Contributions of Microtubule Dynamic Instability and Rotational Diffusion to Kinetochore Capture

Distinct regions of the kinesin-5 C-terminal tail are essential for mitotic spindle midzone localization and sliding force

Kinesin-5 motor proteins play essential roles during mitosis in most organisms. Their tetrameric structure and plus-end-directed motility allow them to bind to and move along antiparallel microtubules, thereby pushing spindle poles apart to assemble a bipolar spindle. Recent work has shown that the C-terminal tail is particularly important to kinesin-5 function: The tail affects motor domain structure, ATP hydrolysis, motility, clustering, and sliding force measured for purified motors, as well as motility, clustering, and spindle assembly in cells. Because previous work has focused on presence or absence of the entire tail, the functionally important regions of the tail remain to be identified. We have therefore characterized a series of kinesin-5/Cut7 tail truncation alleles in fission yeast. Partial truncation causes mitotic defects and temperature-sensitive growth, while further truncation that removes the conserved BimC motif is lethal. We compared the sliding force generated by cut7 mutants using a kinesin-14 mutant background in which some microtubules detach from the spindle poles and are pushed into the nuclear envelope. These Cut7-driven protrusions decreased as more of the tail was truncated, and the most severe truncations produced no observable protrusions. Our observations suggest that the C-terminal tail of Cut7p contributes to both sliding force and midzone localization. In the context of sequential tail truncation, the BimC motif and adjacent C-terminal amino acids are particularly important for sliding force. In addition, moderate tail truncation increases midzone localization, but further truncation of residues N-terminal to the BimC motif decreases midzone localization.

Mechanistic model for nuclear migration in hyphae during mitosis

Saccharomyces cerevisiae and Candida albicans, the two well-known human pathogens, can be found in all three morphologies, i.e., yeast, pseudohyphae, and true hyphae. The cylindrical daughter-bud (germ tube) grows very long for true hyphae, and the cell cycle is delayed compared to the other two morphologies. The place of the nuclear division is specific for true hyphae determined by the position of the septin ring. However, the septin ring can localize anywhere inside the germ tube, unlike the mother-bud junction in budding yeast. Since the nucleus often migrates a long path in the hyphae, the underlying mechanism must be robust for executing mitosis in a timely manner. We explore the mechanism of nuclear migration through hyphae in light of mechanical interactions between astral microtubules and the cell cortex. We report that proper migration through constricted hyphae requires a large dynein pull applied on the astral microtubules from the hyphal cortex. This is achieved when the microtubules frequently slide along the hyphal cortex so that a large population of dyneins actively participate, pulling on them. Simulation shows timely migration when the dyneins from the mother cortex do not participate in pulling on the microtubules. These findings are robust for long migration and positioning of the nucleus in the germ tube at the septin ring.

Distinct regions of the kinesin-5 C-terminal tail are essential for mitotic spindle midzone localization and sliding force

Kinesin-5 motor proteins play essential roles during mitosis in most organisms. Their tetrameric structure and plus-end-directed motility allow them to bind to and move along antiparallel microtubules, thereby pushing spindle poles apart to assemble a bipolar spindle. Recent work has shown that the C-terminal tail is particularly important to kinesin-5 function: the tail affects motor domain structure, ATP hydrolysis, motility, clustering, and sliding force measured for purified motors, as well as motility, clustering, and spindle assembly in cells. Because previous work has focused on presence or absence of the entire tail, the functionally important regions of the tail remain to be identified. We have therefore characterized a series of kinesin-5/Cut7 tail truncation alleles in fission yeast. Partial truncation causes mitotic defects and temperature-sensitive growth, while further truncation that removes the conserved BimC motif is lethal. We compared the sliding force generated by cut7 mutants using a kinesin-14 mutant background in which some microtubules detach from the spindle poles and are pushed into the nuclear envelope. These Cut7-driven protrusions decreased as more of the tail was truncated, and the most severe truncations produced no observable protrusions. Our observations suggest that the C-terminal tail of Cut7p contributes to both sliding force and midzone localization. In the context of sequential tail truncation, the BimC motif and adjacent C-terminal amino acids are particularly important for sliding force. In addition, moderate tail truncation increases midzone localization, but further truncation of residues N terminal to the BimC motif decreases midzone localization.

