concentrations of molecules within the cell but also on the concentrations of molecules, particularly Notch receptors and ligands, on
neighboring cells that are in direct contact with the given cell.
Therefore, before simulating Notch signaling-mediated dynamics,
one must choose a suitable spatial lattice wherein each lattice position is occupied by a single cell. This is essential in order to properly
identify the neighboring cells for each cell in the population. We
will not describe the mathematical form of the ordinary differential
equations here since these equations have been described in detail
previously [4].
Figure 7 (bottom panel) shows the spatial patterns that emerge
via Notch signaling between cells occupying a hexagonal lattice
wherein each cell communicates with six neighboring cells in the
population. The results indicate that spatial epithelial-mesenchymal
heterogeneity can emerge in a population of cancer cells due to the
activity of the Notch signaling mechanism. Cells with differing
expression levels of epithelial and mesenchymal factors can be
Fig. 7 (Top) Coupling between Notch-Delta-Jagged signaling and EMT regulation. (Bottom) Spatial heterogeneity in the expression of epithelial and mesenchymal markers in the presence of Notch-Delta signaling (left)
and in the presence of Notch-Jagged signaling (right)
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Shubham Tripathi et al.