A stochastic model of kinetochore-microtubule attachment accurately describes fission yeast chromosome segregation

Microtubule search-and-capture model evaluates the effect of chromosomal volume conservation on spindle assembly during mitosis

Variation in the chromosome numbers can arise from the erroneous mitosis or fusion and fission of chromosomes. While the mitotic errors lead to an increase or decrease in the overall chromosomal substance in the daughter cells, fission and fusion keep this conserved. Variations in chromosome numbers are assumed to be a crucial driver of speciation. For example, the members of the muntjac species are known to have very different karyotypes with the chromosome numbers varying from 2n=70+3B in the brown brocket deer to 2n=46 in the Chinese muntjac and 2n=6/7 in the Indian muntjac. The chromosomal content in the nucleus of these closely related mammals is roughly the same and various chromosome fusion and fission pathways have been suggested as the evolution process of these karyotypes. Similar trends can also be found in lepidoptera and yeast species which show a wide variation of chromosome numbers. The effect of chromosome number variation on the spindle assembly time and accuracy is still not properly addressed. We computationally investigate the effect of conservation of the total chromosomal substance on the spindle assembly during prometaphase. Our results suggest that chromosomal fusion pathways aid the microtubule-driven search and capture of the kinetochore in cells with monocentric chromosomes. We further report a comparative analysis of the site and percentage of amphitelic captures, dependence on cell shape, and position of the kinetochore in respect to chromosomal volume partitioning.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Strain stiffening of Ndc80 complexes attached to microtubule plus ends

In the mitotic spindle, microtubules attach to chromosomes via kinetochores. The microtubule-binding Ndc80 complex is an integral part of kinetochores, and is essential for kinetochores to attach to microtubules and to transmit forces from dynamic microtubule ends to the chromosomes. The Ndc80 complex has a rod-like appearance with globular domains at its ends that are separated by a long coiled coil. Its mechanical properties are considered important for the dynamic interaction between kinetochores and microtubules. Here, we present a novel method that allows us to time trace the effective stiffness of Ndc80 complexes following shortening microtubule ends against applied force in optical trap experiments. Applying this method to wild-type Ndc80 and three variants (calponin homology (CH) domains mutated or Hec1 tail unphosphorylated, phosphorylated, or truncated), we reveal that each variant exhibits strain stiffening; i.e., the effective stiffness increases under tension that is built up by a depolymerizing microtubule. The strain stiffening relation is roughly linear and independent of the state of the microtubule. We introduce structure-based models that show that the strain stiffening can be traced back to the specific architecture of the Ndc80 complex with a characteristic flexible kink, to thermal fluctuations of the microtubule, and to the bending elasticity of flaring protofilaments, which exert force to move the Ndc80 complexes. Our model accounts for changes in the amount of load-bearing attachments at various force levels and reproduces the roughly linear strain stiffening behavior, highlighting the importance of force-dependent binding affinity.

CellDynaMo–stochastic reaction-diffusion-dynamics model: Application to search-and-capture process of mitotic spindle assembly

We introduce a Stochastic Reaction-Diffusion-Dynamics Model (SRDDM) for simulations of cellular mechanochemical processes with high spatial and temporal resolution. The SRDDM is mapped into the CellDynaMo package, which couples the spatially inhomogeneous reaction-diffusion master equation to account for biochemical reactions and molecular transport within the Langevin Dynamics (LD) framework to describe dynamic mechanical processes. This computational infrastructure allows the simulation of hours of molecular machine dynamics in reasonable wall-clock time. We apply SRDDM to test performance of the Search-and-Capture of mitotic spindle assembly by simulating, in three spatial dimensions, dynamic instability of elastic microtubules anchored in two centrosomes, movement and deformations of geometrically realistic centromeres with flexible kinetochores and chromosome arms. Furthermore, the SRDDM describes the mechanics and kinetics of Ndc80 linkers mediating transient attachments of microtubules to the chromosomal kinetochores. The rates of these attachments and detachments depend upon phosphorylation states of the Ndc80 linkers, which are regulated in the model by explicitly accounting for the reactions of Aurora A and B kinase enzymes undergoing restricted diffusion. We find that there is an optimal rate of microtubule-kinetochore detachments which maximizes the accuracy of the chromosome connections, that adding chromosome arms to kinetochores improve the accuracy by slowing down chromosome movements, that Aurora A and kinetochore deformations have a small positive effect on the attachment accuracy, and that thermal fluctuations of the microtubules increase the rates of kinetochore capture and also improve the accuracy of spindle assembly.

The CellDynaMo package models, in 3D, any cellular subsystem where sufficient detail of the macromolecular players and the kinetics of relevant reactions are available. The package is based on the Stochastic Reaction-Diffusion-Dynamics model that combines the stochastic description of chemical kinetics, Brownian diffusion-based description of molecular transport, and Langevin dynamics-based representation of mechanical processes most pertinent to the system. We apply the model to test the Search-and-Capture mechanism of mitotic spindle assembly. We find that there is an optimal rate of microtubule-kinetochore detachments which maximizes the accuracy of chromosome connections, that chromosome arms improve the attachment accuracy by slowing down chromosome movements, that Aurora A kinase and kinetochore deformations have small positive effects on the accuracy, and that thermal fluctuations of the microtubules increase the rates of kinetochore capture and also improve the accuracy.

