# Controlling Cell Migratory Patterns Under an Electric Field Regulated by a Neural Network-Based Feedback Controller

## TL;DR

This paper introduces a neural network-based feedback controller to precisely regulate cell migration under electric fields, improving on traditional methods.

## Contribution

A novel neural network feedback controller with a projection operator to manage electric field saturation during cell migration control.

## Key findings

- The modified neural network controller outperforms the original design in trajectory tracking under saturation.
- In vitro experiments show the controller effectively directs macrophage migration under a unidirectional electric field.
- The controller outperforms PID in guiding electrotactic migration of macrophages in 2D culture.

## Abstract

Electric fields (EFs) are widely employed to promote tissue regeneration and accelerate wound healing. Despite extensive study, the cellular responses elicited by EFs are complex and not well understood. The present work focuses on cell migration—a process essential to organismal development, immune surveillance, and repair—and seeks to achieve its precise, closed-loop regulation. Effective control is impeded by (i) the nonlinear and stochastic nature of migratory dynamics and (ii) safety constraints that restrict the admissible EF magnitude. To address these challenges, we reformulate a neural network (NN) feedback controller previously developed for single-cell membrane-potential regulation and adapt it to guide population-level cell migration. A projection operator is embedded into the NN weight-update law to prevent maladaptive learning that arises when the control signal saturates at its EF limit. Numerical simulations confirm that the modified controller maintains accurate trajectory tracking under saturation and outperforms the original NN design. Finally, we demonstrate a proof-of-concept by implementing the controller in vitro to direct the electrotactic migration of naïve macrophages in 2D culture under a unidirectional EF. For the in vitro experiments, we compare performance to the standard proportional–integral–derivative (PID) controller.