A model of fibroblast motility on substrates with different rigidities

Abstract

To function efficiently in the body, the biological cells must have the ability to sense the external environment. Mechanosensitivity toward the extracellular matrix was identified as one of the sensing mechanisms affecting cell behavior. It was shown experimentally that a fibroblast cell prefers locomoting over the stiffer substrate when given a choice between a softer and a stiffer substrate. In this article, we develop a discrete model of fibroblast motility with substrate-rigidity sensing. Our model allows us to understand the interplay between the cell-substrate sensing and the cell biomechanics. The model cell exhibits experimentally observed substrate rigidity sensing, which allows us to gain additional insights into the cell mechanosensitivity.

Figure 1

Two-dimensional cell mesh and the cytoskeleton mechanical properties. The nonstretched cell is shown at the initial time moment. Each edge that connects neighboring nodes i and j is modeled as an elastic spring with elasticity coefficient E_ij and viscous dashpot with viscosity coefficient μ, connected in parallel. The active forces F_i are applied only at the front of the cell, at nodes marked by the large solid dots. A representative force is marked by a shaded arrow. The cell center is indicated by a letter C.

Figure 2

The assumed magnitude of cell active force |F_i|, at i^th node, as a function of the substrate rigidity σ_ST. Four considered substrates are marked as I, II, III, and IV. See Table 2 for rigidity values of these substrates.

Figure 3

(a) The calculated steady-state cell speed as a function of substrate rigidity σ_ST. The cell moves more efficiently at the intermediate values of substrate rigidity. (b) The calculated equilibrium cell area as a function of substrate rigidity σ_ST. The model cell has compact shape on soft substrates. This distribution is similar to that seen experimentally (1,8) for fibroblasts. Four considered substrates are marked as I, II, III, and IV.

Figure 4

(a) The fibroblast moves from the soft side of the substrate toward the soft-stiff rigidity boundary and crosses it (reproduced with permission from Lo et al. (1)). Bar, 40 μm. (b) The model cell planted on the soft side of the substrate crosses the boundary and continues to move on the stiff side of the substrate. Bar, 50 μm. The trajectory of the cell center is marked with a bold line.

Figure 5

(a) A fibroblast moves from the stiff side of the substrate toward the stiff-soft rigidity boundary, but does not cross it (reproduced with permission from (reproduced with permission from Lo et al. (1)). Bar, 40 μm. (b) The model cell planted on the stiff side of the substrate does not cross the boundary between two rigidities, but turns away from the boundary and stays on the stiff side. Bar, 50 μm. The trajectory of the cell center is marked with a bold line.