Structural hierarchy governs fibrin gel mechanics

Abstract

Fibrin gels are responsible for the mechanical strength of blood clots, which are among the most resilient protein materials in nature. Here we investigate the physical origin of this mechanical behavior by performing rheology measurements on reconstituted fibrin gels. We find that increasing levels of shear strain induce a succession of distinct elastic responses that reflect stretching processes on different length scales. We present a theoretical model that explains these observations in terms of the unique hierarchical architecture of the fibers. The fibers are bundles of semiflexible protofibrils that are loosely connected by flexible linker chains. This architecture makes the fibers 100-fold more flexible to bending than anticipated based on their large diameter. Moreover, in contrast with other biopolymers, fibrin fibers intrinsically stiffen when stretched. The resulting hierarchy of elastic regimes explains the incredible resilience of fibrin clots against large deformations.

Figure 1

Structural properties of fibrin gels. (A) Atomic force microscopy shows a homogeneous network of thick and straight fibers (5 × 5 μm area). (B) Fibrin fibers have a hierarchical architecture: fibers (top) are bundles of protofibrils (middle), which consist of two half-staggered strands of fibrin monomers with αC-extensions (αC-e) protruding from the surface (bottom). (C–E) Confocal microscopy demonstrates that fibrin gels are homogeneous over a large range of protein concentrations. Scale bars, 10 μm. (F) (Top panel) The mesh size of fibrin gels estimated from confocal images decreases as the square-root of protein concentration (symbols), consistent with the expectation for homogeneous networks of fibers of constant diameter (solid line). (Bottom panel) Concentration dependence of the number of protofibrils per fiber N, measured by turbidimetry.

Figure 2

Low-strain rheology of fibrin gels. (A) Frequency dependence of the elastic (solid symbols) and viscous (open symbols) moduli for a network of 0.6 μM fibrin, measured by rheometry (circles) and microrheology (squares). Solid line shows the viscous modulus of the solvent. (Upper inset) The bulk rheology is measured by applying a small, oscillatory shear stress to a fibrin gel between two plates of a rheometer. (Bottom inset) The local rheology is measured by microrheology: a probe sphere inside the fibrin gel is held by an optical tweezer (dotted red lines). Its thermal fluctuations are tracked with a quadrant photodiode and converted to shear moduli using linear response theory. (B) The low-strain plateau modulus G₀ (blue squares) agrees with an entropic model of semiflexible fibers (blue line) with one adjustable parameter, the distance l_c between cross links (bottom inset). The high-strain plateau modulus K_s (red circles) agrees with a single-fiber stretching model (red line) with one adjustable parameter, the fiber stretch modulus κ_s (upper inset).

Figure 3

High-strain mechanics of fibrin gels. (Top) Increasing levels of shear strain (bar) induce a sequence of distinct elastic regimes. (Bottom) Typical stress-stiffening behavior of a fibrin gel (9 μM). The color coding of the background indicates the transition from a regime dominated by entropic elasticity at the network level (red) to a regime dominated by entropic elasticity at the fiber level (green). The initial, linear network stiffness reflects thermal fluctuations of the fibers (regime 1). Strains of a few percent pull out the thermal slack from fiber segments between cross links, leading to network stiffening (regime 2). Even larger strains cause fiber stretching, resulting in a second linear regime (regime 3). The elastic modulus would remain constant for fibers with a linear stretch modulus (dashed line). Instead, the modulus increases again (regime 4), indicating stretching of flexible regions within the fibers. The increase is consistent with the σ^3/2 response expected for wormlike chains (dashed line). Forced-unfolding of fibrin monomers may start before network rupture (regime 5).

Figure 4

Strain-stiffening transitions of fibrin gels. (A) Critical strain characterizing the onset of the first strain-stiffening regime (regime 2), compared with a model (line) that assumes entropic stretching of fibers (Inset). (B) Critical stress characterizing the onset of the first strain-stiffening regime (regime 2, blue squares) and the onset of the second strain-stiffening regime (regime 4, red circles). Solid lines indicate model predictions for entropic stretching of fibers (blue line) and of loose protofibril bundles (red line and inset).

Figure 5

Intrinsic nonlinear stretch modulus of fibrin fibers. (A) Stress-stiffening curves measured for different polymer concentrations, rescaled by protofibril density. The data collapse onto a mastercurve at large strain, where the network elasticity is governed by stretching of fibers with a nonlinear stretch modulus. The stiffening is consistent with the response of a wormlike chain (dashed line). (B) Stress-stiffening curves predicted for fibrin concentrations of 0.3 (low), 1, 3, and 9 (high) μM. (Inset) The fibers are modeled as loose, parallel arrays of protofibrils that fluctuate independently over a length l₀ = 0.1 μm between cross links to the rest of the fiber. The model combines entropic elasticity of the fibers between network cross links (red line), and intrinsic fiber nonlinear stretching due to entropic elasticity of the protofibrils (blue line). The extension (or compliance) of these two contributions add (black line).

Figure 6

Rupture behavior of fibrin gels. (A) The rupture strain (symbols) increases weakly with fibrin concentration according to a power-law with exponent 0.2 (dashed line). (B) Tension per protofibril calculated from the shear stress where the second strain-stiffening regime starts (open symbols) and from the stress where the network ruptures (solid symbols).