Mathematical Institute, University of Oxford, Oxford, UK.
Department of Quantitative and Computational Biology, Princeton University, Princeton, NJ, USA.
Bull Math Biol. 2024 Jun 19;86(8):95. doi: 10.1007/s11538-024-01319-8.
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.
上皮细胞单层是研究细胞集体迁移的最佳模型之一，因为它们在多细胞系统中非常丰富，而且易于处理。在实验中，可以通过电刺激等方法来稳健地引导上皮细胞单层的集体迁移，这个过程被称为趋电性。然而，从理论上讲，如何设计电场以实现所需的时空运动模式的问题还没有得到充分探索。在这项工作中，我们构建并校准了一个常微分方程模型，以预测细胞单层对电场刺激的质心平均速度。我们使用这个模型，结合最优控制理论，推导出物理上合理的最优电场设计，以实现各种目标，包括最大化单层迁移的总距离、最大化单层速度，以及在刺激过程中保持单层速度恒定。总之，这项工作首次提出了用于集体单层趋电性最优控制的统一框架，并为使用其他外部线索来最优地引导集体迁移提供了蓝图。
