Abstract：
Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model\'s predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.
摘要：
细胞与环境机械地相互作用来感知，例如,地形,来自其他细胞的弹性和机械线索。机械传感对细胞行为有深远的影响，包括运动性。本研究旨在建立平面弹性基底上细胞机械传感的数学模型，并证明该模型对集落中单个细胞运动的预测能力。在模型中,假定细胞传递粘附力，从动态局灶性粘附整合素密度导出，使基底局部变形，并感测源自相邻细胞的基底变形。来自多个单元的基板变形表示为具有空间变化梯度的总应变能密度。细胞位置处的梯度的幅度和方向定义细胞运动。细胞-基质摩擦，局部运动随机性，包括细胞死亡和分裂。对于几种基底弹性和厚度，给出了单个细胞的基底变形和两个细胞的运动性。预测了25个细胞在模拟200µm圆形伤口闭合的均匀基质上的集体运动性，以进行确定性和随机运动。探索了4个细胞和15个细胞在具有不同弹性和厚度的基底上的细胞运动性，后者再次模仿伤口闭合。使用45个细胞的伤口闭合来证明迁移过程中细胞死亡和分裂的模拟。该数学模型可以充分模拟平面弹性基底上机械诱导的集体细胞运动性。该模型适用于扩展到其他细胞和底物形状，并包含趋化线索，提供补充体外和体内研究的潜力。
