A multiscale theory for mesenchymal cell migration in straight or curved channel confinement

Mesenchymal cells navigate the extracellular matrix (ECM) in vivo by processing both its mechanical properties and confinement geometry. Here, we develop a multiscale whole-cell theory to investigate cell spreading and migration in two-dimensional viscoelastic channel confinements of varying width and curvature. Our simulations show that, in straight channels, the cell migration speed depends monotonically on the substrate elastic stiffness, which is otherwise biphasic on an unconfined substrate. This is because confinement enforces directional spreading while reducing the spreading area, which results in lower intracellular viscous drag on the nucleus and a higher net traction force of polarized cells in our model. In contrast, we find that confinement curvature slows down cell migration since the friction forces between the bending cell and the confinement walls increase with curvature. We validate our model with experimental data for cell migration in straight channels spanning a wide range of the ECM stiffness as well as in curved channels. Our model illuminates the intertwined effects of substrate viscoelasticity and confinement geometry on cell spreading and migration in complex microenvironments, revealing that channel curvature can override substrate mechanics to dominate migration regulation. The study paves the way for designing scaffolds that leverage curvature and confinement to steer controllable cell migration.