Modeling mitosis

A theoretical model of anaphase

This paper develops a theory for anaphase in cells. After a brief description of microtubules, the mitotic spindle and the centrosome, a mathematical model for anaphase is introduced and developed in the context of the cell cytoplasm and liquid crystalline structures. Prophase, prometaphase and metaphase are then briefly described in order to focus on anaphase, which is the main study of this paper. The entities involved are modelled in terms of liquid crystal defects and microtubules are represented as defect flux lines. The mathematical techniques employed make extensive use of energy considerations based on the work that was developed by Dafermos (1970) from the classical Frank-Oseen nematic liquid crystal energy (Frank, 1958; Oseen, 1933). With regard to liquid crystal theory we introduce the concept of regions of influence for defects which it is believed have important implications beyond the subject of this paper. The results of this paper align with observed biochemical phenomena and are explored in application to HeLa cells and Caenorhabditis elegans. This unified approach offers the possibility of gaining insight into various consequences of mitotic abnormalities which may result in Down syndrome, Hodgkin lymphoma, breast, prostate and various other types of cancer.

Liquid-liquid phase separation of microtubule-binding proteins in the regulation of spindle assembly

Cell division is a highly regulated process essential for the accurate segregation of chromosomes. Central to this process is the assembly of a bipolar mitotic spindle, a highly dynamic microtubule (MT)-based structure responsible for chromosome movement. The nucleation and dynamics of MTs are intricately regulated by MT-binding proteins. Over the recent years, various MT-binding proteins have been reported to undergo liquid-liquid phase separation, forming either single- or multi-component condensates on MTs. Herein, we provide a comprehensive summary of the phase separation characteristics of these proteins. We underscore their critical roles in MT nucleation, spindle assembly and kinetochore-MT attachment during the cell division process. Furthermore, we discuss the current challenges and various remaining unsolved problems, highlights the ongoing research efforts aimed at a deeper understanding of the role of the phase separation process during spindle assembly and orientation. Our review aims to contribute to the collective knowledge in this area and stimulate further investigations that will enhance our comprehension of the intricate mechanisms governing cell division.

Confinement in fibrous environments positions and orients mitotic spindles

Accurate positioning of the mitotic spindle within the rounded cell body is critical to physiological maintenance. Adherent mitotic cells encounter confinement from neighboring cells or the extracellular matrix (ECM), which can cause rotation of mitotic spindles and, consequently, titling of the metaphase plate (MP). To understand the positioning and orientation of mitotic spindles under confinement by fibers (ECM-confinement), we use flexible ECM-mimicking nanofibers that allow natural rounding of the cell body while confining it to differing levels. Rounded mitotic bodies are anchored in place by actin retraction fibers (RFs) originating from adhesion clusters on the ECM-mimicking fibers. We discover the extent of ECM-confinement patterns RFs in 3D: triangular and band-like at low and high confinement, respectively. A stochastic Monte-Carlo simulation of the centrosome (CS), chromosome (CH), membrane interactions, and 3D arrangement of RFs on the mitotic body recovers MP tilting trends observed experimentally. Our mechanistic analysis reveals that the 3D shape of RFs is the primary driver of the MP rotation. Under high ECM-confinement, the fibers can mechanically pinch the cortex, causing the MP to have localized deformations at contact sites with fibers. Interestingly, high ECM-confinement leads to low and high MP tilts, which mechanistically depend upon the extent of cortical deformation, RF patterning, and MP position. We identify that cortical deformation and RFs work in tandem to limit MP tilt, while asymmetric positioning of MP leads to high tilts. Overall, we provide fundamental insights into how mitosis may proceed in fibrous ECM-confining microenvironments in vivo.

Mitotic Functions and Characters of KIF11 in Cancers

Mitosis mediates the accurate separation of daughter cells, and abnormalities are closely related to cancer progression. KIF11, a member of the kinesin family, plays a vital role in the formation and maintenance of the mitotic spindle. Recently, an increasing quantity of data have demonstrated the upregulated expression of KIF11 in various cancers, promoting the emergence and progression of cancers. This suggests the great potential of KIF11 as a prognostic biomarker and therapeutic target. However, the molecular mechanisms of KIF11 in cancers have not been systematically summarized. Therefore, we first discuss the functions of the protein encoded by KIF11 during mitosis and connect the abnormal expression of KIF11 with its clinical significance. Then, we elucidate the mechanism of KIF11 to promote various hallmarks of cancers. Finally, we provide an overview of KIF11 inhibitors and outline areas for future work.

