A cytokinetic ring-driven cell rotation achieves Hertwig's rule in early development

Abstract

Hertwig's rule states that cells divide along their longest axis, usually driven by forces acting on the mitotic spindle. Here, we show that in contrast to this rule, microtubule-based pulling forces in early Caenorhabditis elegans embryos align the spindle with the short axis of the cell. We combine theory with experiments to reveal that in order to correct this misalignment, inward forces generated by the constricting cytokinetic ring rotate the entire cell until the spindle is aligned with the cell's long axis. Experiments with slightly compressed mouse zygotes indicate that this cytokinetic ring-driven mechanism of ensuring Hertwig's rule is general for cells capable of rotating inside a confining shell, a scenario that applies to early cell divisions of many systems.

Keywords: actomyosin; biophysics; cell biology; cytokinesis; development.

Fig. 1.

Hertwig’s long axis rule is executed in the AB cell. (A) Left: Schematic of a C. elegans two-cell embryo, anterior (A) and posterior (P) are indicated. Right: In utero, the embryo is compressed orthogonal to the anteroposterior (AP) axis such that the AB cell has a long and a short axis in the dorsoventral-left-right (DV-LR) plane. (B) Final angle between the mitotic spindle and the long axis in the DV-LR plane upon different compression strengths. Embryos were dissected and subjected to various degrees of compression, resulting in aspect ratios between 0.4 and 1.1. (C and D) Left panels: Example of an uncompressed (AR > 0.95, C) and compressed embryo (AR > 0.95, D), producing GFP-tubulin, at the beginning of anaphase (t_begin, blue) and at the end (t_end, yellow) viewed in the DV-LR plane. The end point is defined by the starting time point of the cell division skew in the AP-DV plane (SI Appendix, Fig. S1). Dashed lines mark the cell outline, as defined by the Lifeact::mKate2 signal (Movies S1 and S2). Right panels: Time evolution of spindle length (pole-to-pole distance) and angle with the long axis in uncompressed (C) and compressed (D) embryos, plotted in polar coordinates. Traces represent individual embryos. Time is normalized and subsequently color coded in the same manner throughout the manuscript. For uncompressed embryos, in which there is no long axis, the angle with the imaging plane was reported. (Scale bars: 10 μm.)

Fig. 2.

Long axis alignment in the AB cell is achieved by an NMY-2/Myosin-dependent spindle rotation. (A–C) Time evolution of spindle length and angle upon (A) decreased cortical pulling forces, lin-5(RNAi), (B) control, non-RNAi, and (C) increased cortical pulling forces, opto-lin-5. (D) Total absolute angular movement of the spindle (Top) and final spindle angle with the long axis (Bottom). Data points represent individual embryos. Mean with 95% CI is indicated for the total rotation. Statistical tests: Wilcoxon rank-sum test for total angular movement and, because of the periodicity of the data, the Watson U² test for final spindle angles. (E–G) Time evolution of spindle length and angle imaged at 25 °C in (E) control, (F) upon reduced cortical tension-nmy-2(ts) and (G) upon combined cortical tension reduction and increased cortical pulling forces—opto-lin-5; nmy-2(ts). The GFP channel in opto-lin-5 shows GFP::tubulin and PH::GFP::LOV2, which is a membrane-localized LOV2 domain necessary to recruit cytoplasmic LIN-5::ePDZ to the cortex (Materials and Methods). (H) Total absolute angular movement of the spindle (Top) and final spindle angle with the long axis (Bottom), as in (D). Note: As we still observe a rotation of the spindle in nmy-2(ts) embryos, the NMY-2/Myosin activity may not be fully perturbed at 25 °C, or an NMY-2/Myosin-independent pathway exists. The control conditions for opto-lin-5; nmy-2(ts) imaged at 25 °C are shown in SI Appendix, Fig. S4 A and B. n = number of embryos. (Scale bars: 10 μm.)

Fig. 3.

