Aster repulsion drives short-ranged ordering in the Drosophila syncytial blastoderm

Biological systems are highly complex, yet notably ordered structures can emerge. During syncytial stage development of the Drosophila melanogaster embryo, nuclei synchronously divide for nine cycles within a single cell, after which most of the nuclei reach the cell cortex. The arrival of nuclei to the cortex occurs with remarkable positional order, which is important for subsequent cellularisation and morphological transformations. Yet, the mechanical principles underlying this lattice-like positional order of nuclei remain untested. Here, utilising quantification of nuclei position and division orientation together with embryo explants we show that short-ranged repulsive interactions between microtubule asters ensure the regular distribution and maintenance of nuclear positions in the embryo. Such ordered nuclear positioning still occurs with the loss of actin caps and even the loss of the nuclei themselves; the asters can self-organise with similar distribution to nuclei in the wild-type embryo. The explant assay enabled us to deduce the nature of the mechanical interaction between pairs of nuclei. We used this to predict how the nuclear division axis orientation changes upon nucleus removal from the embryo cortex, which we confirmed in vivo with laser ablation. Overall, we show that short-ranged microtubule-mediated repulsive interactions between asters are important for ordering in the early Drosophila embryo and minimising positional irregularity.

Smallest Chimeras Under Repulsive Interactions

We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the repulsive interactions can only establish a symmetry of complete synchrony in the ring, which is broken with increasing repulsive interactions when the junctions pass through serials of asynchronous states (periodic and chaotic) but finally emerge into chimera states. The chimera pattern first appears in chaotic rotational motion of the three junctions when two junctions evolve coherently, while the third junction is incoherent. For larger repulsive coupling, the junctions evolve into another chimera pattern in a periodic state when two junctions remain coherent in rotational motion and one junction transits to incoherent librational motion. This chimera pattern is sensitive to initial conditions in the sense that the chimera state flips to another pattern when two junctions switch to coherent librational motion and the third junction remains in rotational motion, but incoherent. The chimera patterns are detected by using partial and global error functions of the junctions, while the librational and rotational motions are identified by a libration index. All the collective states, complete synchrony, desynchronization, and two chimera patterns are delineated in a parameter plane of the ring of junctions, where the boundaries of complete synchrony are demarcated by using the master stability function.

Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along trajectories of the linearized flow. This is done by an exact integration of the linearized equation, followed by the analysis of the perturbed Hamiltonian equation in action-angle coordinates.