Mechanical Coupling With the Nuclear Envelope Shapes the Schizosaccharomyces pombe Mitotic Spindle

ABSTRACT

The fission yeast Schizosaccharomyces pombe divides via closed mitosis, meaning that spindle elongation and chromosome segregation transpire entirely within the closed nuclear envelope. Both the spindle and nuclear envelope must undergo shape changes and exert varying forces on each other during this process. Previous work has demonstrated that nuclear envelope expansion (Yam, He, Zhang, Chiam, & Oliferenko, 2011; Mori & Oliferenko, 2020) and spindle pole body (SPB) embedding in the nuclear envelope are required for normal S. pombe mitosis, and mechanical modeling has described potential contributions of the spindle to nuclear morphology (Fang et al., 2020; Zhu et al., 2016). However, it is not yet fully clear how and to what extent the nuclear envelope and mitotic spindle each directly shape each other during closed mitosis. Here, we investigate this relationship by observing the behaviors of spindles and nuclei in live mitotic fission yeast following laser ablation. First, we characterize these dynamics in mitotic S. pombe nuclei with increased envelope tension, finding that nuclear envelope tension can both bend the spindle and slow elongation. Next, we directly probe the mechanical connection between spindles and nuclear envelopes by ablating each structure. We demonstrate that envelope tension can be relieved by severing spindles and that spindle compression can be relieved by rupturing the envelope. We interpret our experimental data via two quantitative models that demonstrate that fission yeast spindles and nuclear envelopes are a mechanical pair that can each shape the other's morphology.

1. Introduction

The geometric simplicity and temporal standardization of the Schizosaccharomyces pombe mitotic apparatus have made it a particularly suitable system for molecular perturbation and mechanical modeling (Loïodice et al. 2005; Lamson et al. 2019; Blackwell et al. 2017; Ward et al. 2014; Winters et al. 2019; Kalinina et al. 2013; Vogel et al. 2009). The S. pombe mitotic spindle consists of a single bundle of 10–30 microtubules, held together along their lengths by microtubule crosslinking proteins and motors (Ding et al. 1993; Krüger et al. 2021; Thomas et al. 2020). In the spindle midzone, microtubules of alternating geometric polarity form a square lattice (Ding et al. 1993). During anaphase, motor proteins crosslink and slide apart antiparallel microtubule neighbors, creating extensile force within the spindle and driving spindle elongation (Krüger et al. 2021; Tolić‐Nørrelykke et al. 2004). This elongation is quite dramatic, with spindles elongating from hundreds of nanometers in length to roughly 10 $\mathrm{\mu m}$ over the course of mitosis, with a program that is spatiotemporally stereotyped from cell to cell (Nabeshima et al. 1998; Loïodice et al. 2005).

Unlike some eukaryotes, whose mitotic spindles self‐assemble and elongate in the cytoplasm, S. pombe performs closed mitosis, meaning that the nucleus stays intact throughout cell division. To facilitate this task, during mitosis, the spindle pole body (SPB) embeds in the nuclear envelope, producing a direct mechanical connection between the envelope and the mitotic spindle (Ding et al. 1997; Zheng et al. 2007). Presumably as a result of this physical connection, spindle elongation accompanies a series of shape transitions in the closed nuclear envelope, from a spheroid, through a peanut‐shaped intermediate, to a dumbbell that will ultimately separate into two daughter nuclei (Figure 1A). Like spindle elongation, these shape changes and their timing are highly stereotyped between cells (Toya et al. 2007), making them ripe for modeling (Zhu et al. 2016; Fang et al. 2020). Previous work showing that aberrant nuclear envelope expansion can disrupt spindle form and function (Yam et al. 2011; Takemoto et al. 2016; Mori and Oliferenko 2020) suggests that the mechanics of the mitotic spindle and of the nuclear envelope are deeply intertwined. Yet, direct experiments to probe their physical connection, as well as modeling to quantitatively understand its consequences, have been lacking. Here, we combine acute mechanical perturbation of both the mitotic spindle and the nuclear envelope by laser ablation to probe the forces each exerts that shape the other. We extend our understanding of this system with two mechanical models that quantitatively explain our experimental data.

FIGURE 1.

Increased nuclear envelope tension bends spindles and slows their elongation. (A) Cartoon showing anaphase nuclear deformation and spindle elongation in a S. pombe cell. (B) Typical example of a cerulenin‐treated S. pombe spindle bending as it elongates during anaphase (beginning around 10–11:00). (C) Cartoon of a mechanical model explaining how the nuclear envelope can bend the mitotic spindle. (D) When elongating during anaphase, cerulenin‐treated S. pombe spindles (gold) often begin bending when they are $\sim$5 $\mathrm{\mu m}$ in length, whereas untreated spindles rarely bend. The area of each violin corresponds to the number of data points in that bin, relative to the total number of points. Dark lines: mean of each bin. Outlying data (less than 0.44% of all data), with curvature values greater than 0.3 $\mu m^{-1}$ are not shown here. (E) Spindles in cerulenin‐treated S. pombe (gold) elongate more slowly during anaphase than those in untreated cells (blue). Traces represent average change in arc length, compared to the first frame after ablation, and shaded regions represent average +/− s.e.m. Traces aligned so that t = 0 is the time when the rate of spindle elongation sharply increases.

2. Results and Discussion

2.1. Increased Nuclear Envelope Tension Can Bend Spindles and Slow Their Elongation

During spindle elongation, the spindle and nuclear envelope are mechanically linked at the two SPBs (Ding et al. 1997). Presumably, this connection allows nuclear envelope tension to be transmitted to the spindle (Yam et al. 2011) and vice versa, but we sought to probe this mechanical relationship directly and quantitatively. To do so, we altered the nuclear envelope with cerulenin, a fatty acid synthesis inhibitor (Omura 1976; Funabashi et al. 1989; Yazawa et al. 2012) that prevents the addition of phospholipids to the nuclear envelope during nuclear envelope expansion and has previously been shown to alter S. pombe mitotic spindle and nuclear shape (Yam et al. 2011; Awaya et al. 1975; Saitoh et al. 1996). Extending this previous work from others, we quantified the behaviors of spindles in cerulenin‐treated cells and modeled their mechanics.

