Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics.

Area of Science:

• Cell Biology
• Biophysics
• Computational Biology

Background:

• Cellular behavior, including shape and migration, is significantly influenced by the mechanical properties of the extracellular matrix (ECM).
• Cells exhibit distinct morphologies (rounded, elongated, flattened) and directional migration (durotaxis) in response to varying substrate stiffness.
• Previous mathematical models have not fully unified the explanations for cell shape and durotaxis based on ECM mechanics.

Purpose of the Study:

• To develop a unified mathematical model explaining cell shape and durotaxis based on focal adhesion (FA) dynamics.
• To investigate how cell traction forces and ECM stiffness influence FA stabilization and cell morphology.
• To demonstrate that FA dynamics can simultaneously account for cell spreading, elongation, and durotaxis.

Main Methods:

• Utilized a hybrid cellular Potts and finite-element model.
• Incorporated ordinary differential equation (ODE)-based models for focal adhesion (FA) turnover.
• Developed a 2D cell-shape model to simulate cell-ECM interactions under varying stiffness conditions.

Main Results:

• The model successfully explains the full range of cell shapes (rounded, elongated, flattened) observed on different ECM stiffnesses.
• FA stabilization, driven by cell traction forces that increase with ECM stiffness, leads to cell spreading on stiff substrates.
• Cell elongation on intermediate stiffness substrates is explained by ECM stress further stabilizing FAs.
• Durotaxis is shown to arise from the same fundamental assumptions regarding FA dynamics.

Conclusions:

• Focal adhesion dynamics provide a unified mechanistic explanation for diverse cell responses to extracellular matrix stiffness, including shape changes and durotaxis.
• The developed model offers a new framework for understanding fundamental cell-ECM interactions.
• This work lays the groundwork for more sophisticated computational models of cell-matrix communication.