Topological interactions drive the first fate decision in the Drosophila embryo

During embryogenesis, the first cell fate decision - whether the cell participates in development of the embryo or not - is often linked to the positioning of the nucleus. The cell cycle oscillator and associated cytoskeletal dynamics contribute to the control of nuclear positioning. Yet, the mechanisms that ensure that the correct number of nuclei move to their appropriate place remain poorly understood. Here, we show that the orientation of the mitotic spindle controls the first fate decision in Drosophila embryos using light sheet microscopy experiments. Combining computational methods inspired by integral geometry, manipulation of cell cycle genes and investigation of the relationship between geometry and topology, we show that spindle orientation is controlled by topological interactions and not by internuclear distance. Leveraging physics 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 nuclear density and determine cell fate.