Impact of crosslink heterogeneity on extracellular matrix mechanics and remodeling

Abstract

Mechanical interactions between cells and the extracellular matrix (ECM) lead to the formation of biophysical cues, notably in the form of cell-generated tension, stiffness, and concentration profiles in the ECM. Fibrillar ECMs have nonlinear stiffnesses, linked to the reorientation of fibers under stress and strain, and nonelastic properties, resulting from the force-induced unbinding of transient bonds (crosslinks) that interconnect fibers. Mechanical forces generated by cells can lead to local ECM stiffening and densification. Cell tension is also propagated through the ECM network. The underlying factors that regulate the relative emergence of these signals are not well understood. Here, through computational simulations of 3D ECM fiber networks, we show that the composition of ECM crosslinks is a key determinant of the degree of densification and stiffening that can be achieved by cell-generated forces. This also regulates the sustainability of tensions propagated through the ECM. In particular, highly transient force-sensitive crosslinks promote nonelastic densification and rapid tension relaxation, whereas permanent crosslinks promote nonlinear stiffening and stable tension profiles. A heterogeneous population of crosslinks with different unbinding kinetics enables ECMs to exhibit accumulation, tension propagation, and stiffening simultaneously in response to mechanical interactions with cells.

Keywords: Cell-matrix interactions; Computational modeling; Crosslinking; Extracellular matrix; Mechanobiology.

Graphical abstract

Fig. 1

Schematic of dynamic force loading in an ECM network with crosslink heterogeneity. Local pulling forces, mimicking dynamic cell protrusion-contraction activity, are generated on fiber segments that enter the cell vicinity, i.e. the loading zone, leading to gradual ECM densification. Crosslinks are either transient (force-sensitive) or permanent (force-insensitive). As transient crosslinks unbind, ECM accumulation and network reorganization become nonelastic. Permanent crosslinks do not exhibit force-induced unbinding.

Fig. 2

Simulation examples. An initial 3D uniform fiber network is generated without any applied loading forces. Dynamic pulling forces are then applied to fiber segments that are close to the cell surface (within 2 µm of the left surface). After a loading period, applied forces are stopped to allow for network relaxation. ECMs with different R_P’s (ratio of permanent crosslinks to total crosslinks) exhibit different amounts of remodeling and nonelastic accumulation. The total number of crosslinks is constant. ECM fibers are color-coded by tension based on the color bar at the right (from −300 to + 300 pN). Yellow points are crosslinks. The left and right surfaces are hard boundaries (fibers cannot go through them). Fibers segments that are at the right surface are bound to it. The other four boundaries are periodic. The simulation domain is 20 × 20 × 20 µm³. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3

Stress profiles. a) The stress in the network, calculated by summing the normal tensions of components crossing a plane parallel to the cell surface and then dividing by the area of the surface (20 × 20 µm²), evolves over time for networks with different R_P’s. Dynamic forces are applied from normalized time of 0 to 1, followed by cessation of applied forces. High R_P leads to stable network stresses, whereas low R_P leads to stress profiles that decay over time. b) The peak stress in the network increases with increasing R_P up to a plateau. c) The stress ratio is the ratio of the stress at t = 1 (right before applied forces are stopped) and the peak stress. The stress ratio also increases with R_P up to a plateau.

Fig. 4

ECM accumulation profiles. a) The ECM concentration near the cell surface (within 6 µm) is measured over time. The concentration is normalized to the concentration before force loading. Dynamic forces are loaded at the normalized time from 0 to 1, and applied forces are stopped afterwards to allow for relaxation. High R_P leads to low ECM accumulation that reverts, whereas low R_P leads to high ECM accumulation that does not revert. b) The peak concentration is measured as a function of R_P. This includes both elastic and nonelastic ECM accumulation. c) The nonelastic accumulation (calculated at normalized time = 2, when most simulations have reached a relatively stable state) is measured as a function of R_P. At this point, most of the elastic strains have been relaxed.

Fig. 5

Concentration and stress vs. R_P. We overlay the accumulated ECM concentration, peak stress, and stress ratio vs. R_P curves, demonstrating nonlinearity in the dependence on R_P. There is a range of R_P’s that supports both ECM accumulation and sustaining high stresses. Here, for the purpose of comparing, the curves are all renormalized to range between 0 and 1.

Fig. 6

Stress and stiffness profiles at varying strain. a) Extensional strain is applied to networks of varying R_P, as shown by simulation snapshots. Fibers are color-coded based on tension according to the color bar, which ranges from −300 to 300pN. Yellow spheres are crosslinks. The initial domain size is 20x20x20µm³. b) Extensional stress vs. strain curves are measured for networks with different R_P. Networks with low R_P exhibit stress decay at high strains. c) Heat map of K_E (in Pa) vs. strain and R_P shows increased strain-stiffening capacity for networks with high R_P. Networks with low R_P undergo failure at large strains, and their stiffness is diminished. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)