Enucleation of the C. elegans embryo revealed dynein-dependent spacing between microtubule asters

The intracellular positioning of the centrosome, a major microtubule-organizing center, is important for cellular functions. One of the features of centrosome positioning is the spacing between centrosomes; however, the underlying mechanisms are not fully understood. To characterize the spacing activity in Caenorhabditis elegans embryos, a genetic setup was developed to produce enucleated embryos. The centrosome was duplicated multiple times in the enucleated embryo, which enabled us to characterize the chromosome-independent spacing activity between sister and non-sister centrosome pairs. We found that the timely spacing depended on cytoplasmic dynein, and we propose a stoichiometric model of cortical and cytoplasmic pulling forces for the spacing between centrosomes. We also observed dynein-independent but non-muscle myosin II-dependent movement of centrosomes in the later cell cycle phase. The spacing mechanisms revealed in this study are expected to function between centrosomes in general, regardless of the presence of a chromosome/nucleus between them, including centrosome separation and spindle elongation.

Morphological growth dynamics, mechanical stability, and active microtubule mechanics underlying spindle self-organization

The spindle is a dynamic intracellular structure self-organized from microtubules and microtubule-associated proteins. The spindle’s bipolar morphology is essential for the faithful segregation of chromosomes during cell division, and it is robustly maintained by multifaceted mechanisms. However, abnormally shaped spindles, such as multipolar spindles, can stochastically arise in a cell population and cause chromosome segregation errors. The physical basis of how microtubules fail in bipolarization and occasionally favor nonbipolar assembly is poorly understood. Here, using live fluorescence imaging and quantitative shape analysis in Xenopus egg extracts, we find that spindles of varied shape morphologies emerge through nonrandom, bistable self-organization paths, one leading to a bipolar and the other leading to a multipolar phenotype. The bistability defines the spindle’s unique morphological growth dynamics linked to each shape phenotype and can be promoted by a locally distorted microtubule flow that arises within premature structures. We also find that bipolar and multipolar spindles are stable at the steady-state in bulk but can infrequently switch between the two phenotypes. Our microneedle-based physical manipulation further demonstrates that a transient force perturbation applied near the assembled pole can trigger the phenotypic switching, revealing the mechanical plasticity of the spindle. Together with molecular perturbation of kinesin-5 and augmin, our data propose the physical and molecular bases underlying the emergence of spindle-shape variation, which influences chromosome segregation fidelity during cell division.

Choice between 1- and 2-furrow cytokinesis in Caenorhabditis elegans embryos with tripolar spindles

Excessive centrosomes often lead to multipolar spindles, and thus probably to multipolar mitosis and aneuploidy. In Caenorhabditis elegans, ∼70% of the paternal emb-27APC6 mutant embryonic cells contained more than two centrosomes and formed multipolar spindles. However, only ~30% of the cells with tripolar spindles formed two cytokinetic furrows. The rest formed one furrow, similar to normal cells. To investigate the mechanism via which cells avoid forming two cytokinetic furrows even with a tripolar spindle, we conducted live-cell imaging in emb-27APC6 mutant cells. We observed that the chromatids were aligned on only two of the three sides of the tripolar spindle, and the angle of the tripolar spindle relative to the long axis of the cell correlated with the number of cytokinetic furrows. Our numerical modeling showed that the combination of cell shape, cortical pulling forces, and heterogeneity of centrosome size determines whether cells with a tripolar spindle form one or two cytokinetic furrows.

Is the cell really a machine?

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes.

A computational model of the early stages of acentriolar meiotic spindle assembly

The mitotic spindle is an ensemble of microtubules responsible for the repartition of the chromosomal content between the two daughter cells during division. In metazoans, spindle assembly is a gradual process involving dynamic microtubules and recruitment of numerous associated proteins and motors. During mitosis, centrosomes organize and nucleate the majority of spindle microtubules. In contrast, oocytes lack canonical centrosomes but are still able to form bipolar spindles, starting from an initial ball that self-organizes in several hours. Interfering with early steps of meiotic spindle assembly can lead to erroneous chromosome segregation. Although not fully elucidated, this process is known to rely on antagonistic activities of plus end- and minus end-directed motors. We developed a model of early meiotic spindle assembly in mouse oocytes, including key factors such as microtubule dynamics and chromosome movement. We explored how the balance between plus end- and minus end-directed motors, as well as the influence of microtubule nucleation, impacts spindle morphology. In a refined model, we added spatial regulation of microtubule stability and minus-end clustering. We could reproduce the features of early stages of spindle assembly from 12 different experimental perturbations and predict eight additional perturbations. With its ability to characterize and predict chromosome individualization, this model can help deepen our understanding of spindle assembly.

