Remodeling of fibrous extracellular matrices by contractile cells: predictions from discrete fiber network simulations

Abstract

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element-based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.

Figure 8

Simple shear deformation of collagen network with varying gel concentrations. The characteristic nonlinear strain hardening response with the concentration dependent stiffening observed in experiments is captured well by the model. To see this figure in color, go online.

Figure 9

Stress- strain response and energy of deformation. (A) Response of a single fiber fixed at the bottom and deformed at the top as shown in the inset. The initial deformation is dominated by fiber bending and at ∼10% strain, stretching energy dominates the response. (B) A similar response is observed for networks, however, instead of a well-defined knee, it occurs over a range of strains. In the case of a network, individual fibers make transitions as shown in (A) and the cooperative response is shown in (B). To see this figure in color, go online.

Figure 10

Contraction induced fiber reorientation and alignment. Quadrants encompassing long axes of the cell at 45° and short cell axis at 135° are labeled as LA and SA, respectively. During the contraction of cell, fibers align to the axes and the fraction of fibers aligning to LA is shown in (B) and SA in (C). To see this figure in color, go online.

Figure 11

Fiber alignment computed as the change in orientation parameter before and after cell contraction. Alignment is a function of cell aspect ratio and contractility. More fibers align to the axis of contraction and as the aspect ratio increases and there is a pronounced alignment along longer cell axis. (A) When the cell is circular, alignment along LA and SA is similar. (B) For the spindle-shaped cell, alignment along LA is more than along SA. To see this figure in color, go online.

Figure 1

Collagen gel is modeled using 2D networks of elastic fibers with random orientations (histogram of the fiber distribution is given in the left inset) with edges rigidly fixed. The region corresponding to the elliptical cell is removed and displacement boundary conditions are applied to simulate isotropic cell contraction. The right inset shows the cell shape and boundary conditions. To see this figure in color, go online.

Figure 2

Displacement field after contraction of the cell (strain ∼ 90%). The ellipse (a/b = 4) at the center schematically shows the position of the cell before contraction. Inset A shows the aligned (red) and buckled (blue) fibers near the cell. Deformation is highly heterogeneous and localizes along the major axis of the cell as observed in experiments (inset B, adapted with permission from Gjorevski et al. (15)). Displacement vectors show the magnitude and direction of the deformation. Note the longer aligned vectors along the long axis and shorter vectors along the short axis of the cell and their random orientations. To see this figure in color, go online.

Figure 3

Role of cell aspect ratio on fiber reorganization and deformation anisotropy. (A–C) Shows the networks with cells (aspect ratios a/b = 1, 4, and 16, respectively). (D–F) Fibers along the longer cell axis experience large axial stretching and preferential alignment at higher cell aspect ratios. Axial strains of red fibers exceed 1%, blue fibers are in compression and black to white denote fibers with strains in the range 0% to 1%. (G–I) Strain energy density (SED) of the networks at 25% cell contraction. (J–L) The averaged SED variation is similar along both the LA and the SA for the circular cell and localizes along the LA as the cells become more elliptical. To see this figure in color, go online.

Figure 4

Plot of the ratios of stretching to bending energies $\left({\mathit{E}}_{\mathit{R}}={\mathit{E}}_{\mathit{stretch}}/{\mathit{E}}_{\mathit{bend}}\right)$ as a function of the distance from the cell surface for different levels of contractility and aspect ratios. The shaded zone corresponds to the stretching dominated regime. At higher levels of cell contractility and aspect ratios, more fibers are axially stretched and the deformation becomes stretching dominated. (A) For the circular cell at 40% to 50% cell contractility the size of the fiber stretching dominates region is only r = 2.5r₀. (B) When the cell aspect ratio increases, at the same levels of contractility, the deformation zone extends up to r = 10r₀. Inset in both figures schematically shows the cell shapes before and after contraction. (C) ${\mathit{E}}_{\mathit{R}}$ variation along LA at 50% strain for three aspect ratios. Cells of all aspect ratios have a stretching dominated zone up to certain distance from the cell surface and this increases with the aspect ratio. (D) ${\mathit{E}}_{\mathit{R}}$ along SA—in this case the deformation is entirely bending dominated. To see this figure in color, go online.

Figure 5

Heat map of the deformation zone around a single contracting cell. The zone of influence increases with both contractility and the shape anisotropy. For a circular cell, up to a contractile strain of 35%, the gel around the cell is in the bending-dominated regime of deformation and fiber alignment is not observed. As the contractility increases, collagen fibers are aligned akin to collagen tracts seen in experiments (top left corner). Note that a very strong alignment is seen for spindle-shaped cells at large contractility (top right corner). To see this figure in color, go online.

Figure 6

Interaction between two cells with varying center to center distance at ∼ 90% cell contraction. When the distance is 50 μm, cells of all aspects ratios interact by forming collagen tracts. However, as the separation distance increases, the collagen tracts in the deformation zones around the circular cells do not interact with each other. Axial strains of red fibers exceed 1%, blue fibers are in compression and black to white denote fibers with strains in the range 0% to 1%. (E) Heat maps of critical contraction strains for interaction between two cells as a function of their separation. The interaction is strong at higher aspect ratios and smaller separation distances. For circular cells, when the separation between cells is more than 50 μm, no visible collagen tracts are observed. To see this figure in color, go online.

Figure 7

Displacement fields of the DFN model and the NH material. The cell is circular and the model size is identical in both cases. (A) The displacement is felt at a radius of r ∼ 4r₀ for the fibrous network. (B) For the equivalent 2D plane stress model with a nonlinear hardening NH material, the field in red is only significant for r ∼ r₀. (C) Displacement fields of two cells separated by 50 μm overlap with each other for the DFN model. (D) For the same separation distance and contractility, the displacement fields of NH material remain isolated and no interaction is observed. Regions with displacements exceeding 1 μm are shown in red and the initial cell size is schematically shown by a circle (r₀ = 4 μm). To see this figure in color, go online.