Counteraction between Astrin-PP1 and Cyclin-B-CDK1 pathways protects chromosome-microtubule attachments independent of biorientation

Defects in chromosome-microtubule attachment can cause chromosomal instability (CIN), frequently associated with infertility and aggressive cancers. Chromosome-microtubule attachment is mediated by a large macromolecular structure, the kinetochore. Sister kinetochores of each chromosome are pulled by microtubules from opposing spindle-poles, a state called biorientation which prevents chromosome missegregation. Kinetochore-microtubule attachments that lack the opposing-pull are detached by Aurora-B/Ipl1. It is unclear how mono-oriented attachments that precede biorientation are spared despite the lack of opposing-pull. Using an RNAi-screen, we uncover a unique role for the Astrin-SKAP complex in protecting mono-oriented attachments. We provide evidence of domains in the microtubule-end associated protein that sense changes specific to end-on kinetochore-microtubule attachments and assemble an outer-kinetochore crescent to stabilise attachments. We find that Astrin-PP1 and Cyclin-B-CDK1 pathways counteract each other to preserve mono-oriented attachments. Thus, CIN prevention pathways are not only surveying attachment defects but also actively recognising and stabilising mature attachments independent of biorientation.

Chromosome instability frequently occurs due to issues with chromosome-microtubule attachments. Here the authors show that the Astrin-PP1 and Cyclin-B-CDK1 pathways counteract each other to protect chromosome-microtubule attachments independent of biorientation.

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.

A mathematical model of kinetochore-microtubule attachment regulated by Aurora A activity gradient describes chromosome oscillation and correction of erroneous attachments

Chromosome oscillation during metaphase is attenuated in cancer cell lines, concomitant with the reduction of Aurora A activity on kinetochores, which results in reduced mitotic fidelity. To verify the correlation between Aurora A activity, chromosome oscillation, and error correction efficiency, we developed a mathematical model of kinetochore-microtubule dynamics, based on stochastic attachment/detachment events regulated by Aurora A activity gradient centered at spindle poles. The model accurately reproduced the oscillatory movements of chromosomes, which were suppressed not only when Aurora A activity was inhibited, but also when it was upregulated, mimicking the situation in cancer cells. Our simulation also predicted efficient correction of erroneous attachments through chromosome oscillation, which was hampered by both inhibition and upregulation of Aurora A activity. Our model provides a framework to understand the physiological role of chromosome oscillation in the correction of erroneous attachments that is intrinsically related to Aurora A activity.

Attenuated Chromosome Oscillation as a Cause of Chromosomal Instability in Cancer Cells

Simple Summary

Chromosomal instability (CIN), a condition in which chromosome missegregation occurs at high rates, is widely seen in cancer cells. Causes of CIN in cancer cells are not fully understood. A recent report suggests that chromosome oscillation, an iterative chromosome motion typically seen in metaphase around the spindle equator, is attenuated in cancer cells, and is associated with CIN. Chromosome oscillation promotes the correction of erroneous kinetochore-microtubule attachments through phosphorylation of Hec1, a kinetochore protein that binds to microtubules, by Aurora A kinase residing on the spindle. In this review, we focused on this unappreciated link between chromosome oscillation and CIN.

Abstract

Chromosomal instability (CIN) is commonly seen in cancer cells, and related to tumor progression and poor prognosis. Among the causes of CIN, insufficient correction of erroneous kinetochore (KT)-microtubule (MT) attachments plays pivotal roles in various situations. In this review, we focused on the previously unappreciated role of chromosome oscillation in the correction of erroneous KT-MT attachments, and its relevance to the etiology of CIN. First, we provided an overview of the error correction mechanisms for KT-MT attachments, especially the role of Aurora kinases in error correction by phosphorylating Hec1, which connects MT to KT. Next, we explained chromosome oscillation and its underlying mechanisms. Then we introduced how chromosome oscillation is involved in the error correction of KT-MT attachments, based on recent findings. Chromosome oscillation has been shown to promote Hec1 phosphorylation by Aurora A which localizes to the spindle. Finally, we discussed the link between attenuated chromosome oscillation and CIN in cancer cells. This link underscores the role of chromosome dynamics in mitotic fidelity, and the mutual relationship between defective chromosome dynamics and CIN in cancer cells that can be a target for cancer therapy.

Aurora B Tension Sensing Mechanisms in the Kinetochore Ensure Accurate Chromosome Segregation

The accurate segregation of chromosomes is essential for the survival of organisms and cells. Mistakes can lead to aneuploidy, tumorigenesis and congenital birth defects. The spindle assembly checkpoint ensures that chromosomes properly align on the spindle, with sister chromatids attached to microtubules from opposite poles. Here, we review how tension is used to identify and selectively destabilize incorrect attachments, and thus serves as a trigger of the spindle assembly checkpoint to ensure fidelity in chromosome segregation. Tension is generated on properly attached chromosomes as sister chromatids are pulled in opposing directions but resisted by centromeric cohesin. We discuss the role of the Aurora B kinase in tension-sensing and explore the current models for translating mechanical force into Aurora B-mediated biochemical signals that regulate correction of chromosome attachments to the spindle.

