significant structural alterations including bending (Figure 4A) and kinking (Figure 4B). This agrees well with the previously published experimental data (Protopopova et al., 2015Protopopova et al., 2017Huang et al., 2014Chernysh et al., 2011Medved et al., 1990Hunziker et al., 1988Fowler et al., 1981) and with our AFM images (Figure 4).

The distribution of end-to-end distances (i.e., the distances between centers of the end D:E:D complexes) in FP9/10 from MD simulations is displayed in Figure 4F. The average end-to-end distance in FP9/10 is R = 330 ± 15 nm. With the contour length L0 = 403 nm (9 monomers, 44.8-nm length of monomer), the average persistence length of protofibril FP9/10 is Lp = 320 ± 80 nm (see STAR Methods). There is a variation in experimental estimates of Lp for fibrin protofibrils, with values ranging from ∼100 nm to 500 nm (Piechocka et al., 2016Storm et al., 2005). Based on our AFM images, Lp = 420–480 nm, which is in good agreement with our simulations. The higher value of Lp observed in AFM images can be attributed to the non-covalent interactions (adsorption forces) between the protofibrils’ backbone and the surface. Reversible formation of kinks in the protofibril structure observed in our simulations was due to simultaneous bending of the coiled coils in adjacent strands around the positions identified in the previous simulation studies (Köhler et al., 2015Figure 3). This is in agreement with AFM images, in which kinks were indeed detected (Figure 4E). Deviations of the atomic structures from the AFM images at the protofibril’s tails are due to limited sampling of the conformational space in the MD simulations. The probability distribution of kinking angles from MD simulations for FP9/10 is shown in Figure 4G.

To quantitatively compare the AFM images and the atomic structural models, we computed the distributions of distances between adjacent D regions (Figure 4H), distribution of distances between D and E regions in DED constructs (Figure 4I), and distribution of distances between DED complexes (Figure 4J). To probe the bending rigidity of protofibrils, we computed the distributions of angles formed by three DED complexes (Figure 4K). To extract these characteristics from AFM images, we only selected protofibrils in which these fragments are visible and located their geometric centers; in the simulations, we computed the centers of mass of these fragments. The average values of all four quantities from AFM images and equilibrium MD simulations agree well (see Table S2), although SDs are larger in AFM images.

Structural Transitions in Fibrin Protofibril

Dissociation of A:a Knob-Hole Bonds

The long 10-ms MD simulations of FP9/10 showed that the A:a knob-hole bonds dissociate. This significantly weakens the D:E:D interface, leading to disruption of the D:D junction (Figure 4C), which does not occur when the A:a knob-hole bonds are intact. The D:D junction is the weakest link in the single-stranded fibrin oligomers (Zhmurov et al., 2011Zhmurov et al., 2012). In accord with these findings, AFM images also show irregularly shaped D:E:D fragments, which suggests the D:D interface disruption (see Figures 2E, 2F, 3E, 4D, and 4E). These results point to the importance of γ-γ covalent crosslinking, which reinforces the D:D interface when fibrin protofibrils form.

αC Regions

To sample conformations of the αC regions with flexible βN regions, we performed 10-ms equilibrium MD simulations of the protofibril FP9/10 with a constrained protofibril backbone and free knobs “B” (STAR Methods; see Video S3). We constructed the probability distribution of the distances between the protofibril longitudinal axis and the centers of mass of αC domains and compared it with the experimental histogram of the same quantity. Figure 5B shows that the agreement is very good, albeit the SDs are smaller in the simulations. This might be due to overstabilization of the αC domains in the simulations. The structure of the αC domain is not resolved experimentally, which suggests that it is not stable. Longer αC connectors are typically bent, which explains why the average distance between the αC regions and the protofibril backbone is only 17 nm (Figure 5B).

