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Heliyon
2024 Feb 15;103:e25494. doi: 10.1016/j.heliyon.2024.e25494.
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Switching from weak to strong cortical attachment of microtubules accounts for the transition from nuclear centration to spindle elongation in metazoans.
Tada S
,
Yamazaki Y
,
Yamamoto K
,
Fujii K
,
Yamada TG
,
Hiroi NF
,
Kimura A
,
Funahashi A
.
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The centrosome is a major microtubule organizing center in animal cells. The position of the centrosomes inside the cell is important for cell functions such as cell cycle, and thus should be tightly regulated. Theoretical models based on the forces generated along the microtubules have been proposed to account for the dynamic movements of the centrosomes during the cell cycle. These models, however, often adopted inconsistent assumptions to explain distinct but successive movements, thus preventing a unified model for centrosome positioning. For the centration of the centrosomes, weak attachment of the astral microtubules to the cell cortex was assumed. In contrast, for the separation of the centrosomes during spindle elongation, strong attachment was assumed. Here, we mathematically analyzed these processes at steady state and found that the different assumptions are proper for each process. We experimentally validated our conclusion using nematode and sea urchin embryos by manipulating their shapes. Our results suggest the existence of a molecular mechanism that converts the cortical attachment from weak to strong during the transition from centrosome centration to spindle elongation.
Figure 1. Schema of the configuration of microtubules during spindle elongation in the MT-Fixed and the MT-Variable models. A: The schematic view of the model assuming MT-Fixed. The angle configuration of microtubules is fixed regardless of centrosome migration. B: The schematic view of the model assuming MT-Variable. The configuration of microtubules is changed by centrosome migration, because the ends of the microtubules are fixed on the cell cortex. Also, in spindle elongation, the two centrosomes are controlled independently.
Figure 2. The MT-Fixed—but not the MT-Variable—configuration accounts for centrosome centration. A: Schematic of centrosome centration. We defined migration length normalized to cell size as the position of the nucleus-centrosome complex and defined the angle of nucleus-centrosome complex rotation from an initial state as ϕ. B: Migration length normalized to cell size, 15 minutes after centrosome centration started (n = 50). There was a significant difference between the models (Wilcoxon rank-sum test p <2.2 × 10−16). C: Angle of nucleus-centrosome complex rotation, 15 minutes after centrosome centration started (n = 50). There was a significant difference between the models (Wilcoxon rank-sum test, p = 1.39 × 10−14).
Figure 3. Centrosome centration is achieved by the model assuming MT-Fixed regardless of any initial position, angle, or cell shape. A: Vector field about the movement of the nucleus-centrosome complex plotted against its position and angle. On the horizontal line, we used position normalized to the major axis. The vector field has a stable fixed point at the center and angle 90∘, and two saddle points at the center and angles 0∘ and 180∘. The standard states (Table 1) were used as parameter values in this simulation. B: More ellipsoidal shape (green: the length of minor axis = 10 × 10−6 m) produced more torque (vertical length of arrows) and rotation than the standard state (red). C: In spheres (major axis = 25 × 10−6 m, minor axis = 25 × 10−6 m), the cell center was stable regardless of angle.
Figure 4. MT distribution during the spindle elongation. A: Scheme of MT distribution in a uniform case (i, left) and in a case where MTs are focused toward the spindle and do not grow over the mitotic chromosomes (ii, right). Red and green lines indicate MTs from the left and right centrosome, respectively. Yellow indicates the mitotic chromosomes. In the case of (ii), there will be MT-sparse regions next to the MT-dense region because the MTs are focused toward the chromosomes, and also because the MTs from the farther centrosome do not elongate across the chromosomes. The dotted lines in (ii) indicate expected MTs of the uniform distribution. This will be reflected as the two valleys next to the largest peak when we quantify the MT intensity along a circumference whose center is one of the centrosome (blue circles) as drawn in the lower panels. In the lower panels, the angle of 0 is toward the other centrosome. B: A representative example of the β-tubulin::GFP image of the C. elegans embryo (AZ244 strain) during spindle elongation. See Supplemental Movie S3 for other frames of this embryo. C: A representative plot of the MT intensity within each angle window for 15 to 20 pixel length from the center of the left centrosome in (B). Red circles and bars represent mean and S.E.M. of the intensity of the angle window. Yellow, orange, and purple lines show the best fit lines with uniform, single peak von Mises, and double peak von Mises distribution, respectively. D: Distribution with respect to the number of frames for a better fit to a two-peak distribution for a frame-by-frame one-peak distribution in each sample.
Figure 5. MT distribution is consistent with MT-Variable model during the spindle elongation. A: Scheme of MT distribution for MT-Variable case. As the spindle elongates, the distance between the two valleys across the major peak (blue two-headed-arrows in left and right schematics) will decrease. The colors in the schema (left) are same as in Fig. 4A. B: Plots of the MT intensity at the initial time frame (frame 0) of the elongation and the final time frame (frame 13) before the onset of spindle rocking. The MT intensity was quantified using the β-tubulin::GFP expressing strain (AZ244). The major peaks became sharper, consistent with the MT-variable model. C: The change in angle for 6 centrosomes. The angle between the two valleys were plotted against time-frame normalized to the onset of the spindle elongation.
Figure 6. The MT-Variable—but not the MT-Fixed—configuration accounts for the experimentally obtained aspect-ratio dependency of spindle elongation in the nematode C. elegans. A: Example of aspect ratio and elongated pole-to-pole distance measurements for C. elegans embryos. B: Blue and green lines show the simulation results of the MT-Fixed and MT-Variable models, respectively. The positions of the spindle poles were visualized using γ-tubulin::GFP expressing strains. Each point refers to a result measured experimentally for C. elegans. The distinct shapes of the points represent the distinct strains and gene knockdowns of C. elegans. Strains used are TH27, TH32 and CAL1628 (see Method).
Figure 7. The MT-Variable—but not MT-Fixed—configuration accounts for the experimentally obtained aspect-ratio dependency of spindle elongation in the sea urchin S. mirabilis. A: Example of aspect ratio and elongated pole-to-pole distance measurements for S. mirabilis embryos. B: Blue and green lines show the simulation results of the MT-Fixed and MT-Variable model, respectively. The points refer to the results measured experimentally for S. mirabilis.
