Active forces shape the metaphase spindle through a mechanical instability

Computational tools for cellular scale biophysics

Mathematical models are indispensable for disentangling the interactions through which biological components work together to generate the forces and flows that position, mix, and distribute proteins, nutrients, and organelles within the cell. To illuminate the ever more specific questions studied at the edge of biological inquiry, such models inevitably become more complex. Solving, simulating, and learning from these more realistic models requires the development of new analytic techniques, numerical methods, and scalable software. In this review, we discuss some recent developments in tools for understanding how large numbers of cytoskeletal filaments, driven by molecular motors and interacting with the cytoplasm and other structures in their environment, generate fluid flows, instabilities, and material deformations which help drive crucial cellular processes.

Mechanisms underlying spindle assembly and robustness

The microtubule-based spindle orchestrates chromosome segregation during cell division. Following more than a century of study, many components and pathways contributing to spindle assembly have been described, but how the spindle robustly assembles remains incompletely understood. This process involves the self-organization of a large number of molecular parts - up to hundreds of thousands in vertebrate cells - whose local interactions give rise to a cellular-scale structure with emergent architecture, mechanics and function. In this Review, we discuss key concepts in our understanding of spindle assembly, focusing on recent advances and the new approaches that enabled them. We describe the pathways that generate the microtubule framework of the spindle by driving microtubule nucleation in a spatially controlled fashion and present recent insights regarding the organization of individual microtubules into structural modules. Finally, we discuss the emergent properties of the spindle that enable robust chromosome segregation.

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.

A sePARate phase? Poly(ADP-ribose) versus RNA in the organization of biomolecular condensates

Condensates are biomolecular assemblies that concentrate biomolecules without the help of membranes. They are morphologically highly versatile and may emerge via distinct mechanisms. Nucleic acids-DNA, RNA and poly(ADP-ribose) (PAR) play special roles in the process of condensate organization. These polymeric scaffolds provide multiple specific and nonspecific interactions during nucleation and 'development' of macromolecular assemblages. In this review, we focus on condensates formed with PAR. We discuss to what extent the literature supports the phase separation origin of these structures. Special attention is paid to similarities and differences between PAR and RNA in the process of dynamic restructuring of condensates during their functioning.

Three-dimensional structure of kinetochore-fibers in human mitotic spindles

During cell division, kinetochore microtubules (KMTs) provide a physical linkage between the chromosomes and the rest of the spindle. KMTs in mammalian cells are organized into bundles, so-called kinetochore-fibers (k-fibers), but the ultrastructure of these fibers is currently not well characterized. Here, we show by large-scale electron tomography that each k-fiber in HeLa cells in metaphase is composed of approximately nine KMTs, only half of which reach the spindle pole. Our comprehensive reconstructions allowed us to analyze the three-dimensional (3D) morphology of k-fibers and their surrounding MTs in detail. We found that k-fibers exhibit remarkable variation in circumference and KMT density along their length, with the pole-proximal side showing a broadening. Extending our structural analysis then to other MTs in the spindle, we further observed that the association of KMTs with non-KMTs predominantly occurs in the spindle pole regions. Our 3D reconstructions have implications for KMT growth and k-fiber self-organization models as covered in a parallel publication applying complementary live-cell imaging in combination with biophysical modeling (Conway et al., 2022). Finally, we also introduce a new visualization tool allowing an interactive display of our 3D spindle data that will serve as a resource for further structural studies on mitosis in human cells.

Self-organization of kinetochore-fibers in human mitotic spindles

During eukaryotic cell division, chromosomes are linked to microtubules (MTs) in the spindle by a macromolecular complex called the kinetochore. The bound kinetochore microtubules (KMTs) are crucial to ensuring accurate chromosome segregation. Recent reconstructions by electron tomography (Kiewisz et al., 2022) captured the positions and configurations of every MT in human mitotic spindles, revealing that roughly half the KMTs in these spindles do not reach the pole. Here, we investigate the processes that give rise to this distribution of KMTs using a combination of analysis of large-scale electron tomography, photoconversion experiments, quantitative polarized light microscopy, and biophysical modeling. Our results indicate that in metaphase, KMTs grow away from the kinetochores along well-defined trajectories, with the speed of the KMT minus ends continually decreasing as the minus ends approach the pole, implying that longer KMTs grow more slowly than shorter KMTs. The locations of KMT minus ends, and the turnover and movements of tubulin in KMTs, are consistent with models in which KMTs predominately nucleate de novo at kinetochores in metaphase and are inconsistent with substantial numbers of non-KMTs being recruited to the kinetochore in metaphase. Taken together, this work leads to a mathematical model of the self-organization of kinetochore-fibers in human mitotic spindles.