Targeted human cytolytic fusion proteins at the cutting edge: harnessing the apoptosis-inducing properties of human enzymes for the selective elimination of tumor cells

Patient-specific targeted therapy represents the holy grail of anti-cancer therapeutics, allowing potent tumor depletion without detrimental off-target toxicities. Disease-specific monoclonal antibodies have been employed to bind to oncogenic cell-surface receptors, representing the earliest form of immunotherapy. Targeted drug delivery was first achieved by means of antibody-drug conjugates, which exploit the differential expression of tumor-associated antigens as a guiding mechanism for the specific delivery of chemically-conjugated chemotherapeutic agents to diseased target cells. Biotechnological advances have expanded the repertoire of immunology-based tumor-targeting strategies, also paving the way for the next intuitive step in targeted drug delivery: the construction of recombinant protein drugs consisting of an antibody-based targeting domain genetically fused with a cytotoxic peptide, known as an immunotoxin. However, the most potent protein toxins have typically been derived from bacterial or plant virulence factors and commonly feature both off-target toxicity and immunogenicity in human patients. Further refinement of immunotoxin technology thus led to the replacement of monoclonal antibodies with humanized antibody derivatives, including the substitution of non-human toxic peptides with human cytolytic proteins. Preclinically tested human cytolytic fusion proteins (hCFPs) have proven promising as non-immunogenic combinatory anti-cancer agents, however they still require further enhancement to achieve convincing candidacy as a single-mode therapeutic. To date, a portfolio of highly potent human toxins has been established; ranging from microtubule-associated protein tau (MAP tau), RNases, granzyme B (GrB) and death-associated protein kinase (DAPk). In this review, we discuss the most recent findings on the use of these apoptosis-inducing hCFPs for the treatment of various cancers.

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.

Microtubules and Microtubule-Associated Proteins

Microtubules act as "railways" for motor-driven intracellular transport, interact with accessory proteins to assemble into larger structures such as the mitotic spindle, and provide an organizational framework to the rest of the cell. Key to these functions is the fact that microtubules are "dynamic." As with actin, the polymer dynamics are driven by nucleotide hydrolysis and influenced by a host of specialized regulatory proteins, including microtubule-associated proteins. However, microtubule turnover involves a surprising behavior-termed dynamic instability-in which individual polymers switch stochastically between growth and depolymerization. Dynamic instability allows microtubules to explore intracellular space and remodel in response to intracellular and extracellular cues. Here, we review how such instability is central to the assembly of many microtubule-based structures and to the robust functioning of the microtubule cytoskeleton.

Anti-mitotic agents: Are they emerging molecules for cancer treatment?

Mutations in cancer cells frequently result in cell cycle alterations that lead to unrestricted growth compared to normal cells. Considering this phenomenon, many drugs have been developed to inhibit different cell-cycle phases. Mitotic phase targeting disturbs mitosis in tumor cells, triggers the spindle assembly checkpoint and frequently results in cell death. The first anti-mitotics to enter clinical trials aimed to target tubulin. Although these drugs improved the treatment of certain cancers, and many anti-microtubule compounds are already approved for clinical use, severe adverse events such as neuropathies were observed. Since then, efforts have been focused on the development of drugs that also target kinases, motor proteins and multi-protein complexes involved in mitosis. In this review, we summarize the major proteins involved in the mitotic phase that can also be targeted for cancer treatment. Finally, we address the activity of anti-mitotic drugs tested in clinical trials in recent years.

Measuring Pushing and Braking Forces Generated by Ensembles of Kinesin-5 Crosslinking Two Microtubules

The proper organization of the microtubule-based mitotic spindle is proposed to depend on nanometer-sized motor proteins generating forces that scale with a micron-sized geometric feature, such as microtubule overlap length. However, it is unclear whether such regulation can be achieved by any mitotic motor protein. Here, we employ an optical-trap- and total internal reflection fluorescence (TIRF)-based assay to show that ensembles of kinesin-5, a conserved mitotic motor protein, can push apart overlapping antiparallel microtubules to generate a force whose magnitude scales with filament overlap length. We also find that kinesin-5 can produce overlap-length-dependent "brake-like" resistance against relative microtubule sliding in both parallel and antiparallel geometries, an activity that has been suggested by cell biological studies but had not been directly measured. Together, these findings, along with numerical simulations, reveal how a motor protein can function as an analog converter, "reading" simple geometric and dynamic features in cytoskeletal networks to produce regulated force outputs.

