  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.