As has previously been observed in S. pombe (Yam et al. 2011), we find that cerulenin treatment often causes bending in anaphase spindles, presumably due to increased nuclear envelope tension (Figure 1B, Video S1). Here, we quantify this bending, which we term ‘buckling,’ as the inverse of the radius of curvature, such that a larger radius of curvature produces less ‘buckling’ than a smaller radius of curvature (Figure 1C). When we plot curvature as a function of spindle length, we find that the onset of buckling occurs fairly abruptly when spindles reach a length of 4–5 $\mathrm{\mu m}$ (Figure 1D). In comparison, spindles in control cells rarely show significant curvature. (While Figure 1D shows some bending in very short spindles, < 3 $\mathrm{\mu m}$, this is an artifact of the difficulty in accurately fitting curvature in short spindles.) We further quantify spindle elongation dynamics in both cerulenin‐treated and control cells. Interestingly, while both initially elongate at similar rates, including the increase in elongation rate at the start of Anaphase B, which is well characterized in S. pombe (Nabeshima et al. 1998; Mallavarapu et al. 1999; Tolić‐Nørrelykke et al. 2004), spindle elongation in cerulenin‐treated cells slows down compared to control spindles when they reach a spindle arc length of 4–5 $\mathrm{\mu m}$, the same length at which they tend to buckle (Figure 1E). Previous work from others has concluded that regulation of microtubule growth and sliding, rather than force balance per se, limits spindle elongation speed (Lera‐Ramirez et al. 2022). However, the present data suggest that nuclear envelope tension, when elevated above normal levels, is at least capable of slowing spindle elongation, and that the force that it exerts when it does so is sufficient to bend the spindle.

To estimate the force exerted on the spindle by the nuclear envelope, we built a simple mechanical model that quantitatively relates spindle buckling to nuclear envelope tension. Parameters associated with this model are shown in Table 1. In general, buckling of a rod occurs above a particular threshold force. In this case, we assume that the nuclear envelope applies this buckling force on the spindle via the spindle pole bodies, which connect to the spindle and are embedded in the envelope (Figure 1C). Using a previous model of spindle buckling in S. pombe (Ward et al. 2014), the force needed to buckle spindles is

$$F_b=\frac{A}{L^4}$$ (1)

where the prefactor $A=1.94\times {10}^4$ pN m for wild‐type fission yeast spindles. Consistent with Figure 1D, which shows that spindles only bend above a threshold length, this model predicts a decreasing buckling force as spindle length extends, with predicted $F_b=31$ pN for 5 $\mathrm{\mu m}$‐long spindles (Ward et al. 2014). Because distortion of the nuclear envelope requires that the envelope bend and stretch, this deformation is energetically unfavorable and requires force. Previous modeling work found the characteristic force scale associated with deforming a membrane is

$$f_0=2\pi \sqrt{2\mathit{\sigma \kappa }}$$ (2)

where $\sigma$ and $\kappa$ are the surface tension and bending rigidity of the nuclear envelope, respectively (Derényi et al. 2002; Lamson et al. 2019; Edelmaier et al. 2020). Using values for wild‐type S. pombe (Lim et al. 2007; Lim and Huber 2009) (see Table 1), we estimate the force scale for distorting the fission yeast nuclear envelope as $f_0=6.4$ pN. Therefore, in unperturbed fission yeast, the force generated by the tendency of the envelope to resist deformation is unlikely to reach the $F_b=31$ pN required to induce buckling of 5 $\mathrm{\mu m}$‐long spindles, and indeed, spindle bending is quite rare in unperturbed cells. Assuming that the bending rigidity of the spindle and the nuclear envelope do not change when cells are treated with cerulenin, the increase in surface tension induced by cerulenin treatment can be estimated using the buckling force. To generate enough force for buckling, we estimate that cerulenin is capable of causing as much as a 20‐fold increase in surface tension, with

$$\sigma =\frac{f^2}{8{\pi }^2\kappa }=0.3\mathrm{pN}/\mathrm{nm}.$$ (3)

TABLE 1.

Parameters of the spindle buckling model of Figure 1C.

Variable	Description	Value	Eqn	Source
$A$	Buckling prefactor	1.94 $\times {10}^4$ pN $\mu$ ${\text{m}}^4$	1	(Ward et al. 2014)
$F_b$	Buckling force	31 pN	1	(Ward et al. 2014)
$f_0$	Force scale for nuclear envelope bending	6.4 pN	2	(Derényi et al. 2002; Lamson et al. 2019; Edelmaier et al. 2020) and values below
$\sigma$	Normal nuclear envelope surface tension	0.013 pN/nm	2	(Lim et al. 2007; Lim and Huber 2009)
$\kappa$	Nuclear envelope bending rigidity	40 pN nm	2	(Lim et al. 2007; Lim and Huber 2009)

2.2. Spindle Severing Verifies That Increased Nuclear Envelope Tension Increases Inward Force at SPBs

We next used laser ablation to sever mitotic spindles to further interrogate the impact of increased nuclear envelope tension on the spindle. We began by severing spindles in control S. pombe (Figure 2A). As previously observed, following ablation, the two spindle halves collapse toward each other (Zareiesfandabadi and Elting 2022; Tolić‐Nørrelykke et al. 2004; Khodjakov et al. 2004), bringing the two poles toward each other and reforming a single microtubule bundle (Figure 2A and Video S2). We have previously determined that this collapse is not only passive relaxation driven by nuclear forces (although it is possible such forces may also contribute), but instead is an active process driven by inward‐directed motor activity (Zareiesfandabadi and Elting 2022).

