# Optimal Control of Collective Electrotaxis in Epithelial Monolayers

## TL;DR

This paper introduces a framework to optimally control the movement of epithelial cell layers using electric fields, enabling precise steering of collective cell migration.

## Contribution

The paper presents the first unified framework for optimal control of collective electrotaxis in epithelial monolayers.

## Key findings

- An ordinary differential equation model was developed to predict monolayer velocity in response to electric fields.
- Optimal electric field designs were derived to maximize distance, velocity, or maintain constant velocity.
- The framework can be extended to other external cues for steering collective cell migration.

## Abstract

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.