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# The Distribution of Active Force Generators Controls Mitotic Spindle Position

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Science  25 Jul 2003:
Vol. 301, Issue 5632, pp. 518-521
DOI: 10.1126/science.1086560

## Abstract

During unequal cell divisions a mitotic spindle is eccentrically positioned before cell cleavage. To determine the basis of the net force imbalance that causes spindle displacement in one-cell Caenorhabditis elegans embryos, we fragmented centrosomes with an ultraviolet laser. Analysis of the mean and variance of fragment speeds suggests that the force imbalance is due to a larger number of force generators pulling on astral microtubules of the posterior aster relative to the anterior aster. Moreover, activation of heterotrimeric guanine nucleotide– binding protein (Gprotein) α subunits is required to generate these astral forces.

Cell divisions creating daughter cells of unequal sizes are widespread in developing organisms, where they contribute to the generation of cell fate diversity (1). During such divisions, the mitotic spindle is off-center at the end of anaphase. The cleavage furrow then bisects the spindle in the middle, generating two daughter cells of unequal size (2). During the first division of a C. elegans embryo, the polarity of the cell is established after fertilization through the action of the par genes (3) and associated components (46). At metaphase, the mitotic spindle is positioned in the center of the cell, aligned along the anterior-posterior (AP) axis. At anaphase, the anterior pole remains in a fixed position, whereas the posterior pole moves toward the posterior cortex, resulting in an off-center spindle (7). Displacement of the spindle is caused by a larger net force acting on the posterior spindle pole than on its anterior counterpart (8).

An increase in net force on the posterior pole relative to the anterior one could be determined by differences in the number, strength, or distribution of force-generating interactions between the cell cortex and the astral microtubules that extend out from spindle poles toward the cortex (9, 10). These force-generating interactions could be driven by molecular motors or microtubule depolymerization (1113). To measure the distribution of force generators, we devised an experiment to determine the spatial arrangement of the forces exerted on spindle poles by astral microtubules. We ablated the central region of the centrosome, causing the pericentriolar material to fragment and expand out toward the cortex. We term this procedure optically induced centrosome disintegration (OICD).

After OICD, indirect immunofluorescence showed that separated aster fragments were radially distributed around the original location of the irradiated centrosome, whereas the unirradiated centrosome and its aster remained intact (Fig. 1, A and B). We followed the movement of aster fragments directly in a C. elegans strain containing green fluorescent protein (GFP)–tagged α-tubulin or indirectly by monitoring yolk granules close to the centrosome (14) (Fig. 2A). Both assays revealed the striking effect of OICD: After disintegration, the fragmented aster expanded out toward the cortex (Fig. 2, A to C) (fig. S2 and movies S1 to S4).

Late in anaphase, the anterior spindle pole remains relatively still, whereas the posterior spindle pole oscillates as it moves toward the cortex (7). We measured the OICD-triggered displacement of aster fragments as a function of direction for both asters at this time (14), because this is when the difference in speed between the anterior and posterior spindle poles is greatest. In the differential interference contrast (DIC) assay, typically 15 granules evenly distributed around the centrosome were tracked for each experiment (Fig. 2, B and C). In the GFP assay, microtubule-based structures were directly tracked. In both assays, the displacements over the initial 5 s after OICD were interpolated (14) to generate a curve describing the rate of expansion as a function of direction (figs. S3 and S4). Means and SDs were calculated (30 DIC and 16 GFP experiments for both anterior and posterior OICD), resulting in an angular distribution of mean fragment speeds (Fig. 3, A and B) (fig. S1). Interestingly, fragment movement after OICD was not restricted to a particular angular range. Thus, the posterior movement of the mitotic spindle is not accomplished by confining force generators to a specific cortical region, but instead is due to distributed force generation (15).

The angular dependence of fragment velocities differed markedly between anterior and posterior OICD experiments. After OICD of the stationary anterior pole, fragment movement was symmetric about the AP axis. By contrast, after OICD of the oscillatory posterior pole, fragments traveling in the initial direction of movement of the pole moved at higher speeds than fragments traveling in the opposite direction (Fig. 2, B, C, F, and G; Fig. 3, A and B). Because cytoplasmic viscosity appears to be the same at the anterior and posterior (8), and because anterior and posterior aster fragments were of the same size on average and the size of a fragment and the direction of movement were uncorrelated (Fig. 3A, inset), these differences in speed are likely due to the differences in the force acting on the aster fragments.