FIGURE 2.

Increased nuclear envelope tension accelerates the inward collapse of severed spindles. (A) Typical example of laser ablation of an S. pombe spindle expressing GFP‐Atb2 (MWE2), showing post‐ablation spindle collapse, followed by the reattachment of ablated spindle halves at their plus‐ends. (B) Typical example of spindle ablation in cerulenin‐treated S. pombe (MWE2). Dynamic changes to spindle structure seen here include spindle half straightening (0:00), spindle collapse, and unrepaired spindle half depolymerization (left half, 1:10). (C) Typical example of spindle ablation in cerulenin‐treated S. pombe (MWE16). Dynamic changes to the nuclear envelope seen here include increased circularity and retraction. (D) Cerulenin‐treated S. pombe spindles (gold) collapse much faster and more severely after ablation than ablated spindles in untreated S. pombe (blue). Traces represent average change in pole separation, compared to the last frame immediately prior to ablation, and shaded regions represent average $\pm$ s.e.m.

To verify that compressive force from the nuclear envelope causes spindle buckling, we next selectively ablated mitotic spindles that appear curved (Figure 2B and Video S3). These data suggested that inward forces on SPBs, due to increased nuclear envelope tension caused by cerulenin, were bending the spindle, and that the two spindle fragments were allowed to straighten after they were ablated, when each half spindle now had room to fit within the nucleus. To test this interpretation directly, we visualized the dynamics of both the spindle and the nuclear envelope (via the marker Cut11‐meGFP) (Figure 2C and Video S4). As expected, we observed that nuclear envelope rounding accompanied the straightening of ablated spindle halves. We quantified the inward motion of spindle poles following ablation, and as with spindles in control S. pombe, the two spindle poles collapse toward each other after ablation in cerulenin‐treated cells, but at a much greater rate and to a greater extent (Figure 2D). In addition to the differences in speed, we note that after severance of curved spindles, the incident angle between the two halves is much greater than that of ablated straight spindles (Figure 2B), a geometry that is likely to be less conducive to motor transport. Thus, we interpret the faster collapse in cerulenin‐treated cells as likely due to an increase in compressive force acting on the spindle ends from the higher‐tension nuclear envelope. Interestingly, and consistent with this interpretation, even though the two poles collapse toward each other, these spindles rarely reform a single microtubule bundle and, after failing to reconnect, ablated spindle halves often eventually depolymerize (Figure 2B, left spindle half). The probability of depolymerization for untreated spindles is approximately 5%, whereas in cerulenin‐treated cells, this probability jumps to 65%, suggesting the increased compressive force from the nuclear envelope and the ablation of the spindle is too much to overcome. When these spindle halves do not reconnect, mitosis is delayed.

2.3. Release of Nuclear Envelope Tension Directly Couples to Spindle Relaxation

While increased nuclear envelope tension could directly bend the spindle, other factors, such as chromosome entanglements or associations of the spindle with the nuclear envelope along its length, could also contribute. To further test these alternative possibilities, we performed experiments in which we ablated the nuclear envelope of cerulenin‐treated S. pombe and tracked the changes to the spindle and nucleoplasm (Figure 3A and Video S5). Only in the case that nuclear envelope surface tension is compressing the spindle via the embedding of the SPBs would we expect ablation of the envelope far from the spindle itself to allow mechanical relaxation of the spindle. For these experiments, we use cells expressing both GFP‐Atb2 (to visualize tubulin) and GFP‐NLS (to verify nuclear leakage). Labeling both structures with GFP minimizes photobleaching during laser ablation, but makes it difficult to visualize the spindle clearly until after the NLS leakage. We also image the nuclear envelope directly following its laser ablation, and observe motion consistent with a drop in its tension (Figure 3B and Video S6).

FIGURE 3.

The fission yeast spindle and nuclear envelope are a mechanical pair. (A) Typical example of nuclear envelope ablation in cerulenin‐treated S. pombe cell expressing GFP‐Atb2 and GFP‐NLS (strain MWE48), showing nucleoplasm leakage and spindle relaxation. Following nuclear envelope rupture, the spindle becomes easier to visualize due to reduced signal in the nucleoplasm from GFP‐NLS. Scale bars, 2 $\mathrm{\mu m}$. Timestamps, sec. (B) Typical example of nuclear envelope ablation in cerulenin‐treated S. pombe cell expressing GFP‐Atb2 and Cut11‐meGFP (strain MWE16), showing nuclear envelope retraction, where green arrowheads serve as fiducials to highlight movement of the nuclear envelope. Right, these differences between two particular time points (0 s and 27 s after ablation) are highlighted in cyan and magenta, respectively, with green arrowheads in the same locations as elsewhere in the figure. (C) Example of typical NLS intensity (purple) and spindle curvature (gold) traces, following laser ablation of cerulenin‐treated S. pombe nuclear envelopes. Fit (darker lines) and parameters (see Equations (4) and (5)) are given for each trace. (D) The averages of NLS intensity (purple) and spindle curvature (gold) show similar trajectories following ablation. Traces represent averages across all videos, and shaded regions represent average $\pm$ s.e.m. (E) The initiations of nucleoplasm leakage and spindle relaxation, defined using best fit traces for each individual video (as in Figure 3C), are approximately simultaneous. The line shows 1:1 correlation.

We next quantified the viscoelastic‐like response of the spindle that we observe following ablation of the nuclear envelope. Usually, within a minute after ablation, the spindle straightens from a curved conformation to its relaxed, straight state (Figure 3A,C). This implies a reduction in the compressive force acting on the spindle poles and provides additional evidence of nuclear envelope tension as the source of compression. Furthermore, we typically observe spindle relaxation in concurrence with nucleoplasm leakage, visualized by the weakening intensity of the GFP‐NLS signal in the nucleus (Figure 3A,C). This correlation is apparent at both the single cell and population levels (Figure 3A,C,D).

