Insights into Fibrinogen Mechanics Under Cyclic High-Strain Loading

Abstract

Fibrinogen plays a central role in the physiological processes of blood coagulation and, unfortunately, ischemic stroke, where it is routinely exposed to mechanical forces. In this study, we employed atomistic molecular dynamics simulations to subject fibrinogen to three cycles of high-strain loading (~17.5%–27.5%) and unloading, enabling us to probe its mechanical response under cyclic stress. To capture the effects of pulling direction and structural asymmetry, we simulated the two different fibrinogen molecules present in the crystallographic unit cell. Forces were applied to the γ1 nodule of molecule 1 and the γ2 nodule of molecule 2 in opposite directions. The simulations revealed contrasting mechanical behaviors: γ1 nodule exhibited greater extension with partial elasticity, whereas β-sheet rich γ2 nodule showed higher resistance but sustained irreversible structural damage. After force relaxation, both molecules retained residual strain (6.52%–15.62% across independent replicas), confirming partial irreversibility. Anisotropic Normal Mode Analysis further identified localized reductions in stiffness linked to unfolding of secondary structural elements, including β-sheets and α-helices. Complementary Kelvin–Voigt modeling of the unloading curves further quantified these effects, showing progressive reductions in the effective spring constant (K_spec) and dashpot coefficient (C_spec) across cycles. The model captured the viscoelastic relaxation dynamics. Collectively, these findings demonstrate that fibrinogen’s cyclic response is shaped by both intrinsic structural heterogeneity, revealing viscoelastic behavior with important implications for clot formation and stroke pathogenesis.

1. Introduction

Fibrinogen is a large soluble glycoprotein composed of three pairs of polypeptide chains (Aα, Bβ, and γ) arranged in a trinodular architecture: a central E domain connects two terminal D domains (β and γ nodules) (Figure1a), via Aα, Bβ, and γ chain coiled-coil segments^{1, 2}. Fibrinogen plays an essential role in hemostasis and wound healing³. Upon vascular injury, fibrinogen is cleaved by the enzyme thrombin to generate fibrin monomers, which polymerize into an insoluble fibrin network that stabilizes the formation of blood clot and initiates tissue repair^4–6. γ-nodules play crucial roles in the fibrin polymerization process⁷. In addition, fibrinogen participates in diverse physiological and pathological processes, including tumor metastasis and angiogenesis^{8, 9}. In vivo, fibrinogen is exposed to a variety of mechanical forces, such as shear from blood flow, platelet contraction, and tissue deformation^10–12. These forces induce conformational changes that impact fibrinogen’s mechanical properties and biological function¹³. Experimental studies using atomic force microscopy (AFM) and optical tweezers have demonstrated that fibrinogen and fibrin exhibit non-linear elasticity and can undergo reversible or irreversible structural transitions depending on force magnitude and duration^{14, 15}. In addition, computational molecular dynamics (MD) simulations were used to investigate the impact of mechanical loading on the different regions of fibrinogen^16–20. Notably, α-helices have been shown to unfold reversibly under moderate force^{21, 22}, while β-sheets display higher stiffness but undergo abrupt, often irreversible rupture.

Figure 1.

Structural organization and heterogeneity of fibrinogen γ-nodules. (a) Full-length fibrinogen crystal structure (PDB ID: 3GHG) showing the γ-chain (green), Bβ-chain (magenta), and Aα-chain (blue). The molecule consists of two γ-nodules and two β-nodules located at either end, connected by coiled-coil domains (ABC and DEF) to the central E domain; (b) Structural comparison of the γ-nodules in molecule 1 (blue) and molecule 2 (green). Within each molecule, the two γ-nodules show subtle differences with RMSD values of 0.560 Å (molecule 1) and 0.500 Å (molecule 2). Across molecules, larger conformational differences are observed, with an RMSD of 1.863 Å, reflecting variability introduced by crystal packing and local structural divergence.

Despite these advances, the effect of repeated cyclic mechanical loading, resembling physiological strain from, e.g. vascular pulsatility or clot retraction, on the structural integrity of fibrinogen remains poorly understood. Moreover, existing computational studies have largely assumed symmetry between the two γ-nodules of fibrinogen molecule²³, neglecting the structural variability present in experimentally resolved fibrinogen conformations. In reality, multiple fibrinogen variants circulate in the blood due to genetic polymorphisms and structural isoforms, with the γ-chain being the primary source of variation²⁴.

