Mitotic spindle: lessons from theoretical modeling

Mechanism and regulation of kinesin motors

Kinesins are a diverse superfamily of microtubule-based motors that perform fundamental roles in intracellular transport, cytoskeletal dynamics and cell division. These motors share a characteristic motor domain that powers unidirectional motility and force generation along microtubules, and they possess unique tail domains that recruit accessory proteins and facilitate oligomerization, regulation and cargo recognition. The location, direction and timing of kinesin-driven processes are tightly regulated by various cofactors, adaptors, microtubule tracks and microtubule-associated proteins. This Review focuses on recent structural and functional studies that reveal how members of the kinesin superfamily use the energy of ATP hydrolysis to transport cargoes, depolymerize microtubules and regulate microtubule dynamics. I also survey how accessory proteins and post-translational modifications regulate the autoinhibition, cargo binding and motility of some of the best-studied kinesins. Despite much progress, the mechanism and regulation of kinesins are still emerging, and unresolved questions can now be tackled using newly developed approaches in biophysics and structural biology.

Proliferative advantage of specific aneuploid cells drives evolution of tumor karyotypes

Most tumors have abnormal karyotypes, which arise from mistakes during mitotic division of healthy euploid cells and evolve through numerous complex mechanisms. In a recent mouse model with increased chromosome missegregation, chromosome gains dominate over losses both in pretumor and tumor tissues, whereas T-cell lymphomas are characterized by gains of chromosomes 14 and 15. However, the quantitative understanding of clonal selection leading to tumor karyotype evolution remains unknown. Here we show, by introducing a mathematical model based on a concept of a macro-karyotype, that tumor karyotypes can be explained by proliferation-driven evolution of aneuploid cells. In pretumor cells, increased apoptosis and slower proliferation of cells with monosomies lead to predominant chromosome gains over losses. Tumor karyotypes with gain of one chromosome can be explained by karyotype-dependent proliferation, whereas, for those with two chromosomes, an interplay with karyotype-dependent apoptosis is an additional possible pathway. Thus, evolution of tumor-specific karyotypes requires proliferative advantage of specific aneuploid karyotypes.

Modeling and mechanical perturbations reveal how spatially regulated anchorage gives rise to spatially distinct mechanics across the mammalian spindle

During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al., 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber's response to force remain unclear. Here, we develop a coarse-grained k-fiber model and combine with manipulation experiments to infer underlying anchorage using shape analysis. By systematically testing different anchorage schemes, we find that forces solely at k-fiber ends are sufficient to recapitulate unmanipulated k-fiber shapes, but not manipulated ones for which lateral anchorage over a 3 μm length scale near chromosomes is also essential. Such anchorage robustly preserves k-fiber orientation near chromosomes while allowing pivoting around poles. Anchorage over a shorter length scale cannot robustly restrict pivoting near chromosomes, while anchorage throughout the spindle obstructs pivoting at poles. Together, this work reveals how spatially regulated anchorage gives rise to spatially distinct mechanics in the mammalian spindle, which we propose are key for function.

Length-dependent poleward flux of sister kinetochore fibers promotes chromosome alignment

Chromosome alignment at the spindle equator promotes proper chromosome segregation and depends on pulling forces exerted at kinetochore fiber tips together with polar ejection forces. However, kinetochore fibers are also subjected to forces driving their poleward flux. Here we introduce a flux-driven centering model that relies on flux generated by forces within the overlaps of bridging and kinetochore fibers. This centering mechanism works so that the longer kinetochore fiber fluxes faster than the shorter one, moving the kinetochores toward the center. We develop speckle microscopy in human spindles and confirm the key prediction that kinetochore fiber flux is length dependent. Kinetochores are better centered when overlaps are shorter and the kinetochore fiber flux slower than the bridging fiber flux. We identify Kif18A and Kif4A as overlap and flux regulators and NuMA as a fiber coupler. Thus, length-dependent sliding forces exerted by the bridging fiber onto kinetochore fibers support chromosome alignment.

