Effects of matrix viscoelasticity and geometrical constraint on cell migrations: A multiscale bio-chemo-mechanical model

Abstract

Cells actively sense the extracellular matrix (ECM) biophysical properties and respond by changing migration phenotypes. The regulatory roles of the ECM viscoelasticity and geometrical constraint were separately validated in different experimental studies. However, the extension of the study to more complex microenvironments that combines all these biophysical factors is challenging due to the difficulty of manipulating 3D ECM scaffolds. In this study, we proposed a multiscale model that enabled the sensing of the ECM mechanical properties and contact interactions between a highly deformed cell with the constricted wavy microchannels. The model is validated against experimental data and quantitatively replicates the effects of ECM viscoelasticity and confinement on cell area and speed. We observe a linearly increasing migration speed on stiff substrates with increasing cell aspect ratios in the narrower channels. The reason can be attributed to the increasing net propulsive force as traction forces become progressively polarized and the decreasing viscous drag resulting from the suppressing spreading. Notably, we predict that, on soft viscoelastic substrates, cells concurrently achieve the maximum speed and the largest spreading in which the substrate relaxation time is comparable to the clutch binding timescale. The model also shows the influence of contact guidance by the geometric curvature at the sidewall boundary on cell spreading, morphology, and migration speed. Together, our multiscale model captures varying mechanosensitive migration phenotypes with the underlying mechanism explained from the sub-cellular dynamics and provides experimentally testable predictions on cell migrations in a microenvironment that better mimic the tissue microenvironment.