Y. Xiao

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.

Multiscale simulation of EMT by minimal signaling circuit Introduction We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.

Simulated sheet morphology for YAP knockdown (KD) and overexpression (OE) Introduction We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.

Multiple models in epithelial-mesenchymal transitions (EMT) Introduction We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.