Interestingly, at the individual cell level, we often observe a delay after ablation of the nuclear envelope before substantial spindle and nuclear envelope relaxation (Figure 3C), which we next sought to understand. To quantify this behavior, we fit the curvature to the function

$$C\left(t\right)=\left\{\begin{array}{ll}{A}_{\mathrm{pre}}\left(t-{\tau }_C\right)+C_0& t\le {\tau }_C\\ C_0+\mathrm{\Delta }{C}_f\left(1-e^{-\left(t-{\tau }_C\right)/{\tau }_S}\right)& t>{\tau }_C\end{array}\right.$$ (4)

where $C\left(t\right)$ is spindle curvature, $t$ is time after ablation, and the fit parameters are $C_0$, the curvature at the onset of straightening; $\mathrm{\Delta }{C}_f$, the final change in curvature; ${\tau }_C$, the delay between ablation and straightening; ${\tau }_S$, the timescale of straightening; and $A_{\mathrm{pre}}$, a constant that takes into account variation in curvature before straightening begins. We quantified and fit the NLS intensity to:

$$\begin{array}{l}I\left(t\right)=\\ \left\{\begin{array}{ll}{I}_0{e}^{-t/{\tau }_{\text{bleach}}}+I_{\mathrm{bgd}}& t\le {\tau }_N\\ I_0{e}^{-t/{\tau }_{\text{bleach}}}+\mathrm{\Delta }{I}_{\text{leak}}\left(1-e^{-\left(t-{\tau }_N\right)/{\tau }_{\text{leak}}}\right)+I_{\mathrm{bgd}}& t>{\tau }_N\end{array}\right.\end{array}$$ (5)

where $I\left(t\right)$ is NLS intensity and fit parameters are $I_0$, the intensity at the onset of leakage; $\mathrm{\Delta }{I}_{\text{leak}}$, the total change in intensity due to leakage; $\mathrm{\Delta }{I}_{\text{bleach}}$, the additional change in intensity due to bleaching; ${\tau }_N$, the delay between ablation and leakage; ${\tau }_{\text{leak}}$, the timescale of leakage; ${\tau }_{\text{bleach}}$, the timescale of photobleaching; and $I_{\mathrm{bgd}}$, a constant that takes into account the fluorescent background. When quantifying both curvature and intensity, we observe a delay between ablation and the cell's response. These two delays in spindle straightening (${\tau }_C$) and in nucleoplasm leakage onset (${\tau }_N$) are highly correlated (Figure 3E), suggesting a causative relationship. In other words, we infer that the onset of leakage indicates mechanical failure of the nuclear envelope, resulting in a drop of envelope tension, which in turn allows the spindle to relax.

2.4. Quantitative Comparison of Experimental Data With Mathematical Modeling Allow Estimation of GFP‐NLS Nuclear Transport and Envelope‐Spindle Coupling

We consider a quantitative description of the leakage of GFP‐NLS out of the nucleus following laser ablation. We initially assumed that the drop in intensity we observed was due directly to GFP‐NLS molecules diffusing out of the hole in the envelope generated by ablation. Previous work showed that the escape of a diffusing particle through a round hole leads to an exponential decrease in concentration, with rate $k=1/\tau =4\mathit{Dr}/V$, where $D$ is the particle diffusion coefficient, $r$ is the radius of the hole, and $V$ is the volume of the nucleus (Grigoriev et al. 2002). Thus, estimation of the hole size required us to measure the diffusion coefficient of GFP‐NLS in the nucleus. To measure $D$, we turned to fluorescence correlation spectroscopy (FCS).

In general, FCS requires low concentrations of fluorophores, with small enough numbers present in the confocal volume so that fluctuations in fluorescence intensity due to diffusion are detectable. Initially, the concentration of GFP‐NLS in nuclei was much too high for this to be feasible (Figure 4A). However, we found that by pre‐bleaching nuclei (Figure 4B) before performing FCS, we were able to successfully measure the FCS decay, $G\left(\tau \right)$ (Figure 4C). We fit this decay to a pure diffusion model of the form

$$G\left(\tau \right)=\frac{1}{N\left(1+\frac{\tau }{{\tau }_D}\right)\sqrt{1+\frac{\tau }{{\tau }_D}\frac{{\omega }_0^2}{z_0^2}}},$$ (6)

where $\tau$ is a delay time, $N$ is the average number of molecules in the confocal volume, ${\tau }_D$ is the characteristic diffusion time, ${\omega }_0$ is the lateral beam radius, and $z_0$ is the axial beam radius. We then calculated the diffusion coefficient, $D$ using the relation $D={\omega }_0^2/\left(4{\tau }_D\right)$ after calibration of the effective confocal volume ($V_{\mathrm{eff}}$) and kappa value (${\kappa }_{\mathrm{eff}}=z_0/{\omega }_0$) with several dyes of known diffusion coefficient. We performed similar measurements as in Figure 4 for $N=12$ traces in 4 nuclei, resulting in a measured diffusion coefficient of $D=11\pm 5$ μm/s (mean $\pm$ s.d.). This value is quantitatively in range with what we would expect for diffusion of a particle the size of GFP, based on previous measurements of diffusion in live yeast cells: for example, previous measurements of GEMs (particles $\sim 10$‐fold larger than GFP) diffusing in the nucleus of S. pombe found $D=1$ μm/s (Lemière and Chang 2023), while other measurements of GFP diffusion in S. cerevisiae cytoplasm found $D=18$ μm/s (Fukuda et al. 2019).

FIGURE 4.