For example, the crystal structure of fibrinogen (PDB ID: 3GHG)²⁵ reveals two distinct protein molecules that differ noticeably in the twisting and bending of the coiled-coil domain. These molecules also vary slightly in length, containing 1,914 residues in molecule 1 and 1,947 in molecule 2. The 33-residue difference arises from insertions located in several regions: 12 residues in the N-terminus of the γ-chain I (equivalent to chain C in molecule 1), 9 residues in the N-terminus of the γ-chain L (equivalent to chain F in molecule 1), and 12 residues in the C-terminus of the Aα-chain J (equivalent to chain D in molecule 1). These length variations are not the focus of the present study, which instead centers on pulling the C-terminal region of the γ-nodule.. Structural comparison of the two crystallographic fibrinogen molecules reveals an RMSD of 1.863 Å (Figure 1b), reflecting conformational differences induced by crystal packing that capture alternative protein conformations in solution²⁵. In molecule 1, the γ-nodules at both ends are nearly identical in sequence, with the only distinction being the presence of an additional Gly395 in one nodule. By contrast, the γ-nodules in molecule 2 display greater variability compared to those present in molecule 1, due to extra residues located at the N-terminal region of the γ-chain. These local structural divergences are likely to influence the mechanical response of the protein. Consistent with this, secondary structure analysis reveals measurable differences, with an RMSD of 0.560 Å between the two γ-nodules in molecule 1 and 0.500 Å between the two γ-nodules in molecule 2 (Figure 1b).

In this study, we investigated how this structural asymmetry affects the protein mechanical response. We performed atomistic molecular dynamics simulations of fibrinogen subjected to three cycles of high-strain (ranging between 17.5%–27.5%) loading and unloading to investigate how pulling direction, twisting, and bending affect structural response. By applying harmonic force to one selected γ-nodule in the two distinct protein molecules (γ1 in molecule 1 and γ2 in molecule 2 as shown in Figure S1), we investigated the mechanical asymmetry between them. We further characterized changes in the secondary structure using selected representative structures and assess mechanical resilience through Anisotropic Network Model²⁶ to track stiffness evolution. In addition, the Kelvin–Voigt theoretical framework was employed to extract the protein’s viscoelastic properties and integrate them with the MD simulation results. Collectively, these analyses reveal that both the pulling direction and local structural differences between γ-nodules strongly influence fibrinogen’s mechanical behavior. The β-sheets exhibit early and often irreversible unfolding, while α-helices show greater capacity for recovery under cyclic strain. Notably, γ1 in molecule 1 consistently stretches more and recovers better than γ2 in molecule 2, correlating with its greater α-helical content and fewer β-sheets. These findings suggest that fibrinogen exhibits mechanical anisotropy tied to its native structural heterogeneity, with potential implications for clot formation, elasticity, and pathological remodeling.

2. Materials and Methods

2.1. System Preparation

The crystal structure of single-molecule fibrinogen containing two molecules of the protein was retrieved from the Protein Data Bank (PDB ID: 3GHG)²⁷. Each fibrinogen molecule comprises three pairs of polypeptide chains (Aα, Bβ, and γ) and is organized into a central E domain flanked by two terminal γ-nodules (D domains), connected by coiled-coil regions.

System preparation was performed using GROMACS v2021.3^{28, 29} with the CHARMM27 all-atom force field³⁰. The crystal structure composed of two distinct fibrinogen molecules was solvated in a rectangular periodic box (48.995 nm × 15.584 nm × 23.519 nm) containing 569,914 TIP3P water atoms³¹ and neutralized to physiological ionic strength by adding 31 Na+ ions. The entire system of 1771181 atoms was then minimized using the steepest descent algorithm followed by equilibration in two phases: 100ps NVT and 100ps NPT ensembles. Long-range electrostatics were treated using the Particle Mesh Ewald (PME) method^{32, 33}, and hydrogen bond lengths were constrained using the SHAKE algorithm³⁴, allowing a 2fs integration time step.

