Dynein motion switches from diffusive to directed upon cortical anchoring.

Cytoplasmic dynein is a motor protein that exerts force on microtubules. To generate force for the movement of large organelles, dynein needs to be anchored, with the anchoring sites being typically located at the cell cortex. However, the mechanism by which dyneins target sites where they can generate large collective forces is unknown. Here, we directly observe single dyneins during meiotic nuclear oscillations in fission yeast and identify the steps of the dynein binding process: from the cytoplasm to the microtubule and from the microtubule to cortical anchors. We observed that dyneins on the microtubule move either in a diffusive or directed manner, with the switch from diffusion to directed movement occurring upon binding of dynein to cortical anchors. This dual behavior of dynein on the microtubule, together with the two steps of binding, enables dyneins to self-organize into a spatial pattern needed for them to generate large collective forces.

Cortical dynein controls microtubule dynamics to generate pulling forces that position microtubule asters.

Dynein at the cortex contributes to microtubule-based positioning processes such as spindle positioning during embryonic cell division and centrosome positioning during fibroblast migration. To investigate how cortical dynein interacts with microtubule ends to generate force and how this functional association impacts positioning, we have reconstituted the 'cortical' interaction between dynein and dynamic microtubule ends in an in vitro system using microfabricated barriers. We show that barrier-attached dynein captures microtubule ends, inhibits growth, and triggers microtubule catastrophes, thereby controlling microtubule length. The subsequent interaction with shrinking microtubule ends generates pulling forces up to several pN. By combining experiments in microchambers with a theoretical description of aster mechanics, we show that dynein-mediated pulling forces lead to the reliable centering of microtubule asters in simple confining geometries. Our results demonstrate the intrinsic ability of cortical microtubule-dynein interactions to regulate microtubule dynamics and drive positioning processes in living cells.

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.

Oblique circle method for measuring the curvature and twist of mitotic spindle microtubule bundles.

The highly ordered spatial organization of microtubule bundles in the mitotic spindle is crucial for its proper functioning. The recent discovery of twisted shapes of microtubule bundles and spindle chirality suggests that the bundles extend along curved paths in three dimensions, rather than being confined to a plane. This, in turn, implies that rotational forces, i.e., torques, exist in the spindle in addition to the widely studied linear forces. However, studies of spindle architecture and forces are impeded by a lack of a robust method for the geometric quantification of microtubule bundles in the spindle. In this work, we describe a simple method for measuring and evaluating the shapes of microtubule bundles by characterizing them in terms of their curvature and twist. By using confocal microscopy, we obtain three-dimensional images of spindles, which allows us to trace the entire microtubule bundle. For each traced bundle, we first fit a plane and then fit a circle lying in that plane. With this robust method, we extract the curvature and twist, which represent the geometric information characteristic for each bundle. As the bundle shapes reflect the forces within them, this method is valuable for the understanding of forces that act on chromosomes during mitosis.

Pivoting of microtubules driven by minus-end-directed motors leads to spindle assembly.

BACKGROUND: At the beginning of mitosis, the cell forms a spindle made of microtubules and associated proteins to segregate chromosomes. An important part of spindle architecture is a set of antiparallel microtubule bundles connecting the spindle poles. A key question is how microtubules extending at arbitrary angles form an antiparallel interpolar bundle. RESULTS: Here, we show in fission yeast that microtubules meet at an oblique angle and subsequently rotate into antiparallel alignment. Our live-cell imaging approach provides a direct observation of interpolar bundle formation. By combining experiments with theory, we show that microtubules from each pole search for those from the opposite pole by performing random angular movement. Upon contact, two microtubules slide sideways along each other in a directed manner towards the antiparallel configuration. We introduce the contour length of microtubules as a measure of activity of motors that drive microtubule sliding, which we used together with observation of Cut7/kinesin-5 motors and our theory to reveal the minus-end-directed motility of this motor in vivo. CONCLUSION: Random rotational motion helps microtubules from the opposite poles to find each other and subsequent accumulation of motors allows them to generate forces that drive interpolar bundle formation.