Fluorescence correlation spectroscopy (FCS) demonstrates nuclear diffusion of GFP‐NLS. (A) Pre‐bleached image of S. pombe cell expressing GFP‐NLS. Cells are strain MWE40. (B) Post‐bleached image of S. pombe cell expressing GFP‐NLS. The laser power and intensity scale for B is 10× compared to A. (C) FCS decay (scatter plot) from autocorrelation of fluorescence intensity trace collected at the location circled in B, along with fit to $G\left(\tau \right)$ (black line), as in Equation (6). (D) Following laser ablation, a hole that is diffraction‐limited in size is created in the nuclear envelope, allowing GFP‐NLS to diffuse into the cytoplasm. Meanwhile, nuclear pore complexes continue to pump GFP‐NLS from the cytoplasm back into the nucleus. These two processes are in a fast quasi‐equilibrium. At later times, the hole increases in radius, both allowing more diffusion of GFP‐NLS and lowering the envelope tension, allowing the spindle to straighten.

We can now use our measured value of $D$ to better understand the delay in leakage of GFP from the nucleus following laser ablation. We take $\tau =10$ s as a typical value for the relaxation time constant (Figure 3C,D) and estimate nuclear volume $V\approx 14$ μm (see Table 2). Together, if nuclear concentration were dominated only by diffusion through the ablated hole, these values would predict a hole radius due to laser ablation of

$$r=\frac{V}{4\mathit{D\tau }}\approx 30\mathrm{nm}$$ (7)

TABLE 2.

Parameters of the envelope leakage model of Figure 4D.

Variable	Description	Value	Eqn	Source
${\tau }_c$	Delay between ablation and onset of straightening	11 $\pm$ 3 s	4	Fits to all cells as in Figure 3B (mean $\pm$ s.e.m.)
${\tau }_s$	Timescale of straightening (after straightening begins)	12 $\pm$ 2 s	4	Fits to all cells as in Figure 3B (mean $\pm$ s.e.m.)
${\tau }_N$	Delay between ablation and onset of nuclear leakage	11 $\pm$ 3 s	5	Fits to all cells as in Figure 3B (mean $\pm$ s.e.m.)
${\tau }_{\text{leak}}$	Time scale of leakage (after leakage begins)	7 $\pm$ 3 s	5	Fits to all cells as in Figure 3B (mean $\pm$ s.e.m.)
$D$	Diffusion coefficient of GFP‐NLS in the nucleus	$11\pm 5\mu$ ${\text{m}}^2$/s	7, 10	Fits to all cells as in Figure 4C (mean $\pm$ s.e.m.)
$V$	Volume of the nucleus	$14\mu$ ${\text{m}}^3$	7, 10	$\frac{4}{3}\pi R^3$, $R\sim 1.5\mu$m
$I_{\mathrm{nc}}$	Ratio of nuclear to cytoplasmic intensity of GFP‐NLS	$23\pm 6$	11	Confocal fluorescence imaging of intensity in n = 5 cells (mean $\pm$ s.e.m.)
${\tau }_{\text{in}}$	Timescale of active import into the nucleus	10–30 ms	12	Measured GFP‐NLS diffusion coefficient and (Yang et al. 2004; Kubitscheck et al. 2005; Varberg et al. 2022; Milles et al. 2015)
${\tau }_{\text{passive}}$	Timescale of passive diffusion/leakage	200–600 ms	13	Calculated from intensity ratio and import timescale

This estimate is unphysically small, given that damage due to laser ablation occurs in a diffraction‐limited spot with a characteristic size $\approx 500$ nm (Botvinick et al. 2004; Khodjakov et al. 1997; Magidson et al. 2007). We thus consider additional mechanisms that may control the time course of both GFP‐NLS concentration and spindle curvature.

Because GFP‐NLS is actively imported into the nucleus and active import can occur rapidly, we next considered that the data may reflect a balance between passive diffusion of GFP‐NLS through the hole and active import as the hole size changes over time. We therefore construct a model (Figure 4D, Table 2) that considers both of these effects. We assume that there are $N_n\left(t\right)$ GFP‐NLS molecules in the nucleus and $N_c\left(t\right)$ in the cytoplasm. We additionally assume that over the 1‐min timescale of the ablation experiments that the total number of GFP‐NLS molecules does not significantly change (i.e., that photobleaching is minimal), so that there are a total number $N_0=N_n+N_c$ and concentrations $c_n=N_n/V_n$, $c_c=N_c/V_c$, and $c_{\max }=N_0/V_n$, where $V_n$ is the nuclear volume and $V_c$ the cytoplasmic volume. Here, we have defined $c_{\max }$ as the nuclear GFP concentration that would occur if all molecules were in the nucleus. Then the rate of change of the nuclear GFP‐NLS concentration is

$$\frac{{\mathit{dc}}_n}{\mathit{dt}}=-k_{\text{out}}\left(r\right)c_n+k_{\text{in}}{c}_c$$ (8)

where the first‐order rate constant of leakage $k_{\text{out}}\left(r\right)=4\mathit{Dr}\left(t\right)V_n+k_{\text{diffuse}}$ describes both diffusion through the hole in the nuclear envelope (which depends on the size of the hole) and ongoing passive leakage (through the nuclear pore complexes, assumed constant), while the first‐order rate constant $k_{\text{in}}$ describes active import through the nuclear pore complexes and is assumed constant. Substituting $N_c=N_o-N_n$ and the appropriate volume factors into Equation (8) gives

$$\frac{{\mathit{dc}}_n}{\mathit{dt}}=-\left(k_{\text{out}}\left(r\right)+k_{\text{in}}\tilde{V}\right)c_n+k_{\text{in}}\tilde{V}{c}_{\max }$$ (9)

where $\tilde{V}=V_n/V_c$ is the ratio of nuclear to cytoplasmic volume. We treat Equation (9) quasistatically, assuming that the import and export rates are rapid compared to the tens of seconds required for full relaxation of the GFP‐NLS intensity. Therefore, we set the time derivative term on the left side of Equation (9) to zero, and solve for the fraction of total molecules that are in the nucleus, yielding the following result:

$$\frac{c_n}{c_{\max }}=\frac{1}{1+\frac{k_{\text{out}}\left(r\left(t\right)\right)}{k_{\text{in}}\tilde{V}}}=\frac{1}{1+\frac{4\mathit{Dr}\left(t\right)V_n+k_{\text{passive}}}{k_{\text{in}}\tilde{V}}},$$ (10)