2.2. Pulling Simulations

Pulling simulations were carried out using the OpenMMv8.3.0³⁵, specifically implementing the CustomCentroidBondForce module to apply harmonic forces. To assess the impact of structural asymmetry and pulling direction, each of the two fibrinogen molecules was subjected to pulling from opposite termini: The centroid of residue ILE394 in γ1 of molecule 1 and the centroid of residue GLY395 in γ2 of molecule 2 (Figure S1). γ1 of molecule 1 was selected because it is the only nodule in the two molecules that possesses a truncated C-terminal (terminating at ILE394 rather than Gly395), whereas γ2 of molecule 2 was chosen due to its higher secondary structure content, β-sheets in particular, compared to the other γ-nodule within the same molecule (Figure 1b).

Similar to conventional umbrella sampling, a harmonic potential with a force constant of 1000.0 kJ·mol⁻¹·nm⁻² was applied to the centroid between two pulling groups (ILE394 of γ1 in molecule 1 and Gly395 of γ2 in molecule 2). The chosen force constant matches values used in our previous experimental and computational study³⁶ and was selected to achieve high strain within a short simulation time. For a system of this size, imposing large strains is advantageous for probing molecular differences under cyclic loading. In this setup, the pulling force was directly proportional to the displacement.

Two independent simulations were performed in the form of three cycles of loading (1 ns each) and three cycles of unloading/relaxation (5–6 ns). These relaxation intervals were extended until no further structural recovery was observed. Unlike experimental loading-unloading systems where full recovery may occur, the protein did not return to its original conformation, indicating partial irreversibility and residual strain retention after each cycle. The final frame of each phase was extracted as the representative structure for subsequent analysis.

2.3. Strain Calculation

The strain imposed on the system during pulling was computed as:

$$\mathit{\text{Strain}}=\frac{\Delta L}{L_o}$$ (1)

where ΔL is the displacement between the centroids of the two pulling residues (ILE394 in γ1 of molecule 1 and GLY395 in γ2 of molecule 2), and L₀ is the initial inter-residue distance between the centroids of the two pulling groups. This allowed quantification of accumulated strain during each cycle in the entire system including the two distinct fibrinogen molecules.

2.4. Root-Mean-Square Fluctuation (RMSF)

To identify regions undergoing significant structural fluctuations during cyclic loading, root-mean-square fluctuations (RMSF) were computed for all residues using MDTraj1.9.4³⁷. Comparative analysis of RMSF profiles across simulation cycles time course enabled the identification of the domains highly affected by the cyclic loading.

2.5. α-helix/β-sheet ratio via Ramachandran plot

Ramchandran plots were generated using MDAnalysis2.9.0^{38, 39}. The α-helix/β-sheet ratio was calculated by counting the number of points falling within the angular regions’ characteristic of each secondary structure. α-helices were defined by φ angles between −120° and −30° with ψ angles from −60° to −30°, as well as φ angles between 60° and 90° with ψ angles from 0° to 60°, corresponding to the two major allowed regions for helices. β-sheets were identified within φ angles of −180° to −45° and ψ angles of 60° to 180°, representing the canonical β-sheet region. These angular ranges were selected to capture the primary allowed conformational spaces for α-helices and β-sheets.

2.6. Stiffness Analysis via Anisotropic Network Model

To complement structural observations, stiffness values of the γ nodules were computed using the Anisotropic Network Model^{14, 26} as implemented in the ProDy v2.0 package⁴⁰. ANM extends the Gaussian Network Model (GNM) by considering directionality of motions^{41, 42}, allowing better prediction of anisotropic fluctuations. By calculating the second derivative of the harmonic potential, ANM estimates stiffness as a function of inter-residue contact geometry to estimate the collective motions of the protein. This enables identification of flexible and rigid regions, offering a quantitative analysis of the protein response to the cyclic loading/unloading.

2.7. Kelvin-Voigt Theoretical Model

The Kelvin–Voigt model⁴³ is a simple viscoelastic framework that represents a material (in this case fibrinogen) as a spring and a dashpot connected in parallel. Because the strain curves obtained from our harmonic pulling simulations closely resembled those predicted by the Kelvin–Voigt model, we employed this framework to analyze fibrinogen’s mechanical response. Specifically, the model was fit to the displacement–time profiles extracted from simulation to obtain the elastic modulus E (spring constant) and viscosity η (dashpot coefficient), thereby providing insight into the physical properties of the protein under cyclic loading and unloading.

In its classical form, the Kelvin–Voigt constitutive relation under constant applied stress is expressed as:

$$\sigma \left(t\right)=E\epsilon \left(t\right)+\eta \frac{d\epsilon }{dt}$$ (2)

where: σ(t) is stress, ε(t) is strain, E is elastic modulus (spring constant), and η = viscosity (dashpot coefficient).

