Directional cell locomotion requires symmetry breaking between the front and rear of the cell. In some cells, symmetry breaking manifests itself in a directional flow of actin from the front to the rear of the cell. Many cells, especially in physiological 3D matrices do not show such coherent actin dynamics and present seemingly competing protrusion/retraction dynamics at their front and back. How symmetry breaking manifests itself for such cells is therefore elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar observations for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualization of the matrix displacement and a minimal model with multipolar expansion. We show that our cells embedded in a 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself as cycles with finite area in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser. This leads to directed motion. Our study reveals that these cells control their motility by synchronizing dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers.

中文翻译：

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由振荡力偶极子之间的时间相关性驱动的 3D 单细胞迁移

定向细胞运动需要细胞前部和后部之间的对称性破坏。在一些细胞中，对称性破坏表现为肌动蛋白从细胞前部到细胞后部的定向流动。许多细胞，尤其是在生理 3D 矩阵中，没有显示出这种连贯的肌动蛋白动力学，并且在它们的前后呈现看似竞争的突出/收缩动力学。因此，这种细胞的对称性破坏如何表现出来是难以捉摸的。我们从 Purcell 为牛顿流体中的微型游泳者提出的扇贝定理中获得灵感：在低雷诺数下持续运动的自推进物体必须遵循一个打破时间对称性的形状变化循环。我们报告了在 3D 中爬行的细胞的类似观察结果。我们使用 3D 活细胞成像的组合来量化细胞运动，矩阵位移的可视化和具有多极扩展的最小模型。我们表明，嵌入 3D 基质中的细胞在细胞核的两侧形成肌球蛋白驱动的力偶极子，局部地和周期性地挤压基质。定向细胞运动需要两个偶极子之间存在相移，定向细胞运动在偶极子-四极子图中表现为具有有限面积的循环，这是珀塞尔循环的形式等价物。我们通过用激光触发局部偶极收缩来证实这种机制。这导致定向运动。我们的研究表明，这些细胞通过同步分布在前后的偶极力来控制它们的运动。这一结果为外部控制细胞运动以及微型爬行器的设计开辟了新的策略。