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A flux-driven centering model explains chromosome alignment at the spindle equator

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Kinetochore fiber poleward flux is driven by overlap microtubules

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Kinetochore centering requires faster flux of the longer sister kinetochore fiber

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Chromosome alignment depends on the overlap length of bridging microtubules

Cell division: Naegleria bundles up for mitosis

How well do we understand the range of mechanisms used by eukaryotes for mitosis? A new study in a highly divergent eukaryote shows that unusual tubulin isoforms can create a mitotic spindle exclusively out of microtubule bundles.

Naegleria's mitotic spindles are built from unique tubulins and highlight core spindle features

Naegleria gruberi is a unicellular eukaryote whose evolutionary distance from animals and fungi has made it useful for developing hypotheses about the last common eukaryotic ancestor. Naegleria amoebae lack a cytoplasmic microtubule cytoskeleton and assemble microtubules only during mitosis and thus represent a unique system for studying the evolution and functional specificity of mitotic tubulins and the spindles they assemble. Previous studies show that Naegleria amoebae express a divergent α-tubulin during mitosis, and we now show that Naegleria amoebae express a second mitotic α- and two mitotic β-tubulins. The mitotic tubulins are evolutionarily divergent relative to typical α- and β-tubulins and contain residues that suggest distinct microtubule properties. These distinct residues are conserved in mitotic tubulin homologs of the "brain-eating amoeba" Naegleria fowleri, making them potential drug targets. Using quantitative light microscopy, we find that Naegleria's mitotic spindle is a distinctive barrel-like structure built from a ring of microtubule bundles. Similar to those of other species, Naegleria's spindle is twisted, and its length increases during mitosis, suggesting that these aspects of mitosis are ancestral features. Because bundle numbers change during metaphase, we hypothesize that the initial bundles represent kinetochore fibers and secondary bundles function as bridging fibers.

Non-centrosomal microtubules at kinetochores promote rapid chromosome biorientation during mitosis in human cells

Proper segregation of chromosomes during mitosis depends on "amphitelic attachments"-load-bearing connections of sister kinetochores to the opposite spindle poles via bundles of microtubules, termed as the "K-fibers." Current models of spindle assembly assume that K-fibers arise largely from stochastic capture of microtubules, which occurs at random times and locations and independently at sister kinetochores. We test this assumption by following the movements of all kinetochores in human cells and determine that most amphitelic attachments form synchronously at a specific stage of spindle assembly and within a spatially distinct domain. This biorientation domain is enriched in bundles of antiparallel microtubules, and perturbation of microtubule bundling changes the temporal and spatial dynamics of amphitelic attachment formation. Structural analyses indicate that interactions of kinetochores with microtubule bundles are mediated by non-centrosomal short microtubules that emanate from most kinetochores during early prometaphase. Computational analyses suggest that momentous molecular motor-driven interactions with antiparallel bundles rapidly convert these short microtubules into nascent K-fibers. Thus, load-bearing connections to the opposite spindle poles form simultaneously on sister kinetochores. In contrast to the uncoordinated sequential attachments of sister kinetochores expected in stochastic models of spindle assembly, our model envisions the formation of amphitelic attachments as a deterministic process in which the chromosomes connect with the spindle poles synchronously at a specific stage of spindle assembly and at a defined location determined by the spindle architecture. Experimental analyses of changes in the kinetochore behavior in cells with perturbed activity of molecular motors CenpE and dynein confirm the predictive power of the model.

Biomechanics of chromosome alignment at the spindle midplane

During metaphase, chromosomes are aligned in a lineup at the equatorial plane of the spindle to ensure synchronous poleward movement of chromatids in anaphase and proper nuclear reformation at the end of mitosis. Chromosome alignment relies on microtubules, several types of motor protein and numerous other microtubule-associated and regulatory proteins. Because of the multitude of players involved, the mechanisms of chromosome alignment are still under debate. Here, we discuss the current models of alignment based on poleward pulling forces exerted onto sister kinetochores by kinetochore microtubules, which show length-dependent dynamics and undergo poleward flux, and polar ejection forces that push the chromosome arms away from the pole. We link these models with the recent ideas based on mechanical coupling between bridging and kinetochore microtubules, where sliding of bridging microtubules promotes overlap length-dependent sliding of kinetochore fibers and thus the alignment of sister kinetochores at the spindle equator. Finally, we discuss theoretical models of forces acting on chromosomes during metaphase.