Shake It Off: The Elimination of Erroneous Kinetochore-Microtubule Attachments and Chromosome Oscillation

Cell proliferation and sexual reproduction require the faithful segregation of chromosomes. Chromosome segregation is driven by the interaction of chromosomes with the spindle, and the attachment of chromosomes to the proper spindle poles is essential. Initial attachments are frequently erroneous due to the random nature of the attachment process; however, erroneous attachments are selectively eliminated. Proper attachment generates greater tension at the kinetochore than erroneous attachments, and it is thought that attachment selection is dependent on this tension. However, studies of meiotic chromosome segregation suggest that attachment elimination cannot be solely attributed to tension, and the precise mechanism of selective elimination of erroneous attachments remains unclear. During attachment elimination, chromosomes oscillate between the spindle poles. A recent study on meiotic chromosome segregation in fission yeast has suggested that attachment elimination is coupled to chromosome oscillation. In this review, the possible contribution of chromosome oscillation in the elimination of erroneous attachment is discussed in light of the recent finding.

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.

Chiasmata and the kinetochore component Dam1 are crucial for elimination of erroneous chromosome attachments and centromere oscillation at meiosis I

Establishment of proper chromosome attachments to the spindle requires elimination of erroneous attachments, but the mechanism of this process is not fully understood. During meiosis I, sister chromatids attach to the same spindle pole (mono-oriented attachment), whereas homologous chromosomes attach to opposite poles (bi-oriented attachment), resulting in homologous chromosome segregation. Here, we show that chiasmata that link homologous chromosomes and kinetochore component Dam1 are crucial for elimination of erroneous attachments and oscillation of centromeres between the spindle poles at meiosis I in fission yeast. In chiasma-forming cells, Mad2 and Aurora B kinase, which provides time for attachment correction and destabilizes erroneous attachments, respectively, caused elimination of bi-oriented attachments of sister chromatids, whereas in chiasma-lacking cells, they caused elimination of mono-oriented attachments. In chiasma-forming cells, in addition, homologous centromere oscillation was coordinated. Furthermore, Dam1 contributed to attachment elimination in both chiasma-forming and chiasma-lacking cells, and drove centromere oscillation. These results demonstrate that chiasmata alter attachment correction patterns by enabling error correction factors to eliminate bi-oriented attachment of sister chromatids, and suggest that Dam1 induces elimination of erroneous attachments. The coincidental contribution of chiasmata and Dam1 to centromere oscillation also suggests a potential link between centromere oscillation and attachment elimination.

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.

A stochastic model for error correction of kinetochore-microtubule attachments in budding yeast

To divide replicated chromosomes equally between daughter cells, kinetochores must attach to microtubules emanating from opposite poles of the mitotic spindle (biorientation). An error correction mechanism facilitates this process by destabilizing erroneous kinetochore-microtubule attachments. Here we present a stochastic model of kinetochore-microtubule attachments, via an essential protein Ndc80 in budding yeast, Saccharomyces cerevisiae. Using the model, we calculate the stochastic dynamics of a pair of sister kinetochores as they transition among different attachment states. First of all, we determine the kinase-to-phosphatase balance point that maximizes the probability of biorientation, while starting from an erroneous attachment state. We find that the balance point is sensitive to the rates of microtubule-Ndc80 dissociation and derive an approximate analytical formula that defines the balance point. Secondly, we determine the probability of transition from low-tension amphitelic to monotelic attachment and find that, despite this probability being approximately 33%, biorientation can be achieved with high probability. Thirdly, we calculate the contribution of the geometrical orientation of sister kinetochores to the probability of biorientation and show that, in the absence of geometrical orientation, the biorientation error rate is much larger than that observed in experiments. Finally, we study the coupling of the error correction mechanism to the spindle assembly checkpoint by calculating the average binding of checkpoint-related proteins to the kinetochore during the error correction process.

Mechanics of Multicentrosomal Clustering in Bipolar Mitotic Spindles

To segregate chromosomes in mitosis, cells assemble a mitotic spindle, a molecular machine with centrosomes at two opposing cell poles and chromosomes at the equator. Microtubules and molecular motors connect the poles to kinetochores, specialized protein assemblies on the centromere regions of the chromosomes. Bipolarity of the spindle is crucial for the proper cell division, and two centrosomes in animal cells naturally become two spindle poles. Cancer cells are often multicentrosomal, yet they are able to assemble bipolar spindles by clustering centrosomes into two spindle poles. Mechanisms of this clustering are debated. In this study, we computationally screen effective forces between 1) centrosomes, 2) centrosomes and kinetochores, 3) centrosomes and chromosome arms, and 4) centrosomes and cell cortex to understand mechanics that determines three-dimensional spindle architecture. To do this, we use the stochastic Monte Carlo search for stable mechanical equilibria in the effective energy landscape of the spindle. We find that the following conditions have to be met to robustly assemble the bipolar spindle in a multicentrosomal cell: 1) the strengths of centrosomes' attraction to each other and to the cell cortex have to be proportional to each other and 2) the strengths of centrosomes' attraction to kinetochores and repulsion from the chromosome arms have to be proportional to each other. We also find that three other spindle configurations emerge if these conditions are not met: 1) collapsed, 2) monopolar, and 3) multipolar spindles, and the computational screen reveals mechanical conditions for these abnormal spindles.