Force Generation by Molecular-Motor-Powered Microtubule Bundles; Implications for Neuronal Polarization and Growth

The heavily cross-linked microtubule (MT) bundles found in neuronal processes play a central role in the initiation, growth and maturation of axons and dendrites; however, a quantitative understanding of their mechanical function is still lacking. We here developed computer simulations to investigate the dynamics of force generation in 1D bundles of MTs that are cross-linked and powered by molecular motors. The motion of filaments and the forces they exert are investigated as a function of the motor type (unipolar or bipolar), MT density and length, applied load, and motor connectivity. We demonstrate that only unipolar motors (e.g., kinesin-1) can provide the driving force for bundle expansion, while bipolar motors (e.g., kinesin-5) oppose it. The force generation capacity of the bundles is shown to depend sharply on the fraction of unipolar motors due to a percolation transition that must occur in the bundle. Scaling laws between bundle length, force, MT length and motor fraction are presented. In addition, we investigate the dynamics of growth in the presence of a constant influx of MTs. Beyond a short equilibration period, the bundles grow linearly in time. In this growth regime, the bundle extends as one mass forward with most filaments sliding with the growth velocity. The growth velocity is shown to be dictated by the inward flux of MTs, to inversely scale with the load and to be independent of the free velocity of the motors. These findings provide important molecular-level insights into the mechanical function of the MT cytoskeleton in normal axon growth and regeneration after injury.

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.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

A mathematical model of force generation by flexible kinetochore-microtubule attachments

Important mechanical events during mitosis are facilitated by the generation of force by chromosomal kinetochore sites that attach to dynamic microtubule tips. Several theoretical models have been proposed for how these sites generate force, and molecular diffusion of kinetochore components has been proposed as a key component that facilitates kinetochore function. However, these models do not explicitly take into account the recently observed flexibility of kinetochore components and variations in microtubule shape under load. In this paper, we develop a mathematical model for kinetochore-microtubule connections that directly incorporates these two important components, namely, flexible kinetochore binder elements, and the effects of tension load on the shape of shortening microtubule tips. We compare our results with existing biased diffusion models and explore the role of protein flexibility inforce generation at the kinetochore-microtubule junctions. Our model results suggest that kinetochore component flexibility and microtubule shape variation under load significantly diminish the need for high diffusivity (or weak specific binding) of kinetochore components; optimal kinetochore binder stiffness regimes are predicted by our model. Based on our model results, we suggest that the underlying principles of biased diffusion paradigm need to be reinterpreted.

HSP70 colocalizes with PLK1 at the centrosome and disturbs spindle dynamics in cells arrested in mitosis by arsenic trioxide

Heat shock protein 70 (HSP70) has been shown to be a substrate of Polo-like kinase 1 (PLK1), and it prevents cells arrested in mitosis by arsenic trioxide (ATO) from dying. Here, we report that HSP70 participates in ATO-induced spindle elongation, which interferes with mitosis progression. Our results demonstrate that HSP70 and PLK1 colocalize at the centrosome in ATO-arrested mitotic cells. HSP70 located at the centrosome was found to be phosphorylated by PLK1 at Ser⁶³¹ and Ser⁶³³. Moreover, unlike wild-type HSP70 (HSP70(wt)) and its phosphomimetic mutant (HSP70(SS631,633DD)), a phosphorylation-resistant mutant of HSP70 (HSP70(SS631,633AA)) failed to localize at the centrosome. ATO-induced spindle elongation was abolished in cells overexpressing HSP70(SS631,633AA). Conversely, mitotic spindles in cells ectopically expressing HSP70(SS631,633DD) were more resistant to nocodazole-induced depolymerization than in those expressing HSP70(wt) or HSP70(SS631,633AA). In addition, inhibition of PLK1 significantly reduced HSP70 phosphorylation and induced early onset of apoptosis in ATO-arrested mitotic cells. Taken together, our results indicate that PLK1-mediated phosphorylation and centrosomal localization of HSP70 may interfere with spindle dynamics and prevent apoptosis of ATO-arrested mitotic cells.

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.

A computational model for the formation of lamin-B mitotic spindle envelope and matrix

Recent reports show that, after nuclear envelope breakdown, lamin-B, a component of the nuclear lamina in interphase, localizes around the mitotic spindle as a membranous network. How this process occurs, however, and how it influences mitotic spindle morphogenesis is unclear. Here, we develop a computational model based on a continuum description to represent the abundance and location of various molecular species involved during mitosis, and use the model to test a number of hypotheses regarding the formation of the mitotic matrix. Our model illustrates that freely diffusible nuclear proteins can be captured and transported to the spindle poles by minus-end-directed microtubule (MT) motors. Moreover, simulations show that these proteins can be used to build a shell-like region that envelopes the mitotic spindle, which helps to improve the focusing of the mitotic spindle by spatially restricting MT polymerization and limiting the effective diffusion of the free MTs. Simulations also confirm that spatially dependent regulation of the spindle network through the Ran system improves spindle focusing and morphology. Our results agree with experimental observations that lamin-B reorganizes around the spindle and helps to maintain spindle morphology.

