Optimal Control of Collective Electrotaxis in Epithelial Monolayers.

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.

Optimal control of collective electrotaxis in epithelial monolayers.

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.

Spatial heterogeneity in collective electrotaxis: continuum modelling and applications to optimal control.

Collective electrotaxis is a phenomenon that occurs when a cellular collective, for example an epithelial monolayer, is subjected to an electric field. Biologically, it is well known that the velocity of migration during the collective electrotaxis of large epithelia exhibits significant spatial heterogeneity. In this work, we demonstrate that the heterogeneity of velocities in the electrotaxing epithelium can be accounted for by a continuum model of cue competition in different tissue regions. Having established a working model of competing migratory cues in the migrating epithelium, we develop and validate a reaction-convection-diffusion model that describes the movement of an epithelial monolayer as it undergoes electrotaxis. We use the model to predict how tissue size and geometry affect the collective migration of MDCK monolayers, and to propose several ways in which electric fields can be designed such that they give rise to a desired spatial pattern of collective migration. We conclude with two examples that demonstrate practical applications of the method in designing bespoke stimulation protocols.