Straintaxis: cell migration driven by substrate deformation gradients

During annual fish epiboly, between the egg yolk and the enveloping layer cells (EVL), there is a group of deep cells that move in contact with the EVL layer. It has been experimentally observed that these cells migrate toward the EVL borders and move freely on them. It was conjectured that the phenomenon is due to the elastic properties of the EVLs: either a difference in the Young modulus on the border or a stress gradient inside the cell. In this work, a model is developed to demonstrate that cells can migrate due to differences in the internal stresses of the substrate cells. Based on a durotaxis model, we study the elastic response of a substrate that is already deformed by the action of the internal tensions, and the implications in the cell dynamics. It is shown that cells migrate in the direction of increasing strain of the substrate. We consider a circular geometry for the substrate cells, showing that if the contractive circumferential stress component increases with the radial distance, the cell migrates in the right direction and with similar speeds, reproducing the experimental observations. In conclusion, we have identified a new mechanism, straintaxis, which directs the motion of cells when they move on top of a pre-deformed thin elastic substrate. Finally, in the reported experiment, the cell migration could be described by straintaxis instead of durotaxis.