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 (2D) 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 (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 geometric curvature can hierarchically 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. Significance statementCell migration occurs within a 3D extracellular matrix in vivo, which confines cell movement into narrow openings. However, most studies focus on migration on open surfaces, overlooking these extra constraints. Here, we develop a theory to reveal how the mechanical properties of the substrate and confinement geometry jointly regulate migration. Our model provides new insights into how cells navigate tissue openings in vivo or channels in vitro, and highlights how curves along the cells trajectories modulate their migration efficiency. Our findings not only improve our understanding of cell motility in development, immune response, and cancer invasion, but also pave the way for the design of biomimetic platforms that control cell movement for tissue engineering and regenerative medicine.