Critically important biological phenomena in health and disease, such as wound healing, cancer metastasis, and embryonic development, are governed by collective cell migration. This highly complex process depends not only on cellular features, but also on different stimuli from the local cell environment. Cell migration is promoted by the combination of physico-chemical cues, including the mechanical properties of the extracellular matrix (ECM). Stiffness gradients within ECM have recently been demonstrated to result into preferred directions of cell migration. However, the specific mechanisms driving this directed collective cell migration and their relative roles remain unclear. Here, we develop a continuum formulation and its finite element (FE) implementation to test different hypotheses on the cause of spatial heterogeneities during cell migration on heterogeneous-stiffness substrates. We evaluate two key hypotheses: (i) cell polarisation is promoted by stiffness gradients within the ECM and; (ii) propulsion forces are weighted by ECM stiffness. Ultimately, we provide a robust in silico framework to explain experimental observations and guide future research.

在健康和疾病中至关重要的生物学现象，例如伤口愈合，癌症转移和胚胎发育，是由集体细胞迁移决定的。这个高度复杂的过程不仅取决于细胞特征，还取决于与局部细胞环境不同的刺激。物理化学提示的结合促进了细胞迁移，包括细胞外基质（ECM）的机械性能。最近已证明ECM内的刚度梯度可导致细胞迁移的首选方向。但是，驱动这种定向的集体细胞迁移的具体机制及其相对作用仍不清楚。这里，我们开发了一个连续体公式及其有限元（FE）实现，以测试在异质刚度基质上细胞迁移过程中空间异质性原因的不同假设。我们评估了两个关键假设：（i）细胞极化是由ECM内的刚度梯度促进的；以及 （ii）推进力由ECM刚度加权。最终，我们提供了强大的功能在计算机框架中解释实验观察并指导未来研究。