Before ablation, there is no hole, and we predict $c_n/c_{\max }=1/\left(1+k_{\text{passive}}/k_{\text{in}}\tilde{V}\right)$. This can be rewritten in terms of the ratio of the nuclear to cytoplasmic concentration. Since average fluorescence intensity is proportional to concentration, this gives a prediction for the nuclear to cytoplasmic intensity ratio

$$I_{\mathit{nc}}=\frac{c_n}{c_c}=\frac{k_{\text{in}}}{k_{\text{passive}}}.$$ (11)

We measured the average fluorescence intensity of GFP‐NLS in the nucleus relative to the cytoplasm $I_{\mathit{nc}}$ and found an average value $23\pm 6$ (n = 5 cells). This result shows that the active nuclear import rate is significantly higher than the passive export rate through the nuclear pore complex, as expected due to the presence of the NLS tag. Even once the ablated hole in the envelope is present, we expect that diffusion through the hole is initially slow compared to transport rates through the nuclear pore, since the single hole initially has a much smaller area than that of all nuclear pores together. That is, $4{\mathit{DrV}}_n\ll k_{\text{passive}}$, so the denominator of Equation (10) does not initially increase. This could explain the initial delay observed in traces, as in Figure 3C, where the GFP‐NLS concentration is initially approximately constant for $\sim 10$ s following ablation.

The GFP‐NLS concentration will first begin to show a noticeable decrease when the rate of GFP‐NLS leakage through the ablated hole is comparable to the rate of passive nuclear export, meaning $4\mathit{Dr}\left(t\right)V_n\approx k_{\text{passive}}$. To estimate the hole size where this crossover occurs, we estimated $k_{\text{in}}$ and $k_{\text{passive}}$. Measurements of active transport through the nuclear pore complex find very short residence times of transported particles in the pore, in the range of ${\tau }_{\text{trans}}\sim$ 1–10 ms (Yang et al. 2004; Kubitscheck et al. 2005), and that the timescale of nuclear transport is typically limited by the time required for molecules to diffuse to a nuclear pore complex (Milles et al. 2015). In fission yeast, nuclear pore complexes are typically separated by about 0.4 μm (Varberg et al. 2022), making this a typical distance that a GFP‐NLS must diffuse to reach a nuclear pore complex and re‐enter the nucleus. This diffusive timescale for GFP‐NLS is approximately ${\tau }_D\sim {\mathrm{\ell }}^2/D\sim 15$ ms. This suggests that the timescale of active import is in the range of

$${\tau }_{\text{in}}={\tau }_D+{\tau }_{\text{trans}}\sim 10-30\mathrm{ms}$$ (12)

reflecting the variability in transport rate (Frey et al. 2018). The timescale for passive export is approximately 20 times larger, based on our intensity ratio estimate. Therefore, we estimate the export timescale

$${\tau }_{\text{passive}}=\frac{1}{k_{\text{passive}}}=I_{\mathit{nc}}{k}_{\text{in}}\sim 200-600\mathrm{ms}$$ (13)

Based on the prediction of our model that noticeable GFP‐NLS diffusion through the hole will occur once $4\mathit{Dr}\left(t\right)V_n\approx k_{\text{passive}}$, we therefore estimate that the hole size must grow to a radius $r=V_n/\left(4D{\tau }_{\text{passive}}\right)$ before the intensity decrease is observable. This gives an estimated range of hole size $r\sim 0.5-1.5\mathrm{\mu }$m at which the nuclear intensity would be predicted to change due to significant diffusion of GFP‐NLS out of the hole in the nuclear envelope. This micron‐sized hole is physically reasonable to result from ablation.

This model therefore explains why the drop in GFP‐NLS intensity in the nucleus and the drop in spindle curvature have the same timescale. The decrease in intensity is likely limited not by the rate of diffusion through the hole, but by the hole size, which must therefore change over time. While the hole caused by ablation is likely initially small in area, it may trigger a subsequent catastrophic event in which the hole expands and nuclear envelope tension plummets, allowing the spindle to straighten. Such a response would explain the delay between ablation and both the beginning of nuclear leakage and the beginning of spindle straightening (Figure 3E): this delay indicates the time between ablation and envelope rupture to a sufficiently large hole size to compete with active GFP‐NLS import. Additionally, the estimated size at which the hole allows a significant drop in GFP‐NLS concentration, $r\sim 1\mu$m, is physically consistent with the size of deformation we would expect to be required to allow the spindle to straighten. Determining what underlies the timescale of the rupture itself will be an interesting area of further investigation: one can imagine that it might depend on nuclear envelope material properties, larger‐scale rearrangements of the cytoplasm, nucleoplasm, nuclear envelope, and spindle, or a combination.

In total, our results demonstrate significant mechanical coupling during mitosis between the mitotic spindle and nuclear envelope in S. pombe. While such coupling has been previously assumed, the results here directly demonstrate how directly these two crucial structures in closed mitosis shape each other. The rapid spindle collapse following spindle ablation in cerulenin‐treated cells suggests the presence of a compressive force on the spindle poles, resulting from increased nuclear envelope tension. Indeed, such force appears capable of not only bending the spindle but of slowing its elongation. Likewise, the simultaneous nuclear envelope rupture and spindle relaxation after nuclear envelope ablation imply this compressive force can be lessened by relieving tension in the nuclear envelope. It is interesting that nuclear envelope tension is insufficient to bend the spindle during normal cell division and suggests that the forces of each structure may be well‐tuned or coordinated to ensure that they are each of appropriate magnitudes to ensure robust function. Future work could provide further insight into how the mechanical properties of these two functionally integrated structures, the mitotic spindle and the nuclear envelope, may have co‐evolved to support robust chromosome segregation and genetic integrity.

