The elasticity of an individual fibrin fiber in a clot

Abstract

A blood clot needs to have the right degree of stiffness and plasticity to stem the flow of blood and yet be digestable by lytic enzymes so as not to form a thrombus, causing heart attacks, strokes, or pulmonary emboli, but the origin of these mechanical properties is unknown. Clots are made up of a three-dimensional network of fibrin fibers stabilized through ligation with a transglutaminase, factor XIIIa. We developed methods to measure the elastic moduli of individual fibrin fibers in fibrin clots with or without ligation, using optical tweezers for trapping beads attached to the fibers that functioned as handles to flex or stretch a fiber. Here, we report direct measurements of the microscopic mechanical properties of such a polymer. Fibers were much stiffer for stretching than for flexion, as expected from their diameter and length. Elastic moduli for individual fibers in plasma clots were 1.7 +/- 1.3 and 14.5 +/- 3.5 MPa for unligated and ligated fibers, respectively. Similar values were obtained by other independent methods, including analysis of measurements of fluctuations in bead force as a result of Brownian motion. These results provide a basis for understanding the origin of clot elasticity.

Fig. 1.

Confocal scanning light micrographs of plasma clots with and without ligation. These clots were prepared in the same way as those used for the laser tweezers measurements. The fibers are labeled with 5-nm colloidal gold and viewed in reflectance mode. This image is a two-dimensional projection from 150 optical sections made with Zeiss software. (A) Unligated clot formed with DDITS, an inhibitor of factor XIIIa. (B) Ligated clot formed without inhibitor of factor XIIIa. (Scale bar, 5 μm.)

Fig. 2.

An individual fibrin fiber with attached bead ≈1 μm in diameter that is being flexed by the optical tweezers. The curvature of the fiber is not obvious, because deflections were small. The fiber and bead are seen in differential interference contrast mode. In this experiment, the bead was oscillating at 3 Hz, and 170 frames (5.7 s) of video were digitized, so 18 frames with the bead at its maximum position upward were averaged to generate this image. (Scale bar, 1 μm.)

Fig. 3.

Elastic curves of a bent fiber and diagram showing the measured parameters used for calculation of the elastic modulus. (A) Plot of the coordinates of the center of a flexed fiber from transverse line profiles of averaged bitmap differential interference contrast images along the length of the fiber at maximum deflection. For each experiment, four fiber segments were measured on either side of the bead (represented here as a dashed circle) at maximum deflection in either direction. (B) The same fiber curve with the vertical displacement exaggerated to better show the fitting of each segment to a third-order polynomial curve. The curves of best fit were used to calculate the maximum displacement as well as the extrapolation to the fiber “end points” where there was no movement. (C) Diagram of fiber with attached bead that is being flexed by optical tweezers. The movement of bead and fiber in the vertical direction here is also exaggerated for the sake of illustration of the parameters measured. The elastic modulus of a fiber was calculated from the formula for the relationship between loading and deflection of a simple beam (27) E = (pab/6IyL)(L² - b² - a²), where E is elastic modulus (in Pa), p is force applied (in pN), a is distance from left-hand end point to bead (in nm), b is distance from right-hand endpoint to bead (in nm), y is deflection at the point load (in nm), L is effective length of fiber segment (in nm), and I is second moment of circular plane area (in nm²), which is the observed shape of fibrin fibers, I = (πr⁴)/4, where r is fiber radius (in nm).

Fig. 4.

Time course of changes in variance in position of a fibrin fiber in a clot determined from measurement of bead fluctuations as a result of Brownian motion. The magnitude of the fluctuations of a bead attached to a fiber is inversely related to the stiffness of the fiber. Circles, clot formed in the presence of factor XIIIa inhibitor DDITS (little change in fluctuations over time); squares, clot formed in the absence of DDITS (ligation by factor XIIIa occurs over time, resulting in a decrease in fluctuations or increase in stiffness).