B:b Knob-Hole Interactions

We explored the conformational transitions in the βN regions with knobs “B.” The GHR active sequence does not drift far away from the central nodule, making the intra-protofibril B:b highly unlikely to form (Figure 5E). This suggests that additional structural changes in the protofibril are required for the B:b knob-hole bonds to form within the protofibril, in full agreement with earlier reports (Medved et al., 2001). These transitions (B:b knob-hole bond formation) cannot be sampled in MD simulations due to the limited time span (10 ms), and there might be additional putative inter-atomic contacts that guide the βN regions toward the holes “b.” There is experimental evidence suggesting that the B:b knob-hole bonds can form both between the fibrin strands inside the protofibril and between the protofibrils (Litvinov et al., 2007Blombäck et al., 1978Weisel, 1986). For this reason, we recreated two protofibril constructs: one with knobs “B” bound to holes “b,” and the other with free knobs “B”; see the PDB files in Data S1 for knobs-in structure and Data S2 for knobs-out structure.

Hydrodynamic Parameters of Fibrin Oligomers and Protofibril

We calculated the (hydro)dynamic molecular characteristics for double-stranded fibrin oligomers and protofibrils (STAR Methods) and profiled them as a function of their size (Figure 6 and Table 1). First, we compared our theoretical predictions with available experimental values for some of these quantities. Very good agreement was found for the (translational) diffusion coefficient D, i.e., (1.5–2.2) × 10−7 cm2/s (experiment for full-length fibrinogen; Raynal et al., 2013) versus (2.5 ± 0.3) × 10−7cm2/s (our simulations for truncated fibrin monomer without αC regions). Slightly lower values of D obtained for the full-length fibrin monomer can be attributed to the presence of bulky αC appendages, which are absent in truncated fibrin variants. Using confocal microscopy, Chernysh et al. (2011) estimated the diffusion coefficient (D) for 500-nm-long protofibril to be D = 3.7 × 10−8 cm2/s. This is in very good agreement with our values for FP9/10, i.e., D = (3.4 ± 0.2) × 10−8 cm2/s for the full-length molecules and D = (4.0 ± 0.1) × 10−8 cm2/s for those with truncated αC region (Table 1). Given these values of the diffusion coefficient the time needed for the protofibrils to travel toward one another will be fractions of a second, which is significantly shorter than overall polymerization timescale of minutes under similar conditions (Protopopova et al., 2017). Thus, the lateral aggregation of protofibrils is not limited by their diffusion.

The density of fibrin oligomers (1.34–1.36 g/cm3) was also found to be in good agreement with experiments (ρ = 1.38 g/cm3Adamczyk et al., 2012). The density of fibrin with flexible αC regions (1.32–1.33 g/cm3) was lower than the density of fibrin without αC regions (1.34–1.36 g/cm3). Theoretical values of the intrinsic viscosity ηfor the truncated fibrin (24 ± 9 cm3/g) and full-length fibrin monomer (38 ± 19 cm3/g) are also within the experimental range (21–48 cm3/g; Adamczyk et al., 2012). Larger variability in the theoretical values of η for the full-length fibrinogen is due to higher extensibility of αC appendages (Table 1). This supports our findings, namely that fibrinogen in solution exists in two conformational populations: one population with a lower value of η corresponding to conformations of fibrin’s αC domains attached to the central nodule; and the other population with a higher value of η that corresponds to conformations with free αC regions (Zuev et al., 2017). The agreement between experimental and theoretical values of Dρ, and η we have obtained for fibrin monomers and the structures we have recreated enabled us to predict the values of Dρ, and η and radius of gyration Rg for fibrin oligomers and protofibrils not available experimentally (Table 1). We also derived analytical expressions that allow for the extrapolation of these quantities to fibrin protofibrils of arbitrary length (Figure 6).

