A dynamical analysis of the alignment mechanism between two interacting cells

by Vivienne Leech, Mohit P. Dalwadi, and Angelika Manhart

In biology, organisms often align their body orientation to coordinate their movement. Famous examples are schools of fish or flocks of birds. Here we focus on aligning cells, such as bacterial cells or skin cells, whose collective dynamics affects the behaviour of the bacterial colony or the properties of the skin tissue (relevant e.g. in scar formation). We zoom into the collective alignment dynamics and focus on the interactions between two cells on a 2D surface. The cells move, turn and deform in order to avoid overlapping. We thoroughly mathematically analyse the resulting non-linear system of ordinary differential equations. This allows to understand the role the model ingredients, such as self-propulsion, play for alignment dynamics.

Mathematically analysing cell alignment.