Quantifying Yeast Microtubules and Spindles Using the Toolkit for Automated Microtubule Tracking (TAMiT)

Fluorescently labeled proteins absorb and emit light, appearing as Gaussian spots in fluorescence imaging. When fluorescent tags are added to cytoskeletal polymers such as microtubules, a line of fluorescence and even non-linear structures results. While much progress has been made in techniques for imaging and microscopy, image analysis is less well-developed. Current analysis of fluorescent microtubules uses either manual tools, such as kymographs, or automated software. As a result, our ability to quantify microtubule dynamics and organization from light microscopy remains limited. Despite the development of automated microtubule analysis tools for in vitro studies, analysis of images from cells often depends heavily on manual analysis. One of the main reasons for this disparity is the low signal-to-noise ratio in cells, where background fluorescence is typically higher than in reconstituted systems. Here, we present the Toolkit for Automated Microtubule Tracking (TAMiT), which automatically detects, optimizes, and tracks fluorescent microtubules in living yeast cells with sub-pixel accuracy. Using basic information about microtubule organization, TAMiT detects linear and curved polymers using a geometrical scanning technique. Images are fit via an optimization problem for the microtubule image parameters that are solved using non-linear least squares in Matlab. We benchmark our software using simulated images and show that it reliably detects microtubules, even at low signal-to-noise ratios. Then, we use TAMiT to measure monopolar spindle microtubule bundle number, length, and lifetime in a large dataset that includes several S. pombe mutants that affect microtubule dynamics and bundling. The results from the automated analysis are consistent with previous work and suggest a direct role for CLASP/Cls1 in bundling spindle microtubules. We also illustrate automated tracking of single curved astral microtubules in S. cerevisiae, with measurement of dynamic instability parameters. The results obtained with our fully-automated software are similar to results using hand-tracked measurements. Therefore, TAMiT can facilitate automated analysis of spindle and microtubule dynamics in yeast cells.

The kinesin-5 protein Cut7 moves bidirectionally on fission yeast spindles with activity that increases in anaphase

Kinesin-5 motors are essential to separate mitotic spindle poles and assemble a bipolar spindle in many organisms. These motors crosslink and slide apart antiparallel microtubules via microtubule plus-end-directed motility. However, kinesin-5 localization is enhanced away from antiparallel overlaps. Increasing evidence suggests this localization occurs due to bidirectional motility or trafficking. The purified fission-yeast kinesin-5 protein Cut7 moves bidirectionally, but bidirectionality has not been shown in cells, and the function of the minus-end-directed movement is unknown. Here, we characterized the motility of Cut7 on bipolar and monopolar spindles and observed movement toward both plus- and minus-ends of microtubules. Notably, the activity of the motor increased at anaphase B onset. Perturbations to microtubule dynamics only modestly changed Cut7 movement, whereas Cut7 mutation reduced movement. These results suggest that the directed motility of Cut7 contributes to the movement of the motor. Comparison of the Cut7 mutant and human Eg5 (also known as KIF11) localization suggest a new hypothesis for the function of minus-end-directed motility and spindle-pole localization of kinesin-5s.