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.

Dynein, microtubule and cargo: a ménage à trois.

To exert forces, motor proteins bind with one end to cytoskeletal filaments, such as microtubules and actin, and with the other end to the cell cortex, a vesicle or another motor. A general question is how motors search for sites in the cell where both motor ends can bind to their respective binding partners. In the present review, we focus on cytoplasmic dynein, which is required for a myriad of cellular functions in interphase, mitosis and meiosis, ranging from transport of organelles and functioning of the mitotic spindle to chromosome movements in meiotic prophase. We discuss how dynein targets sites where it can exert a pulling force on the microtubule to transport cargo inside the cell.

Self-organization of dynein motors generates meiotic nuclear oscillations.

Meiotic nuclear oscillations in the fission yeast Schizosaccharomyces pombe are crucial for proper chromosome pairing and recombination. We report a mechanism of these oscillations on the basis of collective behavior of dynein motors linking the cell cortex and dynamic microtubules that extend from the spindle pole body in opposite directions. By combining quantitative live cell imaging and laser ablation with a theoretical description, we show that dynein dynamically redistributes in the cell in response to load forces, resulting in more dynein attached to the leading than to the trailing microtubules. The redistribution of motors introduces an asymmetry of motor forces pulling in opposite directions, leading to the generation of oscillations. Our work provides the first direct in vivo observation of self-organized dynamic dynein distributions, which, owing to the intrinsic motor properties, generate regular large-scale movements in the cell.

Kinetochore- and chromosome-driven transition of microtubules into bundles promotes spindle assembly.

Mitotic spindle assembly is crucial for chromosome segregation and relies on bundles of microtubules that extend from the poles and overlap in the middle. However, how these structures form remains poorly understood. Here we show that overlap bundles arise through a network-to-bundles transition driven by kinetochores and chromosomes. STED super-resolution microscopy reveals that PRC1-crosslinked microtubules initially form loose arrays, which become rearranged into bundles. Kinetochores promote microtubule bundling by lateral binding via CENP-E/kinesin-7 in an Aurora B-regulated manner. Steric interactions between the bundle-associated chromosomes at the spindle midplane drive bundle separation and spindle widening. In agreement with experiments, theoretical modeling suggests that bundles arise through competing attractive and repulsive mechanisms. Finally, perturbation of overlap bundles leads to inefficient correction of erroneous kinetochore-microtubule attachments. Thus, kinetochores and chromosomes drive coarsening of a uniform microtubule array into overlap bundles, which promote not only spindle formation but also chromosome segregation fidelity.

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.

Mitotic spindle: lessons from theoretical modeling.

Cell biology is immensely complex. To understand how cells work, we try to find patterns and suggest hypotheses to identify underlying mechanisms. However, it is not always easy to create a coherent picture from a huge amount of experimental data on biological systems, where the main players have multiple interactions or act in redundant pathways. In such situations, when a hypothesis does not lead to a conclusion in a direct way, theoretical modeling is a powerful tool because it allows us to formulate hypotheses in a quantitative manner and understand their consequences. A successful model should not only reproduce the basic features of the system but also provide exciting predictions, motivating new experiments. Much is learned when a model based on generally accepted knowledge cannot explain experiments of interest, as this indicates that the original hypothesis needs to be revised. In this Perspective, we discuss these points using our experiences in combining experiments with theory in the field of mitotic spindle mechanics.

Mechanobiology of the Mitotic Spindle.

The mitotic spindle is a microtubule-based assembly that separates the chromosomes during cell division. As the spindle is basically a mechanical micro machine, the understanding of its functioning is constantly motivating the development of experimental approaches based on mechanical perturbations, which are complementary to and work together with the classical genetics and biochemistry methods. Recent data emerging from these approaches in combination with theoretical modeling led to novel ideas and significant revisions of the basic concepts in the field. In this Perspective, we discuss the advances in the understanding of spindle mechanics, focusing on microtubule forces that control chromosome movements.

