The mechanical basis of cell rearrangement I. Epithelial morphogenesis during Fundulus epiboly

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Abstract
Many morphogenetic processes are accomplished by coordinated cell rearrangements. These rearrangements are accompanied by substantial shifts in the neighbor relationships between cells. Here we propose a model for studying morphogenesis in epithelial sheets by directed cell neighbor change. Our model describes cell rearrangements by accounting for the balance of forces between neighboring cells within an epithelium. Cell rearrangement and cell shape changes occur when these forces are not in mechanical equilibrium. We will show that cell rearrangement within the epidermal enveloping layer (EVL) of the teleost fish Fundulus during epiboly can be explained solely in terms of the balance of forces generated among constituent epithelial cells. Within a cell, we account for circumferential elastic forces and the force generated by hydrostatic and osmotic pressure. The model treats epithelial cells as two-dimensional polygons where the mechanical forces are applied to the polygonal nodes. A cell node protrudes or contracts when the nodal forces are not in mechanical equilibrium. In an epithelial sheet, adjacent cells share common boundary nodes; in this way, mechanical force is transmitted from cell to cell, mimicking junctional coupling. These junctional nodes can slide, and nodes may appear or disappear, so that the number of polygonal sides is variable. Computer graphics allows us to compare numerical simulations of the model with time-lapse cinemicroscopy of cell rearrangements in the living embryo, and data obtained from fixed and silver stained embryos. By manipulating the mechanical properties of the model cells we can study the conditions necessary to reproduce normal cell behavior during Fundulus epiboly. We find that simple stress relaxation is sufficient to account for cell rearrangements among interior cells of the EVL when they are isotropically contractile. Experimental observations show that the number of EVL marginal cells continuously decreases throughout epiboly. In order for the simulation to reproduce this behavior, cells at the EVL boundary must generate protrusive forces rather than contractile tension forces. Therefore, the simulation results suggest that the mechanical properties of EVL marginal cells at their leading edge must be quite different from EVL interior cells.