Kinesin-8 Motors Improve Nuclear Centering by Promoting Microtubule Catastrophe

In fission yeast, microtubules push against the cell edge, thereby positioning the nucleus in the cell center. Kinesin-8 motors regulate microtubule catastrophe; however, their role in nuclear positioning is not known. Here we develop a physical model that describes how kinesin-8 motors affect nuclear centering by promoting a microtubule catastrophe. Our model predicts the improved centering of the nucleus in the presence of motors, which we confirmed experimentally in living cells. The model also predicts a characteristic time for the recentering of a displaced nucleus, which is supported by our experiments where we displaced the nucleus using optical tweezers.

Figure 1

The model. Scheme of the cell (top) and of the model (bottom). The MTs of lengths $L_i^{\pm }$ (green) extend from the $i$th MTOC (magenta) at position $x_i$, toward the cell periphery. MTs in contact with the cell edge exert a pushing force $f_i^{-}$ on the MTOC. The nucleus [dark gray shape (top), gray circle (bottom)] is at position $x_{\text{nuc}}$ and is connected to the MTOC by a spring of stiffness $\kappa$. Klp5 motors (black pictograms) attach to MTs with a rate $k_{\text{on}}$, and detach with a rate $k_{\text{off}}$. Klp5 motors walk toward the MT plus ends with velocity ${\upsilon }_m$ and accumulate at the MT plus end. The number of motors at the MT plus end is denoted $Q_i^{-}$. The origin of the coordinate system is in the cell center. The total length of the cell is denoted $L$. $u$ denotes positive direction of the coordinate in the direction of the MT plus end.

Figure 2

Centering of the nucleus and of the SPB in wild-type and $klp5\mathrm{\Delta }$ cells. Time-lapse images of wild-type (WT) (a) and of $klp5\mathrm{\Delta }$ (d) cells. Time between images is 30 s. Schemes corresponding to the first images are shown on the left. (b),(e) Histograms of the nuclear positions, theory (black) and experiment (green). (c),(f) Histograms of the MTOC (theory, black) and of the SPB (experiment, magenta) positions. Results (b),(c) with and (e),(f) without kinesin-8 motors (for experimental procedure, see Ref. [37]). The number of events is normalized, error bars represent SEM. (g) Histograms of the position of the division plane in wild-type (black) and $klp5\mathrm{\Delta }$ (magenta) cells. Fitting the histogram of the length difference of the two sibling cells, $|L_{\text{cell}1}-L_{\text{cell}2}|$, with a Gaussian gives a value of $0.50\pm 0.02\mu \mathrm{m}$ for wild-type cells and $1.03\pm 0.11\mu \mathrm{m}$ for $klp5\mathrm{\Delta }$ cells. (h) Theoretical results for the velocity of the nucleus (lower line) and of a MTOC (upper line) as a function of their distance when a single MT pushes against the cell edge. (i) Experimental results for the velocity of the nucleus (lower lines) and of the SPB (upper lines) as a function of their distance, for wild-type (black) and $klp5\mathrm{\Delta }$ (magenta) cells, when only one MT is in contact with the cell edge. The parameters for the model are given in Table 1.

Figure 3

Recentering of a displaced nucleus. (a) Theory, the position of the nucleus as a function of time, for the starting position $1\mu \mathrm{m}$ away from the cell center. The average curve (black) and 6 individual traces (colors) are shown. (b) Left, scheme of the optical tweezers experiment (see Ref. [37]); right, images of a cell with a displaced nucleus and the corresponding schemes. After displacing the nucleus, methyl benzimidazol-2-yl-carbamate (MBC) was washed out to allow the repolymerization of MTs. (c) The experimentally measured position of the nucleus after the MBC washout as a function of time, normalized to the distance by which the nucleus was displaced. An exponential fit (dashed line) to the average data (black circles, error bars represent standard deviation) gives a characteristic time of $22\pm 1\min$ ($\text{mean}\pm \text{standard error of the mean}$); the colored lines represent individual wild-type cells ($n=6$).