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The mechanism of embryonic polarity establishment in mammals has long been controversial. Whereas some claim prepatterning in the egg, we recently presented evidence that mouse embryonic polarity is not established until blastocyst and proposed the mechanical constraint model. Here we apply computer simulation to clarify the minimal cellular properties required for this morphology. The simulation is based on three assumptions: (1) behavior of cell aggregates is simulated by a 3D vertex dynamics model; (2) all cells have equivalent mechanical properties; (3) an inner cavity with equivalent surface properties is gradually enlarged. However, an initial attempt reveals a requirement for an additional assumption: (4) the surface of the cavity is firmer than intercellular surfaces, suggesting the presence of a basement membrane lining the blastocyst cavity, which is indeed confirmed by published data. The simulation thus successfully produces a structure recapitulating the mouse blastocyst. The axis of the blastocyst, however, remains variable, leading us to an additional assumption: (5) the aggregate is enclosed by a capsule, equivalent to the zona pellucida in vivo. Whereas a spherical capsule does not stabilize the blastocyst axis, an ellipsoidal capsule eventually orients the axis in accordance with its longest diameter. These predictions are experimentally verified by time-lapse recordings of mouse embryos. During simulation, equivalent cells form two distinct populations composed of smaller inner cells and larger outer cells. These results reveal a unique feature of early mammalian development: an asymmetry may emerge autonomously in an equivalent population with no need for a priori intrinsic differences.

During development, certain cells intercalate with each other towards tissue-elongation, exemplified in sea-urchin gut-elongation, amphibian gastrulation, and Drosophila germ-band extension. Their mechanism is not universal among intercalation events. To clarify the minimal cellular properties required for cellintercalation, we computer-simulated the process using three-dimensional geometrical cell-models. We identified two different mechanisms: (1) cell-junction-remodeling by cell-junction contraction along a specific direction, as observed in Drosophila germ-band extension, and (2) cell-shuffling by orientated cell-extension of bipolar cells, as observed in amphibian gastrulation. The cell-junction-remodeling was characterized by well-defined accumulation of contractile molecules along a specific direction of celljunctions. Length contraction of approximately one cell-junction per cell is enough for the entire tissueelongation. The cell-shuffling was characterised by rhythmic cell-extension and orientated movement of cytoskeleton within the elongated cells. Furthermore, tissue-elongation along a polarized axis was limited to a 2.5-fold increase in the cell-junction-remodeling, while no limit was defined for the cell-shuffling.

The mechanism of wound closure in epithelial tissues, i.e., cell monolayer sheets, is investigated through computer simulations. A wound means an area in which some cells have been removed from the normal tissue. The vertex dynamics cell model [T. Nagai and H. Honda, Philos. Mag. B 81, 699 (2001)], which describes morphogenesis of epithelial tissues using the concepts of statistical physics, is modified and applied to the closure of small wounds without mitosis. It is shown that cell-basal-lamina adhesion governs the wound closure competing with cell-cell adhesion and cell elasticity. The simulation results reproduce the actual wound closure process qualitatively and partly quantitatively. The closing proceeds with the translation of the edges of wound polygons toward the wound center and the intermittent reduction in the number of polygon edges. Over time, the process leads to an exponential decrease in the wound area. A shape factor is introduced to describe the wound shape quantitatively and is used to examine the time variation thereof. A method for determining model parameters by comparison with the experiments is given.