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. 2016 Nov 7;27(22):3550-3562.
doi: 10.1091/mbc.E16-06-0430. Epub 2016 Oct 12.

Stronger Net Posterior Cortical Forces and Asymmetric Microtubule Arrays Produce Simultaneous Centration and Rotation of the Pronuclear Complex in the Early Caenorhabditis Elegans Embryo

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Stronger Net Posterior Cortical Forces and Asymmetric Microtubule Arrays Produce Simultaneous Centration and Rotation of the Pronuclear Complex in the Early Caenorhabditis Elegans Embryo

Valerie C Coffman et al. Mol Biol Cell. .
Free PMC article

Abstract

Positioning of microtubule-organizing centers (MTOCs) incorporates biochemical and mechanical cues for proper alignment of the mitotic spindle and cell division site. Current experimental and theoretical studies in the early Caenorhabditis elegans embryo assume remarkable changes in the origin and polarity of forces acting on the MTOCs. These changes must occur over a few minutes, between initial centration and rotation of the pronuclear complex and entry into mitosis, and the models do not replicate in vivo timing of centration and rotation. Here we propose a model that incorporates asymmetry in the microtubule arrays generated by each MTOC, which we demonstrate with in vivo measurements, and a similar asymmetric force profile to that required for posterior-directed spindle displacement during mitosis. We find that these asymmetries are capable of and important for recapitulating the simultaneous centration and rotation of the pronuclear complex observed in vivo. The combination of theoretical and experimental evidence provided here offers a unified framework for the spatial organization and forces needed for pronuclear centration, rotation, and spindle displacement in the early C. elegans embryo.

