Optimal Control of Collective Electrotaxis in Epithelial Monolayers

Area of Science:

• Cellular dynamics and biophysics
• Mathematical modeling of biological systems
• Collective cell migration

Background:

• Epithelial monolayers are widely used models for collective cell migration.
• Electrotaxis, steering cell migration with electric fields, is experimentally established but theoretically underexplored for precise control.
• Designing electric fields for specific spatiotemporal cell movement patterns remains a challenge.

Purpose of the Study:

• To develop a theoretical framework for optimal control of collective monolayer electrotaxis.
• To construct and calibrate a mathematical model predicting cell monolayer velocity under electric field stimulation.
• To derive optimal electric field designs for achieving desired migration patterns.

Main Methods:

• Development and calibration of an ordinary differential equation (ODE) model for monolayer center-of-mass velocity.
• Application of optimal control theory to the ODE model.
• Derivation of electric field designs for specific migration objectives (e.g., maximizing distance, velocity).

Main Results:

• A calibrated ODE model accurately predicts monolayer velocity in response to electric fields.
• Optimal control theory yielded physically realistic electric field designs for steering collective migration.
• Demonstrated ability to maximize monolayer travel distance, velocity, or maintain constant velocity.

Conclusions:

• This study presents the first unified framework for optimal control of collective monolayer electrotaxis.
• The derived methods provide a blueprint for precisely steering collective cell migration using electric fields.
• The framework can be extended to control collective migration using other external cues.