Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

Figure 1

Realizations of 3D ECM networks with randomly oriented fibers with $\mathrm{\Omega }=0.5$ (a) and horizontally aligned fibers with $\mathrm{\Omega }=0.88$ (b), generated using stochastic reconstruction techniques. For better visualization, only small subnetworks with a linear size of $50\mu \text{m}$ are shown here. Panels (c) and (d), respectively, show the coordination distribution $P_Z$ and fiber length distribution $P_f$ for the networks, which are computed based on confocal images of a 2 mg/ml collagen gel. The statistical descriptors of the simulated networks almost perfectly match the corresponding target descriptors obtained from the experiments and thus, are visually indistinguishable from one another.

Figure 2

Schematic illustration of the nonlinear elastic fiber model, including a linear elastic regime, which is followed by a strong strain-hardening regime upon compression and buckling upon compression.

Figure 3

Schematic illustration of the computational model for a migrating cell. (a) Protrusions (yellow dashed lines) generated by polymerization of actin filaments can lead to focal adhesion formation (yellow dots) in a region within $\delta R_s$ (effective protrusion length) from the cell surface (red sphere), which is enclosed by the dashed circle. (b) New focal adhesion (red dots) formation is modeled by adding new filaments (yellow solid lines) connecting the center of mass of the cell (i.e., the center of the cytoplasm sphere) to a randomly selected node of the ECM network within $\delta R_s$ from the cell surface, with a probability depending on the persistent direction of the cell (dashed arrow) and the local stress state of the fibers. (c) Active contraction of actin filaments generates active forces in the ECM network and leads to deformation of ECM. (d) Locomotion of the cell due to actin filament contraction.

Figure 4

Left panel: 3D visualization of a single MCF-10A cell migrating on isotropic collagen gel with randomly oriented fibers. The contraction of the actin filaments generates active tensile forces, which are transmitted to the collagen fibers (shown in red or dark gray in print version). Right panel: Confocal microscopy image of a migrating MCF-10A cell (bright blue) on collagen gel. The collagen fibers are shown in dark blue (or dark gray in print version). The linear size of the system is $\sim 100\mu \text{m}$.

Figure 5

Comparison of the mean-squared displacement (MSD) of a single MCF-10A cell migrating on isotropic collagen gel with randomly oriented fibers, respectively, obtained from computer simulation (left panel) and in vitro experiment (right panel). The reported results are, respectively, ensemble averages of 15 independent experiments and 20 independent simulations. The regions enclosed by the dashed lines represent the range of standard deviations. The insets show the trajectories of the cells.

Figure 6

A typical trajectory of MCF-10A cell migrating on 3D collagen gel with horizontally aligned fibers obtained from simulations.

Figure 7

Mean-squared displacement (MSD) of MCF-10A cell migrating on 3D collagen gel with horizontally aligned fibers (along the $x$ direction), respectively, along the $x$ direction (left panel) and $y$ direction (right panel). Anisotropy in migration can be clearly observed, i.e., the cell tends to move along the direction of fiber aligned, a phenomenon known as contact guidance. The reported results are ensemble averages of 20 independent simulations. The regions enclosed by the dashed lines represent the range of standard deviations.

Figure 8

A typical trajectory of MCF-10A cell migrating on 3D collagen gel with a stiffness gradient along the $x$ direction obtained from simulations.

Figure 9

Mean-squared displacement (MSD) of MCF-10A cell migrating on 3D collagen gel with a stiffness gradient (along the $x$ direction), respectively, along the $x$ direction (left panel) and $y$ direction (right panel). Anisotropy in migration can be clearly observed, i.e., the cell tends to move up against the stiffness gradient, a phenomenon known as durotaxis. The reported results are ensemble averages of 20 independent simulations. The regions enclosed by the dashed lines represent the range of standard deviations.

Figure 10

Left panel: 3D visualization of two closely spaced MCF-10A cells migrating on an isotropic collagen gel with randomly oriented fibers. The collagen fibers carrying large tensile forces generated by actin filament contraction are highlighted in red. Right panel: Confocal microscopy image of a pair of migrating MCF-10A cells (bright blue) on collagen gel. The collagen fibers are shown in dark blue (or dark gray in print version).

Figure 11

Comparison of the velocity correlation function $S\left(r\right)$ (see the text for definition) of MCF-10A cells migrating on isotropic collagen gels with randomly oriented fibers, respectively, obtained from computer simulation (solid curve) and in vitro experiment (dashed curve).

Figure 12

Successive snapshots over 30 min showing the positions of two nearby cells obtained from simulations (upper panels) and experiments (lower panels). These results indicate the two cells move towards one another, as indicated by the short-range negative values of the corresponding velocity correlation functions shown in Fig. 11.