Aurora B and condensin are dispensable for chromosome arm and telomere separation during meiosis II

In mitosis, while the importance of kinetochore (KT)-microtubule (MT) attachment has been known for many years, increasing evidence suggests that telomere dysfunctions also perturb chromosome segregation by contributing to the formation of chromatin bridges at anaphase. Recent evidence suggests that Aurora B kinase ensures proper chromosome segregation during mitosis not only by controlling KT-MT attachment but also by regulating telomere and chromosome arm separation. However, whether and how Aurora B governs telomere separation during meiosis has remained unknown. Here, we show that fission yeast Aurora B localizes at telomeres during meiosis I and promotes telomere separation independently of the meiotic cohesin Rec8. In meiosis II, Aurora B controls KT-MT attachment but appears dispensable for telomere and chromosome arm separation. Likewise, condensin activity is nonessential in meiosis II for telomere and chromosome arm separation. Thus, in meiosis, the requirements for Aurora B are distinct at centromeres and telomeres, illustrating the critical differences in the control of chromosome segregation between mitosis and meiosis II.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

Before a cell divides, it must make a copy of its genetic material and then promptly split in two. This process, called mitosis, is coordinated by many different molecular machines. The DNA is copied, then the duplicated chromosomes line up at the middle of the cell. Next, an apparatus called the mitotic spindle latches onto the chromosomes before pulling them apart. The mitotic spindle is a bundle of long, thin filaments called microtubules. It attaches to chromosomes at the kinetochore, the point where two copied chromosomes are cinched together in their middle.

Proper cell division is vital for the healthy growth of all organisms, big and small, and yet some parts of the process remain poorly understood despite extensive study. Specifically, there is more to learn about how the mitotic spindle self-assembles, and how microtubules and kinetochores work together to correctly orient and segregate chromosomes into two sister cells. These nanoscale processes are happening a hundred times a minute, so computer simulations are a good way to test what we know.

Edelmaier et al. developed a computer model to simulate cell division in fission yeast, a species of yeast often used to study fundamental processes in the cell. The model simulates how the mitotic spindle assembles, how its microtubules attach to the kinetochore and the force required to pull two sister chromosomes apart. Building the simulation involved modelling interactions between the mitotic spindle and kinetochore, their movement and forces applied. To test its accuracy, model simulations were compared to recordings of the mitotic spindle – including its length, structure and position – imaged from dividing yeast cells.

Running the simulation, Edelmaier et al. found that several key effects are essential for the proper movement of chromosomes in mitosis. This includes holding chromosomes in the correct orientation as the mitotic spindle assembles and controlling the relative position of microtubules as they attach to the kinetochore. Misaligned attachments must also be readily deconstructed and corrected to prevent any errors. The simulations also showed that kinetochores must begin to exert more force (to separate the chromosomes) once the mitotic spindle is attached correctly.

Altogether, these findings improve the current understanding of how the mitotic spindle and its counterparts control cell division. Errors in chromosome segregation are associated with birth defects and cancer in humans, and this new simulation could potentially now be used to help make predictions about how to correct mistakes in the process.

Centromere mechanical maturation during mammalian cell mitosis

During mitosis, tension develops across the centromere as a result of spindle-based forces. Metaphase tension may be critical in preventing mitotic chromosome segregation errors, however, the nature of force transmission at the centromere and the role of centromere mechanics in controlling metaphase tension remains unknown. We combined quantitative, biophysical microscopy with computational analysis to elucidate the mechanics of the centromere in unperturbed, mitotic human cells. We discovered that the mechanical stiffness of the human centromere matures during mitotic progression, which leads to amplified centromere tension specifically at metaphase. Centromere mechanical maturation is disrupted across multiple aneuploid cell lines, leading to a weak metaphase tension signal. Further, increasing deficiencies in centromere mechanical maturation are correlated with rising frequencies of lagging, merotelic chromosomes in anaphase, leading to segregation defects at telophase. Thus, we reveal a centromere maturation process that may be critical to the fidelity of chromosome segregation during mitosis.

During mitosis, tension at the centromere occurs from the spindle but the role of centromere mechanics in controlling metaphase tension is poorly understood. Here, the authors report that mechanical stiffnness of the centromere matures during mitotic progression and is amplified specifically at metaphase.

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.

Stochastic Modeling Yields a Mechanistic Framework for Spindle Attachment Error Correction in Budding Yeast Mitosis

Proper segregation of the replicated genome requires that kinetochores form and maintain bioriented, amphitelic attachments to microtubules from opposite spindle poles and eliminate erroneous, syntelic attachments to microtubules from the same spindle pole. Phosphorylation of kinetochore proteins destabilizes low-tension kinetochore-microtubule attachments, yet tension stabilizes bioriented attachments. This conundrum for forming high-tension amphitelic attachments is recognized as the "initiation problem of biorientation (IPBO)." A delay before kinetochore-microtubule detachment solves the IPBO, but it lacks a mechanistic framework. We developed a stochastic mathematical model for kinetochore-microtubule error correction in yeast that reveals: (1) under low chromatin tension, requiring a large number of phosphorylation events at multiple sites to achieve detachment provides the necessary delay; and (2) kinetochore-induced microtubule depolymerization generates tension in amphitelic, but not syntelic, attachments. With these requirements, the model provides a mechanistic framework for the delay before detachment to solve the IPBO and demonstrates the high degree of amphitely observed experimentally for wild-type spindles under optimal conditions.