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.

Collective behavior of antagonistically acting kinesin-1 motors.

In many subcellular force-generating systems, groups of motor proteins act antagonistically. Here, we present an experimental study of the tug of war between superprocessive kinesin-1 motors acting on antiparallel microtubule doublets in vitro. We found distinct modes of slow and fast movements, as well as sharp transitions between these modes and regions of coexistence. We compare our experimental results to a quantitative theory based on the physical properties of individual motors. Our results show that mechanical interactions between motors can collectively generate coexisting transport regimes with distinct velocities.

Helical Twist and Rotational Forces in the Mitotic Spindle.

The mitotic spindle segregates chromosomes into two daughter cells during cell division. This process relies on the precise regulation of forces acting on chromosomes as the cell progresses through mitosis. The forces in the spindle are difficult to directly measure using the available experimental techniques. Here, we review the ideas and recent advances of how forces can be determined from the spindle shape. By using these approaches, it has been shown that tension and compression coexist along a single kinetochore fiber, which are balanced by a bridging fiber between sister kinetochore fibers. An extension of this approach to three dimensions revealed that microtubule bundles have rich shapes, and extend not simply like meridians on the Earth's surface but, rather, twisted in a helical manner. Such complex shapes are due to rotational forces, which, in addition to linear forces, act in the spindle and may be generated by motor proteins such as kinesin-5. These findings open new questions for future studies, to understand the mechanisms of rotational forces and reveal their biological roles in cells.

Pivot-and-bond model explains microtubule bundle formation.

During mitosis, microtubules form a spindle, which is responsible for proper segregation of the genetic material. A common structural element in a mitotic spindle is a parallel bundle, consisting of two or more microtubules growing from the same origin and held together by cross-linking proteins. An interesting question is what are the physical principles underlying the formation and stability of such microtubule bundles. Here we show, by introducing the pivot-and-bond model, that random angular movement of microtubules around the spindle pole and forces exerted by cross-linking proteins can explain the formation of microtubule bundles as observed in our experiments. The model predicts that stable parallel bundles can form in the presence of either passive crosslinkers or plus-end directed motors, but not minus-end directed motors. In the cases where bundles form, the time needed for their formation depends mainly on the concentration of cross-linking proteins and the angular diffusion of the microtubule. In conclusion, the angular motion drives the alignment of microtubules, which in turn allows the cross-linking proteins to connect the microtubules into a stable bundle.

Hierarchical structure of cascade of primary and secondary periodicities in Fourier power spectrum of alphoid higher order repeats.

BACKGROUND: Identification of approximate tandem repeats is an important task of broad significance and still remains a challenging problem of computational genomics. Often there is no single best approach to periodicity detection and a combination of different methods may improve the prediction accuracy. Discrete Fourier transform (DFT) has been extensively used to study primary periodicities in DNA sequences. Here we investigate the application of DFT method to identify and study alphoid higher order repeats. RESULTS: We used method based on DFT with mapping of symbolic into numerical sequence to identify and study alphoid higher order repeats (HOR). For HORs the power spectrum shows equidistant frequency pattern, with characteristic two-level hierarchical organization as signature of HOR. Our case study was the 16 mer HOR tandem in AC017075.8 from human chromosome 7. Very long array of equidistant peaks at multiple frequencies (more than a thousand higher harmonics) is based on fundamental frequency of 16 mer HOR. Pronounced subset of equidistant peaks is based on multiples of the fundamental HOR frequency (multiplication factor n for nmer) and higher harmonics. In general, nmer HOR-pattern contains equidistant secondary periodicity peaks, having a pronounced subset of equidistant primary periodicity peaks. This hierarchical pattern as signature for HOR detection is robust with respect to monomer insertions and deletions, random sequence insertions etc. For a monomeric alphoid sequence only primary periodicity peaks are present. The 1/fbeta- noise and periodicity three pattern are missing from power spectra in alphoid regions, in accordance with expectations. CONCLUSION: DFT provides a robust detection method for higher order periodicity. Easily recognizable HOR power spectrum is characterized by hierarchical two-level equidistant pattern: higher harmonics of the fundamental HOR-frequency (secondary periodicity) and a subset of pronounced peaks corresponding to constituent monomers (primary periodicity). The number of lower frequency peaks (secondary periodicity) below the frequency of the first primary periodicity peak reveals the size of nmer HOR, i.e., the number n of monomers contained in consensus HOR.