The mitotic spindle and cytokinetic ring rotate together, and this coincides with cytokinetic ring formation. (A) Still images of a two-cell embryo producing GFP::tubulin (cyan) and Lifeact::mKate2 (magenta and inverted) viewed in the DV-LR plane (Top) and AP-DV plane (Bottom). Arrows mark the position of the cytokinetic ring. (Scale bar: 10 μm.) (B) Time evolution of the angular velocity of the mitotic spindle and (C) the normalized F-actin intensity in the ring (SI Appendix, Eq. S3). t₀ (=t_begin) is defined as the rotation onset. Red lines show the mean. As the angular velocity is noisy, data points in (B) represent a moving average with 45 s as sliding window. (D) Angle of the spindle and ring during the rotation plotted over time. Note that the angles for spindle and ring are with respect to the long axis and short axis, respectively. The red diagonal is a guide to the eye to indicate the similarity of spindle and ring orientation. Color-coded data points in (B–D) represent individual measurements at respective time points.

Fig. 4.

Physical model of long axis alignment driven by the emerging cytokinetic ring. (A) Schematic of the AB cell in the DV-LR plane: Rigid eggshell enforces shape of the embryo by exerting forces (red arrows) normal to the embryo surface that balance forces resulting from active surface tension in the cell cortex (colored contour). The cytokinetic ring (black contour) is a region of high tension (red) relative to the cell poles (blue), where astral microtubules (gray) inhibit actomyosin. This results in normal forces driving ring ingression and pole expansion that are balanced by the eggshell. When the ring is not aligned perpendicular to the long axis (Left) a torque arises driving a rotation (black arrows) that aligns the ring perpendicular to the long axis and the spindle with the long axis. (B) Same as in (A) but for a scenario where normal forces are primarily due to cortical pulling by astral microtubules. In such a scenario, the cell poles are pulled inward, resulting in alignment of the spindle axis with the short axis of the cell. (C–E) Quantitative analysis of the dynamics of the angle ϕ between the ring and the short axis and the NMY-2 concentration M in the ring. (C) Scatter plot of effective force driving alignment determined from the speed of cortical rotation Ω and the ring angle ϕ vs. NMY-2 ring intensity M (SI Appendix, Eq. S7). We observe a striking correlation (rho = −0.8, P-value < 1e−3). (D) Trajectories of the absolute ring angle |ϕ|. (E) Same trajectories as in (D) but plotted vs. the change in ring intensity relative to the ring intensity at |ϕ| = 30°. Trajectories collapse onto an exponential decay of the tangent of ϕ as predicted by our model for a linear relationship between active tension and NMY-2 concentration.

Fig. 5.

Hertwig’s rule execution in slightly compressed mouse embryos coincides with ring ingression. (A) Top panels: Example of a mildly compressed mouse zygote, imaged using Differential Interference Contrast (DIC) microscopy, undergoing cell division inside a glass capillary. For mild compression, embryos inside a capillary with inner diameter between 80 and 90 µm were used. The dashed line indicates the shape of the zona pellucida. Left images show anaphase onset (t_begin, blue), and Right images show the zygote upon completion of cytokinesis (t_end, yellow). The embryo is slightly compressed such that the zona pellucida has a long and a short axis. During metaphase, the mitotic spindle is not aligned with the long axis of the zona pellucida, but during anaphase, it rotates toward the long axis. Arrows mark the cytokinetic ring. Bottom panels: Still images overlaid with the cytoplasmic flow field as measured by PIV. Spindle poles, marked with filled circles, were manually identified at anaphase onset (Left), and their positions were inferred by using the interpolated local flow field (Materials and Methods). Spindle pole time traces of the displayed zygote are shown on the lower right. (B) Time evolution of spindle length (pole-to-pole distance) and angle with the long axis in mildly compressed mouse zygotes, plotted in polar coordinates. During ring ingression, the spindle rotates toward long axis alignment. In 2 out of 10 embryos, long axis alignment was not finished upon completion of cytokinesis. In these embryos, a slower rotation into long axis alignment occurred in the two-cell embryo, see Movie S14. (C) Final angle with the long axis and total absolute spindle rotation in degrees. Each data point represents an individual embryo. Mean with 95% CI is indicated for the total rotation. n = number of embryos. AO = anaphase onset. PIV vector scale bar: 1 μm/min. (Scale bar: 20 μm.)