Modelling biological gel contraction by cells: mechanocellular formulation and cell traction force quantification

Area of Science:

• Cellular mechanics
• Biophysics
• Tissue engineering

Background:

• Cell traction forces are vital for biological tissue organization.
• Quantifying these forces is challenging due to complex cell-matrix interactions.
• Existing methods use experimental devices with gels between holders.

Purpose of the Study:

• To formulate a mathematical model for cell-gel dynamics in traction force measurement devices.
• To theoretically analyze and simulate system behavior under varying conditions.
• To provide a theoretical basis for an experimental device to estimate endothelial cell traction forces.

Main Methods:

• Developed a mathematical model based on mechanical force balance of the gel's viscoelastic response.
• Simulated the displacement of the free moving boundary under different cell and gel concentrations.
• Utilized an experimental setup with endothelial cells on a fibrin gel between floating holders, one fixed and one with a force sensor.

Main Results:

• The model successfully simulated gel boundary displacement.
• Comparison between simulated and experimental data allowed estimation of endothelial cell traction forces.
• Different analytical expressions for cell traction were proposed and compared.

Conclusions:

• The developed mathematical model provides a robust framework for quantifying cell traction forces.
• The experimental device, based on this model, effectively estimates endothelial cell forces on fibrin gels.
• Findings contribute to understanding cell-matrix interactions and their role in tissue development.