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.

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.

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.

Analysis of mitotic protein dynamics and function in Drosophila embryos by live cell imaging and quantitative modeling.

Mitosis depends upon the mitotic spindle, a dynamic protein machine that uses ensembles of dynamic microtubules (MTs) and MT-based motor proteins to assemble itself, control its own length (pole-pole spacing), and segregate chromosomes during anaphase A (chromosome-to-pole motility) and anaphase B (spindle elongation). In this review, we describe how the molecular and biophysical mechanisms of these processes can be analyzed in the syncytial Drosophila embryo by combining (1) time-lapse imaging and other fluorescence light microscopy techniques to study the dynamics of mitotic proteins such as tubulins, mitotic motors, and chromosome or centrosome proteins; (2) the perturbation of specific mitotic protein function using microinjected inhibitors (e.g., antibodies) or mutants to infer protein function; and (3) mathematical modeling of the qualitative models derived from these experiments, which can then be used to make predictions which are in turn tested experimentally. We provide details of the methods we use for embryo preparation, fluorescence imaging, and mathematical modeling.

Patronin mediates a switch from kinesin-13-dependent poleward flux to anaphase B spindle elongation.

Anaphase B spindle elongation contributes to chromosome segregation during Drosophila melanogaster embryo mitosis. We propose that this process is driven by a kinesin-5-generated interpolar microtubule (MT; ipMT) sliding filament mechanism that engages when poleward flux is turned off. In this paper, we present evidence that anaphase B is induced by the minus end-stabilizing protein patronin, which antagonizes the kinesin-13 depolymerase KLP10A at spindle poles, thereby switching off the depolymerization of the minus ends of outwardly sliding ipMTs to suppress flux. Although intact cortices, kinetochore MTs, and midzone augmentation are dispensable, this patronin-based change in ipMT minus-end dynamics is sufficient to induce the elongation of spindles capable of separating chromosomes.

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

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.

Intraflagellar transport delivers tubulin isotypes to sensory cilium middle and distal segments.

Sensory cilia are assembled and maintained by kinesin-2-dependent intraflagellar transport (IFT). We investigated whether two Caenorhabditis elegans α- and ß-tubulin isotypes, identified through mutants that lack their cilium distal segments, are delivered to their assembly sites by IFT. Mutations in conserved residues in both tubulins destabilize distal singlet microtubules. One isotype, TBB-4, assembles into microtubules at the tips of the axoneme core and distal segments, where the microtubule tip tracker EB1 is found, and localizes all along the cilium, whereas the other, TBA-5, concentrates in distal singlets. IFT assays, fluorescence recovery after photobleaching analysis and modelling indicate that the continual transport of sub-stoichiometric numbers of these tubulin subunits by the IFT machinery can maintain sensory cilia at their steady-state length.

Mitotic force generators and chromosome segregation.

The mitotic spindle uses dynamic microtubules and mitotic motors to generate the pico-Newton scale forces that are needed to drive the mitotic movements that underlie chromosome capture, alignment and segregation. Here, we consider the biophysical and molecular basis of force-generation for chromosome movements in the spindle, and, with reference to the Drosophila embryo mitotic spindle, we briefly discuss how mathematical modeling can complement experimental analysis to illuminate the mechanisms of chromosome-to-pole motility during anaphase A and spindle elongation during anaphase B.

Prometaphase spindle maintenance by an antagonistic motor-dependent force balance made robust by a disassembling lamin-B envelope.

We tested the classical hypothesis that astral, prometaphase bipolar mitotic spindles are maintained by balanced outward and inward forces exerted on spindle poles by kinesin-5 and -14 using modeling of in vitro and in vivo data from Drosophila melanogaster embryos. Throughout prometaphase, puncta of both motors aligned on interpolar microtubules (MTs [ipMTs]), and motor perturbation changed spindle length, as predicted. Competitive motility of purified kinesin-5 and -14 was well described by a stochastic, opposing power stroke model incorporating motor kinetics and load-dependent detachment. Motor parameters from this model were applied to a new stochastic force-balance model for prometaphase spindles, providing a good fit to data from embryos. Maintenance of virtual spindles required dynamic ipMTs and a narrow range of kinesin-5 to kinesin-14 ratios matching that found in embryos. Functional perturbation and modeling suggest that this range can be extended significantly by a disassembling lamin-B envelope that surrounds the prometaphase spindle and augments the finely tuned, antagonistic kinesin force balance to maintain robust prometaphase spindles as MTs assemble and chromosomes are pushed to the equator.

Dynamic partitioning of mitotic kinesin-5 cross-linkers between microtubule-bound and freely diffusing states.

The dynamic behavior of homotetrameric kinesin-5 during mitosis is poorly understood. Kinesin-5 may function only by binding, cross-linking, and sliding adjacent spindle microtubules (MTs), or, alternatively, it may bind to a stable "spindle matrix" to generate mitotic movements. We created transgenic Drosophila melanogaster expressing fluorescent kinesin-5, KLP61F-GFP, in a klp61f mutant background, where it rescues mitosis and viability. KLP61F-GFP localizes to interpolar MT bundles, half spindles, and asters, and is enriched around spindle poles. In fluorescence recovery after photobleaching experiments, KLP61F-GFP displays dynamic mobility similar to tubulin, which is inconsistent with a substantial static pool of kinesin-5. The data conform to a reaction-diffusion model in which most KLP61F is bound to spindle MTs, with the remainder diffusing freely. KLP61F appears to transiently bind MTs, moving short distances along them before detaching. Thus, kinesin-5 motors can function by cross-linking and sliding adjacent spindle MTs without the need for a static spindle matrix.

