Modeling Chemotaxis Cell Adhesion and Cell Sorting Examples

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

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

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

Outline • Introduction • Design of Model • Results • Conclusions & Future Work

The Model. • 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

A Representation of the Deformability of Each Axis

di dj

Rotation

Forces (static)

Force equations Equation of motion

Temporal Evolution of the Model • 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.

R Foty 1996

Sorting Ebb > Eab >Eaa Random Eab > Eaa, Ebb Separation Eaa , Ebb > Eab

Type Color Adhesion Limb Bud Green 20. 1 Pigm. Epith. Red 12. 6 Heart Yellow 8. 5 Liver Blue N. Retina Orange 1. 6 4. 6 R Foty 1996

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

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 c. AMP signals.

Aggregation. Pacemaker Cells in Red

Aggregation. 1 to 1 Pacemaker Cells in Red

Aggregation, 1 -1. Reduced Diffusion

Simulations of 2 -D slugs The Red Cells in the front are c. AMP Pacemakers

Slug with c. AMP 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 c. AMP 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