Mathematical modeling accurately predicts the dynamics and scaling of nuclear growth in discrete cytoplasmic volumes.

Scaling of nuclear size with cell size has been observed in many species and cell types. In this work we formulate a modeling framework based on the limiting component hypothesis. We derive a family of spatio-temporal mathematical models for nuclear size determination based on different transport and growth mechanisms. We analyse model properties and use in vitro experimental data to identify the most probable mechanism. This suggests that nuclear volume scales with cell volume and that a nucleus controls its import rate as it grows. We further test the model by comparing to data of early frog development, where rapid cell divisions set the relevant time scales.

In vivo mitotic spindle scaling can be modulated by changing the levels of a single protein: the microtubule polymerase XMAP215.

In many organisms, early embryonic development is characterized by a series of reductive cell divisions that result in rapid increases in cell number and concomitant decreases in cell size. Intracellular organelles, such as the nucleus and mitotic spindle, also become progressively smaller during this developmental window, but the molecular and mechanistic underpinnings of these scaling relationships are not fully understood. For the mitotic spindle, changes in cytoplasmic volume are sufficient to account for size scaling during early development in certain organisms. This observation is consistent with models that evoke a limiting component, whereby the smaller absolute number of spindle components in smaller cells limits spindle size. Here we investigate the role of a candidate factor for developmental spindle scaling, the microtubule polymerase XMAP215. Microinjection of additional XMAP215 protein into Xenopus laevis embryos was sufficient to induce the assembly of larger spindles during developmental stages 6.5, 7, and 8, whereas addition of a polymerase-incompetent XMAP215 mutant resulted in a downward shift in the in vivo spindle scaling curve. In sum, these results indicate that even small cells are able to produce larger spindles if microtubule growth rates are increased and suggest that structural components are not limiting.

Centrosomal clustering contributes to chromosomal instability and cancer.

Cells assemble mitotic spindles during each round of division to insure accurate segregation of their duplicated genome. In animal cells, stereotypical spindles have two poles, each containing one centrosome, from which microtubules are nucleated. By contrast, many cancer cells often contain more than two centrosomes and form transient multipolar spindle structures with more than two poles. In order to divide and produce viable progeny, the multipolar spindle intermediate must be reshaped into a pseudo-bipolar structure via a process called centrosomal clustering. Pseudo-bipolar spindles appear to function normally during mitosis, but they occasionally give rise to aneuploid and transformed daughter cells. Agents that inhibit centrosomal clustering might therefore work as a potential cancer therapy, specifically targeting mitosis in supernumerary centrosome-containing cells.

Changes in cytoplasmic volume are sufficient to drive spindle scaling.

The mitotic spindle must function in cell types that vary greatly in size, and its dimensions scale with the rapid, reductive cell divisions that accompany early stages of development. The mechanism responsible for this scaling is unclear, because uncoupling cell size from a developmental or cellular context has proven experimentally challenging. We combined microfluidic technology with Xenopus egg extracts to characterize spindle assembly within discrete, geometrically defined volumes of cytoplasm. Reductions in cytoplasmic volume, rather than developmental cues or changes in cell shape, were sufficient to recapitulate spindle scaling observed in Xenopus embryos. Thus, mechanisms extrinsic to the spindle, specifically a limiting pool of cytoplasmic component(s), play a major role in determining spindle size.