Physical Model for Cell Migration Guided by Elastic Properties of the Substrate

Abstract

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 EVL layer. It is experimentally observed that these cells migrate toward the EVL borders and move freely on them. Apparently,the phenomenon is due to 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 elucidate how this kind of migration works and what are sensing the cells. It considers a cell modelled as a circle with four contacts on a thin elastic membrane,representing the EVL layer. Each of the four contacts simulates a random protrusion which elongates their end out of the center of the cell,attach rigidly to the substrate, and contracts without gliding. We study the elastic response of the substrate and its implications in the cell dynamics when it has different stiffness and when it is under internal tensions. In the first case, the substrate has a stiffer strip which simulates the EVL border which in theory has a higher Young modulus. In this case,the results do not show the expected durotaxis effect. In fact, the cell shows a random walk movement added to a slight repulsion generated by the border so that a stiffer strip on a thin plate is not enough to reproduce the phenomenon. In the second case,when the substrate is under internal applied tensions,the results show that in a substrate with circular geometry,if the contractive circumferential stress component increases with the radial distance,the cell migrates and reproduce experimental observations. We conclude that cell migration could be due to differences in internal tensions instead of thickness or stiffness differences.