Helical flow states in active nematics

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.

Mechanical Torque Promotes Bipolarity of the Mitotic Spindle Through Multi-centrosomal Clustering

Intracellular forces shape cellular organization and function. One example is the mitotic spindle, a cellular machine consisting of multiple chromosomes and centrosomes which interact via dynamic microtubule filaments and motor proteins, resulting in complicated spatially dependent forces. For a cell to divide properly, it is important for the spindle to be bipolar, with chromosomes at the center and multiple centrosomes clustered into two 'poles' at opposite sides of the chromosomes. Experimental observations show that in unhealthy cells, the spindle can take on a variety of patterns. What forces drive each of these patterns? It is known that attraction between centrosomes is key to bipolarity, but what prevents the centrosomes from collapsing into a monopolar configuration? Here, we explore the hypothesis that torque rotating chromosome arms into orientations perpendicular to the centrosome-centromere vector promotes spindle bipolarity. To test this hypothesis, we construct a pairwise-interaction model of the spindle. On a continuum version of the model, an integro-PDE system, we perform linear stability analysis and construct numerical solutions which display a variety of spatial patterns. We also simulate a discrete particle model resulting in a phase diagram that confirms that the spindle bipolarity emerges most robustly with torque. Altogether, our results suggest that rotational forces may play an important role in dictating spindle patterning.

The Xenopus spindle is as dense as the surrounding cytoplasm

The mitotic spindle is a self-organizing molecular machine, where hundreds of different molecules continuously interact to maintain a dynamic steady state. While our understanding of key molecular players in spindle assembly is significant, it is still largely unknown how the spindle's material properties emerge from molecular interactions. Here, we use correlative fluorescence imaging and label-free three-dimensional optical diffraction tomography (ODT) to measure the Xenopus spindle's mass density distribution. While the spindle has been commonly referred to as a denser phase of the cytoplasm, we find that it has the same density as its surrounding, which makes it neutrally buoyant. Molecular perturbations suggest that spindle mass density can be modulated by tuning microtubule nucleation and dynamics. Together, ODT provides direct, unbiased, and quantitative information of the spindle's emergent physical properties-essential to advance predictive frameworks of spindle assembly and function.

Two dimensional automatic active shape model of degenerative disc repaired by low-intensity laser

OBJECTIVE

Intervertebral disc degeneration is the main factor causing low back pain, and the related long-term treatment can improve the situation of degeneration. This study aimed to investigate the effect of low-intensity laser irradiation on the repair of degenerative intervertebral disc by two dimensional automatic active shape model (2D-AASM).

METHODS

Nine Bama miniature pigs were randomly divided into three groups: control group (Con), model group (Mod) and laser treatment group (Las). After one month, the discs were treated with low-energy laser for another month. MRI was performed for one month, and the statistical shape model and 2D-AASM of intervertebral disc were established based on the minimum description length method.

RESULTS

The model established by the proposed method is more accurate and the segmentation result is more accurate. From the segmented T2-weighted image, the signal intensity of the Mod group decreased significantly, and the signal intensity in the Las group was moderate and high compared with the Mod group. The HE staining display the structure of Con group was damaged, and the construction of Las group was restored compared with Mod group.

CONCLUSIONS

The 2D-AASM method effectively improves the accuracy of intervertebral disc segmentation. The low-intensity laser has a protective effect on the repair of the degenerative intervertebral disc.

Mechanical Mechanisms of Chromosome Segregation

Chromosome segregation—the partitioning of genetic material into two daughter cells—is one of the most crucial processes in cell division. In all Eukaryotes, chromosome segregation is driven by the spindle, a microtubule-based, self-organizing subcellular structure. Extensive research performed over the past 150 years has identified numerous commonalities and contrasts between spindles in different systems. In this review, we use simple coarse-grained models to organize and integrate previous studies of chromosome segregation. We discuss sites of force generation in spindles and fundamental mechanical principles that any understanding of chromosome segregation must be based upon. We argue that conserved sites of force generation may interact differently in different spindles, leading to distinct mechanical mechanisms of chromosome segregation. We suggest experiments to determine which mechanical mechanism is operative in a particular spindle under study. Finally, we propose that combining biophysical experiments, coarse-grained theories, and evolutionary genetics will be a productive approach to enhance our understanding of chromosome segregation in the future.