Discussion

Fibrin oligomers and protofibrils are important intermediate products formed early during fibrin polymerization. Resolution of atomic structures of fibrin oligomers and protofibrils is needed to illuminate the mechanisms of the early stages of fibrin formation, including lateral aggregation of protofibrils, and to characterize the remarkable extensibility and viscoelasticity of fibrin fibers (Liu et al., 2010Litvinov and Weisel, 2017). Yet experimental determination of the structure and characterization of the properties of double-stranded fibrin polymers is difficult due to their elongated shape and highly unstable nature. We employed a powerful combination of the state-of-the-art experimental AFM imaging technique and theoretical approaches to multiscale modeling accelerated on a GPU to gather the atomic-level information about the structure and properties of fibrin oligomers and protofibrils. Using the full-atomic structure of a short fibrin oligomer FO2/3 (Figure 1Zhmurov et al., 2016), here we have reconstructed the atomic structures of longer fibrin oligomers FO3/4–FO7/8 up to a 19-mer protofibril FP9/10 (Figures 2 and 3Table 1). These constructs involve γ-γ crosslinking, A:a and B:b knob-hole bonds, and αC regions—all important functional elements of fibrin—and carbohydrates. The double-stranded fibrin structures were successfully validated through the direct comparison with high-resolution AFM images of oligomers and protofibrils (Figures 2 and 3Data S1 and S2).

Early products of fibrin polymerization are two-stranded oligomers (Fowler et al., 1981Chernysh et al., 2011Huang et al., 2014). A common feature of fibrin oligomers visualized with transmission electron microscopy is their twisted helical shape, although reported parameters of the oligomers’ helicity are highly variable. Medved et al. (1990) showed that some protofibrils form twisted structures with a helical pitch of ∼100 nm, whereas other protofibrils are nearly straight. In agreement with this study, we found that the helical pitch decreases from 3,300 nm to 400 nm (Figure 3) following the transition from the straight conformation (PDB: 1N86) to the bent conformation (PDB: 1FZG) of the D:D interface (Figures 3A, 3B, and S2), and the helical radius decreases from 650 nm to 5 nm. This points to the important role played by the D:D interfacial flexibility in early stages of fibrin polymerization. We did not observe a helical pitch <400 nm, which might be due to the experimental conditions used in previous studies (Medved et al., 1990) or to crystal packing forces in the atomic structures used. In most experiments, fibrin protofibrils are straight and thin, which agrees with our results. After reaching a certain length, fibrin protofibrils aggregate laterally to form thick twisted fibers. Fibrin fibers have a 20- to 60-nm helical radius and ∼2,000-nm helical pitch (Weisel et al., 1987), and continue to twist as they grow.

The reconstructed double-stranded fibrin oligomers and protofibrils correspond to the known ultrastructures, but surpass the available experimental data in spatial resolution. We are aware of other models of fibrin protofibrils (Yang et al., 2000Pechik et al., 2006Huang et al., 2014). The model proposed by Yang et al. (2000)captures the main structural features of fibrin oligomers, including the half-staggered molecular overlay formed by two fibrin strands. However, this model is ad hoc rather than systematic, and lacks a detailed analysis of the crystal forms. This model provides a static view of fibrin structure with missing γ-γ crosslinking, A:a and B:b knob-hole bonds, and αC regions. Another model (Huang et al., 2014) captures the half-staggered molecular arrangement of fibrin strands, and has a helical pitch of 90 nm. Yet a closer look reveals major steric clashes in the DED regions, which make the A-a bond formation unlikely. Also, this model is lacking γ-γ crosslinking, knob-hole bonds, and αC regions, and is based on the chicken fibrinogen structure (PDB: 1M1J).

We employed equilibrium MD simulations of fibrin protofibril FP9/10 to explore the dynamic structural transitions that occur in double-stranded fibrin polymers. Fibrin protofibrils behave like other double-stranded biopolymers, such as double-stranded DNA, but with a longer 320-nm persistence length, and show a high degree of bending. A theoretical probability density curve shows that due to bending, the end-to-end distance in FP9/10 decreases from ∼400 nm (contour length) to ∼330 nm (Figure 4F). This might be important for the fiber formation and fiber branching (Figure 4). Experimental AFM images reveal more bending flexibility than the in silico structures, and the protofibril’s bending becomes more pronounced with increasing length. We also observe reversible kinking of the protofibril backbone with the 80° to 140° kinking angle range and an average kinking angle of 115° (Figure 4G). Protofibril bending and kinking could be one of the mechanisms of initiation of branch points in growing fibrin fibers.

