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First published online March 21, 2008
doi: 10.1242/10.1242/dev.014555

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Computer simulation of emerging asymmetry in the mouse blastocyst

Hisao Honda^1,*, Nami Motosugi^2,, Tatsuzo Nagai³, Masaharu Tanemura⁴ and Takashi Hiiragi^2,,,*

¹ Hyogo University, Kakogawa, Hyogo 675-0195, Japan.
² Department of Developmental Biology, Max-Planck Institute of Immunobiology, Freiburg D-79108, Germany.
³ Physics Department, Kyushu Kyoritsu University, Kitakyushu 807-8585, Japan.
⁴ Institute of Statistical Mathematics, Tokyo 106-8569, Japan.

View larger version (13K): [in this window] [in a new window]   Fig. 1. Model and elements of the computer simulation. (A) Polyhedral cells and polygonal surfaces are defined by vertices. (B) Reconnection of neighboring vertices. (C) Formation of a tetrahedral intercellular space at a vertex, corresponding to the blastocyst cavity. (D) Process of expanding the blastocyst cavity in the computer simulation. Volume of the intercellular space (VIstd) is forced to increase linearly until t=500.

View larger version (39K): [in this window] [in a new window]   Fig. 2. Mouse blastocyst morphology under various conditions. The initial cell aggregate (A) and the simulated blastocyst at t=2000 (B-F) are shown in cross-sectional views of xz-(left column) and yz-(right column) planes. (A) The initial cell aggregate, in which either a central (black circle) or peripheral (blue circle) vertex is replaced by a tetrahedron (t=0), followed by enlargement under various conditions specified in B-F. (B) An aggregate without zona pellucida (ZP) and with cavitation initiated from a central vertex. (C) An aggregate enclosed with a spherical ZP with cavitation initiated from a central point. (D) An aggregate enclosed with the ellipsoidal (long y-axis) ZP and cavitation from the center. (E) The ellipsoidal (long z-axis) ZP with cavitation initiated from a peripheral vertex. (F) The ellipsoidal (long y-axis) ZP with cavitation from a peripheral point.

View larger version (28K): [in this window] [in a new window]   Fig. 3. Experimental verification of the predictions based on the computer simulation. (A) Scheme illustrating the tilt angle (dark green) between the shortest ZP axis at the 2-cell stage and the Em-Ab boundary in the blastocyst. (B) The proportion of mouse embryos with tilt angles within a certain range, in relation to the ratio of the longest to the shortest diameter of the ZP. Embryos in Group I have the longest ZP diameter, 20% longer than that of the shortest. Embryos in Group II have the spherical ZP that results from its partial digestion and enlargement. Numbers within the bars indicate the number of embryos with tilt angles within the range specified on the right. (C) Sequential DIC images of embryos with enlarged and spherical ZP developing from the 2-cell to the blastocyst stage. Solid and dashed colored lines indicate, for each embryo, the shortest ZP axis at the 2-cell stage and the Em-Ab boundaries at the mid-blastocyst stage, respectively. The tilt angle for each embryo is measured by superimposing these two lines. White arrowheads indicate the ZP. In each frame, time is given in hours:minutes after human chorionic gonadotropin (hCG) injection. Scale bar: 50 µm.

View larger version (46K): [in this window] [in a new window]   Fig. 4. Computer simulation of mammalian blastocyst morphology. Drawing (top left) shows cross-sections by xz- and yz-planes of the simulated aggregate. (A) An example of the calculation process to a stable state, viewed from cross-sections of the yz-plane. Numbers indicate the time point of the simulation (t). A vertex (a black circle in the sample at t=0) is replaced by a tetrahedron (see Fig. 1C) and is enlarged until its volume reaches half the initial total volume (at t=500; see Fig. 1D). The blastocyst axis keeps changing during t=500-2000 (see text) until it is localized and stabilized at one end of the long axis of the ellipsoidal ZP (t=2000), when it no longer migrates (t=2000-3500). Several cells are marked (green, red, orange and blue) to illustrate their movement. In addition, four cells surrounding the orange cell at t=1000 are marked by black and red squares and circles. Some of these cells are not visible at certain time points because they are moving in 3D. (B) The simulated blastocyst at t=2000 in cross-sectional views of xz- and yz-planes. (C) A stereoscopic view of the blastocyst at t=2000, in which the ZP and some of the TE cells are removed for internal view.

View larger version (12K): [in this window] [in a new window]   Fig. 5. Volume of inner cells and outer cells of the blastocyst after simulations. The data are based on a total of five simulations under various conditions (differing in direction of the long axis of the ellipsoidal ZP, and in the initial position of the cavity). Average volumes (±s.d.) of the inner cells (black bars) and of the outer cells (gray bars) are 0.702±0.0088 (n=56) and 0.744±0.0136 (n=144), respectively.

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