Figures

FIGURE 1:
FIGURE 1:
Pronuclear centration and rotation occur simultaneously between pronuclear meeting and NEBD. (A) Schematic of events before NEBD in the single-celled embryo (top to bottom): MTOCs (green) duplicate, mature, and nucleate MT arrays (blue); pronuclei (yellow) meet; entire complex rotates and centers; MTOC axis aligns with the long axis of the embryo. Anterior is at the left in this and all subsequent images. (B) EBP-2::GFP reveals MTOC positions during centration and rotation of the PNC. Time (s) is in the corner of each image. The pronuclei meet at time 0, and NEBD occurs at time 165. (C) A maximum-intensity projection through time of the embryo in B. Scale bars: 10 μm. (D) Graph of centration and rotation of the PNC in individual embryos (gray lines) and mean (black line, n = 11). The angle of the MTOC axis (y-axis) is time matched to the Euclidean distance of the PNC from the center of the embryo (x-axis) from pronuclear meeting to NEBD. The diagonal (blue line) lies below the majority of the curves. (E) Graph of the change in angle over the change in distance (y-axis) vs. time (x-axis) from polynomial curve fits of the data in D vs. time (n = 10; see Materials and Methods).
FIGURE 2:
FIGURE 2:
Overview of our 2D stochastic mathematical model. (A) Schematic of the components of the model in their initial configuration. A rigid rod centered at (xp,yp) (open circle) with respect to the center of the embryo (black point) is assumed to have two points from which rigid MTs nucleate (red and blue). Each MT can grow to contact the cortex and subsequently generate either pulling force (Fpull) or pushing force (Fpush), depending on its cortical attachment position. The cortical band, centered on the cortex at 60% EL (blue square) extends in both directions symmetrically with arc length s (yellow bars). Different probabilities of pulling contacts exist to the left (P = 0.65, orange curved bar) and right (P = 1, green curved bar) of the cortical band. MTs experience dynamic instability with growth speed vg and shortening speed vs throughout the cytoplasm and catastrophe with speed vsc after contact with the cortex (see the text for detailed model description). The 5 μm grid behind the embryo shows the scale. (B) Zoomed view of example MT contacts in one cortical region (see the text for description). (C) Flowchart showing sequence of model calculations at each time step.
FIGURE 3:
FIGURE 3:
Simulations with and without cortical force asymmetry due to LET-99 produce centration and rotation. (A–C) Model with no LET-99 activity. (A) Graph of the Euclidean distance of the PNC from the center of the embryo over time in 10 individual simulations (gray) and mean (black, n = 100 runs) from the start of the simulation (time = 0) to the completion of centration and rotation to within ∼20° of the long axis (time = 80). The dashed line at 30 min is a reference point for comparison with simulations in Figure 6. Inset, Schematic of cortical forces in these simulations: anterior (orange) and posterior (green) zones meet at 60% EL (blue line) with no band. The two MTOCs are equivalent in NMT and arrayRange parameters. (B) Graph of PNC rotation in 10 individual simulations (gray) and mean (black, n = 100 runs). All angles are transformed to run from 90° (vertical) to 0° (horizontal). (C) Histogram of the final angle (at 80 min) of the MTOC axis (n = 100 runs). Unlike in B, the angles are not transformed. (D–F) Model including a region of LET-99 activity. (D) Graph of the Euclidean distance of the PNC from the center of the embryo over time in 10 individual simulations (gray) and mean (black, n = 100 runs). Inset, Schematic of cortical forces in these simulations: anterior (orange) and posterior (green) zones are separated by the cortical band (yellow) centered at 60% EL (blue line). The two MTOCs are equivalent in NMT and arrayRange parameters. (E) Graph of PNC rotation in 10 individual simulations (gray) and mean (black, n = 100 runs). All angles are transformed to run from 90° (vertical) to 0° (horizontal). (F) Histogram of the final angle (at 80 min) of the MTOC axis (n = 100 runs). Unlike in E, the angles are not transformed.
FIGURE 4:
FIGURE 4:
Simulations with or without LET-99 activity do not produce appropriate timing of centration and rotation. (A, B) Model with no LET-99 activity (same simulations as Figure 3, A–C). (A) Graph of centration and rotation of PNC in 10 individual simulations (gray lines) and mean (black line, n = 100). The angle of the MTOC axis (y-axis) is time matched to the Euclidean distance of the PNC from the center of the embryo (x-axis) from 0 to 80 min. The diagonal (blue line) is for comparison with Figure 1D. Mean data from Figure 1D are included (brown line). (B) Graph of the change in angle over the change in distance vs. time from mean simulation data in A. (C, D) Model including a region of LET-99 activity (same simulations as Figure 3, D–F). (C) Graph of centration and rotation of PNC in 10 individual simulations (gray lines) and mean (black line, n = 100). The angle of the MTOC axis (y-axis) is time matched to the Euclidean distance of the PNC from the center of the embryo (x-axis) from 0 to 80 min. The diagonal (blue line) is for compared with Figure 1D. Mean data from Figure 1D are included (brown line). (D) Graph of the change in angle over the change in distance vs. time from mean simulation data in C.
FIGURE 5:
FIGURE 5:
The MTOC that leads pronuclear rotation has a larger, denser MT array. (A) Schematic of the C. elegans embryo at pronuclear meeting showing the orientation of the images in D (yellow boxes). (B) Single-plane image of an embryo expressing GFP::TBB-2 just after rotation has begun. Scale bar: 10 μm. (C) Same image as in B, rotated and cropped with the leading centrosome on the bottom. Approximate array angles are marked (dashed yellow lines). Scale bar: 2 μm. (D) Thresholded images of EBP-2::GFP signal after implementation of an edge-preserving rolling average (see Materials and Methods). Dashed yellow lines indicate the nucleation angle span as measured. Time 0 is at NEBD. Scale bar: 2 μm. (E) Graph of nucleation angle span measurements from the time of pronuclear meeting until NEBD (time 0), n = 11. Error bars represent SD, and linear curve fits are included. (F) EBP-2::GFP intensity from leading and lagging MT arrays normalized to the time-averaged leading MTOC value for each embryo (see Materials and Methods).
FIGURE 6:
FIGURE 6:
Simulations with a posterior-lateral band and MT array asymmetry produce appropriate relative timing of centration and rotation. (A) Graph of centration and rotation of the PNC in 10 individual simulations (gray lines) and mean (black line, n = 100 runs). The angle of the MTOC axis (y‑axis) is time matched to the Euclidean distance of the PNC from the center of the embryo (x-axis) from the beginning of the simulation (time = 0) to the time the PNC reaches the center (time = 30 min). The diagonal (blue line) is for comparison with Figure 1D. Mean data from Figure 1D are included (brown line). Inset, Schematic of cortical forces in these simulations: anterior (orange) and posterior (green) zones are separated by the cortical band (yellow) centered at 60% EL (blue line). The two MTOCs are not equivalent, with NMT1 > NMT2 and arrayRange1 > arrayRange2. (B) Graph of the change in angle over the change in distance vs. time from mean simulation data in A from the start of the simulation until the PNC reaches the center. (C) Graph of individual MTOC trajectories, anterior (orange) and posterior (green), from time-lapse microscopy of EBP-2::GFP (mean traces in black), scaled to the embryo size (gray ellipse). (D) Graph of individual MTOC trajectories, anterior (red) and posterior (blue), and mean trajectories (black, n = 100 runs) from simulations, scaled to the embryo size (gray ellipse). (E) Histogram of the final angle (at 30 min) of the MTOC axis when MT arrays are asymmetric (n = 100 runs).

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