Abstract
Astral microtubules are elongated greatly during anaphase and telophase in sea urchin eggs. The surface density of microtubules reaching the cell surface can be defined at each surface point. Gradients of the surface-density function were assumed to drive membrane proteins whose accumulation causes the formation of contractile-ring microfilaments. An equation was constructed to calculate the movements of the membrane proteins on a curved surface. The equation was applied to eggs compressed between a coverslip and a glass slide by regarding the egg shape as an oblate spheroid. The simulations explained the observations that contractile-ring microfilaments locally appeared and then developed into a complete ring in compressed eggs. When one aster in the mitotic apparatus stopped growing during anaphase, the equation predicted that the zone of contractile-ring microfilaments is displaced toward the inactivated aster, curves in the view from above and tapers off toward the cell edge. The curve gets sharper as eggs are compressed more greatly and as microtubules from the growing aster penetrate more deeply into the opposite hemisphere. The predictions were compared with the observations by Ishii and Shimizu in 1995 and by Hamaguchi in 1998 regarding the furrow formation by the asymmetric mitotic apparatus.
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Yoshigaki, T. The cleavage plane will bend when one aster of the mitotic apparatus stops growing in compressed sea urchin eggs. Bull. Math. Biol. 64, 643–672 (2002). https://doi.org/10.1006/bulm.2002.0298
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DOI: https://doi.org/10.1006/bulm.2002.0298