A zipper network model of the failure mechanics of extracellular matrices

Abstract

Mechanical failure of soft tissues is characteristic of life-threatening diseases, including capillary stress failure, pulmonary emphysema, and vessel wall aneurysms. Failure occurs when mechanical forces are sufficiently high to rupture the enzymatically weakened extracellular matrix (ECM). Elastin, an important structural ECM protein, is known to stretch beyond 200% strain before failing. However, ECM constructs and native vessel walls composed primarily of elastin and proteoglycans (PGs) have been found to fail at much lower strains. In this study, we hypothesized that PGs significantly contribute to tissue failure. To test this, we developed a zipper network model (ZNM), in which springs representing elastin are organized into long wavy fibers in a zipper-like formation and placed within a network of springs mimicking PGs. Elastin and PG springs possessed distinct mechanical and failure properties. Simulations using the ZNM showed that the failure of PGs alone reduces the global failure strain of the ECM well below that of elastin, and hence, digestion of elastin does not influence the failure strain. Network analysis suggested that whereas PGs drive the failure process and define the failure strain, elastin determines the peak and failure stresses. Predictions of the ZNM were experimentally confirmed by measuring the failure properties of engineered elastin-rich ECM constructs before and after digestion with trypsin, which cleaves the core protein of PGs without affecting elastin. This study reveals a role for PGs in the failure properties of engineered and native ECM with implications for the design of engineered tissues.

Fig. 1.

Failure of the ZNM and an engineered ECM construct. (Left) Images of the ZNM being stretched to various strains. The elastin fibers are drawn as thick lines and the PGs as thin lines. Note that the elastin does not percolate across the network. The color scale shows the relative forces on each spring. (Right) Phase-contrast images of a region of a tissue sample undergoing failure taken at strains comparable with those in the network model on the left.

Fig. 2.

The fraction of broken PG springs (solid line) and the maximum strain on the PGs (dashed line) as a function of global strain during a failure test of the ZNM. Curves represent the average of 7 simulations.

Fig. 3.

Failure curves and the corresponding peak stresses and failure strains of the ZNM. (A) Sample stress–strain curves for model simulations with and without simulated elastase digestion. Peak stress and stress at failure, or failure stress, are indicated by arrows. (B) Failure data comparing control (n = 7) and elastase (n = 7) digestion simulations. Digestion leads to a significant drop in peak stress but no change in failure strain. Stress is in arbitrary units. *, P < 0. 001.

Fig. 4.

Stress–strain curves of the model undergoing graded removal of PGs. (Inset) Stiffness of the model evaluated at 20% strain for the various PG digestion simulations. Stress and stiffness are in arbitrary units.

Fig. 5.

The mean and SD of stiffness measured at 20% strain as a function of time for control (n = 11) and trypsin-digested (n = 13) engineered ECM constructs. Values are normalized to the baseline at time 0. (Inset) Peak stress and failure strain for the control and trypsin digested groups. *, P < 0.05.

Fig. 6.

Images of a network that contains 2 elastin fibers at network strains of 0% and 65% strains. Note that at 0% strain, the fibers are not aligned with the direction of strain.