Top-Down Mathematical Modeling of Cell Shape and Migration

Biophys. J. 94:3671-3683 (2008)

A coarse grain, top-down model is developed to understand the circuit that coordinates cellular activities to generate shape changes and migration. The model contains four simple components of extension, retraction, local positive feedback, and global negative feedback. However it is surprisingly versatile, capable of generating a wide range of shapes and migration patterns mimicking different cell types.

Migration of a Dictyostelium discoidium Amoeba under Agar and Its Computer Simulation

The condition to simulate Dictyostelium shape and migration is generated by using a social biology type optimization algorithm that searches the noisy multi-dimensional parameter space of the model for conditions that reproduce the Dictyostelium behavior.

Migration of a Dictyostelium discoidium Amoeba under Agar and Treated with Nocodazole to Disassemble Microtubules

Nocodazole causes the cell area to become slightly larger and less stable, and the migration to become less persistent. However these effects are subtle visually.

Computer Simulation of Nocodazole-Treated Dictyostelium

Key changes from the control include a higher rate of tail retraction, a faster decay of protrusion signals, and a decrease in negative feedback for suppressing secondary protrusions.

Simulation of a Fibroblast

Fibroblast-like behavior may be generated by adding adhesion sites, which form stochastically at the leading edge and disappear with a finite half life, to an amoebae.

Simulation of a Keratocyte

The simulated keratocyte shows some key characteristics, including the formation of a broad lamellipodium, lateral propagation of shape irregularities, and a strong persistence of migration.. Crucial conditions include a high diffusion rate. strong positive feedback of protrusion signals, and a high rate of retraction.

Simulation of a Neuron

The simulated neuron shows some key characteristics of nerve cells, including the formation of multiple neurites followed by the stabilization of a dominant axon and retraction of other processes. Crucial conditions include limited diffusion and decay of protrusion signals, a low rate of spontaneous protrusions, and a low rate of retraction.