Mechanics of microtubule organizing center clustering and spindle positioning in budding yeast Cryptococcus neoformans

The dynamic process of mitotic spindle assembly depends on multitudes of inter-dependent interactions involving kinetochores (KTs), microtubules (MTs), spindle pole bodies (SPBs), and molecular motors. Before forming the mitotic spindle, multiple visible microtubule organizing centers (MTOCs) coalesce into a single focus to serve as an SPB in the pathogenic budding yeast, Cryptococcus neoformans. To explain this unusual phenomenon in the fungal kingdom, we propose a “search and capture” model, in which cytoplasmic MTs (cMTs) nucleated by MTOCs grow and capture each other to promote MTOC clustering. Our quantitative modeling identifies multiple redundant mechanisms mediated by a combination of cMT-cell cortex interactions and inter-cMT coupling to facilitate MTOC clustering within the physiological time limit as determined by time-lapse live-cell microscopy. Besides, we screen various possible mechanisms by computational modeling and propose optimal conditions that favor proper spindle positioning—a critical determinant for timely chromosome segregation. These analyses also reveal that a combined effect of MT buckling, dynein pull, and cortical push maintains spatiotemporal spindle localization.

Figure 1

Cell cycle stages in C. neoformans wild-type cell as observed from live-cell imaging. (a) Time series snapshots showing the localization of MTs (GFP-Tub1, depicted in green in the MERGE panel) and KTs (mCherry-CENP-A, depicted in red in the MERGE panel) at different stages of the cell cycle in a wild-type cell. The cell was subjected to time-lapse video microscopy for 60 min. The timestamp (in min) for each image is annotated in the uppermost TUB1 panel. Bar, $5\mu \mathrm{m}$. (b), (c) Clustering of MTOCs and KTs during mitosis in C. neoformans. Images of cells showing the localization of (b) Spindle pole body protein, Spc98 and (c) KT marker CENP-A at different cell cycle stages in the wild-type cells. Bar, $5\mu \mathrm{m}$. The snapshots of the co-localization of Spc98 and CENP-A (using a different strain) were shown in Ref. [20]. (d) Schematic depicting the simultaneous happening of the processes shown in panels (b) and (c). (e) Progression of bud growth with time. (f) Number of MTOCs in the cell as a function of time estimated from the bud size.

Figure 2

Representative schematic diagrams illustrating the computational and mathematical model. (a) Model schematic depicts the cell cycle stages in C. neoformans which are simulated utilizing the computational model. Plausible interactions of cMTs with the cell cortex and on the nuclear envelope are shown. Arrows indicate the direction of forces. (b) Schematic of the one-dimensional mathematical model for spindle positioning in C. neoformans. The origin $O(0,0)$ is located at the center of the mother bud, while the center of the daughter bud is located on the axis of symmetry (namely the $X$ axis) at $(d,0)$. The instantaneous position of the spindle is denoted by $x$ measured from the origin. $l_c$ denotes the cortex's width, filled with mesh-like actins and dyneins. $SPB\left(L\right)$ and $SPB\left(R\right)$ denote the leftward and rightward SPBs, and the green lines represent microtubules. In the mother bud, the section “PR” is the “uncurled” MT segment in the cortical region, and the segment “PQ” is the “curled” MT segment undergoing sliding within the mother cortex where cortical dyneins pull on both the segments. A similar interaction occurs in the daughter cortex as well. Localized cortical dynein patch in the daughter cortex around the axis of symmetry signifies the differential spatial distribution of dynein in the mother and daughter bud [16]. (c) The direction of the forces acting on the spindle in the mathematical model.

Figure 3

Cooperative interactions among MTs and motors govern MTOC clustering. (a) Model schematic depicting MT-mediated ‘search and capture’ processes and forces required for the clustering of MTOCs. Arrows indicate the direction of forces. Plausible clustering mechanisms illustrated are: a growing cMT directly capturing an MTOC (‘direct search and capture'), sliding of antiparallel cMTs via crosslinking minus end-directed motors on the NE (inter cMT coupling at the NE), and cMT plus-ends interacting with cell cortex (MT-cortex interaction). (b) Clustering time in the sole presence of inter cMT coupling at the NE increases as the minus-ended motor-generated inward force at MT-MT overlap decreases. The MT number is fixed at 4 per MTOC. (c) Clustering solely via MT-cell cortex interaction. The clustering is faster when the Bim1 bias is enhanced. $|{\vec{f}}_{\text{dyn}}|$ ($|{\vec{f}}_{\mathrm{Bim}1}|$) represents the magnitude of the force generated by a single dynein (Bim1) on each MT at mother cortex. (d) Time progression of MTOC clustering in different mechanisms. The first/fifth bar in part (c) denotes the parameter values corresponding to the magenta/cyan curve in part (d), respectively. (e) Comparison between MTOC clustering timescales via MT-cell cortex interaction, inter cMT coupling on NE and Bim1 bias with suppressed dynein activity at cell cortex ($|\overrightarrow{f_{\text{dyn}}}|=0.0$ pN, $|\overrightarrow{f_{\mathrm{Bim}1}}|=0.5$ pN). In all figures, sample size $n>2000$ for simulation and red bars indicate SEM (wherever shown).

Figure 4

MTOC clustering and nuclear migration: sensitivity to model parameters. (a)–(c) Time required for complete MTOC clustering and proper nuclear migration to daughter bud when Bim1 bias force per MT (a), number of MT per MTOC (b), and average cMT length (c) are varied. For MTOC clustering, solely the mechanism of “MT-cell cortex interaction with diminished cortical pull and enhanced Bim1 bias” is considered. In all figures, sample size $n>2000$ for simulation and red bars indicate SEM (wherever shown).

Figure 5

The mechanistic models of force balance explain spindle positioning in C. neoformans. (a) Spindle stably collapses onto the cell cortex as dynein density in the daughter cortex (${\lambda }_{\text{dyn}}^D$) is varied. Dynein density in the mother cortex (${\lambda }_{\text{dyn}}^M$) is fixed and instantaneous cortical push is present in both mother and daughter cortex. Color bars represent the net force on the spindle and white solid lines denote the center of the daughter and mother buds. (b), (c) MT buckling is present combined with instantaneous push and cortical pull. Increasing dynein density in the daughter cortex (${\lambda }_{\text{dyn}}^D$) steadily brings the spindle into the daughter, localizing near the septin ring (b). Spindle position varies depending on the average MT length $L_{\text{MT}}^{\text{av}}$ (c). (d), (e) Spindle distance from septin ring in the absence (d) or presence (e) of MT buckling at the cortex as observed in the agent-based simulation. The values within the bars indicate the percentage of spindles in mother or daughter across the cell population. (f) Spindle position depending on the variation in average MT length ($L_{\text{MT}}^{\text{av}}$) as observed in the agent-based simulation when instantaneous cortical push, dynein pull, and MT buckling are acting in tandem. In plots A–F, -ve/$+\mathrm{ve}$ distance refers to the spindle in the mother (M) and daughter (D) bud.

Figure 6

Summary of model outcomes describing mechanistic aspects of MTOC clustering and spindle positioning in C. neoformans. The agent-based model depicts redundant mechanisms for the timely clustering of MTOCs. Inter cMT coupling at NE and/or cortical interaction of MTs with suppressed dynein pull and enhanced Bim1 bias may facilitate timely clustering, either independently or in unison. Furthermore, the analytical model supported by agent-based simulations suggests that proper spindle positioning in the daughter bud near the septin ring requires MT buckling from the cell cortex.