MAARS: a novel high-content acquisition software for the analysis of mitotic defects in fission yeast

Faithful segregation of chromosomes during cell division relies on multiple processes such as chromosome attachment and correct spindle positioning. Yet mitotic progression is defined by multiple parameters, which need to be quantitatively evaluated. To study the spatiotemporal control of mitotic progression, we developed a high-content analysis (HCA) approach that combines automated fluorescence microscopy with real-time quantitative image analysis and allows the unbiased acquisition of multiparametric data at the single-cell level for hundreds of cells simultaneously. The Mitotic Analysis and Recording System (MAARS) provides automatic and quantitative single-cell analysis of mitotic progression on an open-source platform. It can be used to analyze specific characteristics such as cell shape, cell size, metaphase/anaphase delays, and mitotic abnormalities including spindle mispositioning, spindle elongation defects, and chromosome segregation defects. Using this HCA approach, we were able to visualize rare and unexpected events of error correction during anaphase in wild-type or mutant cells. Our study illustrates that such an expert system of mitotic progression is able to highlight the complexity of the mechanisms required to prevent chromosome loss during cell division.

Physical determinants of bipolar mitotic spindle assembly and stability in fission yeast

Mitotic spindles use an elegant bipolar architecture to segregate duplicated chromosomes with high fidelity. Bipolar spindles form from a monopolar initial condition; this is the most fundamental construction problem that the spindle must solve. Microtubules, motors, and cross-linkers are important for bipolarity, but the mechanisms necessary and sufficient for spindle assembly remain unknown. We describe a physical model that exhibits de novo bipolar spindle formation. We began with physical properties of fission-yeast spindle pole body size and microtubule number, kinesin-5 motors, kinesin-14 motors, and passive cross-linkers. Our model results agree quantitatively with our experiments in fission yeast, thereby establishing a minimal system with which to interrogate collective self-assembly. By varying the features of our model, we identify a set of functions essential for the generation and stability of spindle bipolarity. When kinesin-5 motors are present, their bidirectionality is essential, but spindles can form in the presence of passive cross-linkers alone. We also identify characteristic failed states of spindle assembly-the persistent monopole, X spindle, separated asters, and short spindle, which are avoided by the creation and maintenance of antiparallel microtubule overlaps. Our model can guide the identification of new, multifaceted strategies to induce mitotic catastrophes; these would constitute novel strategies for cancer chemotherapy.

A mathematical model of Aurora B activity in prophase and metaphase

Aurora B kinase is a protein that controls several processes in mitosis when it is found associated with INCENP, Survivin and Borealin in a complex known as the Chromosomal Passenger Complex. Aurora B in complex with INCENP is phosphorylated on three sites, resulting in the full activation of Aurora B. In prophase and metaphase, Aurora B is activated at centromeres, the region of chromatin linking sister chromatids, due to an autophosphorylation mechanism, and it has been hypothesised that Aurora B is activated throughout the cytoplasm due to its concentration at centromeres. In this article, we first develop a time-dependent model of Aurora B activation that does not incorporate spatial variation. This model is used to demonstrate the various qualitative behaviours that the activation of Aurora B is capable of displaying for different model parameters. Next, we develop a spatio-temporal model of Aurora B activation that includes diffusion of soluble Aurora B and binding of Aurora B to immobile centromeric binding sites. This model describes the activation of Aurora B throughout the cytoplasm due to its concentration-dependent activation at centromeres. The models demonstrate the effects that a soluble phosphatase concentration, multisite phosphorylation and diffusion have on the activation of Aurora B.

Kinesin-8 effects on mitotic microtubule dynamics contribute to spindle function in fission yeast

Kinesin-8 motor proteins destabilize microtubules and increase chromosome loss in mitosis. In fission yeast, aberrant microtubule-driven kinetochore pushing movements, tripolar mitotic spindles, and fluctuations in metaphase spindle length occurred in kinesin-8–deletion mutants. A mathematical model can explain these results.

Kinesin-8 motor proteins destabilize microtubules. Their absence during cell division is associated with disorganized mitotic chromosome movements and chromosome loss. Despite recent work studying effects of kinesin-8s on microtubule dynamics, it remains unclear whether the kinesin-8 mitotic phenotypes are consequences of their effect on microtubule dynamics, their well-established motor activity, or additional, unknown functions. To better understand the role of kinesin-8 proteins in mitosis, we studied the effects of deletion of the fission yeast kinesin-8 proteins Klp5 and Klp6 on chromosome movements and spindle length dynamics. Aberrant microtubule-driven kinetochore pushing movements and tripolar mitotic spindles occurred in cells lacking Klp5 but not Klp6. Kinesin-8–deletion strains showed large fluctuations in metaphase spindle length, suggesting a disruption of spindle length stabilization. Comparison of our results from light microscopy with a mathematical model suggests that kinesin-8–induced effects on microtubule dynamics, kinetochore attachment stability, and sliding force in the spindle can explain the aberrant chromosome movements and spindle length fluctuations seen.