The corresponding force equation can be written as a function of the material properties (Eq. 3)

$$F=k_{\mathit{\text{spec}}}e+c_{\mathit{\text{spec}}}\frac{de}{dt}$$ (3)

where $k_{\mathit{\text{spec}}}$ is spring constant, $c_{\mathit{\text{spec}}}$ is the dashpot coefficient, and e is the instantaneous displacement. These parameters are related to the length and the cross-sectional area of the protein through (Eq. 4 and 5)

$$k_{\mathit{\text{spec}}}=E\frac{A}{L}$$ (4)

$$c_{\mathit{\text{spec}}=}\eta \frac{A}{L}$$ (5)

Where A is cross-sectional area and L is the length of the protein

Since our simulations employed a harmonic potential, the equations were modified to account for the constant force constant k imposed during pulling. The harmonic force is given by:

$$F=k\left(e_0-e\right)$$ (6)

where e₀ is the target displacement and e is the instantaneous displacement. Substituting Eq. (6) into Eq. (3) yields:

$$c_{\mathit{\text{spec}}}\frac{de}{dt}+{(k}_{\mathit{\text{spec}}}+k)e=k{e}_0$$ (7)

During the loading phase, the evolution of displacement follows:

$$\frac{de}{dt}=-\frac{{(k}_{\mathit{\text{spec}}}+k)}{c_{\mathit{\text{spec}}}}e+\frac{k}{c_{\mathit{\text{spec}}}}{e}_0$$ (8)

During unloading (when e₀ is removed), this reduces to:

$$\frac{de}{dt}=-\frac{k_{\mathit{\text{spec}}}}{c_{\mathit{\text{spec}}}}e$$ (9)

By fitting displacement–time curves to the Kelvin–Voigt formulation, the slope corresponds to $-\lambda$, where ${\lambda }_{\mathit{\text{load}}}$ is $\frac{{(k}_{\mathit{\text{spec}}}+k)}{c_{\mathit{\text{spec}}}}$ and ${\lambda }_{\mathit{\text{unload}}}$ is $\frac{k_{\mathit{\text{spec}}}}{c_{\mathit{\text{spec}}}}$ and the intercept b in during loading is $\frac{k}{c_{\mathit{\text{spec}}}}{e}_0$

Thus, the harmonic form of Kelvin-Voigt model can be represented by the following equation

$$\frac{de}{dt}=-\lambda e+b$$ (10)

The material-specific parameters are then recovered as:

$$k_{\mathit{\text{spec}}}=k\frac{{\lambda }_{\mathit{\text{unload}}}}{{{\lambda }_{\mathit{\text{load}}}-\lambda }_{\mathit{\text{unload}}}}$$ (11)

$$c_{\mathit{\text{spec}}}=\frac{k_{\mathit{\text{spec}}}}{{\lambda }_{\mathit{\text{unload}}}}$$ (12)

3. Results and Discussion

3.1. Cyclic Loading Reveals Irreversible Structural Changes and Asymmetric Behavior Between γ-Nodules

To investigate the structural response of fibrinogen to mechanical stress, γ1 in molecule 1 and γ2 in molecule 2 were subjected to three successive cycles of pulling and relaxation using a harmonic restraint with a force constant of 1000 kJ/mol·nm² (Figure 2). Each pulling phase (Pull1-Pull3) resulted in a sharp increase in strain within the first 100ps, followed by a plateau. In Pull1, the strain measured between the centroids of the two pulling residues in the two distinct fibrinogen molecules (γ1 of molecule 1 and γ2 of molecule 2) reached a maximum of 17.5% in replica 1. The final frame was selected as the representative structure for this pulling phase. During Relax1, the strain initially decreased, but a late rise was observed after 6ns time frame, thus the last frame at the 6ns mark was used as representation for this phase (Relax 1). Despite relaxation, ~6.5% strain was retained, indicating partial irreversibility. In Pull2, the strain increased again, reaching ~27.5%, incorporating residual strain from Pull1. Similar stabilization occurred after 100ps, and the final frame was selected. Relax2 allowed partial recovery, and the final 5ns frame was used for analysis. In Pull3, the strain rose more slowly and peaked around 22.5%, suggesting the system retained a strain from prior cycles. Relax3 revealed differential recovery: replica 1 regained compactness (retained a strain percent of 6.54%), whereas replica 2 did not (retained a strain percent of 15.62%), implying structural deformation. The strain response varied across the three cycles, reflecting changes in the protein’s mechanical resistance. During the first cycle, the protein resisted deformation, reaching a maximum strain of ~17.5%. By the second and third cycles, higher strain levels of 27.5% and 22.5% were observed, suggesting a progressive loss of resistance to pulling forces and resulting in structural deformation.

