Cell spreading and migration on viscoelastic substrates: a bio-chemo-mechanical multiscale model

The extracellular matrix (ECM) is viscoelastic in nature. Recent evidence has shown that cells can sense both elasticity and viscous response of the ECM via focal adhesions. Although the sub-cellular level theories using the motor-clutch models revealed the critical role of the ECM viscoelasticity in focal adhesion dynamics, elucidating the cell mechanosensitive response demands a whole-cell model. To investigate the mechano-sensing of a mesenchymal cell on a viscoelastic substrate, we formulated a multiscale bio-chemo-mechanical model for the modeling of a whole cell. The proposed framework takes into account the feedback between the biochemical and biomechanical events and integrates the motor-clutch model at the sub-cellular scale with the cell structural analysis at the global level. Our model can quantitatively capture variations of the spreading area and migration speed in response to the ECM stiffness, in agreement with experiments. It further predicts the significant influence of the viscosity on cell spreading and migration on soft substrates. The intermediate substrate viscosity maximizes cell spreading while the maximum migration speed is achieved at high viscosity. These findings pave the way for designing biomaterials that optimize cell spreading and migration.