Mitotic motors and chromosome segregation: the mechanism of anaphase B

Anaphase B spindle elongation plays an important role in chromosome segregation. In the present paper, we discuss our model for anaphase B in Drosophila syncytial embryos, in which spindle elongation depends on an ip (interpolar) MT (microtubule) sliding filament mechanism generated by homotetrameric kinesin-5 motors acting in concert with poleward ipMT flux, which acts as an 'on/off' switch. Specifically, the pre-anaphase B spindle is maintained at a steady-state length by the balance between ipMT sliding and ipMT depolymerization at spindle poles, producing poleward flux. Cyclin B degradation at anaphase B onset triggers: (i) an MT catastrophe gradient causing ipMT plus ends to invade the overlap zone where ipMT sliding forces are generated; and (ii) the inhibition of ipMT minus-end depolymerization so flux is turned 'off', tipping the balance of forces to allow outward ipMT sliding to push apart the spindle poles. We briefly comment on the relationship of this model to anaphase B in other systems.

Model of myosin node aggregation into a contractile ring: the effect of local alignment

Actomyosin bundles frequently form through aggregation of membrane-bound myosin clusters. One such example is the formation of the contractile ring in fission yeast from a broad band of cortical nodes. Nodes are macromolecular complexes containing several dozens of myosin-II molecules and a few formin dimers. The condensation of a broad band of nodes into the contractile ring has been previously described by a search, capture, pull and release (SCPR) model. In SCPR, a random search process mediated by actin filaments nucleated by formins leads to transient actomyosin connections among nodes that pull one another into a ring. The SCPR model reproduces the transport of nodes over long distances and predicts observed clump-formation instabilities in mutants. However, the model does not generate transient linear elements and meshwork structures as observed in some wild-type and mutant cells during ring assembly. As a minimal model of node alignment, we added short-range aligning forces to the SCPR model representing currently unresolved mechanisms that may involve structural components, cross-linking and bundling proteins. We studied the effect of the local node alignment mechanism on ring formation numerically. We varied the new parameters and found viable rings for a realistic range of values. Morphologically, transient structures that form during ring assembly resemble those observed in experiments with wild-type and cdc25-22 cells. Our work supports a hierarchical process of ring self-organization involving components drawn together from distant parts of the cell followed by progressive stabilization.

Can molecular cell biology explain chromosome motions?

BACKGROUND

Mitotic chromosome motions have recently been correlated with electrostatic forces, but a lingering "molecular cell biology" paradigm persists, proposing binding and release proteins or molecular geometries for force generation.

RESULTS

Pole-facing kinetochore plates manifest positive charges and interact with negatively charged microtubule ends providing the motive force for poleward chromosome motions by classical electrostatics. This conceptual scheme explains dynamic tracking/coupling of kinetochores to microtubules and the simultaneous depolymerization of kinetochore microtubules as poleward force is generated.

CONCLUSION

We question here why cells would prefer complex molecular mechanisms to move chromosomes when direct electrostatic interactions between known bound charge distributions can accomplish the same task much more simply.

Mitotic membrane helps to focus and stabilize the mitotic spindle

During mitosis, microtubules (MTs), aided by motors and associated proteins, assemble into a mitotic spindle. Recent evidence supports the notion that a membranous spindle matrix aids spindle formation; however, the mechanisms by which the matrix may contribute to spindle assembly are unknown. To search for a mechanism by which the presence of a mitotic membrane might help spindle morphology, we built a computational model that explores the interactions between these components. We show that an elastic membrane around the mitotic apparatus helps to focus MT minus ends and provides a resistive force that acts antagonistically to plus-end-directed MT motors such as Eg5.

Cell-size-dependent control of organelle sizes during development

During development, cells differentiate into diverse cell types with different sizes. The size of intracellular organelles often correlates with the size of the cell, which may be important for cell homeostasis. The nucleus is a well-known example of an organelle whose size correlates with cell size. However, the mechanical basis of the correlation is unknown. The lengths of the mitotic spindle and contractile ring are emerging as model system to investigate the cell-size-dependent control mechanisms of organelle size. Mechanistic models are proposed for the cell-size-dependent control of these organelles. Understanding the cell-size dependency of organelle sizes is expected to impact not only on the morphogenesis of the individual organelle, but also on cell homeostasis, cell cycle progression, and cell differentiation.

