Mechanics of Metric Frustration in Contorted Filament Bundles: From Local Symmetry to Columnar Elasticity

Biomechanical origins of inherent tension in fibrin networks

Blood clots form at the site of vascular injury to seal the wound and prevent bleeding. Clots are in tension as they perform their biological functions and withstand hydrodynamic forces of blood flow, vessel wall fluctuations, extravascular muscle contraction and other forces. There are several mechanisms that generate tension in a blood clot, of which the most well-known is the contraction/retraction caused by activated platelets. Here we show through experiments and modeling that clot tension is generated by the polymerization of fibrin. Our mathematical model is built on the hypothesis that the shape of fibrin monomers having two-fold symmetry and off-axis binding sites is ultimately the source of inherent tension in individual fibers and the clot. As the diameter of a fiber grows during polymerization the fibrin monomers must suffer axial twisting deformation so that they remain in register to form the half-staggered arrangement characteristic of fibrin protofibrils. This deformation results in a pre-strain that causes fiber and network tension. Our results for the pre-strain in single fibrin fibers is in agreement with experiments that measured it by cutting fibers and measuring their relaxed length. We connect the mechanics of a fiber to that of the network using the 8-chain model of polymer elasticity. By combining this with a continuum model of swellable elastomers we can compute the evolution of tension in a constrained fibrin gel. The temporal evolution and tensile stresses predicted by this model are in qualitative agreement with experimental measurements of the inherent tension of fibrin clots polymerized between two fixed rheometer plates. These experiments also revealed that increasing thrombin concentration leads to increasing internal tension in the fibrin network. Our model may be extended to account for other mechanisms that generate pre-strains in individual fibers and cause tension in three-dimensional proteinaceous polymeric networks.