Relevance of Cell-ECM Interactions: From a Biological Perspective to the Mathematical Modeling

Abstract

Cell migration across fibre networks and micro-channel structures has been widely demonstrated to be strongly influenced by the interactions between moving indi- viduals and the surrounding extracellular matrix as well as by the mechanical properties of cell nucleus. In this respect, our work will be devoted to describe several mathemat- ical models, which deal either with cell adhesion mechanics or with suitable analysis of the role played in cell movement by nucleus stiffness. In particular, the presented approaches span from discrete individual-based methods to continuous models and pro- vide useful insights into selected determinant underlying cell migration within two- and three-dimensional matrix environments. The extracellular environment cells live and migrate in is mainly composed of an aqueous intersti- tial fluid and of an insoluble protein infrastructure, which is generally called extracellular matrix (and shortened as ECM). The ECM is an interlinked network formed by filamentary molecules secreted by many cell types, mainly fibroblasts. The specific composition of the ECM can considerably change, as it can involve several constituents like collagen, elastin, proteoglycan, fibronectin. The ECM provides structural and biochemical support to the ensemble of cells. In particular, cell-matrix interactions are mediated by transmembrane adhesion molecules, among which integrins are the most important ones: their regulatory activity is fundamental for inside-out signaling ex- changes between the cells and the external environment. Specifically, cell-ECM interactions regu- late both migration-related processes, as it happens during wound healing and spread of metastasis, and proliferation-related mechanisms, critical in the case of tumor growth, tissue development, and organogenesis. Entering in more details, cell migratory ability and migratory mode are significantly determined by chemical composition, mechanical properties, and topological microstructure of the surrounding extracellular matrix. In this respect, cell response to mechanical and biochemical cues coming from the ECM environment mainly depends from two mechanisms: mechanosensing and mechanotrans- duction. The former defines how cells sense the mechanical forces exerted on them by fibrous matrix proteins, i.e., either through membrane-bound ion channels, that open or close up under stress or shear to modulate the influx/outflux of ions, or through a direct transmission of stress and shear from the ECM to the actin cytoskeleton (via adhesion complexes and transmembrane adhesion protein, e.g., of the integrin family). The latter has to do with the effective cell response to mechanical cues. This