Spindle Dynamics Model Explains Chromosome Loss Rates in Yeast Polyploid Cells.

Faithful chromosome segregation, driven by the mitotic spindle, is essential for organismal survival. Neopolyploid cells from diverse species exhibit a significant increase in mitotic errors relative to their diploid progenitors, resulting in chromosome nondisjunction. In the model system Saccharomyces cerevisiae, the rate of chromosome loss in haploid and diploid cells is measured to be one thousand times lower than the rate of loss in isogenic tetraploid cells. Currently it is unknown what constrains the number of chromosomes that can be segregated with high fidelity in an organism. Here we developed a simple mathematical model to study how different rates of chromosome loss in cells with different ploidy can arise from changes in (1) spindle dynamics and (2) a maximum duration of mitotic arrest, after which cells enter anaphase. We apply this model to S. cerevisiae to show that this model can explain the observed rates of chromosome loss in S. cerevisiae cells of different ploidy. Our model describes how small increases in spindle assembly time can result in dramatic differences in the rate of chromosomes loss between cells of increasing ploidy and predicts the maximum duration of mitotic arrest.

Metaphase kinetochore movements are regulated by kinesin-8 motors and microtubule dynamic instability.

During metaphase, sister chromatids are connected to microtubules extending from the opposite spindle poles via kinetochores to protein complexes on the chromosome. Kinetochores congress to the equatorial plane of the spindle and oscillate around it, with kinesin-8 motors restricting these movements. Yet, the physical mechanism underlying kinetochore movements is unclear. We show that kinetochore movements in the fission yeast Schizosaccharomyces pombe are regulated by kinesin-8-promoted microtubule catastrophe, force-induced rescue, and microtubule dynamic instability. A candidate screen showed that among the selected motors only kinesin-8 motors Klp5/Klp6 are required for kinetochore centering. Kinesin-8 accumulates at the end of microtubules, where it promotes catastrophe. Laser ablation of the spindle resulted in kinetochore movement toward the intact spindle pole in wild-type and klp5Δ cells, suggesting that kinetochore movement is driven by pulling forces. Our theoretical model with Langevin description of microtubule dynamic instability shows that kinesin-8 motors are required for kinetochore centering, whereas sensitivity of rescue to force is necessary for the generation of oscillations. We found that irregular kinetochore movements occur for a broader range of parameters than regular oscillations. Thus, our work provides an explanation for how regulation of microtubule dynamic instability contributes to kinetochore congression and the accompanying movements around the spindle center.

The mitotic spindle is chiral due to torques within microtubule bundles.

Mitosis relies on forces generated in the spindle, a micro-machine composed of microtubules and associated proteins. Forces are required for the congression of chromosomes to the metaphase plate and their separation in anaphase. However, besides forces, torques may exist in the spindle, yet they have not been investigated. Here we show that the spindle is chiral. Chirality is evident from the finding that microtubule bundles in human spindles follow a left-handed helical path, which cannot be explained by forces but rather by torques. Kinesin-5 (Kif11/Eg5) inactivation abolishes spindle chirality. Our theoretical model predicts that bending and twisting moments may generate curved shapes of bundles. We found that bundles turn by about -2 deg µm-1 around the spindle axis, which we explain by a twisting moment of roughly -10 pNµm. We conclude that torques, in addition to forces, exist in the spindle and determine its chiral architecture.