Control of mitotic spindle length

The mitotic spindle accurately segregates genetic instructions by moving chromosomes to spindle poles (anaphase A) and separating the poles (anaphase B) so that, in general, the chromosomes and poles are positioned near the centers of the nascent daughter cell products of each cell division. Because the size of different types of dividing cells, and thus the spacing of their daughter cell centers, can vary significantly, the length of the metaphase or postanaphase B spindle often scales with cell size. However, significant exceptions to this scaling rule occur, revealing the existence of cell size–independent, spindle-associated mechanisms of spindle length control. The control of spindle length reflects the action of mitotic force-generating mechanisms, and its study may illuminate general principles by which cells regulate the size of internal structures. Here we review molecules and mechanisms that control spindle length, how these mechanisms are deployed in different systems, and some quantitative models that describe the control of spindle length.

Influence of centriole number on mitotic spindle length and symmetry

The functional role of centrioles or basal bodies in mitotic spindle assembly and function is currently unclear. Although supernumerary centrioles have been associated with multipolar spindles in cancer cells, suggesting centriole number might dictate spindle polarity, bipolar spindles are able to assemble in the complete absence of centrioles, suggesting a level of centriole-independence in the spindle assembly pathway. In this report we perturb centriole number using mutations in Chlamydomonas reinhardtii, and measure the response of the mitotic spindle to these perturbations in centriole number. Although altered centriole number increased the frequency of monopolar and multipolar spindles, the majority of spindles remained bipolar regardless of the centriole number. But even when spindles were bipolar, abnormal centriole numbers led to asymmetries in tubulin distribution, half-spindle length and spindle pole focus. Half spindle length correlated directly with number of centrioles at a pole, such that an imbalance in centriole number between the two poles of a bipolar spindle correlated with increased asymmetry between half spindle lengths. These results are consistent with centrioles playing an active role in regulating mitotic spindle length. Mutants with centriole number alteration also show increased cytokinesis defects, but these do not correlate with centriole number in the dividing cell and may therefore reflect downstream consequences of defects in preceding cell divisions.

Lamin B counteracts the kinesin Eg5 to restrain spindle pole separation during spindle assembly

Lamin B is a component of the membranous spindle matrix isolated from Xenopus egg extracts, and it is required for proper spindle morphogenesis. Besides lamin B, the spindle matrix contains spindle assembly factors (SAFs) such as Eg5 and dynein which are known to regulate microtubule organization and SAFs known to promote microtubule assembly such as Maskin and XMAP215. Because lamin B does not bind directly to microtubules, it must affect spindle morphogenesis indirectly by influencing the function of spindle matrix-associated SAFs. Using different assays in Xenopus egg extracts, we found that depleting lamin B caused formation of elongated and multipolar spindles, which could be reversed by partially inhibiting the kinesin Eg5, revealing an antagonistic relationship between Eg5 and lamin B. However, lamin B only very weakly antagonizes Eg5 in mediating poleward microtubule-flux based on fluorescence speckle microscopy. Depleting lamin B led to a very small but statistically significant increase in flux. Furthermore, flux reduction caused by partial Eg5 inhibition is only slightly reversed by removing lamin B. Because lamin B does not bind to Eg5, our studies suggest two nonexclusive mechanisms by which lamin B can indirectly antagonize Eg5. It could function in a network that restricts Eg5-driven microtubule sliding only when microtubules come into transient contact with the network. Lamin B could also function to sequester microtubule polymerization activities within the spindle. Without lamin B, increased microtubule assembly caused by the released SAFs would lead to excessive microtubule sliding that results in formation of elongated and multipolar spindles.

Reaction-diffusion systems in intracellular molecular transport and control

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

Cytoskeletal dynamics in fission yeast: a review of models for polarization and division

We review modeling studies concerning cytoskeletal activity of fission yeast. Recent models vary in length and time scales, describing a range of phenomena from cellular morphogenesis to polymer assembly. The components of cytoskeleton act in concert to mediate cell-scale events and interactions such as polarization. The mathematical models reduce these events and interactions to their essential ingredients, describing the cytoskeleton by its bulk properties. On a smaller scale, models describe cytoskeletal subcomponents and how bulk properties emerge.