Figure 2.

Two independent replicas of three rounds of applying harmonic potential for 1ns on γ1 in molecule 1 and γ2 in molecule 2 followed by three rounds of unloading allowing the protein to relax for 8ns in cycle 1, 5ns in cycle 2, and 6ns in cycle 3 (left); Selected representative structures for each cycle

Qualitative inspection of representative structures (Figure 2) showed distinct responses between γ1 and γ2. In Pull1, γ1 in molecule 1 exhibited greater extension than γ2 in molecule 2. Interestingly, γ2 retained more compactness during Relax1. Similar trends persisted in Pull2 and Relax2, where γ2 demonstrated greater structural recovery. By Pull3, both γ-nodules showed reduced extension capacity, and during Relax3, both exhibited curled structures indicating irreversible damage and loss of elasticity. These differences in strain accumulation and relaxation behavior between the two γ-nodules support the hypothesis of structural asymmetry in fibrinogen. The unequal mechanical responses between γ1 and γ2 prompted further investigation through RMSF analysis to localize regions of high flexibility and deformation.

3.2. Structural Changes trigger altered behavior

3.2.1. γ-Nodules and Coiled-Coil Domains Are Most Susceptible to Cyclic Pulling-Induced Fluctuations

To evaluate the localized structural response of fibrinogen to repeated high-strain loading, root mean square fluctuation (RMSF) analyses were conducted across three pulling cycles. These calculations allowed the identification of regions that change under cyclic high-strain mechanical loading.

In Pull 1, the γ1 nodule in molecule 1 (residue index 696–956, highlighted in blue in Figure 3a) exhibited elevated fluctuations, with RMSF values ranging from 0.4 to 0.6 nm. This region was directly subjected to the applied pulling force. In addition, the γ2 nodule in molecule 2 (residue index 3599–3860, highlighted in green in Figure 3a) also showed increased RMSF values (up to 0.8 nm). In Pull 2, the asymmetry in response became more pronounced. γ1 (molecule 1) continued to fluctuate within a range of 0.25–0.75 nm, while γ2 (molecule 2) experienced markedly higher fluctuations, reaching 1.75 nm. This sharp increase indicates severe local instability or partial unfolding of the γ2 nodule during this cycle. In Pull 3, the trend persisted: γ2 showed fluctuations of up to 1.0 nm, whereas γ1 remained more stable (maximum RMSF ≈ 0.5 nm).

Figure 3.

RMSF profiles reveal the fluctuations of different regions under cyclic pulling.for both fibrinogen copies. The highest fluctuations are consistently observed at the pulling sites: γ1 of molecule 1 (highlighted in blue) and γ2 of molecule 2 (highlighted in green). Moderate fluctuations are also detected in the coiled-coil domains (highlighted in purple), particularly during Pull 1. (a) Cycle 1 of pulling (Pull1); (b) Cycle 2 of pulling (Pull2), fluctuations in the coiled-coil structure were minimal and therefore not highlighted in purple. (c) Cycle 3 of pulling (Pull3).

In addition to the γ-nodules, the coiled-coil domains, specifically regions ABC (residue indices 20–174, 193–314, and 583–696 in molecule 1; 1935–2089, 2108–2229, and 2508–2621 in molecule 2) and DEF (residue indices 976–1130, 1149–1270, 1539–1652 in molecule 1; 2901–3067, 3086–3207, and 3485–3598 in copy 2) also exhibited moderate fluctuations, highlighted in purple. These helically structured linkers experienced RMSF values between 0.2 and 0.4 nm during Pull 1, consistent with their role as elastic but mechanically responsive connectors. Interestingly, these coiled-coil regions were less responsive in Pull 2 and Pull 3, with fluctuations decreasing to ~0.2 nm or less, suggesting that initial strain absorption and unfolding were more dominant in the earlier stages of cyclic loading.

