Attractive internuclear force drives the collective behavior of nuclear arrays in Drosophila embryos
Fig 6
The intrinsic properties of the force fields generate the characteristic features of the collective behaviors of the nuclear array.
(A) Asymmetric distribution of the nuclear density is stabilized by the attractive but not repulsive force field. As the nuclear density is high in the middle of the embryo, for a nucleus (orange circle), its nearest neighboring nuclei on the pole side (dark blue circles) are fewer in number but larger in the internuclear distance than those on the middle side (light blue circles) of the embryo. Since the attractive force increases with distance, the pair-wise force is stronger on the pole side (thicker arrows) than that on the middle side (thin arrows). Hence the net force on a given nucleus is balanced. In contrast, the repulsive force decreases with distance, the pair-wise force is stronger on the middle side, and the net force cannot be balanced. (B) Collective motion is driven by the age-dependent force field. The nuclei on the pole side (dark blue circle) have a greater nuclear age T than those in the middle (light blue circle). This age difference leads to a greater (weaker) attractive force from the pole side in the first (second) half period of the standing wave, hence the nuclei (orange circle) collectively move towards (away from) the pole. (C) The dampening standing wave of the nuclear speed is generated due to the greater net force in the first half period compared with the second half period. In the first half period, the amplitude of the attractive force from the pole side (Fp) is much greater than the force from the middle side (Fm). But in the second half period, the amplitude difference between Fp and Fm is much smaller.