Quantifying yeast microtubules and spindles using the Toolkit for Automated Microtubule Tracking (TAMiT)

Fluorescently labeled proteins absorb and emit light, appearing as Gaussian spots in fluorescence imaging. When fluorescent tags are added to cytoskeletal polymers such as microtubules, a line of fluorescence and even non-linear structures results. While much progress has been made in techniques for imaging and microscopy, image analysis is less well developed. Current analysis of fluorescent microtubules uses either manual tools, such as kymographs, or automated software. As a result, our ability to quantify microtubule dynamics and organization from light microscopy remains limited. Despite development of automated microtubule analysis tools for in vitro studies, analysis of images from cells often depends heavily on manual analysis. One of the main reasons for this disparity is the low signal-to-noise ratio in cells, where background fluorescence is typically higher than in reconstituted systems. Here, we present the Toolkit for Automated Microtubule Tracking (TAMiT), which automatically detects, optimizes and tracks fluorescent microtubules in living yeast cells with sub-pixel accuracy. Using basic information about microtubule organization, TAMiT detects linear and curved polymers using a geometrical scanning technique. Images are fit via an optimization problem for the microtubule image parameters that is solved using non-linear least squares in Matlab. We benchmark our software using simulated images and show that it reliably detects microtubules, even at low signal-to-noise ratios. Then, we use TAMiT to measure monopolar spindle microtubule bundle number, length, and lifetime in a large dataset that includes several S. pombe mutants that affect microtubule dynamics and bundling. The results from the automated analysis are consistent with previous work, and suggest a direct role for CLASP/Cls1 in bundling spindle microtubules. We also illustrate automated tracking of single curved astral microtubules in S. cerevisiae , with measurement of dynamic instability parameters. The results obtained with our fully-automated software are similar to results using hand-tracked measurements. Therefore, TAMiT can facilitate automated analysis of spindle and microtubule dynamics in yeast cells.

Non-centrosomal microtubules at kinetochores promote rapid chromosome biorientation during mitosis in human cells

Proper segregation of chromosomes during mitosis depends on "amphitelic attachments"-load-bearing connections of sister kinetochores to the opposite spindle poles via bundles of microtubules, termed as the "K-fibers." Current models of spindle assembly assume that K-fibers arise largely from stochastic capture of microtubules, which occurs at random times and locations and independently at sister kinetochores. We test this assumption by following the movements of all kinetochores in human cells and determine that most amphitelic attachments form synchronously at a specific stage of spindle assembly and within a spatially distinct domain. This biorientation domain is enriched in bundles of antiparallel microtubules, and perturbation of microtubule bundling changes the temporal and spatial dynamics of amphitelic attachment formation. Structural analyses indicate that interactions of kinetochores with microtubule bundles are mediated by non-centrosomal short microtubules that emanate from most kinetochores during early prometaphase. Computational analyses suggest that momentous molecular motor-driven interactions with antiparallel bundles rapidly convert these short microtubules into nascent K-fibers. Thus, load-bearing connections to the opposite spindle poles form simultaneously on sister kinetochores. In contrast to the uncoordinated sequential attachments of sister kinetochores expected in stochastic models of spindle assembly, our model envisions the formation of amphitelic attachments as a deterministic process in which the chromosomes connect with the spindle poles synchronously at a specific stage of spindle assembly and at a defined location determined by the spindle architecture. Experimental analyses of changes in the kinetochore behavior in cells with perturbed activity of molecular motors CenpE and dynein confirm the predictive power of the model.

Quantification of Microtubule Stutters: Dynamic Instability Behaviors that are Strongly Associated with Catastrophe

Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting DI mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA) that identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term “stutters.” During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our in vitro experiments and dimer-scale MT simulations, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anticatastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared with previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.

Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies

The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.