Directly probing the mechanical properties of the spindle and its matrix

Several recent models for spindle length regulation propose an elastic pole to pole spindle matrix that is sufficiently strong to bear or antagonize forces generated by microtubules and microtubule motors. We tested this hypothesis using microneedles to skewer metaphase spindles in Xenopus laevis egg extracts. Microneedle tips inserted into a spindle just outside the metaphase plate resulted in spindle movement along the interpolar axis at a velocity slightly slower than microtubule poleward flux, bringing the nearest pole toward the needle. Spindle velocity decreased near the pole, which often split apart slowly, eventually letting the spindle move completely off the needle. When two needles were inserted on either side of the metaphase plate and rapidly moved apart, there was minimal spindle deformation until they reached the poles. In contrast, needle separation in the equatorial direction rapidly increased spindle width as constant length spindle fibers pulled the poles together. These observations indicate that an isotropic spindle matrix does not make a significant mechanical contribution to metaphase spindle length determination.

Ase1/Prc1-dependent spindle elongation corrects merotely during anaphase in fission yeast

The tug of war that ensues when a kinetochore binds microtubules from both spindle poles is resolved by Ase1/Prc1.

Faithful segregation of sister chromatids requires the attachment of each kinetochore (Kt) to microtubules (MTs) that extend from opposite spindle poles. Merotelic Kt orientation is a Kt–MT misattachment in which a single Kt binds MTs from both spindle poles rather than just one. Genetic induction of merotelic Kt attachment during anaphase in fission yeast resulted in intra-Kt stretching followed by either correction or Kt disruption. Laser ablation of spindle MTs revealed that intra-Kt stretching and merotelic correction were dependent on MT forces. The presence of multiple merotelic chromosomes linearly antagonized the spindle elongation rate, and this phenomenon could be solved numerically using a simple force balance model. Based on the predictions of our mechanical model, we provide in vivo evidence that correction of merotelic attachment in anaphase is tension dependent and requires an Ase1/Prc1-dependent mechanism that prevents spindle collapse and thus asymmetric division and/or the appearance of the cut phenotype.

Mechanisms of chromosome behaviour during mitosis

For over a century, scientists have strived to understand the mechanisms that govern the accurate segregation of chromosomes during mitosis. The most intriguing feature of this process, which is particularly prominent in higher eukaryotes, is the complex behaviour exhibited by the chromosomes. This behaviour is based on specific and highly regulated interactions between the chromosomes and spindle microtubules. Recent discoveries, enabled by high-resolution imaging combined with the various genetic, molecular, cell biological and chemical tools, support the idea that establishing and controlling the dynamic interaction between chromosomes and microtubules is a major factor in genomic fidelity.

Systems biology and inflammation

Inflammation is a complex, multiscale biological response to threats - both internal and external - to the body, which is also required for proper healing of injured tissue. In turn, damaged or dysfunctional tissue stimulates further inflammation. Despite continued advances in characterizing the cellular and molecular processes involved in the interactions between inflammation and tissue damage, there exists a significant gap between the knowledge of mechanistic pathophysiology and the development of effective therapies for various inflammatory conditions. We have suggested the concept of translational systems biology, defined as a focused application of computational modeling and engineering principles to pathophysiology primarily in order to revise clinical practice. This chapter reviews the existing, translational applications of computational simulations and related approaches as applied to inflammation.

New look inside the spindle: microtubule-dependent microtubule generation within the spindle

The structure, dynamics, and mechanics of mitotic and meiotic spindles have been progressively elucidated through the advancements in microscopic technology, identification of the genes involved, and construction of theoretical frameworks. Here, we review recent works that have utilized quantitative image analysis to advance our understanding of the complex spindle structure of animal cells. In particular, we discuss how microtubules (MTs) are nucleated and distributed inside the spindle. Accumulating evidence supports the presence of MT-dependent MT generation within the spindle. This mechanism would produce dense arrays of intraspindle MTs with various lengths, which may contribute to efficient spindle assembly and stabilize the metaphase spindle. RNA interference (RNAi) screens with quantitative image analysis led to the identification of the augmin complex that plays a key role in this MT generation process.

Walking, hopping, diffusing and braking modes of kinesin-5

It is clear that the main cellular mission of the molecular motor kinesin-5 (known as Eg5 in vertebrates) is to cross-link antiparallel microtubules and to slide them apart, thus playing a critical role during bipolar spindle formation. Nonetheless, important questions about the cell biological and biophysical mechanisms of Eg5 remain unanswered. With the 20th 'birthday' of Eg5 approaching, we discuss recent insights into the in vitro and in vivo functions of Eg5, in the context of our own recent work.