Taken together, the RMSF profiles across the pulling cycles confirm that γ-nodules are the primary sites of mechanical deformation, while coiled-coil domains act as intermediate dampeners, absorbing part of the applied force without undergoing extensive unfolding. The progressive loss of structural stability in γ2, despite its relatively low extension (Figure 2) emphasizes the importance of local secondary structure (notably β-sheets) in defining regional mechanical fragility under cyclic loading.

3.2.2. Asymmetric Extension: γ1 Experiences Higher Strain Than γ2

As γ nodules were found to be the most affected regions by the pulling forces, as revealed by the RMSF profiles (Figure 3), it was essential to investigate the corresponding structural changes at the molecular level. This was achieved by analyzing the changes in the secondary structures in the selected representative structures.

In Pull1, γ1 experienced significant structural disruption, with the loss of four β-sheets (Gly188–197, Phe215-Leu218, Ala279-Gly284, and Lys380-Pro386) and two α-helices, Ala289-Asp291 and Phe389–Thr393 (Figure 4). In Relax1, none of the disrupted β-sheets recovered their structure, highlighting the potential irreversible nature of β-sheet unfolding. However, the α-helix Lys356-Ser358 formed during this relaxation phase, notably matching a native α-helix observed in γ1 in molecule 2. In Pull2, this newly formed α-helix unfolded again, along with further disruption of the Ala279-Gly284 β-sheet. In Relax2, the β-sheet originally spanning Ala245-Ala263 became fragmented into two separate strands (Ala245-Asp252 and Gly255-Ala263), indicating further deformation of the secondary structure. In Pull3, partial recovery was observed; Ala289-Asp291 reformed its α-helical structure, while the Gly255-Ala263 and Ala279-Gly284 β-sheets exhibited further unfolding. This cycle exhibited minimal additional secondary structure loss, consistent with the reduced RMSF values observed in this phase (Figure 3). In Relax3, a new α-helix (Ser300-Thr305) emerged, while Ala289-Asp291 was again disrupted and the Ala279-Gly284 β-sheet was lost. The reduced extent of structural change during Pull3 likely reflects the lower strain applied, as the system had already absorbed significant deformation during Pull1 and Pull2.

Figure 4.

The impact of the cyclic loading and unloading on the structural changes in γ1 in molecule 1 of the single molecule fibrinogen. Changes in α-helices are represented in purple and changes in β-sheets are represented in orange. Only the affected regions are labeled in each cycle.

In contrast, γ2 underwent more severe structural degradation (Figure 5). Seven β-sheets were lost during Pull1 (Gly188-Arg197, Phe215-Leu218, Tyr280-Gly283, Tyr244-Leu246, Gln311-Ser313, Trp334-Met336, and Lys380-Pro386), along with two α-helices (Phe389-Gly395 and Pro269-Lys273). Interestingly, a short α-helix (Lys356-Ser358), native to γ1 in copy 2, formed transiently in γ2 but was lost during Relax1, alongside unfolding of Thr257-Val267. In Pull2, Asp288-Gly292 formed a short α-helix that again unfolded in Relax2. Pull3 did not show further significant unfolding, while in Relax3, some recovery of α-helices was noted, specifically Pro269-Lys273 and Asp288-Gly292.

Figure 5.

The impact of the cyclic loading and unloading on the structural changes in γ2 of molecule 2 of the protein. Changes in α-helices are represented in purple and changes in β-sheets are represented in orange. Only the affected regions are labeled in each cycle.

In summary, γ1 (molecule 1) stretched more extensively but preserved much of its secondary structure, especially α-helices, due to their ability to reversibly unfold and refold. γ2 (molecule 2), richer in β-sheets, suffered greater irreversible damage early in the simulation and resisted further extension, thereby preserving its overall compactness (Figure 2). This structural degradation explains the elevated RMSF values observed in γ2 across all three pulling cycles (Figure 3). The greater abundance of β-sheets in γ2 made it more susceptible to early structural unfolding compared to γ1. These observations reflect the distinct mechanical behavior of β-sheets and α-helices. β-sheets, while initially stiff, unfold irreversibly under tension due to abrupt hydrogen bond rupture and poor re-alignment, making recovery unlikely⁴⁴. α-helices²², in contrast, display a more elastic and reversible behavior, able to unwind under low to moderate force and re-form during relaxation phases. This behavior is consistent with prior single-molecule pulling simulations, where α-helices act like entropic springs and β-sheets exhibit brittle failure^{22, 44}.

