Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.

细胞外基质的刚性显着调节许多细胞过程。然而，细胞如何检测和响应基质刚性仍不完全清楚。在这里，我们提出了一个统一的二维多尺度框架来解释化学机械反馈，以探索相互关联的细胞机械传感、极化和迁移，它们构成了细胞对基质刚度响应的动态级联，但在以前的理论中通常单独建模。通过结合整合素动力学和细胞内力转导，我们发现基质硬度可以充当激活或停用细胞极化的开关。我们的理论定量地再现了在广泛的细胞类型中报道的丰富的刚度依赖性细胞动力学，包括扩散、极性选择、迁移模式、杜罗轴，甚至负杜罗轴，并协调了一些不一致的实验观察结果。我们发现特定的双极化模式可以确定最佳的基底刚度，从而实现最快的细胞迁移，而不是细胞在基底上施加的最大牵引力。我们发现这种机械适应源于整个细胞的力平衡。这些发现可以对组织形态发生、伤口愈合和癌症侵袭背景下的各种刚度介导的细胞过程产生普遍的见解。