L. Edelstein-Keshet: Mathematical Models in Cell Biology

Spatial relaxation oscillator produces spatial dynamics and spiral waves Introduction We consider a full spatial variant of the Morpheus Model ID: M2012"model of a F-actin negative feedback to GTPase system.

ODEs for GTPase interacting with F-actin Introduction Here, we explore the time behavior of a well-mixed GTPase model with negative feedback from F-actin to the GTPase. Description We assume that GTPase ($G$) leads to actin assembly, and that F-actin, denoted by the variable ($F$), leads to GTPase inactivation:

Simulations of a diffusing field Introduction Here, we build up a simulation of diffusion over three successive files by: Starting with 1D and a short time scale in Diffusion1a_main.

Waves produced by an excitable FitzHugh–Nagumo PDE. Introduction We will here take a closer look at waves produced by an excitable FitzHugh–Nagumo PDE in a periodic 1D domain, in a periodic 2D domain.

Simulations of four types of cells with different shapes to demonstrate how the combined target volume, surface area, and medium contact interaction determine the shape of the cell Introduction By setting the volume, surface, and length constraints, a CPM simulation can produce a variety of cell shapes.

Hybrid continuum-chemical and agent-based cell model Introduction The idea that the diffusion of extracellular signaling molecules sets up non-local cellular communications can also be used to simulate non-local forces using chemoattraction and repulsion.

Spatial distribution of GTPase activity Introduction The actin cytoskeleton is regulated by a set of proteins called Small GTPases. The spatial distribution of GTPase activity changes on a timescale of seconds in rapidly moving cells like white blood cells (neutrophils).

An agent-based model where each cell’s position and velocity is tracked Introduction We expand our exploration of local and non-local models to the class of agent-based models. Description Instead of tracking continuous distributions of cell density, neural activity, or other properties that vary continuously across space, we adopt a different kind of modeling approach by tracking the trajectories and behavior of individual cells.

A simplified version of the Morpheus cell sorting example Introduction A simplified version of the Morpheus built-in example of M0021"cell sorting showing the effect of cell-cell and cell-medium contact energies on the tissue configuration.

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.