Adherent cells are able to actively generate internal forces, channelled by cytoskeletal protein filaments and transmitted through transmembrane receptors to the surrounding environment by means of focal adhesions. Cells also dynamically interact with extracellular matrix by sensing external chemo-mechanical stimuli and then inducing formation of stress fibres mediated by polymerization/de-polymerization processes which continuously redesign the interplay between structural organization and contractility activities in the cytoskeleton, so orchestrating selected signal pathways at the basis of many important cell’s physiological functions like adhesion, migration and division. Despite chemo- and duro-taxis have been intensively studied in the last years to understand how cells move on a substrate, their polarization and reorientation – observed during gastrulation, wound healing and morphogenesis – are only partially understood. By starting from the evidence highlighted in some recent studies that cells reorient in response to substrata deformation by essentially obeying a pure mechanical interaction, we propose to interpret the seeming overall cells’ rotation resulting from the reconfiguration of their cytoskeleton – here named mechanotropism – as a nonlinear optimization problem in which the adherent cell aims to align along directions leading it to minimize a physically coherent measure of work spent to deform the elastic substrate while retaining a prescribed level of homeostatic contractile force. To do this, the single-cell is simply modelled as a finite size contractile force dipole that acts on the boundary of a half-space perturbed by applied point loads. The effects of fences of forces acting orthogonally and tangentially on the boundary of the adhesion medium and encircling the cell are then investigated, so obtaining solutions that predict multiple non-trivial cell polarizations as functions of number, direction, relative magnitude and distance from the cell-dipole of the forces, as well as of the substrate’s Poisson ratio, with unprecedented outcomes under the hypothesis of auxetic (i.e. negative Poisson ratio) materials. The results lead to envisage that the proposed theoretical model might contribute to unveil the mechanobiological principles ruling in vivo cells orientation processes by guiding the design of novel experimental strategies and to conceive new mechanics-based markers for guessing cells’ pathological conditions from their mechanotropism.

粘附细胞能够主动产生内力，该内力由细胞骨架蛋白丝引导，并通过粘膜粘附通过跨膜受体传递到周围环境。细胞还可以通过感知外部化学机械刺激与细胞外基质动态相互作用，然后诱导由聚合/解聚过程介导的应激纤维的形成，从而不断重新设计细胞骨架中结构组织和收缩活动之间的相互作用，从而协调选择的信号通路。许多重要细胞的生理功能（如粘附，迁移和分裂）的基础。尽管最近几年对化学和硬出租车进行了深入研究，以了解细胞如何在基质上移动，它们的极化和重新定向（在胃形成，伤口愈合和形态发生过程中观察到）仅得到部分了解。从最近的一些研究中强调的证据开始，即细胞通过基本上遵循纯机械相互作用来响应基质变形而重新定向，我们建议解释由于细胞骨架的重新配置而产生的看似整体细胞的旋转-这里称为趋向性–作为一种非线性优化问题，其中贴壁细胞旨在沿其方向对齐，从而最大限度地减少了物理变形的工作量，以使弹性基材变形，同时保持规定水平的稳态收缩力。为此，可以将单单元简单地建模为有限大小的收缩力偶极子，该偶极子作用在受外加点载荷扰动的半空间的边界上。围栏的影响然后研究了正交和切向作用在粘附介质边界上并环绕细胞的力的分布，因此获得了预测多个非平凡细胞极化的解决方案，这些极化是数量，方向，相对大小和与细胞偶极的距离的函数力，以及底物的泊松比，在膨胀（即泊松比为负）材料的假设下具有空前的结果。结果导致设想所提出的理论模型可能通过指导新颖的实验策略的设计和构思新的基于力学的标志物来推测细胞的病理状况，从而揭示揭示了体内细胞定向过程的力学生物学原理，从而推测它们的致病性。