A Statistical Mechanics Approach to Describe Cell Reorientation Under Stretch.

Area of Science:

• Cell biology
• Biophysics
• Statistical mechanics

Background:

• Cells cultured on elastic substrates exhibit reorientation when subjected to cyclic stretching.
• Stochastic effects lead to a broad distribution of cell orientation angles, typically reported experimentally.

Purpose of the Study:

• To determine the evolution and stationary state of cell orientation probability density functions.
• To model cell reorientation using Fokker-Planck equations derived from microscopic rules.
• To compare model predictions with experimental results.

Main Methods:

• Utilizing Fokker-Planck equations derived from microscopic rules for cell reorientation.
• Employing a stochastic differential equation based on a general elastic energy minimization principle.
• Implementing discrete-time random processes and optimal control problems to model reorientation mechanisms.

Main Results:

• The time integration and stationary state results from the Fokker-Planck equation showed excellent agreement with experimental data.
• The developed models accurately predict the statistical distribution of cell orientations under cyclic stretching.
• The study successfully linked microscopic cell behaviors to macroscopic orientation patterns.

Conclusions:

• Fokker-Planck equations provide a robust framework for modeling cell reorientation dynamics on elastic substrates.
• The models developed offer insights into the underlying mechanisms of cell response to mechanical stimuli.
• The findings have implications for understanding tissue development and mechanobiology.