Microtubule pivoting enables mitotic spindle assembly in S. cerevisiae

To assemble a bipolar spindle, microtubules emanating from two poles must bundle into an antiparallel midzone, where plus end–directed motors generate outward pushing forces to drive pole separation. Midzone cross-linkers and motors display only modest preferences for antiparallel filaments, and duplicated poles are initially tethered together, an arrangement that instead favors parallel interactions. Pivoting of microtubules around spindle poles might help overcome this geometric bias, but the intrinsic pivoting flexibility of the microtubule–pole interface has not been directly measured, nor has its importance during early spindle assembly been tested. By measuring the pivoting of microtubules around isolated yeast spindle poles, we show that pivoting flexibility can be modified by mutating a microtubule-anchoring pole component, Spc110. By engineering mutants with different flexibilities, we establish the importance of pivoting in vivo for timely pole separation. Our results suggest that passive thermal pivoting can bring microtubules from side-by-side poles into initial contact, but active minus end–directed force generation will be needed to achieve antiparallel alignment.

Chemically Fueled Self-Assembly in Biology and Chemistry

Life is a non-equilibrium state of matter maintained at the expense of energy. Nature uses predominantly chemical energy stored in thermodynamically activated, but kinetically stable, molecules. These high-energy molecules are exploited for the synthesis of other biomolecules, for the activation of biological machinery such as pumps and motors, and for the maintenance of structural order. Knowledge of how chemical energy is transferred to biochemical processes is essential for the development of artificial systems with life-like processes. Here, we discuss how chemical energy can be used to control the structural organization of organic molecules. Four different strategies have been identified according to a distinguishable physical-organic basis. For each class, one example from biology and one from chemistry are discussed in detail to illustrate the practical implementation of each concept and the distinct opportunities they offer. Specific attention is paid to the discussion of chemically fueled non-equilibrium self-assembly. We discuss the meaning of non-equilibrium self-assembly, its kinetic origin, and strategies to develop synthetic non-equilibrium systems.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.

Tell the Difference Between Mitosis and Meiosis: Interplay Between Chromosomes, Cytoskeleton, and Cell Cycle Regulation

Meiosis is a specialized style of cell division conserved in eukaryotes, particularly designed for the production of gametes. A huge number of studies to date have demonstrated how chromosomes behave and how meiotic events are controlled. Yeast substantially contributed to the understanding of the molecular mechanisms of meiosis in the past decades. Recently, evidence began to accumulate to draw a perspective landscape showing that chromosomes and microtubules are mutually influenced: microtubules regulate chromosomes, whereas chromosomes also regulate microtubule behaviors. Here we focus on lessons from recent advancement in genetical and cytological studies of the fission yeast Schizosaccharomyces pombe, revealing how chromosomes, cytoskeleton, and cell cycle progression are organized and particularly how these are differentiated in mitosis and meiosis. These studies illuminate that meiosis is strategically designed to fulfill two missions: faithful segregation of genetic materials and production of genetic diversity in descendants through elaboration by meiosis-specific factors in collaboration with general factors.

Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.

Spatio-temporal correlations between catastrophe events in a microtubule bundle: a computational study

We explore correlations between dynamics of different microtubules in a bundle, via numerical simulations, using a one-dimensional stochastic model of a microtubule. The guanosine triphosphate (GTP)-bound tubulins undergo diffusion-limited binding to the tip. Random hydrolysis events take place along the microtubule and converts the bound GTP in tubulin to guanosine diphosphate (GDP). The microtubule starts depolymerising when the monomer at the tip becomes GDP-bound; in this case, detachment of GDP-tubulin ensues and continues until either GTP-bound tubulin is exposed or complete depolymerisation is achieved. In the latter case, the microtubule is defined to have undergone a "catastrophe". Our results show that, in general, the dynamics of growth and catastrophe in different microtubules are coupled to each other; the closer the microtubules are, the stronger the coupling. In particular, all microtubules grow slower, on average, when brought closer together. The reduction in growth velocity also leads to more frequent catastrophes. More dramatically, catastrophe events in the different microtubules forming a bundle are found to be correlated; a catastrophe event in one microtubule is more likely to be followed by a similar event in the same microtubule. This propensity of bunching disappears when the microtubules move farther apart.

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.

