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

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.

Computer simulation of merotelic kinetochore-microtubule attachments: corona size is more important than other cell parameters

The even chromosome segregation between daughter cells during mitosis is crucial for genome integrity and is mostly regulated by proper attachments of spindle microtubules to kinetochores. Abnormalities in this process can lead to chromosome mis-segregation and potentially result in severe developmental disorders such as aneuploidy and cancer. Merotelic attachments when tubulin microtubules captured by the kinetochore of one chromatid originate from both spindle poles are considered as one of the key molecular processes that cause such abnormalities. In this paper, we use computer modeling and the Monte Carlo approach to reveal the reasons for retaining merotelic attachments at the end of metaphase. To this end, we varied, in small increments, the basic cell parameters within ensembles of 100, 500, and 1000 virtual cells. The analysis of configurations that ensure the preservation of the largest fraction of merotelic attachments enabled us to conclude that only a change in the size of the kinetochore corona can significantly increase the number of merotelic attachments and the angle between the centromere axis and the spindle axis. The effect of the other changes in model parameters, if any, was steadily suppressed by the end of metaphase. In addition, our computer model was validated by successfully reproducing the results of third-party theoretical studies as well as some experimental observations. We also found that the orientation of chromosomes and the number of merotelic attachments do not have an explicit correlation with each other and within some limits can change independently.

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.

Theory of Cytoskeletal Reorganization during Cross-Linker-Mediated Mitotic Spindle Assembly

Cells grow, move, and respond to outside stimuli by large-scale cytoskeletal reorganization. A prototypical example of cytoskeletal remodeling is mitotic spindle assembly, during which microtubules nucleate, undergo dynamic instability, bundle, and organize into a bipolar spindle. Key mechanisms of this process include regulated filament polymerization, cross-linking, and motor-protein activity. Remarkably, using passive cross-linkers, fission yeast can assemble a bipolar spindle in the absence of motor proteins. We develop a torque-balance model that describes this reorganization because of dynamic microtubule bundles, spindle-pole bodies, the nuclear envelope, and passive cross-linkers to predict spindle-assembly dynamics. We compare these results to those obtained with kinetic Monte Carlo-Brownian dynamics simulations, which include cross-linker-binding kinetics and other stochastic effects. Our results show that rapid cross-linker reorganization to microtubule overlaps facilitates cross-linker-driven spindle assembly, a testable prediction for future experiments. Combining these two modeling techniques, we illustrate a general method for studying cytoskeletal network reorganization.

Leader of the SAC: molecular mechanisms of Mps1/TTK regulation in mitosis

Discovered in 1991 in a screen for genes involved in spindle pole body duplication, the monopolar spindle 1 (Mps1) kinase has since claimed a central role in processes that ensure error-free chromosome segregation. As a result, Mps1 kinase activity has become an attractive candidate for pharmaceutical companies in the search for compounds that target essential cellular processes to eliminate, for example, tumour cells or pathogens. Research in recent decades has offered many insights into the molecular function of Mps1 and its regulation. In this review, we integrate the latest knowledge regarding the regulation of Mps1 activity and its spatio-temporal distribution, highlight gaps in our understanding of these processes and propose future research avenues to address them.

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.

Anaphase B

Anaphase B spindle elongation is characterized by the sliding apart of overlapping antiparallel interpolar (ip) microtubules (MTs) as the two opposite spindle poles separate, pulling along disjoined sister chromatids, thereby contributing to chromosome segregation and the propagation of all cellular life. The major biochemical “modules” that cooperate to mediate pole–pole separation include: (i) midzone pushing or (ii) braking by MT crosslinkers, such as kinesin-5 motors, which facilitate or restrict the outward sliding of antiparallel interpolar MTs (ipMTs); (iii) cortical pulling by disassembling astral MTs (aMTs) and/or dynein motors that pull aMTs outwards; (iv) ipMT plus end dynamics, notably net polymerization; and (v) ipMT minus end depolymerization manifest as poleward flux. The differential combination of these modules in different cell types produces diversity in the anaphase B mechanism. Combinations of antagonist modules can create a force balance that maintains the dynamic pre-anaphase B spindle at constant length. Tipping such a force balance at anaphase B onset can initiate and control the rate of spindle elongation. The activities of the basic motor filament components of the anaphase B machinery are controlled by a network of non-motor MT-associated proteins (MAPs), for example the key MT cross-linker, Ase1p/PRC1, and various cell-cycle kinases, phosphatases, and proteases. This review focuses on the molecular mechanisms of anaphase B spindle elongation in eukaryotic cells and briefly mentions bacterial DNA segregation systems that operate by spindle elongation.

