Force-free cell and cluster migration driven by cortical actomyosin flow

Many fundamental biological processes depend on cell migration. While the mechanical basis of single-cell motility is relatively well understood, the mechanism by which clusters of adherent cells migrate collectively remains elusive due to the complex interplay of actomyosin contraction, hydrostatic pressure, substrate friction, and intercellular forces. We present a two-dimensional continuous membrane model that reproduces both single-cell and cluster migration driven by cortical actomyosin flow. In the model, contraction, adhesion, pressure, and frictional forces acting on the cell surface are always balanced, neglecting inertia, i.e., the model satisfies the force-free conditions. When cell polarity is introduced as a direction-dependent surface tension, a steady cortical flow spontaneously arises from front to rear, generating unidirectional migration not only for single cells but also for cell clusters. The same mechanism can be extended to three dimensions, where cells migrate while maintaining the balance of contractile, frictional, and hydrostatic forces. This force-free mechanism can provide a unified physical basis for understanding collective cell migration observed in developmental morphogenesis, wound healing, and cancer invasion.