The differences in α-helix and β-sheet populations were further quantified using Ramachandran plots of the γ-nodules from representative structures subjected to cyclic pulling (Figure S2). To assess secondary structure balance, the α-helix/β-sheet ratio was calculated (Figure S3). Across all three pulling cycles, γ1 in molecule 1 consistently exhibited a higher α/β ratio compared to γ2 in molecule 2 (Pull1: 0.352 vs. 0.348, Pull2: 0.362 vs. 0.357, Pull3: 0.414 vs. 0.379). These results confirm that γ1, enriched in α-helices, responds to cyclic loading with greater extensibility, whereas γ2, containing more β-sheets, is less resilient. This structural asymmetry underlies the differential mechanical response of the two γ-nodules.

3.3. Stiffness Analysis of γ-Nodules Under Cyclic Loading

Stiffness calculations of the γ-nodules were performed using the Anisotropic Network Model¹⁴ to quantify the mechanical impact of repeated cyclic loading and structural asymmetry between the two fibrinogen molecules. These calculations, based on the selected representative structures extracted at the end of each pulling and relaxation phase to provide insight into the local mechanical resilience of each γ-nodule under directional force application.

When γ1 in molecule 1 was directly subjected to pulling forces (Figure 6a), its stiffness dropped dramatically 0.048. This sharp decrease indicates that γ1 undergoes significant structural softening upon force application. In contrast, molecule 2, which was not directly pulled in this condition, maintained consistently high γ1 stiffness across all three cycles. This mechanical preservation highlights how pulling direction strongly results in localized deformation. Similarly, when γ2 in molecule 2 was pulled (Figure 6b), its stiffness was markedly reduced to 0.088 in Pull, whereas γ2 in molecule 1, not subjected to direct pulling, retained higher stiffness throughout. Notably, the lowest stiffness values for the pulled nodules in both panels occurred in Pull2, corresponding to the phase with the highest recorded strain and most extensive secondary structure disruption (particularly β-sheet unfolding). This correlation supports the conclusion that stiffness loss is closely tied to irreversible structural deformation. Interestingly, in Pull3, stiffness partially recovered for both γ-nodules. This trend may reflect reduced strain accumulation in this final pulling cycle, as well as the reformation of some α-helices. In the relaxation phases, stiffness of the non-pulled nodules remained relatively stable, while the pulled nodules showed modest recovery; most notably in γ2, whose stiffness rose from 0.033 in Pull2 to 0.209 in Relax3.

Figure 6.

Stiffness analysis highlights the effects of pulling direction and structural asymmetry. (a) Stiffness values of γ1 in the two distinct fibrinogen molecules (Molecule 1 shown in blue and Molecule 2 in green) across three cycles of loading and unloading when γ1 in molecule 1 is the pulling point. (b) Stiffness values of γ2 in both copies during the same simulation protocol when γ2 in copy 2 is subjected to pulling.

Together, the mechanical response is asymmetric between γ1 and γ2, with γ2 exhibiting generally higher stiffness, likely due to its greater β-sheet content. These insights highlight the importance of considering both pulling direction and local structural composition when evaluating protein mechanical behavior under physiological or pathological forces to the pulling force.

3.4. Kelvin-Voigt Theoretical Model

The cyclic loading–unloading simulations were analyzed using the Kelvin–Voigt viscoelastic model to characterize the relaxation dynamics of fibrinogen under repeated strain (Figure 7). During each cycle, the loading phase showed an almost instantaneous rise in displacement as the harmonic potential was applied, reflecting the direct impact of the force on the γ-nodules. In contrast, the unloading phases displayed a gradual exponential-like decay in displacement, which was well approximated by the Kelvin–Voigt fits. The model successfully reproduced the relaxation slopes and corresponding time constants (λ), thereby providing estimates of the effective elastic modulus and viscosity. In all cycles, residual strain persisted at the end of unloading, and this irreversibility accumulated over successive cycles, indicative of structural damage and irreversible deformation that the Kelvin–Voigt model captures.

Figure 7.

Cyclic loading–unloading simulations of fibrinogen analyzed using the Kelvin–Voigt (KV) viscoelastic model. Displacement–time curves are shown for three consecutive cycles (Cycle 1–3) in Replica 1 (left) and Replica 2. Blue curves represent loading under harmonic pulling, while orange curves represent unloading. Dashed green and red lines correspond to Kelvin–Voigt fits for loading and unloading phases, respectively.