3. Materials and Methods

3.1. Fission Yeast Strains and Culture

For strain details, see Table 3. S. pombe strain MWE2 is from Fred Chang's lab stock (original strain FC2861). MWE48 was created by crossing S. pombe strains MWE2 and MWE40, which were from Gautam Dey's lab stock (original strain GD208 (Dey et al. 2020)). The cross was performed by tetrad dissection using standard methods (Forsburg and Rhind 2006). All strains were cultured at 25°C on YE5S plates using standard techniques (Forsburg and Rhind 2006). For imaging, liquid cultures were grown in YE5S media at 25°C with shaking by a rotating drum for 12–24 h before imaging. To ensure that cells were in the growth phase for imaging, we measured OD595 with a target of 0.1–0.2. If cells had grown beyond this point, we diluted them and allowed them to recover for 1 h before imaging. As a method of increasing nuclear envelope tension in S. pombe, cells were treated with 0.3‐1 mM cerulenin for between 1 and 4 h before imaging, from stock solutions at 50 mM in DMSO, as previously described (Yam et al. 2011; Awaya et al. 1975).

TABLE 3.

Strains.

Genotype	Original source	Strain identifier
S. pombe h+ GFP‐atb2:kanMX ade6‐ leu1‐32 ura4‐D18	Gift of F. Chang (FC2861)	MWE2
S. pombe h− pBIP1‐NLS‐GFP‐NLS:leu1+ ade‐ leu1‐32 ura4D‐18	Gift of G. Dey (GD208) (Dey et al. 2020)	MWE40
S. pombe pBIP1‐NLS‐GFP‐NLS:leu1+ GFP‐atb2:kanMX	This work (cross of MWE2 and MWE40)	MWE48
S. pombe h+ nmt41‐GFP‐atb2‐hpnMX6 + Cut11‐meGFP‐KanMX6	Gift of C. Laplante (CL579‐1)	MWE16

3.2. Live Cell Imaging, Laser Ablation, and Fluorescence Correlation Spectroscopy

Prior to imaging, samples were placed onto gelatin pads on microscope glass slides. For gelatin pads, 125 mg gelatin was added to 500 $\mathrm{\mu L}$ EMM5S and heated in a tabletop dry heat bath at 90°C for at least 20 min. A small sample volume ($\sim 5$ $\mathrm{\mu L}$) of the gelatin mixture was pipetted onto each slide, covered with a coverslip, and given a minimum of 30 min to solidify. For each microscope slide, 1 mL volume of cells suspended in YE5S liquid growth media was centrifuged (enough to see a pellet), using a tabletop centrifuge. Nearly all the supernatant was decanted and the cells were resuspended in the remaining supernatant. Next, 2 $\mathrm{\mu L}$ of the resuspended cells were pipetted onto the center of the gelatin pad, which was immediately covered with a cover slip. Finally, the coverslip was sealed using VALAP (1:1:1: Vaseline:lanolin:paraffin). All samples, sealed between the gelatin pads and coverslips, were imaged at room temperature ($\sim 22$°C). Spinning disk confocal live imaging and laser ablation experiments were performed similar to those described previously (Begley et al. 2021; Zareiesfandabadi and Elting 2022; Uzsoy et al. 2021). Live videos were captured using a Nikon Ti‐E stand on an Andor Dragonfly spinning disk confocal fluorescence microscope; spinning disk dichroic Chroma ZT405/488/561/640rpc; 488 nm (50 mW) diode laser (240 ms exposures) with Borealis attachment (Andor); emission filter Chroma ET525/50 m; and an Andor iXon3 camera. Imaging was performed with a 100 × 1.45 Ph3 Nikon objective and a 1.5 × magnifier (built‐in to the Dragonfly system). An Andor Micropoint attachment with galvo‐controlled steering was used for targeted laser ablation, delivering 20–30 3 ns pulses of 551 nm light at 20 Hz. Each cell was imaged until either spindle repair had been completed or the spindle had failed to repair after 5 min. For spindle ablation videos, frames were collected every 3.5 s, while frames were collected every 280 ms for nuclear envelope ablation videos. Andor Fusion software was used to manage imaging and Andor IQ software was used to simultaneously manipulate the laser ablation system. We used GFP as a marker in all cases due to its greater robustness against photobleaching when we ablate. Due to differences in localization, we were able to discriminate between the GFP‐Atb2 and GFP‐NLS signals.

FCS (Magde et al. 1972, 1974; Elson and Magde 1974) measurements were performed with a time‐resolved confocal fluorescence microscope (MicroTime 200, PicoQuant) with SymPhoTime64 software for data acquisition and analysis. A picosecond pulsed diode laser (485 nm) controlled by a laser driver module (SEPIA II) was used to excite the sample with a 60 × 1.2 numerical aperture water immersion lens (Olympus UPlanSApo, Superachromat). A fast galvo beam scanning module (FLIMbee) was used for laser beam scanning. Time‐correlated single photon counting (TCSPC) with a multichannel event timer (MultiHarp 150) in time‐tagged time‐resolved (TTTR) measurement mode applied time tags to individual photons detected at a single photon avalanche diode (SPAD) with a 511/20 bandpass filter. Detected photons were also marked with a location in the beam scan of the sample to enable fluorescence lifetime imaging microscopy (FLIM). A FLIM image was acquired, and the nuclei of cells were selectively pre‐bleached by scanning with an average laser power density of $\sim 3$ kW/cm. FCS measurements were acquired by point clicking on a bleached location within the nucleus and collecting photons from diffusing GFP‐NLS molecules. An autocorrelation was performed on the fluorescence intensity trace and the decay fitted to a pure diffusion model to extract a diffusion time. The diffusion coefficient was calculated by characterizing the effective confocal volume ($\sim 1$ femtoliter) and kappa value ($\sim 6$) with several fluorescent dyes with a known diffusion coefficient. Simultaneous detection of the fluorescence lifetime of the diffusing species ($\sim 2.7$ ns) was consistent with GFP.