Pivot-and-bond model explains microtubule bundle formation

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

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

BACKGROUND

At the beginning of mitosis, the cell forms a spindle made of microtubules and associated proteins to segregate chromosomes. An important part of spindle architecture is a set of antiparallel microtubule bundles connecting the spindle poles. A key question is how microtubules extending at arbitrary angles form an antiparallel interpolar bundle.

RESULTS

Here, we show in fission yeast that microtubules meet at an oblique angle and subsequently rotate into antiparallel alignment. Our live-cell imaging approach provides a direct observation of interpolar bundle formation. By combining experiments with theory, we show that microtubules from each pole search for those from the opposite pole by performing random angular movement. Upon contact, two microtubules slide sideways along each other in a directed manner towards the antiparallel configuration. We introduce the contour length of microtubules as a measure of activity of motors that drive microtubule sliding, which we used together with observation of Cut7/kinesin-5 motors and our theory to reveal the minus-end-directed motility of this motor in vivo.

CONCLUSION

Random rotational motion helps microtubules from the opposite poles to find each other and subsequent accumulation of motors allows them to generate forces that drive interpolar bundle formation.

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.

Search and Capture Efficiency of Dynamic Microtubules for Centrosome Relocation during IS Formation

Upon contact with antigen-presenting cells, cytotoxic T lymphocytes (T cells) establish a highly organized contact zone denoted as the immunological synapse (IS). The formation of the IS implies relocation of the microtubule organizing center (MTOC) toward the contact zone, which necessitates a proper connection between the MTOC and the IS via dynamic microtubules (MTs). The efficiency of the MTs finding the IS within the relevant timescale is, however, still illusive. We investigate how MTs search the three-dimensional constrained cellular volume for the IS and bind upon encounter to dynein anchored at the IS cortex. The search efficiency is estimated by calculating the time required for the MTs to reach the dynein-enriched region of the IS. In this study, we develop simple mathematical and numerical models incorporating relevant components of a cell and propose an optimal search strategy. Using the mathematical model, we have quantified the average search time for a wide range of model parameters and proposed an optimized set of values leading to the minimal capture time. Our results show that search times are minimal when the IS formed at the nearest or at the farthest sites on the cell surface with respect to the perinuclear MTOC. The search time increases monotonically away from these two specific sites and is maximal at an intermediate position near the equator of the cell. We observed that search time strongly depends on the number of searching MTs and distance of the MTOC from the nuclear surface.

Microtubules assemble near most kinetochores during early prometaphase in human cells

Correlative light electron microscopy reveals microtubule assembly near most kinetochores at the onset of mitosis in human cells. Conversion of the initially lateral interactions between these microtubules and kinetochores into end-on attachments is facilitated by the kinesin CenpE. This work suggests that kinetochore fibers predominately form via capture of locally nucleated noncentrosomal microtubules.

For proper segregation during cell division, each chromosome must connect to the poles of the spindle via microtubule bundles termed kinetochore fibers (K-fibers). K-fibers form by two distinct mechanisms: (1) capture of astral microtubules nucleated at the centrosome by the chromosomes’ kinetochores or (2) attachment of kinetochores to noncentrosomal microtubules with subsequent transport of the minus ends of these microtubules toward the spindle poles. The relative contributions of these alternative mechanisms to normal spindle assembly remain unknown. In this study, we report that most kinetochores in human cells develop K-fibers via the second mechanism. Correlative light electron microscopy demonstrates that from the onset of spindle assembly, short randomly oriented noncentrosomal microtubules appear in the immediate vicinity of the kinetochores. Initially, these microtubules interact with the kinetochores laterally, but end-on attachments form rapidly in the first 3 min of prometaphase. Conversion from lateral to end-on interactions is impeded upon inhibition of the plus end–directed kinetochore-associated kinesin CenpE.

