Cell migration in the extracellular matrix

Mathematical Framework to Model Migration of Cell Population in Extracellular Matrix

Cell migration is an essential feature of both normal and pathological bio- logical phenomena. Tissue formation in embryonic development requires cell movements and coordination among cells. Migration of cells plays a fundamen- tal role in immune response and tissue homeostasis in mature multicellular organisms. It is also the main process of metastasis dissemination and tumor invasion in cancer.
The characteristics of migration may vary considerably, being either intrin- sic properties of the cells or resulting from their adaptation to the environ- ment. Cell movement is partially regulated by external factors that may in- clude diffusive (such as chemoattractant) and nondiffusive (like ligands bound to the extracellular matrix or ECM) chemicals. Physical interactions of cells and the ECM also play an important role in cell movement.

A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism

Cell migration involves different mechanisms in different cell types and tissue environments. Changes in migratory behaviour have been observed experimentally and associated with phenotypic switching in various situations, such as the migration–proliferation dichotomy of glioma cells, the epithelial–mesenchymal transition or the mesenchymal–amoeboid transition of fibrosarcoma cells in the extracellular matrix (ECM). In the present study, we develop a modelling framework to account for changes in migratory behaviour associated with phenotypic switching. We take into account the influence of the ECM on cell motion and more particularly the alignment process along the fibers. We use a mesoscopic description to model two cell populations with different migratory properties. We derive the  corresponding continuum (macroscopic) model by appropriate rescaling, which leads to a generic reaction–diffusion system for the two cell phenotypes. We investigate phenotypic adaptation to dense and sparse environments and propose two complementary transition mechanisms. We study these mechanisms by using a combination of linear stability analysis and numerical simulations. Our investigations reveal that when the cell migratory ability is reduced by a crowded environment, a diffusive instability may appear and lead to the formation of aggregates of cells of the same phenotype. Finally, we discuss the importance of the results from a biological perspective.

Modeling cell movement in anisotropic and heterogeneous network tissues

Cell motion and interaction with the extracellular matrix is studied deriving a kinetic model and considering its diffusive limit. The model takes into account the chemotactic and haptotactic effects, and obtains friction as a result of the interactions between cells and between cells and the fibrous environment. The evolution depends on the fibre distribution, as cells preferentially move along the fibre direction and tend to cleave and remodel the extracellular matrix when their direction of motion is not aligned with the fibre direction. Simulations are performed to describe the behavior of an ensemble of cells under the action of a chemotactic field and in the presence of heterogeneous and anisotropic fibre networks.

Modeling the motion of a cell population in the extracellular matrix

The paper aims at describing the motion of cells in fibrous tissues taking into account the interaction with the network fibers and among cells, chemotaxis, and contact guidance from network fibers. Both a kinetic model and its continuum limit are described.