Cutting edge science: Laser surgery illuminates viscoelasticity of merotelic kinetochores

Increasing evidence in eukaryotic cells suggests that mechanical forces are essential for building a robust mitotic apparatus and correcting inappropriate chromosome attachments. In this issue, Cojoc et al. (2016. J. Cell Biol., http://dx.doi.org/10.1083/jcb.201506011) use laser microsurgery in vivo to measure and study the viscoelastic properties of kinetochores.

Aurora B kinase controls the separation of centromeric and telomeric heterochromatin

The segregation of chromosomes is coordinated at multiple levels to prevent chromosome loss, a phenotype frequently observed in cancers. We recently described an essential role for telomeres in the physical separation of chromosomes and identified Aurora B kinase as a double agent involved in the separation of centromeric and telomeric heterochromatin.

Fission yeast kinesin-8 controls chromosome congression independently of oscillations

In higher eukaryotes, efficient chromosome congression relies, among other players, on the activity of chromokinesins. Here, we provide a quantitative analysis of kinetochore oscillations and positioning in Schizosaccharomyces pombe, a model organism lacking chromokinesins. In wild-type cells, chromosomes align during prophase and, while oscillating, maintain this alignment throughout metaphase. Chromosome oscillations are dispensable both for kinetochore congression and stable kinetochore alignment during metaphase. In higher eukaryotes, kinesin-8 family members control chromosome congression by regulating their oscillations. By contrast, here, we demonstrate that fission yeast kinesin-8 controls chromosome congression by an alternative mechanism. We propose that kinesin-8 aligns chromosomes by controlling pulling forces in a length-dependent manner. A coarse-grained model of chromosome segregation implemented with a length-dependent process that controls the force at kinetochores is necessary and sufficient to mimic kinetochore alignment, and prevents the appearance of lagging chromosomes. Taken together, these data illustrate how the local action of a motor protein at kinetochores provides spatial cues within the spindle to align chromosomes and to prevent aneuploidy.

Highlighted Article: Quantitative analysis in S. pombe reveals that chromosome oscillations are dispensable for kinetochore congression in mitosis. Kinesin-8 controls chromosome congression through length-dependent pulling forces.

Accurate chromosome segregation by probabilistic self-organisation

Background

For faithful chromosome segregation during cell division, correct attachments must be established between sister chromosomes and microtubules from opposite spindle poles through kinetochores (chromosome bi-orientation). Incorrect attachments of kinetochore microtubules (kMTs) lead to chromosome mis-segregation and aneuploidy, which is often associated with developmental abnormalities such as Down syndrome and diseases including cancer. The interaction between kinetochores and microtubules is highly dynamic with frequent attachments and detachments. However, it remains unclear how chromosome bi-orientation is achieved with such accuracy in such a dynamic process.

Results

To gain new insight into this essential process, we have developed a simple mathematical model of kinetochore–microtubule interactions during cell division in general, i.e. both mitosis and meiosis. Firstly, the model reveals that the balance between attachment and detachment probabilities of kMTs is crucial for correct chromosome bi-orientation. With the right balance, incorrect attachments are resolved spontaneously into correct bi-oriented conformations while an imbalance leads to persistent errors. In addition, the model explains why errors are more commonly found in the first meiotic division (meiosis I) than in mitosis and how a faulty conformation can evade the spindle assembly checkpoint, which may lead to a chromosome loss.

Conclusions

The proposed model, despite its simplicity, helps us understand one of the primary causes of chromosomal instability—aberrant kinetochore–microtubule interactions. The model reveals that chromosome bi-orientation is a probabilistic self-organisation, rather than a sophisticated process of error detection and correction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-015-0172-y) contains supplementary material, which is available to authorized users.

Aurora B Overexpression Causes Aneuploidy and p21Cip1 Repression during Tumor Development

Aurora kinase B, one of the three members of the mammalian Aurora kinase family, is the catalytic component of the chromosomal passenger complex, an essential regulator of chromosome segregation in mitosis. Aurora B is overexpressed in human tumors although whether this kinase may function as an oncogene in vivo is not established. Here, we report a new mouse model in which expression of the endogenous Aurkb locus can be induced in vitro and in vivo. Overexpression of Aurora B in cultured cells induces defective chromosome segregation and aneuploidy. Long-term overexpression of Aurora B in vivo results in aneuploidy and the development of multiple spontaneous tumors in adult mice, including a high incidence of lymphomas. Overexpression of Aurora B also results in a reduced DNA damage response and decreased levels of the p53 target p21(Cip1) in vitro and in vivo, in line with an inverse correlation between Aurora B and p21(Cip1) expression in human leukemias. Thus, overexpression of Aurora B may contribute to tumor formation not only by inducing chromosomal instability but also by suppressing the function of the cell cycle inhibitor p21(Cip1).

