A phase oscillator model of cell cycles reveals nuclear density control in a branched fungal network

Multinucleate cells are widespread in biology, from human skeletal muscle and placenta to many filamentous fungi, yet their basic cell biology remains poorly understood. Maintaining an appropriate nuclear-to-cytoplasmic ratio is essential across cell types for physiological function, and mechanisms of size control have been extensively studied in mononucleate cells. Much less is known about how comparable control is achieved in cells where many nuclei share a common cytoplasm. The filamentous fungus Ashbya gossypii forms a branching mycelial network in which individual nuclei divide asynchronously, while the number of nuclei per cell volume (the nuclear density) is tightly controlled. How global regulation of nuclear density coexists with local cell cycle asynchrony remains unclear. We address this by combining a mathematical model of nuclear division in a growing and branching cell with live-cell microscopy. We model nuclei as a dividing population of phase oscillators within a branching cell network and parameterize the model with measurements from Ashbya cells. The model demonstrates that asynchrony is required to prevent large density fluctuations that would result from synchronous division, and that introducing a nuclear-density checkpoint to the cell cycles leads to synchrony if it is the only mechanism of density control. We find that coupling branch formation to nuclear density both stabilizes nuclear density and prevents the emergence of synchronous cycles. Our results indicate that asynchronous nuclear cycles together with density-responsive branching maintain a constant nuclear density, revealing a strategy for regulating the nuclear-to-cytoplasmic ratio in large multinucleate cells.