Abstract
In collective cell migration, the motion results from forces produced by each cell and transmitted to the neighboring cells and to the substrate. Because inertia is negligible and the migration occurs over long time scales, the cell layer exhibits viscous behavior, where force and motion are connected by an apparent friction that results from the breaking and forming of adhesive bonds at the cell–cell and cell–substrate interfaces. Most theoretical models for collective migration include an apparent friction to connect force and motion, with many models making predictions that depend on the ratio of cell–cell and cell–substrate friction. However, little is known about factors that affect friction, leaving predictions of many theoretical models untested. Here, we considered how substrate stiffness and the number of adhesions affected friction at the cell–substrate interface. The experimental data were interpreted through prior theoretical models, which led to the same conclusion, that increased substrate stiffness increased the number of cell–substrate adhesions and caused increased cell–substrate friction. In turn, the friction affected the collective migration by altering the curvature at the edge of the cell layer. By revealing underlying factors affecting friction and demonstrating how friction perturbs the collective migration, this work provides experimental evidence supporting prior theoretical models and motivates the study of other ways to alter the collective migration by changing friction.
Highlights
IntroductionTheoretical models for collective cell m igration[11,12,13,16,17,18,19,29,30] define viscosity η as the ratio of stress and velocity gradient (i.e., the difference in velocity) at the cell–cell interface with units of (force)(time)/(length)[2] and friction ξ as the ratio of the cell–substrate force density (force)(time)/(length)[4]
Variable k represents the combined stiffness of the cell, bonds, and substrate[22], and given that cells can adapt their stiffness to match that of the substrate[23], it is feasible that all are of the same order of magnitude, suggesting that increasing substrate stiffness would directly increase variable k, thereby increasing the friction force
We focused on one aspect of those interactions, the resisting force that creates apparent viscosity and friction at the cell–cell and cell–substrate interfaces
Summary
Theoretical models for collective cell m igration[11,12,13,16,17,18,19,29,30] define viscosity η as the ratio of stress and velocity gradient (i.e., the difference in velocity) at the cell–cell interface with units of (force)(time)/(length)[2] and friction ξ as the ratio of the cell–substrate force density (force)(time)/(length)[4]. Other studies found the ratio of viscosity to friction to be large, with λ on the order of hundreds of microns or larger[12,19,31]. These conflicting experimental observations are likely caused in part by different experimental conditions. Predicting a biphasic relationship between velocity correlation length and speed, depending on the balance of viscosity and friction[14], and the second by Alert et al predicting that length scale λ is proportional to the size of a protrusion at the edge of the cell layer[18]
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