A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells

We present a chemomechanical whole-cell theory for the spreading and
migration dynamics of mesenchymal cells that can actively reinforce their
adhesion to an underlying viscoelastic substrate as a function of its
stiffness. Our multiscale model couples the adhesion reinforcement effect
at the subcellular scale with the nonlinear mechanics of the
nucleus-cytoskeletal network complex at the cellular scale to explain the
concurrent monotonic area-stiffness and non-monotonic speed-stiffness
relationships observed in experiments: We consider that large cell
spreading on stiff substrates flattens the nucleus, increasing the viscous
drag force on it. The resulting force balance dictates a reduction in the
migration speed on stiff substrates. We also reproduce the experimental
influence of the substrate viscosity on the cell spreading area and
migration speed by elucidating how the viscosity may either maintain
adhesion reinforcement or prevent it depending on the substrate stiffness.
Additionally, our model captures the experimental directed migration
behavior of the adhesion-reinforced cells along a stiffness gradient,
known as durotaxis, as well as up or down a viscosity gradient (viscotaxis
or anti-viscotaxis), the cell moving towards an optimal viscosity in
either case. Overall, our theory explains the intertwined mechanics of the
cell spreading, migration speed and direction in the presence of the
molecular adhesion reinforcement mechanism.