Phospho-regulated interaction between kinesin-6 Klp9p and microtubule bundler Ase1p promotes spindle elongation

The spindle midzone-composed of antiparallel microtubules, microtubule-associated proteins (MAPs), and motors-is the structure responsible for microtubule organization and sliding during anaphase B. In general, MAPs and motors stabilize the midzone and motors produce sliding. We show that fission yeast kinesin-6 motor klp9p binds to the microtubule antiparallel bundler ase1p at the midzone at anaphase B onset. This interaction depends upon the phosphorylation states of klp9p and ase1p. The cyclin-dependent kinase cdc2p phosphorylates and its antagonist phosphatase clp1p dephosphorylates klp9p and ase1p to control the position and timing of klp9p-ase1p interaction. Failure of klp9p-ase1p binding leads to decreased spindle elongation velocity. The ase1p-mediated recruitment of klp9p to the midzone accelerates pole separation, as suggested by computer simulation. Our findings indicate that a phosphorylation switch controls the spatial-temporal interactions of motors and MAPs for proper anaphase B, and suggest a mechanism whereby a specific motor-MAP conformation enables efficient microtubule sliding.

Data harvesting from fields of spindles

The mitotic spindle is essential for chromosome segregation and must be large enough to accommodate all of the chromatin in the dividing cell. In this issue, Dinarina et al. (2009) grow "fields" of spindles on coverslips to investigate the relationship between chromatin and spindle size as well as intrinsic mechanisms of spindle assembly.

A quantitative systems view of the spindle assembly checkpoint

The idle assembly checkpoint acts to delay chromosome segregation until all duplicated sister chromatids are captured by the mitotic spindle. This pathway ensures that each daughter cell receives a complete copy of the genome. The high fidelity and robustness of this process have made it a subject of intense study in both the experimental and computational realms. A significant number of checkpoint proteins have been identified but how they orchestrate the communication between local spindle attachment and global cytoplasmic signalling to delay segregation is not yet understood. Here, we propose a systems view of the spindle assembly checkpoint to focus attention on the key regulators of the dynamics of this pathway. These regulators in turn have been the subject of detailed cellular measurements and computational modelling to connect molecular function to the dynamics of spindle assembly checkpoint signalling. A review of these efforts reveals the insights provided by such approaches and underscores the need for further interdisciplinary studies to reveal in full the quantitative underpinnings of this cellular control pathway.

Kinesin-5-dependent poleward flux and spindle length control in Drosophila embryo mitosis

We used antibody microinjection and genetic manipulations to dissect the various roles of the homotetrameric kinesin-5, KLP61F, in astral, centrosome-controlled Drosophila embryo spindles and to test the hypothesis that it slides apart interpolar (ip) microtubules (MT), thereby controlling poleward flux and spindle length. In wild-type and Ncd null mutant embryos, anti-KLP61F dissociated the motor from spindles, producing a spatial gradient in the KLP61F content of different spindles, which was visible in KLP61F-GFP transgenic embryos. The resulting mitotic defects, supported by gene dosage experiments and time-lapse microscopy of living klp61f mutants, reveal that, after NEB, KLP61F drives persistent MT bundling and the outward sliding of antiparallel MTs, thereby contributing to several processes that all appear insensitive to cortical disruption. KLP61F activity contributes to the poleward flux of both ipMTs and kinetochore MTs and to the length of the metaphase spindle. KLP61F activity maintains the prometaphase spindle by antagonizing Ncd and another unknown force-generator and drives anaphase B, although the rate of spindle elongation is relatively insensitive to the motor's concentration. Finally, KLP61F activity contributes to normal chromosome congression, kinetochore spacing, and anaphase A rates. Thus, a KLP61F-driven sliding filament mechanism contributes to multiple aspects of mitosis in this system.

Kinesin-5 is not essential for mitotic spindle elongation in Dictyostelium

The proper assembly and operation of the mitotic spindle is essential to ensure the accurate segregation of chromosomes and to position the cytokinetic furrow during cell division in eukaryotes. Not only are dynamic microtubules required but also the concerted actions of multiple motor proteins are necessary to effect spindle pole separation, chromosome alignment, chromatid segregation, and spindle elongation. Although a number of motor proteins are known to play a role in mitosis, there remains a limited understanding of their full range of functions and the details by which they interact with other spindle components. The kinesin-5 (BimC/Eg5) family of motors is largely considered essential to drive spindle pole separation during the initial and latter stages of mitosis. We have deleted the gene encoding the kinesin-5 member in Dictyostelium, (kif13), and find that, in sharp contrast with results found in vertebrate, fly, and yeast organisms, kif13(-) cells continue to grow at rates indistinguishable from wild type. Phenotype analysis reveals a slight increase in spindle elongation rates in the absence of Kif13. More importantly, there is a dramatic, premature separation of spindle halves in kif13(-) cells, suggesting a novel role of this motor in maintaining spindle integrity at the terminal stages of division.