Scale-independent topological interactions drive the first fate decision in the Drosophila embryo

During embryogenesis, the earliest cell fate decision is often linked to nuclear positioning, whose control arises from the integration of the cell cycle oscillator and associated cytoskeletal dynamics. Yet, the mechanisms that ensure that the correct number of nuclei move to the appropriate place remain poorly understood. Here, using light sheet microscopy, we show that in Drosophila embryos spindle orientation controls which nuclei migrate towards the cortex and which remains inside the embryo, thereby determining nuclear fate and the number of cells undergoing development. Combining computational methods inspired by integral geometry and manipulations of cell cycle genes, we show that spindle orientation is controlled by topological spindle-spindle interactions and not by internuclear distance. Using arguments describing the behavior of space-filling systems, we develop a theory for topological dependency in microtubule structures. Our work shows how topological interplay of microtubule mechanics can ensure robust control of density and cell fate determination. ### Competing Interest Statement The authors have declared no competing interest.