The progressive reduction in peak displacement from cycle 1 to cycle 3 highlights the cumulative weakening of the fibrinogen structure under repeated stress. This is consistent with irreversible unfolding of β-sheet motifs, which fail to refold upon unloading, in contrast to α-helical segments that display partial recovery. Replica 1 and Replica 2 both followed this general viscoelastic–plastic trend, though Replica 2 exhibited slightly slower relaxation.

Kelvin–Voigt fitting of the cyclic loading–unloading simulations revealed progressive changes in the viscoelastic properties of fibrinogen (Table S1). During the first cycle, both replicas exhibited relatively high stiffness (K_spec = 10.06 and 7.85 kJ·mol⁻¹·nm⁻²) and large dashpot coefficients (~12,000–13,000 kJ·mol⁻¹·nm⁻²·ps), reflecting the intact structure’s ability to resist deformation. By the second cycle, Replica 1 displayed a noticeable reduction in stiffness (6.34 kJ·mol⁻¹·nm⁻²) while Replica 2 remained largely unchanged (8.01 kJ·mol⁻¹·nm⁻²), although both retained high viscous damping. In the third cycle, both replicas underwent dramatic softening, with Replica 1 and Replica 2 decreasing to 3.39 and 0.57 kJ·mol⁻¹·nm⁻², respectively. Viscosity also declined significantly (C_spec ≈ 6,400–10,000), indicating diminished capacity for deformation resistance. The deviations in the spring constants and dashpot coefficients observed between the two independent replicas across cycles can be attributed to differences in retained strain (Figure 2). Replica 2 exhibited a higher residual strain during Relax3 (Cycle 3), which corresponded to a greater reduction in both the spring constant and the dashpot coefficient. These results suggest that, while the overall mechanical trends of the two replicas are consistent, the absolute values diverge depending on the extent of strain retained, reflecting variability in fibrinogen’s response under different loading conditions.

Compared to elastin and fibrin fibers^{15, 45–47} (Table S2), fibrinogen is less resilient, showing irreversible softening after repeated cycles. Compared to collagen^{48, 49}, it is softer and more dissipative, allowing it to absorb energy but at the cost of plastic deformation. Its behavior most closely resembles viscoelastic synthetic polymers or cytoskeletal networks⁵⁰, which also exhibit creep, residual strain, and cycle-dependent weakening. This highlights fibrinogen’s unique mechanical role: a sacrificial protein optimized for energy dissipation and irreversible remodeling during clot formation, rather than for permanent load-bearing like collagen.

4. Conclusion

The mechanical response of fibrinogen is shaped by structural variability among circulating variants, driven by genetic polymorphisms and isoforms, with the γ-chain as a major source of heterogeneity. Our simulations highlight a striking asymmetry between the γ1 and γ2 nodules of the two fibrinogen molecules: γ1 undergoes greater extension with partial recovery, whereas the β-sheet–rich γ2 resists deformation but sustains irreversible damage. This directional dependence underscores that fibrinogen’s mechanics differ across domains, with β-sheets being more susceptible to disruption while α-helices retain greater resilience. Kelvin-Voigt modeling quantified these differences, revealing progressive reductions in both spring constant (K_spec) and dashpot coefficient (C_spec) across cycles. The model captured viscoelastic relaxation and residual strain, demonstrating that fibrinogen’s cyclic mechanics can be effectively described within a viscoelastic framework.

Statement of significance.

Fibrinogen is an essential clotting protein that is constantly exposed to mechanical forces in the bloodstream. Despite its importance, how fibrinogen responds to repeated mechanical stress has remained unclear. Using atomistic simulations, we show that its two terminal γ nodules, surprisingly, respond asymmetrically: the γ1 nodule stretches with partial recovery, while the β-sheet–rich γ2 nodule resists deformation but accumulates irreversible damage. Across multiple loading cycles, both molecules retained residual strain, indicating incomplete reversibility. By combining structural analysis with Kelvin–Voigt viscoelastic modeling, we demonstrate how fibrinogen integrates elasticity, viscosity, and plasticity. These findings provide molecular insight into the mechanical response of the fibrinogen under high-strain cyclic loading (~17.5%–27.5%).

Data availability

The crystal structure including the two distinct fibrinogen molecules was retrieved from the protein data bank (PDB ID: 3GHG). All data and simulation trajectories supporting the findings of this study are available from the corresponding author upon request.