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PeerJ
2015 Dec 10;3:e1490. doi: 10.7717/peerj.1490.
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On the embryonic cell division beyond the contractile ring mechanism: experimental and computational investigation of effects of vitelline confinement, temperature and egg size.
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Embryonic cell division is a mechanical process which is predominantly driven by contraction of the cleavage furrow and response of the remaining cellular matter. While most previous studies focused on contractile ring mechanisms of cytokinesis, effects of environmental factors such as pericellular vitelline membrane and temperature on the mechanics of dividing cells were rarely studied. Here, we apply a model-based analysis to the time-lapse imaging data of two species (Saccoglossus kowalevskii and Xenopus laevis) with relatively large eggs, with the goal of revealing the effects of temperature and vitelline envelope on the mechanics of the first embryonic cell division. We constructed a numerical model of cytokinesis to estimate the effects of vitelline confinement on cellular deformation and to predict deformation of cellular contours. We used the deviations of our computational predictions from experimentally observed cell elongation to adjust variable parameters of the contractile ring model and to quantify the contribution of other factors (constitutive cell properties, spindle polarization) that may influence the mechanics and shape of dividing cells. We find that temperature affects the size and rate of dilatation of the vitelline membrane surrounding fertilized eggs and show that in native (not artificially devitellinized) egg cells the effects of temperature and vitelline envelope on mechanics of cell division are tightly interlinked. In particular, our results support the view that vitelline membrane fulfills an important role of micromechanical environment around the early embryo the absence or improper function of which under moderately elevated temperature impairs normal development. Furthermore, our findings suggest the existence of scale-dependent mechanisms that contribute to cytokinesis in species with different egg size, and challenge the view of mechanics of embryonic cell division as a scale-independent phenomenon.
Figure 1. Embryonic cell division.(A, C) show the begining and (B, D) the end of the first embryonic division of Sk (A, B) and Xl (C, D) cells. While vitelline unconstrained Sk cells demonstrate free extension of their polar length during the cleavage, tight mechanical confinement restrains Xl cells to deform within the vitelline sphere.
Figure 2. Image processing and contour extraction.(A) shows segmentation of Sk embryonic cells (colored areas and isosurfaces) in a single 2D microscopic image and (B) in entire 3D (2D image + time) stack. (C) Cellular contours are extracted from the boundary of segmented cells. (D) To quantify the cellular shape at every time step (s) of the image sequence, the lengths of the furrow F and the embryonic polar axis L are calculated.
Figure 3. Detection of the first embryonic division of Sk cells in image time series.Median-smoothed time series of the furrow (dark blue) and polar (pink) lengths are combined to detect start ss and end se time steps of the first embryonic cell cleavage using the sum of their derivative magnitudes |F′(s)| + |L′(s)| (light blue). Based on ss and se, dimensionless time interval t ∈ [0; 1] of the cleavage is introduced.
Figure 4. Microscopic images vs. Finite Element simulation of the first embryonic cell division.(A, C) show three sample stages of the cleavage of vitelline-unconfined Sk cell vs. vitelline-confined Xl cell (C) vs. Finite Element simulation (B) of Neumann (A) and sliding (C) boundary conditions given on the vitelline membrane. The green stripe in the equatorial plane of the initial FE cell model (B) indicates the cleavage furrow. Apparently, mechanical vitelline confinement essentially determines the cellular shape during the cleavage.
Figure 5. Simulation of cell elongation for variable values of furrow width and polar stiffness gradient.Dots show simulated relative cell elongation (Ln) corresponding to the first 10% contraction of the cleavage furrow as a function of the ratio between equatorial and polar cell stiffness (log(Ee/Ep)) for four discrete values of the furrow width (4, 8, 16, 20 μm).
Figure 6. Comparison of polar elongation measurements of Sk cells between two different temperatures (18 °C and 26 °C) vs. FE simulation of egg cleavage resulting from contraction of equatorial furrow.Dots represent cumulative measurements of relative elongation of embryonic Sk cells under the given temperature condition as a function of dimensionless cleavage time Ln(t). Each dot corresponds to simulated re. measured polar cell length Ln(t) at a distinctive time point (t = [0, 1]) of the cleavage. Lines depict polynomial data fits.
Figure 7. Visualization of the relative geometrical proportion of the maximum spindle length (60 μm) to the size of Sk (400 μm) and Cj (100 μm) cells.Effects of spindle polarization on mechanics of small Cj cells are significantly more pronounced in comparison to four time larger Sk cells.
Figure 8. Comparison of our cumulative measurements of polar elongation of Sk (400 μm) embryonic cells vs. Cj (100 μm) data (Hiramoto, 1958) vs. FE simulations of spindle-free (i.e., Sk) and spindle-extended (i.e., Cj) contractile ring models.FE simulation of Sk cleavage is performed under assumption of vanishing effects of spindle polarization and constant furrow width (FW = 8 μm, i.e., 2% of the Sk egg cross-section), while division of the Cj cell is modeled by iterative fitting of variable furrow width (FW = 3.6â13 μm, i.e., 3.6â13% of the Cj egg cross-section) and spindle length (SL = 30â53.6 μm) to polar elongation measurements.
Figure 9. Plots of furrow width (A) and spindle length (B) as a function of dimensionless cleavage time.The values of FW and SL are estimated by a stepwise fitting of our FE cleavage model to Cj data (Hiramoto, 1958), cf. Table 2 (raws 5 and 6).
Figure 10. Vitelline membrane cross-section to polar cell length ratio (V/C) as a function of dimensionless cleavage time (t â [0, 1]).In the late phase of cleavage (t ⥠0.7), polar elongation of 18 °C Sk cells is hindered by a tight vitelline membrane (i.e., median(V/C) = 1.0). In contrast, 26 °C Sk cells do not experience such a boundary constraint (i.e., median(V/C) > 1).
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