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Cell size is a critical factor for cell cycle regulation. In  Xenopus  embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in  Caenorhabditis elegans  embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to  C. elegans  founder cell lineages (1.2, 0.81, and <0.39 in radius, respectively). Thus, the power law relationship is conserved in  Xenopus  and  C. elegans , while the absolute powers in  C. elegans  were different from that in  Xenopus . Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic  C. elegans  cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures.

Power law relationship between cell cycle duration and cell volume in the early embryonic development of Caenorhabditis elegans