Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist.

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

Left/right asymmetric collective migration of parapineal cells is mediated by focal FGF signaling activity in leading cells.

The ability of cells to collectively interpret surrounding environmental signals underpins their capacity to coordinate their migration in various contexts, including embryonic development and cancer metastasis. One tractable model for studying collective migration is the parapineal, a left-sided group of neurons that arises from bilaterally positioned precursors that undergo a collective migration to the left side of the brain. In zebrafish, the migration of these cells requires Fgf8 and, in this study, we resolve how FGF signaling correlates with-and impacts the migratory dynamics of-the parapineal cell collective. The temporal and spatial dynamics of an FGF reporter transgene reveal that FGF signaling is activated in only few parapineal cells usually located at the leading edge of the parapineal during its migration. Overexpressing a constitutively active Fgf receptor compromises parapineal migration in wild-type embryos, while it partially restores both parapineal migration and mosaic expression of the FGF reporter transgene in fgf8-/- mutant embryos. Focal activation of FGF signaling in few parapineal cells is sufficient to promote the migration of the whole parapineal collective. Finally, we show that asymmetric Nodal signaling contributes to the restriction and leftwards bias of FGF pathway activation. Our data indicate that the first overt morphological asymmetry in the zebrafish brain is promoted by FGF pathway activation in cells that lead the collective migration of the parapineal to the left. This study shows that cell-state differences in FGF signaling in front versus rear cells is required to promote migration in a model of FGF-dependent collective migration.