Modeling Chemotaxis, Cell Adhesion and Cell Sorting. Examples with Dictyostelium Eirikur Pálsson Dept of Biology, Simon Fraser University

Throughout gastrulation and embryogenesis. In wound healing. Carcinoma cell invasion. Limb bud regeneration. Cell movement in Dictyostelium discoideum. Examples of Processes Where Cell Movement Is Important:

Purpose of a Cell Movement model Visualization of cell movements in 3-D Understand how simple cell-cell interactions, signaling and adhesion lead to complex cell movements Simplification; Revealing the most important things Gives constraints. Suggests what behavior is possible

Introduction Design of Model Results Conclusions & Future Work Outline

The basic unit of the model is an ellipsoidal cell Deformation of the cell depends on the history of the forces acting on it The cell conserves volume with variable ellipsoidal semi-axes The cell may adhere to other cells or to the substrate When the cell moves it sends out a pseudopod, attaches it to either a neighbor or the surface The cell responds to chemotactic signals The Model.

A Representation of the Deformability of Each Axis

didi djdj

Rotation

Forces (static)

Force equations Equation of motion

All the neighbor cells are found The chemical gradient around each cell is calculated The cells orient towards the chemical gradient and apply an active force in that direction All the forces acting on a cell are determined. These are of two types; The passive and the active forces The cells are moved and deformed according to the equations of motion The chemical concentration is updated. Temporal Evolution of the Model

R Foty 1996

Sorting E aa,E bb > E ab E ab > E aa, E bb E bb > E ab >E aa Separation Random

Limb Bud Pigm. Epith. Heart Liver N. Retina Green Red Yellow Blue Orange Adhesion ColorType R Foty 1996

Sorting Time Sorting Time Sorting: With or Without Random Cell Movement Sorting: Changing Cell Stiffness and Adhesion Normal Cell Stiffer Cell Stiffer and more Adhesive Cell Not Random Random Motion

Sorting of Pre-spore and Pre-Stalk Cells Takeuchi 1986

Sorting due to specific Cell Adhesion

Dictyostelium discoideum Life Cycle

Camp Waves During Aggregation 1 mm K Lee Princeton U

Aggregation (Firtel)

Simulations of Dictyostelium discoideum Aggregation in Response to cAMP signals.

Aggregation. Pacemaker Cells in Red

Aggregation. 1 to 1 Pacemaker Cells in Red

Aggregation,1-1. Reduced Diffusion

Bonner 1999

Simulations of 2-D slugs The Red Cells in the front are cAMP Pacemakers

Slug with cAMP wave

Slug moving straight, Pacemaker graft

Cell Sorting. The Chemotactic force is 50 % Larger in the Grey Cells

Slug with 2 different Cell types, same adhesion

Slug with 2 different cell types, specific cell adhesion Grey cells more adhesive than green

Thicker Slug with 2 different cell types, specific cell adhesion Grey cells more adhesive than green

Thicker Slug with 2 different cell types, specific cell adhesion Grey cells more adhesive than green (Cross section)

Conclusions The model reproduces well the observed behavior and properties of cell aggregates The chemotactic movement of cells in response to a cAMP wave are in qualitative agreement with experiments New Findings Random movement, cell stiffness and cell adhesion affect the rate of cell sorting Cell specific adhesion enhances chemotactic sorting and may be necessary to achieve cell sorting in a timely manner