A multiscale theory for opposing durotactic regimes in mesenchymal cell migration

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix (ECM) significantly affect cell motility. As a function of stiffness and viscosity, malignant cells rationally switch between durotaxis (migration to stiffer regions) and negative durotaxis (migration to softer regions) in biological tissues. To discern the underlying parameters of this rich behavior we developed a multiscale single-cell model for mesenchymal migration: At the sub-cellular scale, our framework translates the coupling between the viscoelastic substrate, chemical signaling pathways involving Rac and Rho GTPases, the intracellular dynamics of actomyosin complexes and microtubules to the emergent chemo-mechanical forces. At the cellular scale, the model integrates the gradients of the sub-cellular information from different parts of the cell to determine the polarity, which in turn drives the migration by concerted localized protrusions and contractions at opposite ends of the cell, a hallmark of mesenchymal mode. Through the dynamical feedback across these two scales, our simulated cell (i) yields a biphasic migration speed profile in response to the ECM stiffness; (ii) can exhibit both durotaxis and negative durotaxis, in either case migrating toward the region with an optimal stiffness from softer and stiffer regions, respectively; (iii) reveals that high actomyosin contractions driven by steep RhoA GTPase gradients can steer cells against stiffness gradients. Our simulations further predict that viscosity gradients along a substrate can induce migration toward softer regions, preempting stiffness-induced durotaxis. Overall, our multiscale model demonstrates that opposing durotactic behaviors can emerge from predominantly mechanical interactions between the cell and the external medium in quantitative agreement with experiments, thereby elucidating complex mechano-sensing at a single-cell level.