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

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

Mitotic spindle: kinetochore fibers hold on tight to interpolar bundles

When a cell starts to divide, it forms a spindle, a micro-machine made of microtubules, which separates the duplicated chromosomes. The attachment of microtubules to chromosomes is mediated by kinetochores, protein complexes on the chromosome. Spindle microtubules can be divided into three major classes: kinetochore microtubules, which form k-fibers ending at the kinetochore; interpolar microtubules, which extend from the opposite sides of the spindle and interact in the middle; and astral microtubules, which extend towards the cell cortex. Recent work in human cells has shown a close relationship between interpolar and kinetochore microtubules, where interpolar bundles are attached laterally to kinetochore fibers almost all along their length, acting as a bridge between sister k-fibers. Most of the interpolar bundles are attached to a pair of sister kinetochore fibers and vice versa. Thus, the spindle is made of modules consisting of a pair of sister kinetochore fibers and a bundle of interpolar microtubules that connects them. These interpolar bundles, termed bridging fibers, balance the forces acting at kinetochores and support the rounded shape of the spindle during metaphase. This review discusses the structure, function, and formation of kinetochore fibers and interpolar bundles, with an emphasis on how they interact. Their connections have an impact on the force balance in the spindle and on chromosome movement during mitosis because the forces in interpolar bundles are transmitted to kinetochore fibers and hence to kinetochores through these connections.

Tau-based fluorescent protein fusions to visualize microtubules

The ability to visualize cytoskeletal proteins and their dynamics in living cells has been critically important in advancing our understanding of numerous cellular processes, including actin- and microtubule (MT)-dependent phenomena such as cell motility, cell division, and mitosis. Here, we describe a novel set of fluorescent protein (FP) fusions designed specifically to visualize MTs in living systems using fluorescence microscopy. Each fusion contains a FP module linked in frame to a modified phospho-deficient version of the MT-binding domain of Tau (mTMBD). We found that expressed and purified constructs containing a single mTMBD decorated Xenopus egg extract spindles more homogenously than similar constructs containing the MT-binding domain of Ensconsin, suggesting that the binding affinity of mTMBD is minimally affected by localized signaling gradients generated during mitosis. Furthermore, MT dynamics were not grossly perturbed by the presence of Tau-based FP fusions. Interestingly, the addition of a second mTMBD to the opposite terminus of our construct caused dramatic changes to the spatial localization of probes within spindles. These results support the use of Tau-based FP fusions as minimally perturbing tools to accurately visualize MTs in living systems.

Kinesin-5-independent mitotic spindle assembly requires the antiparallel microtubule crosslinker Ase1 in fission yeast

Bipolar spindle assembly requires a balance of forces where kinesin-5 produces outward pushing forces to antagonize the inward pulling forces from kinesin-14 or dynein. Accordingly, Kinesin-5 inactivation results in force imbalance leading to monopolar spindle and chromosome segregation failure. In fission yeast, force balance is restored when both kinesin-5 Cut7 and kinesin-14 Pkl1 are deleted, restoring spindle bipolarity. Here we show that the cut7Δpkl1Δ spindle is fully competent for chromosome segregation independently of motor activity, except for kinesin-6 Klp9, which is required for anaphase spindle elongation. We demonstrate that cut7Δpkl1Δ spindle bipolarity requires the microtubule antiparallel bundler PRC1/Ase1 to recruit CLASP/Cls1 to stabilize microtubules. Brownian dynamics-kinetic Monte Carlo simulations show that Ase1 and Cls1 activity are sufficient for initial bipolar spindle formation. We conclude that pushing forces generated by microtubule polymerization are sufficient to promote spindle pole separation and the assembly of bipolar spindle in the absence of molecular motors.

Bipolar spindle assembly requires a balance of kinesin 14 pulling and kinesin 5 pushing forces. Here, the authors show that in fission yeast, spindle formation can occur in the absence of kinesin 5 (Cut7) and 14 (Pkl1) but requires the microtubule-associated protein Ase1 for spindle bipolarity.

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.