The Mitotic Spindle in the One-Cell C . elegans Embryo Is Positioned with High Precision and Stability

Abstract

Precise positioning of the mitotic spindle is important for specifying the plane of cell division, which in turn determines how the cytoplasmic contents of the mother cell are partitioned into the daughter cells, and how the daughters are positioned within the tissue. During metaphase in the early Caenorhabditis elegans embryo, the spindle is aligned and centered on the anterior-posterior axis by a microtubule-dependent machinery that exerts restoring forces when the spindle is displaced from the center. To investigate the accuracy and stability of centering, we tracked the position and orientation of the mitotic spindle during the first cell division with high temporal and spatial resolution. We found that the precision is remarkably high: the cell-to-cell variation in the transverse position of the center of the spindle during metaphase, as measured by the standard deviation, was only 1.5% of the length of the short axis of the cell. Spindle position is also very stable: the standard deviation of the fluctuations in transverse spindle position during metaphase was only 0.5% of the short axis of the cell. Assuming that stability is limited by fluctuations in the number of independent motor elements such as microtubules or dyneins underlying the centering machinery, we infer that the number is ∼1000, consistent with the several thousand of astral microtubules in these cells. Astral microtubules grow out from the two spindle poles, make contact with the cell cortex, and then shrink back shortly thereafter. The high stability of centering can be accounted for quantitatively if, while making contact with the cortex, the astral microtubules buckle as they exert compressive, pushing forces. We thus propose that the large number of microtubules in the asters provides a highly precise mechanism for positioning the spindle during metaphase while assembly is completed before the onset of anaphase.

Physical Limits on the Precision of Mitotic Spindle Positioning by Microtubule Pushing forces

“…The measured drag coefficient and associated relaxation time [58] also accord with the pushing model. The correlation time associated with spindle fluctuations [38] also agrees with the pushing model.…”

“…Fluctuations in the number of microtubules associated with the pushing mechanism are expected to lead to positional fluctuations [50] ; the measured amplitude of these fluctuations [38] (Figure 4D-F) accords with the pushing model (see Comparisons of the astral pushing model to experimental data). Furthermore, the stability increases, rather than decreases, following GPR-1/2 RNAi, as expected if the cortical pulling forces are anti-centering.…”

“…Within this complex choreography (Figure 2B,C), there is a period of few minutes, roughly corresponding to metaphase and termed the maintenance phase , during which the spindle is relatively quiescent (green line in Figure 2C). During this period, while spindle assembly is being completed, the spindle is precisely oriented along the anterior-posterior (AP) axis [38] . Because of its long duration, the maintenance phase has proved amenable to mechanical experiments, allowing detailed quantitation of the microtubule-based forces acting on the spindle.…”

“…Growth occurs by the addition of GTP-tubulin whose concentration in cytoplasm ([T] = 10μM) is much higher than the critical concentration of GTP-tubulin required for growth ( K T ≈ 0.5 μM, based on studies with the non-hydrolyzable GTP analog GMPCPP [45] ). If the addition of a tubulin dimer increases the length of a microtubule by δ = 0.6 nm (the 8-nm length of a tubulin dimer divided by the 13 dimers per cross-section of the hollow cylinder), then the maximum pushing force is ( kT / δ )ln([T]/ K T ) ≈ 12 pN, where kT is the Boltzmann constant times absolute temperature [38] . This force is consistent with measurements of maximum pushing forces of 5-10 pN using purified tubulin [46,47] .…”

“…4E), corresponding to σ x / R = 1%, with an upper estimate of 1.3% at the 95% confidence level [38] . The total number of pushing microtubules in the entire bipolar spindle was estimated to be Mp 0 = 418, similar to independent estimates from [62] .…”