DiffEqn

Derived from the seminal Hodgkin-Huxley and FitzHugh-Nagumo models, the Barkley model is probably the simplest continuous model for excitable media. It replaces the cubic term in the FitzHugh-Nagumo model with a piece-wise linear term as a simplification that enables fast simulation.

Introduction This example model cell fate decisions during early patterning of the pancreas (de Back et al., 2012). The simple gene regulatory network of each cell is coupled to adjacent cells by lateral (juxtacrine) signaling.

Let’s go through an example. We’ll construct a model in which an intracellular cell cycle network (ODE) regulates the division of motile cells which (CPM) release a diffusive cytokine (PDE) which, in turn, controls the cell cycle (ODE).

Diffusion model with cells endowed with chemotactic ability Introduction Previously developed diffusion models can be used to model chemotaxis by adding cells endowed with chemotactic ability. Here, chemotaxis of a group of cells towards a chemical diffusing into the domain with a high level at the right boundary is demonstrated, as well as in a second model, Keller-Segel cells being the sources of their own attractant.