The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.

中文翻译：

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细胞外基质弹性变形对细胞迁移的影响

已知细胞外基质的机械特性，特别是其刚度会影响细胞迁移。在本文中，我们开发了单个细胞在弹性矩阵上迁移的数学模型，该模型解释了由细胞施加的力引起的矩阵变形，并研究了刚度如何影响迁移的方向和速度。我们将一维细胞建模为通过弹性弹簧连接到许多粘附位点的细胞核。细胞通过随机更新其粘附位点的位置来迁移。我们首先研究单元弹簧恒定的情况，然后继续假设它们取决于矩阵刚度、均匀刚度矩阵以及具有刚度梯度的矩阵。我们发现，单元弹簧取决于基板刚度的假设对于有效的硬度响应是必要和充分的。我们将模拟与最近表现出 durotaxis 的人类癌细胞的实验观察结果进行比较，这显示出良好的定性一致性。