Reverse engineering of force integration during mitosis in the Drosophila embryo.

The mitotic spindle is a complex macromolecular machine that coordinates accurate chromosome segregation. The spindle accomplishes its function using forces generated by microtubules (MTs) and multiple molecular motors, but how these forces are integrated remains unclear, since the temporal activation profiles and the mechanical characteristics of the relevant motors are largely unknown. Here, we developed a computational search algorithm that uses experimental measurements to 'reverse engineer' molecular mechanical machines. Our algorithm uses measurements of length time series for wild-type and experimentally perturbed spindles to identify mechanistic models for coordination of the mitotic force generators in Drosophila embryo spindles. The search eliminated thousands of possible models and identified six distinct strategies for MT-motor integration that agree with available data. Many features of these six predicted strategies are conserved, including a persistent kinesin-5-driven sliding filament mechanism combined with the anaphase B-specific inhibition of a kinesin-13 MT depolymerase on spindle poles. Such conserved features allow predictions of force-velocity characteristics and activation-deactivation profiles of key mitotic motors. Identified differences among the six predicted strategies regarding the mechanisms of prometaphase and anaphase spindle elongation suggest future experiments.

Mitotic motors: kinesin-5 takes a brake.

A kinesin-5-dependent 'sliding filament' mechanism is commonly used to actively push apart the poles during mitotic spindle assembly and elongation, but a recent study now shows that, in C. elegans, kinesin-5 is deployed as a brake to slow down spindle-pole separation.

Quantitative analysis of an anaphase B switch: predicted role for a microtubule catastrophe gradient.

Anaphase B in Drosophila embryos is initiated by the inhibition of microtubule (MT) depolymerization at spindle poles, which allows outwardly sliding interpolar (ip) MTs to drive pole-pole separation. Using fluorescence recovery after photobleaching, we observed that MTs throughout the preanaphase B spindle are very dynamic and display complete recovery of fluorescence, but during anaphase B, MTs proximal to the poles stabilize and therefore display lower recovery than those elsewhere. Fluorescence microscopy of the MT tip tracker EB1 revealed that growing MT plus ends localize throughout the preanaphase B spindle but concentrate in the overlap region of interpolar MTs (ipMTs) at anaphase B onset. None of these changes occurred in the presence of nondegradable cyclin B. Modeling suggests that they depend on the establishment of a spatial gradient of MT plus-end catastrophe frequencies, decreasing toward the equator. The resulting redistribution of ipMT plus ends to the overlap zone, together with the suppression of minus-end depolymerization at the poles, could constitute a mechanical switch that initiates spindle elongation.

A homotetrameric kinesin-5, KLP61F, bundles microtubules and antagonizes Ncd in motility assays.

BACKGROUND: Mitosis depends upon the cooperative action of multiple microtubule (MT)-based motors. Among these, a kinesin-5, KLP61F, and the kinesin-14, Ncd, are proposed to generate antagonistic-sliding forces that control the spacing of the spindle poles. We tested whether purified KLP61F homotetramers and Ncd homodimers can generate a force balance capable of maintaining a constant spindle length in Drosophila embryos. RESULTS: Using fluorescence microscopy and cryo-EM, we observed that purified full-length, motorless, and tailless KLP61F tetramers (containing a tetramerization domain) and Ncd dimers can all cross-link MTs into bundles in MgATP. In multiple-motor motility assays, KLP61F and Ncd drive plus-end and minus-end MT sliding at 0.04 and 0.1 microm/s, respectively, but the motility of either motor is decreased by increasing the mole fraction of the other. At the "balance point," the mean velocity was zero and MTs paused briefly and then oscillated, taking approximately 0.3 microm excursions at approximately 0.02 microm/s toward the MT plus end and then the minus end. CONCLUSIONS: The results, combined with quantitative analysis, suggest that these motors could act as mutual brakes to modulate the rate of pole-pole separation and could maintain a prometaphase spindle displaying small fluctuations in its steady-state length.

Mechanism of transport of IFT particles in C. elegans cilia by the concerted action of kinesin-II and OSM-3 motors.

The assembly and function of cilia on Caenorhabditis elegans neurons depends on the action of two kinesin-2 motors, heterotrimeric kinesin-II and homodimeric OSM-3-kinesin, which cooperate to move the same intraflagellar transport (IFT) particles along microtubule (MT) doublets. Using competitive in vitro MT gliding assays, we show that purified kinesin-II and OSM-3 cooperate to generate movement similar to that seen along the cilium in the absence of any additional regulatory factors. Quantitative modeling suggests that this could reflect an alternating action mechanism, in which the motors take turns to move along MTs, or a mechanical competition, in which the motors function in a concerted fashion to move along MTs with the slow motor exerting drag on the fast motor and vice versa. In vivo transport assays performed in Bardet-Biedl syndrome (BBS) protein and IFT motor mutants favor a mechanical competition model for motor coordination in which the IFT motors exert a BBS protein-dependent tension on IFT particles, which controls the IFT pathway that builds the cilium foundation.

Modeling mitosis.

The mitotic spindle is a fascinating protein machine that uses bipolar arrays of dynamic microtubules and many mitotic motors to coordinate the accurate segregation of sister chromatids. Here we discuss recent mathematical models and computer simulations that, in concert with experimental studies, help explain the molecular mechanisms by which the spindle machinery performs its crucial functions. We review current models of spindle assembly, positioning, maintenance and elongation; of chromosome capture and congression; and of the spindle assembly checkpoint. We discuss some limitations of the application of modeling to other aspects of mitosis and the feasibility of building more comprehensive system-level models.