Higher forces could be due to more force generators per fragment or to a larger force per individual force generator. These possibilities can be distinguished by the analysis of the fluctuation in the speed of fragments from one experiment to the next. The variance in speed in any given direction initially increased as the mean speed increased, reached a maximum, and surprisingly decreased at high mean speeds (Fig. 3C). This nonlinearity was statistically significant (second-order coefficients were significantly different from 0; Student t test, |t| > 10, P < 1015). Whereas most sources of error are expected to cause a monotonic increase in variance (14), a decrease in variance is observed for two-state systems such as ion channels that are either open or closed. In this case, the current variance falls as all channels saturate in their open state (16). By analogy, our data suggest that a two-state process is acting to move aster fragments, and that the fall in variance is due to saturation of a limited number of active force generators that are pulling on the fragments.

The initial slopes of the mean-variance curves were similar for anterior and posterior experiments, but the anterior variance peaked at a lower speed (Fig. 3C). This can be interpreted by formulating a two-state model in which each fragment interacts with N force generators on the cortex, and the speed of a fragment is proportional to the number of active force generators (in what we call the force-limited regime). The mean speed $Math$ and the variance $Math$ are then given by $Math$(1) $Math$(2) $Math$(3) (14, 16, 17), where υe is the elementary speed due to a single force generator that exerts a force f, p is the probability of a force generator being in its active state, and γ is the drag coefficient of a fragment. Expressing the variance in terms of the mean speed results in a parabolic relationship, $Math$(4) This equation provided a good fit to the data (R2 = 0.96 for anterior and R2 = 0.94 for posterior OICD, DIC assay; Table 1). Thus, a two-state model for force generators is consistent with the experimental data. Although our data do not favor any molecular mechanism, a microtubule-based motor such as dynein (18, 19) could be actively engaged with the end of a microtubule in one state, whereas it could be detached in the other.

Table 1.

Fit parameters. The elementary speed υe, the number of force generators per fragment N, the determination coefficient R2 (30), the reduced χ2, and the corresponding one-sided probability of the χ2 distribution (P) are given for anterior (A) and posterior (P) wild-type fragmentation experiments using the DIC and GFP assays (14). Deviations between assays were expected (31).

Assay υe (μm s-1) NR2 Reduced χ2P
DIC A 0.22 ± 0.01 1.42 ± 0.11 0.96 0.60 0.18
P 0.24 ± 0.01 2.15 ± 0.15 0.94 0.87 0.44
GFP A 0.18 ± 0.01 1.91 ± 0.15 0.72 0.48 0.07
P 0.18 ± 0.01 2.62 ± 0.29 0.91 0.93 0.48

The elementary speeds of anterior and posterior fragments were 0.22 ± 0.01 μm s1 and 0.24 ± 0.01 μm s1, respectively (DIC assay; Table 1). Because the sizes of fragments were the same and the viscosity is homogeneous, this equality of elementary speeds suggests that the elementary forces themselves are equal. We cannot reliably estimate the absolute value of the force because of uncertainty in the absolute value of the drag coefficient.

The similarity of the elementary speeds provides experimental evidence that the force generators are the same throughout the embryo (i.e., they have the same unitary force and velocity) and that differences in speeds of aster fragments are due to differences in the number of force generators that are moving them. In agreement with this expectation, the average number of force generators for anterior and posterior fragments differed (1.42 ± 0.11 and 2.15 ± 0.15, respectively, DIC assay; Table 1). The finding that N is greater than 1 supports our assumption that force generators are operating in the force-limited regime (20). Interestingly, the total number of active force generators is quite small, probably fewer than 50 (an exact number critically depends on the average number of fragments generated) (21). Because the total number of force generators is greater on the posterior than on the anterior side, we suggest that the force imbalance during spindle displacement (8) is due to an increase in the number of active force generators rather than an increase in the elementary force.

The G protein α subunit (Gα) signaling pathway is required for spindle displacement (22, 23). OICD in gpr-1/2(RNAi) embryos, in which Gα activity is inhibited and net forces on spindle poles are severely compromised (2427), did not result in the expansion of aster fragments toward the cortex (Fig. 1C), and the mean fragment speeds were greatly reduced (14) (Fig. 2, D, E, H, and I; Fig. 3A). Therefore, spindle displacement is defective in the absence of Gα activity because of a complete lack of active force generators. We suggest that the asymmetrically localized GPR-1/2 (25, 26) increases the pool of cortical protein complexes that are available to interact with the plus ends of the astral microtubules on the posterior side, ultimately leading to spindle displacement and unequal cleavage.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S7

References

Movies S1 to S7

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