In the simulations, we observed the dissociation of A:a knob-hole non-covalent bonds, which was followed by the disruption of the D:E:D interface. This suggests a secondary role played by the D:D interface in fibrin polymerization, and also potentially supports the so-called Y-ladder model of fibrin fiber growth (Rocco et al., 2014). According to this model, the D:E:D interface becomes stable only after both knobs “A” are bound to their corresponding holes “a” (Rocco et al., 2014). Since upon the disruption of D:E:D interface and D-region rotation one A:a knob-hole bond is completely dissociated, a knob “A” and a hole “a” might become available for inter-protofibril cross-coupling. Another fibrin monomer from another protofibril could then bind, thus initiating a branch point. Formation of branch points is visible in some of the protofibril images (Figure 4E). We did not observe formation of new A:a knob-hole bonds in the millisecond timescale of simulations, hence this transition occurs in a longer timescale.

The length of αC connectors is very important for mechanical properties of fibrin fibers (Falvo et al., 2008). Since the αC domains are capable of interacting with each other (Tsurupa et al., 2011Tsurupa et al., 2012Litvinov et al., 2007) and with the globular parts of fibrin molecules (Tsurupa et al., 2009), it is important that they have an optimal length. When the αC connectors are long (as in human fibrinogen) their αC domains tend to form non-covalent bonds with other αC domains within the same protofibril and between the protofibrils. When the αC connectors are short (as in chicken fibrinogen), the αC domains hardly form binding contacts between protofibrils but only within the protofibril. We see in the simulations and in AFM images that the span of the αC regions is long enough so that the αC domains can form the αC-αC contacts within the protofibril and between protofibrils (Figure 5). The experimental histogram of the lengths of αC region shows the 10- to 35-nm range and an average length of 17.3 nm; the theoretical probability density curve reveals a smaller 10- to 20-nm range and a similar average length of 14.7 nm. This large variability also explains why in AFM images were on average 1.6 αC regions per fibrin monomer (<2). Our results imply that the conformational dynamics of αC regions plays a role in defining the thickness of fibrin fibers (number of protofibrils in a fiber).

The physiological role of B:b knob-hole bonds is not yet fully understood (Weisel and Litvinov, 2017). Although knobs “B” are long enough to reach and bind to the corresponding holes “b” in the same protofibril, our simulations of FP9/10 with free knobs “B” show that they have a limited span due to thermal fluctuations (Figure 5E). Hence, formation of intra-protofibril B:b contacts is possible only when Nβ regions are close to the globular parts of fibrin, interacting with γ and β nodules of adjacent molecules (Moskowitz and Budzynski, 1994). These interactions can guide the knob “B” to the hole “b” or/and to the thrombin active-site cleft (Pechik et al., 2006). Upon formation of B:b knob-hole bonds, the β nodule dissociates from the α-helical coiled coil, which results in the exposure of the tissue plasminogen activator and plasminogen binding cites in the coiled coil (Medved et al., 2001). This transition might help to bring holes “b” of adjacent protofibril closer to knobs “B,” thus facilitating the inter-protofibril contacts’ formation. Our simulations for protofibril FP9/10 suggest that the intra-protofibril B:b contacts are less probable than the inter-protofibril B:b contacts, which also explains why the formation of fibrin fibers occurs even in the absence of knobs “B” (Moskowitz and Budzynski, 1994Weisel, 1986).

We calculated the molecular hydrodynamic parameters for double-stranded fibrin oligomers and protofibrils, which are not available experimentally (Table 1), and extracted the scaling laws for RgDη, and ρ as functions of their size N (number of fibrin monomers; Figure 6). The protein density ρ was found to depend on Nexponentially (Figure 6C) in full agreement with the predictions made by Fischer et al. (2004). The profile of Rg shows a linear increase with N starting from 5 to 7 monomers (Figure 6A), because at larger N fibrin oligomers are pseudo-one-dimensional with size growing with N. This also explains why the intrinsic viscosity ηincreases quadratically with N. According to the Flory theory, η = ΦRg3/M, where Φis a universal constant and M is the molar mass (Doi and Edwards, 1986). Indeed, for a linear polymer Rg ∼ N and M ∼ N, and so η ∼ N2 (Figure 6D).

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