L. Edelstein-Keshet: Mathematical Models in Cell Biology

ODEs for the FitzHugh–Nagumo well-mixed system Introduction The FitzHugh–Nagumo (FN) model is commonly used as a toy model for neuronal excitation. Description Everything is well-mixed and two ODEs are solved for two variables, $u$ (voltage) and $v$ (recovery variable).

Simple model for neuronal firing Introduction This is one of the simplest models used to depict neuronal firing. Description A simple model for neuronal firing consists of the basic ‘integrate-and-fire’ system ODE:

Time sequence showing the changing shape of a CPM cell Introduction Not all cell shapes are circular. In this example, a single cell undergoes a whole series of deformations resulting in the development of irregular cell shapes.

Unbiased and biased random walkers Introduction We can simulate the swimming motion of a cell, such as a bacterium, by interspersing short periods of directed motion with random turns or random scrambling of the cell’s velocity.

Two-parameter plane showing all possible regimes of behavior for a single CPM cell Introduction The idea is based on figure 3 in the referenced paper. Description But here, we use two dimensionless parameters:

Creating patterns using the Schnakenberg reaction-diffusion system Introduction We use the Schnakenberg system to generate patterns using a pair of reaction-diffusion (RD) equations, build up from 1D to 2D and explore parameter dependence.

Example demonstrating how adhesion energies affect cell shape and the cell-cell contact region Introduction We simulate two CPM cells of the same type to demonstrate how adhesion energies affect cell shape and the cell-cell contact region.

Particles moving left and right (as well as up) to mimic actin filament barbed ends Introduction Particles are moving left and right (as well as up) to mimic actin filament barbed ends as motivated by the referenced paper.