Active matter, then and now

Historically, living was divided from dead, inert matter by its autonomous activity. Today, a number of materials not themselves alive are characterized as having inherent activity, and this activity has become the subject of a hot new field of physics, "Active Matter", or "Soft matter become alive." For active matter scientists, the relation of physics to biology is guaranteed in one direction by the assertion that the cell is a material, and hence its study can be considered a branch of material science, and in the other direction, by the claim that the physical dynamics of this material IS what brings the cell to life, and therefore its study is a proper branch of biology. I will examine these claims in relation to the concerns of nineteenth century scientists on the one hand, and on the other, in relation to future prospects of the division between animate and inanimate.

Mechanism for Anaphase B: Evaluation of "Slide-and-Cluster" versus "Slide-and-Flux-or-Elongate" Models

Elongation of the mitotic spindle during anaphase B contributes to chromosome segregation in many cells. Here, we quantitatively test the ability of two models for spindle length control to describe the dynamics of anaphase B spindle elongation using experimental data from Drosophila embryos. In the slide-and-flux-or-elongate (SAFE) model, kinesin-5 motors persistently slide apart antiparallel interpolar microtubules (ipMTs). During pre-anaphase B, this outward sliding of ipMTs is balanced by depolymerization of their minus ends at the poles, producing poleward flux, while the spindle maintains a constant length. Following cyclin B degradation, ipMT depolymerization ceases so the sliding ipMTs can push the poles apart. The competing slide-and-cluster (SAC) model proposes that MTs nucleated at the equator are slid outward by the cooperative actions of the bipolar kinesin-5 and a minus-end-directed motor, which then pulls the sliding MTs inward and clusters them at the poles. In assessing both models, we assume that kinesin-5 preferentially cross-links and slides apart antiparallel MTs while the MT plus ends exhibit dynamic instability. However, in the SAC model, minus-end-directed motors bind the minus ends of MTs as cargo and transport them poleward along adjacent, parallel MT tracks, whereas in the SAFE model, all MT minus ends that reach the pole are depolymerized by kinesin-13. Remarkably, the results show that within a narrow range of MT dynamic instability parameters, both models can reproduce the steady-state length and dynamics of pre-anaphase B spindles and the rate of anaphase B spindle elongation. However, only the SAFE model reproduces the change in MT dynamics observed experimentally at anaphase B onset. Thus, although both models explain many features of anaphase B in this system, our quantitative evaluation of experimental data regarding several different aspects of spindle dynamics suggests that the SAFE model provides a better fit.

Small Molecule Approach to Study the Function of Mitotic Kinesins

Mitotic motor proteins of the kinesin superfamily are critical for the faithful segregation of chromosomes and the formation of the two daughter cells during meiotic and mitotic M-phase. Of the 45 human kinesins, roughly a dozen are involved in the assembly of the bipolar spindle, alignment of chromosomes at the spindle equator, chromosome segregation, and cytokinesis. The functions of kinesins in these processes are highly diverse and include the transport of cargo molecules, sliding and bundling of microtubules, and regulation of microtubule dynamics. In light of this multitude of diverse functions and the complex functional interplay of different kinesins during M-phase, it is not surprising that one of the greatest challenges in cell biology is the functional dissection of individual motor proteins. Reversible and fast acting small molecules are powerful tools to accomplish this challenge. However, the validity of conclusions drawn from small molecule studies strictly depends on compound specificity. In this chapter, we present methods for the identification of small molecule inhibitors of a motor protein of interest. In particular, we focus on a protein-based large throughput screen to identify inhibitors of the ATPase activity of kinesins. Furthermore, we provide protocols and guidelines for secondary screens to validate hits and select for specific inhibitors.

Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics

Kinetochores are multi-protein complexes that mediate the physical coupling of sister chromatids to spindle microtubule bundles (called kinetochore (K)-fibres) from respective poles. These kinetochore-attached K-fibres generate pushing and pulling forces, which combine with polar ejection forces (PEF) and elastic inter-sister chromatin to govern chromosome movements. Classic experiments in meiotic cells using calibrated micro-needles measured an approximate stall force for a chromosome, but methods that allow the systematic determination of forces acting on a kinetochore in living cells are lacking. Here we report the development of mathematical models that can be fitted (reverse engineered) to high-resolution kinetochore tracking data, thereby estimating the model parameters and allowing us to indirectly compute the (relative) force components (K-fibre, spring force and PEF) acting on individual sister kinetochores in vivo. We applied our methodology to thousands of human kinetochore pair trajectories and report distinct signatures in temporal force profiles during directional switches. We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature. There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude. This data driven reverse engineering approach is sufficiently flexible to allow fitting of more complex mechanistic models; mathematical models of kinetochore dynamics can therefore be thoroughly tested on experimental data for the first time. Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

To achieve proper cell division, newly duplicated chromosomes must be segregated into daughter cells with high fidelity. This occurs in mitosis where during the crucial metaphase stage chromosomes are aligned on an imaginary plate, called the metaphase plate. Chromosomes are attached to a structural scaffold—the mitotic spindle, which is composed of dynamic fibres called microtubules—by protein machines called kinetochores. Observation of kinetochores during metaphase reveals they undergo a series of forward and backward movements. The mechanical system generating this oscillatory motion is not well understood. By tracking kinetochores in live cell 3D confocal microscopy and reverse engineering their trajectories we decompose the forces acting on kinetochores into the three main force generating components. Kinetochore dynamics are dominated by K-fibre forces, although changes in the minor spring force over time suggests an important role in controlling directional switching. In addition, we show that the strength of forces can vary both spatially within cells throughout the plate and between cells.

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.

The microtubule cross-linker Feo controls the midzone stability, motor composition, and elongation of the anaphase B spindle in Drosophila embryos

The antiparallel MT-MT cross-linking nonmotor MAP, Feo, controls the organization, stability, and motor composition of the Drosophila embryo anaphase B spindle midzone, thereby facilitating the kinesin-5-driven sliding filament mechanism underlying proper anaphase B spindle elongation and chromosome segregation.

Chromosome segregation during anaphase depends on chromosome-to-pole motility and pole-to-pole separation. We propose that in Drosophila embryos, the latter process (anaphase B) depends on a persistent kinesin-5–generated interpolar (ip) microtubule (MT) sliding filament mechanism that “engages” to push apart the spindle poles when poleward flux is turned off. Here we investigated the contribution of the midzonal, antiparallel MT-cross-linking nonmotor MAP, Feo, to this “slide-and-flux-or-elongate” mechanism. Whereas Feo homologues in other systems enhance the midzone localization of the MT-MT cross-linking motors kinesin-4, -5 and -6, the midzone localization of these motors is respectively enhanced, reduced, and unaffected by Feo. Strikingly, kinesin-5 localizes all along ipMTs of the anaphase B spindle in the presence of Feo, including at the midzone, but the antibody-induced dissociation of Feo increases kinesin-5 association with the midzone, which becomes abnormally narrow, leading to impaired anaphase B and incomplete chromosome segregation. Thus, although Feo and kinesin-5 both preferentially cross-link MTs into antiparallel polarity patterns, kinesin-5 cannot substitute for loss of Feo function. We propose that Feo controls the organization, stability, and motor composition of antiparallel ipMTs at the midzone, thereby facilitating the kinesin-5–driven sliding filament mechanism underlying proper anaphase B spindle elongation and chromosome segregation.