Cell size modulates oscillation, positioning and length of mitotic spindles

Mitotic spindle is the main subcellular structure that accomplishes the chromosome segregation between daughter cells during cell division. However, how mitotic spindles sense and control their size, position and movement inside the cell still remains unclear. In this paper, we focus on the size effects of mitotic spindles, i.e., how cell size controls various interesting phenomena in the metaphase, such as oscillation, positioning and size limit of mitotic spindles. We systematically studied the frequency doubling phenomenon during chromosome oscillation and found that cell size can regulate the period and amplitude of chromosome oscillation. We found that the relaxation time of the positioning process increases exponentially with cell size. We also showed that the stabler microtubule-kinetochore attachments alone can directly lead to an upper limit of spindle size. Our work not only explains the existing experimental observations, but also provides some interesting predictions that can be verified or rejected by further experiments.

Aurora B prevents chromosome arm separation defects by promoting telomere dispersion and disjunction

The segregation of centromeres and telomeres at mitosis is coordinated at multiple levels to prevent the formation of aneuploid cells, a phenotype frequently observed in cancer. Mitotic instability arises from chromosome segregation defects, giving rise to chromatin bridges at anaphase. Most of these defects are corrected before anaphase onset by a mechanism involving Aurora B kinase, a key regulator of mitosis in a wide range of organisms. Here, we describe a new role for Aurora B in telomere dispersion and disjunction during fission yeast mitosis. Telomere dispersion initiates in metaphase, whereas disjunction takes place in anaphase. Dispersion is promoted by the dissociation of Swi6/HP1 and cohesin Rad21 from telomeres, whereas disjunction occurs at anaphase after the phosphorylation of condensin subunit Cnd2. Strikingly, we demonstrate that deletion of Ccq1, a telomeric shelterin component, rescued cell death after Aurora inhibition by promoting the loading of condensin on chromosome arms. Our findings reveal an essential role for telomeres in chromosome arm segregation.

Pericentromere tension is self-regulated by spindle structure in metaphase

Pericentromere tension in yeast is substantial and is tightly self-regulated by the metaphase mitotic spindle through adjustments in spindle structure.

During cell division, a mitotic spindle is built by the cell and acts to align and stretch duplicated sister chromosomes before their ultimate segregation into daughter cells. Stretching of the pericentromeric chromatin during metaphase is thought to generate a tension-based signal that promotes proper chromosome segregation. However, it is not known whether the mitotic spindle actively maintains a set point tension magnitude for properly attached sister chromosomes to facilitate robust mechanochemical checkpoint signaling. By imaging and tracking the thermal movements of pericentromeric fluorescent markers in Saccharomyces cerevisiae, we measured pericentromere stiffness and then used the stiffness measurements to quantitatively evaluate the tension generated by pericentromere stretch during metaphase in wild-type cells and in mutants with disrupted chromosome structure. We found that pericentromere tension in yeast is substantial (4–6 pN) and is tightly self-regulated by the mitotic spindle: through adjustments in spindle structure, the cell maintains wild-type tension magnitudes even when pericentromere stiffness is disrupted.

Modelling chromosome dynamics in mitosis: a historical perspective on models of metaphase and anaphase in eukaryotic cells

Mitosis is the process by which the genome is segregated to form two identical daughter cells during cell division. The process of cell division is essential to the maintenance of every form of life. However, a detailed quantitative understanding of mitosis has been difficult owing to the complexity of the process. Indeed, it has been long recognized that, because of the complexity of the molecules involved, their dynamics and their properties, the mitotic events that mediate the segregation of the genome into daughter nuclei cannot be fully understood without the contribution of mathematical/quantitative modelling. Here, we provide an overview of mitosis and describe the dynamic and mechanical properties of the mitotic apparatus. We then discuss several quantitative models that emerged in the past decades and made an impact on our understanding of specific aspects of mitosis, including the motility of the chromosomes within the mitotic spindle during metaphase and anaphase, the maintenance of spindle length during metaphase and the switch to spindle elongation that occurs during anaphase.

Stochastic modelling of chromosomal segregation: errors can introduce correction

Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.

Dynamical scenarios for chromosome bi-orientation

Chromosome bi-orientation at the metaphase spindle is essential for precise segregation of the genetic material. The process is error-prone, and error-correction mechanisms exist to switch misaligned chromosomes to the correct, bi-oriented configuration. Here, we analyze several possible dynamical scenarios to explore how cells might achieve correct bi-orientation in an efficient and robust manner. We first illustrate that tension-mediated feedback between the sister kinetochores can give rise to a bistable switch, which allows robust distinction between a loose attachment with low tension and a strong attachment with high tension. However, this mechanism has difficulties in explaining how bi-orientation is initiated starting from unattached kinetochores. We propose four possible mechanisms to overcome this problem (exploiting molecular noise; allowing an efficient attachment of kinetochores already in the absence of tension; a trial-and-error oscillation; and a stochastic bistable switch), and assess their impact on the bi-orientation process. Based on our results and supported by experimental data, we put forward a trial-and-error oscillation and a stochastic bistable switch as two elegant mechanisms with the potential to promote bi-orientation both efficiently and robustly.

