Mathematical Model for Early Development of the Sea Urchin Embryo

Abstract

In Xenopus and Drosophila, the nucleocytoplasmic ratio controls many aspects of cell-cycle remodeling during the transitory period that leads from fast and synchronous cell divisions of early development to the slow, carefully regulated growth and divisions of somatic cells. After the fifth cleavage in sea urchin embryos, there are four populations of differently sized blastomeres, whose interdivision times are inversely related to size. The inverse relation suggests nucleocytoplasmic control of cell division during sea urchin development as well. To investigate this possibility, we developed a mathematical model based on molecular interactions underlying early embryonic cell-cycle control. Introducing the nucleocytoplasmic ratio explicitly into the molecular mechanism, we are able to reproduce many physiological features of sea urchin development.