8 - Spatiotemporal Patterning by the Cells

Summary

In this chapter, we introduce various modeling approaches capable of addressing pattern formation by cell populations. Firstly, we discuss the Delta–Notch system as an example of pattern formation by local interaction. We then explore the Kessler–Levin model, which combines cellular automaton and continuous system approaches, illustrating the evolution of cAMP waves in cellular slime molds. Next, our attention turns to methodologies requiring active consideration of cellular arrangements and deformations, including models involving cell proliferation and movement. We present reaction–diffusion systems that explain structures formed in bacterial colonies resembling Diffusion Limited Aggregation (DLA). Additionally, we introduce the cellular Potts model to investigate pattern formation among moving cells, incorporating variations in cellular adhesion force. The cell-vertex model represents a cell population as a collection of vertices of a polygon or polyhedron. We also discuss the phase field model, employing partial differential equations to depict relatively simple morphological changes in complex structures. By employing these modeling techniques, we can capture the characteristics of various pattern formations orchestrated by cell populations.