Three wise centromere functions: see no error, hear no break, speak no delay

The main function of the centromere is to promote kinetochore assembly for spindle microtubule attachment. Two additional functions of the centromere, however, are becoming increasingly clear: facilitation of robust sister-chromatid cohesion at pericentromeres and advancement of replication of centromeric regions. The combination of these three centromere functions ensures correct chromosome segregation during mitosis. Here, we review the mechanisms of the kinetochore-microtubule interaction, focusing on sister-kinetochore bi-orientation (or chromosome bi-orientation). We also discuss the biological importance of robust pericentromeric cohesion and early centromere replication, as well as the mechanisms orchestrating these two functions at the microtubule attachment site.

Analysis and Modeling of Chromosome Congression During Mitosis in the Chemotherapy Drug Cisplatin

The chemotherapy drug Cisplatin (cis-diamminedichloroplatinum(II)) induces crosslinks within and between DNA strands, and between DNA and nearby proteins. Therefore, Cisplatin-treated cells which progress into cell division may do so with altered chromosome mechanical properties. This could have important consequences for the successful completion of mitosis. Using Total Internal Reflection Fluorescence (TIRF) microscopy of live Cisplatin-treated Saccharomyces cerevisiae cells, we found that metaphase mitotic spindles have disorganized kinetochores relative to untreated cells, and also that there is increased variability in the chromosome stretching distance between sister centromeres. This suggests that chromosome stiffness may become more variable after Cisplatin treatment. We explored the effect of variable chromosome stiffness during mitosis using a stochastic model in which kinetochore microtubule dynamics were regulated by tension imparted by stretched sister chromosomes. Consistent with experimental results, increased variability of chromosome stiffness in the model led to disorganization of kinetochores in simulated metaphase mitotic spindles. Furthermore, the variability in simulated chromosome stretching tension was increased as chromosome stiffness became more variable. Because proper chromosome stretching tension may serve as a signal that is required for proper progression through mitosis, tension variability could act to impair this signal and thus prevent proper mitotic progression. Our results suggest a possible mitotic mode of action for the anti-cancer drug Cisplatin.

Dynamic bonds and polar ejection force distribution explain kinetochore oscillations in PtK1 cells

A computational model of kinetochore dynamics suggests that differences in the distribution of polar ejection forces at the periphery and in the middle of PtK1 cell spindles underlie the observed position-dependence of metaphase chromosome behavior.

Duplicated mitotic chromosomes aligned at the metaphase plate maintain dynamic attachments to spindle microtubules via their kinetochores, and multiple motor and nonmotor proteins cooperate to regulate their behavior. Depending on the system, sister chromatids may display either of two distinct behaviors, namely (1) the presence or (2) the absence of oscillations about the metaphase plate. Significantly, in PtK1 cells, in which chromosome behavior appears to be dependent on the position along the metaphase plate, both types of behavior are observed within the same spindle, but how and why these distinct behaviors are manifested is unclear. Here, we developed a new quantitative model to describe metaphase chromosome dynamics via kinetochore–microtubule interactions mediated by nonmotor viscoelastic linkages. Our model reproduces all the key features of metaphase sister kinetochore dynamics in PtK1 cells and suggests that differences in the distribution of polar ejection forces at the periphery and in the middle of PtK1 cell spindles underlie the observed dichotomy of chromosome behavior.

Pericentric chromatin loops function as a nonlinear spring in mitotic force balance

During mitosis, cohesin- and condensin-based pericentric chromatin loops function as a spring network to balance spindle microtubule force.

The mechanisms by which sister chromatids maintain biorientation on the metaphase spindle are critical to the fidelity of chromosome segregation. Active force interplay exists between predominantly extensional microtubule-based spindle forces and restoring forces from chromatin. These forces regulate tension at the kinetochore that silences the spindle assembly checkpoint to ensure faithful chromosome segregation. Depletion of pericentric cohesin or condensin has been shown to increase the mean and variance of spindle length, which have been attributed to a softening of the linear chromatin spring. Models of the spindle apparatus with linear chromatin springs that match spindle dynamics fail to predict the behavior of pericentromeric chromatin in wild-type and mutant spindles. We demonstrate that a nonlinear spring with a threshold extension to switch between spring states predicts asymmetric chromatin stretching observed in vivo. The addition of cross-links between adjacent springs recapitulates coordination between pericentromeres of neighboring chromosomes.

Identifying network motifs that buffer front-to-back signaling in polarized neutrophils

Neutrophil polarity relies on local, mutual inhibition to segregate incompatible signaling circuits to the leading and trailing edges. Mutual inhibition alone should lead to cells having strong fronts and weak backs or vice versa. However, analysis of cell-to-cell variation in human neutrophils revealed that back polarity remains consistent despite changes in front strength. How is this buffering achieved? Pharmacological perturbations and mathematical modeling revealed a functional role for microtubules in buffering back polarity by mediating positive, long-range crosstalk from front to back; loss of microtubules inhibits buffering and results in anticorrelation between front and back signaling. Furthermore, a systematic, computational search of network topologies found that a long-range, positive front-to-back link is necessary for back buffering. Our studies suggest a design principle that can be employed by polarity networks: short-range mutual inhibition establishes distinct signaling regions, after which directed long-range activation insulates one region from variations in the other.