3.3. Quantification and Statistical Analysis

3.3.1. Image and Video Preparation and Editing

To optimize the identification and tracking of spindle and nuclear envelope features, modifications were made to fluorescence microscopy images and videos using FIJI (Schindelin et al. 2012). First, images and videos were cropped to show only cells of interest, and extra frames were eliminated. Typically, linear adjustments were made to the brightness and contrast of the images in order to track features more clearly. For measurements of NLS intensity, however, pixel intensities were measured from unadjusted images. For immunofluorescence images, the same brightness and contrast scaling was used for all images in each set.

3.3.2. Tracking of Spindle Features in Ablation Videos

All quantitative data regarding post‐ablation spindle dynamics were collected via a tracking program, home‐written in Python. For each ablated spindle, the two spindle poles were tracked following ablation, using this program, and the ‘line’ tool in FIJI was used to measure the length of each spindle immediately prior to ablation (Figure 5A,B). These data were then used to calculate the change in pole separation (length) for each spindle over time, following ablation (Figure 5C). Additionally, the positions of the two new plus‐ends of each ablated spindle half were tracked throughout the video. Our tracking program includes a method for indicating whether or not spindle repair has occurred, with the reconnection of the two ablated spindle halves, in each frame. The data for frames collected before the reformation of a single spindle was used to compute time traces for the change in spindle half length (Figure 5D).

FIGURE 5.

Data analysis pipeline for quantification of spindle length. (A) Screenshot showing the measurement of pre‐ablation spindle length, using the line tool in FIJI. (B) Screenshot of a window from a home‐written Python program used to label spindle poles and spindle half‐ablated plus‐ends in the frames following ablation. (C) Example trace of post‐ablation spindle pole separation for the spindle shown in panels A and B, and Supplemental Video S1. (D) Example trace of post‐ablation spindle half‐length for the two ablated spindle halves shown in panel B and Video S3.

3.3.3. Quantification of Spindle Relaxation and Nucleoplasm Leakage

For all nuclear envelope ablation videos, data were collected on the time evolution of spindle curvature using a home‐written Matlab program. The program takes microscope image files and fits a quadratic function to a chosen object in the image. It then outputs curvature and length data from that fitted curve. For videos, this process was semi‐automated to perform the fit frame by frame. Another program, home‐written in Python, was used to track the rate of nucleoplasm leakage from the nucleus of each cell following nuclear envelope ablation. This program requires the unadjusted video, spindle curvature data, and spindle length data as inputs. Using these inputs, nuclear intensity is calculated for each frame as the average GFP intensity (after background subtraction) of a 25‐pixel square near the center of the nucleus. Both NLS and spindle curvature traces are normalized to their highest value for that video. This same program is then used to compute least squares fit curves for both post‐ablation spindle curvature and nuclear intensity using the equations given in the main text.

Author Contributions

Experimental design: M.A.B., T.M., P.Z., S.J.L., M.D.B., M.W.E. Experimental data collection and analysis: M.A.B., T.M., C.P.M., P.Z., M.B.R., M.T., S.J.L., M.W.E. Theoretical modeling: M.D.B. and M.W.E. Manuscript writing and editing: M.A.B., T.M., S.J.L., M.D.B., M.W.E. Obtaining funding: S.J.L., M.D.B., M.W.E. All authors have given final approval of the version to be published.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Video S1. Typical example of an elongating spindle in an Schizosaccharomyces pombe cell expressing GFP‐Atb2 and treated with cerulenin. The spindle is prone to bending, as it elongates under the compressive force exerted on the spindle poles by the nuclear envelope (3:00–9:50), and eventually breaks into two pieces (10:00–15:00).

Video S2. Typical example of an ablated spindle in an S. pombe cell expressing GFP‐Atb2. Following ablation, the spindle collapses as the distance between the two spindle poles decreases. Eventually, the mechanical connection between the two ablated spindle halves is re‐established, restoring the spindle to a single bundle.

Video S3. Typical example of an ablated curved spindle in an S. pombe cell expressing GFP‐Atb2 and treated with cerulenin. Post‐ablation spindle collapse is more rapid and severe than in untreated S. pombe. Commonly, ablated spindle halves will depolymerize after failing to reform a spindle.

Video S4. Typical example of an ablated curved spindle in an S. pombe cell expressing GFP‐Atb2 and Cut11‐meGFP (which marks the nuclear envelope) and treated with cerulenin. Post‐ablation the nuclear envelope becomes rounder, presumably due to the drop in surface tension that occurs when the spindle is severed. Commonly, ablated spindle halves will depolymerize after failing to reform a spindle, as can be seen here in the left half of the severed spindle.

Video S5. Typical example of an ablated deformed nuclear envelope in an S. pombe cell expressing GFP‐Atb2 and GFP‐NLS and treated with cerulenin. Both nucleoplasm leakage and spindle relaxation can be seen, following ablation of the nuclear envelope distal to the curved spindle.

Video S6. Typical example of an ablated, deformed nuclear envelope in an S. pombe cell expressing GFP‐Atb2 and Cut11‐meGFP and treated with cerulenin. In this particular example, the spindle is in a different focal plane and is difficult to see in most frames. In response to the ablation of the nuclear envelope, the remaining envelope relaxes away from the site of ablation and, on the side of the nucleus opposite the site of ablation, relaxes toward the remaining chromosomes and spindle.

Begley, M. A. , Mahoney T., Medina C. P., et al. 2026. “Mechanical Coupling With the Nuclear Envelope Shapes the Schizosaccharomyces pombe Mitotic Spindle.” Cytoskeleton 83, no. 1: 40–52. 10.1002/cm.22035.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.