A driving and coupling "Pac-Man" mechanism for chromosome poleward translocation in anaphase A

Treadmilling FtsZ polymers drive the directional movement of sPG-synthesis enzymes via a Brownian ratchet mechanism

The FtsZ protein is a central component of the bacterial cell division machinery. It polymerizes at mid-cell and recruits more than 30 proteins to assemble into a macromolecular complex to direct cell wall constriction. FtsZ polymers exhibit treadmilling dynamics, driving the processive movement of enzymes that synthesize septal peptidoglycan (sPG). Here, we combine theoretical modelling with single-molecule imaging of live bacterial cells to show that FtsZ's treadmilling drives the directional movement of sPG enzymes via a Brownian ratchet mechanism. The processivity of the directional movement depends on the binding potential between FtsZ and the sPG enzyme, and on a balance between the enzyme's diffusion and FtsZ's treadmilling speed. We propose that this interplay may provide a mechanism to control the spatiotemporal distribution of active sPG enzymes, explaining the distinct roles of FtsZ treadmilling in modulating cell wall constriction rate observed in different bacteria.

Biophysics of Microtubule End Coupling at the Kinetochore

The main physiological function of mitotic kinetochores is to provide durable attachment to spindle microtubules, which segregate chromosomes in order to partition them equally between the two daughter cells. Numerous kinetochore components that can bind directly to microtubules have been identified, including ATP-dependent motors and various microtubule-associated proteins with no motor activity. A major challenge facing the field is to explain chromosome motions based on the biochemical and structural properties of these individual kinetochore components and their assemblies. This chapter reviews the molecular mechanisms responsible for the motions associated with dynamic microtubule tips at the single-molecule level, as well as the activities of multimolecular ensembles called couplers. These couplers enable persistent kinetochore motion even under load, but their exact composition and structure remain unknown. Because no natural or artificial macro-machines function in an analogous manner to these molecular nano-devices, understanding their underlying biophysical mechanisms will require conceptual advances.

Electrostatic forces drive poleward chromosome motions at kinetochores

BACKGROUND

Recent experiments regarding Ndc80/Hec1 in force generation at kinetochores for chromosome motions have prompted speculation about possible models for interactions between positively charged molecules at kinetochores and negative charge at and near the plus ends of microtubules.

DISCUSSION

A clear picture of how kinetochores and centrosomes establish and maintain a dynamic coupling to microtubules for force generation during the complex motions of mitosis remains elusive. The current paradigm of molecular cell biology requires that specific molecules, or molecular geometries, for force generation be identified. However, it is possible to explain several different mitotic motions-including poleward force production at kinetochores-within a classical electrostatics approach in terms of experimentally known charge distributions, modeled as surface and volume bound charges interacting over nanometer distances.

CONCLUSION

We propose here that implicating Ndc80/Hec1 as a bound volume positive charge distribution in electrostatic generation of poleward force at kinetochores is most consistent with a wide range of experimental observations on mitotic motions, including polar production of poleward force and chromosome congression.

Directed and persistent movement arises from mechanochemistry of the ParA/ParB system

The segregation of DNA before cell division is essential for faithful genetic inheritance. In many bacteria, segregation of low-copy number plasmids involves an active partition system composed of a nonspecific DNA-binding ATPase, ParA, and its stimulator protein ParB. The ParA/ParB system drives directed and persistent movement of DNA cargo both in vivo and in vitro. Filament-based models akin to actin/microtubule-driven motility were proposed for plasmid segregation mediated by ParA. Recent experiments challenge this view and suggest that ParA/ParB system motility is driven by a diffusion ratchet mechanism in which ParB-coated plasmid both creates and follows a ParA gradient on the nucleoid surface. However, the detailed mechanism of ParA/ParB-mediated directed and persistent movement remains unknown. Here, we develop a theoretical model describing ParA/ParB-mediated motility. We show that the ParA/ParB system can work as a Brownian ratchet, which effectively couples the ATPase-dependent cycling of ParA-nucleoid affinity to the motion of the ParB-bound cargo. Paradoxically, this resulting processive motion relies on quenching diffusive plasmid motion through a large number of transient ParA/ParB-mediated tethers to the nucleoid surface. Our work thus sheds light on an emergent phenomenon in which nonmotor proteins work collectively via mechanochemical coupling to propel cargos-an ingenious solution shaped by evolution to cope with the lack of processive motor proteins in bacteria.

Intercentrosomal angular separation during mitosis plays a crucial role for maintaining spindle stability

Cell division through proper spindle formation is one of the key puzzles in cell biology. In most mammalian cells, chromosomes spontaneously arrange to achieve a stable bipolar spindle during metaphase which eventually ensures proper segregation of the DNA into the daughter cells. In this paper, we present a robust three-dimensional mechanistic model to investigate the formation and maintenance of a bipolar mitotic spindle in mammalian cells under different physiological constraints. Using realistic parameters, we test spindle viability by measuring the spindle length and studying the chromosomal configuration. The model strikingly predicts a feature of the spindle instability arising from the insufficient intercentrosomal angular separation and impaired sliding of the interpolar microtubules. In addition, our model successfully reproduces chromosomal patterns observed in mammalian cells, when activity of different motor proteins is perturbed.

Accurate phosphoregulation of kinetochore-microtubule affinity requires unconstrained molecular interactions

Accurate regulation of kinetochore–microtubule affinity is driven by incremental phosphorylation of an NDC80 molecular “lawn,” in which NDC80–microtubule bonds reorganize dynamically in response to the number and stability of microtubule attachments.

Accurate chromosome segregation relies on dynamic interactions between microtubules (MTs) and the NDC80 complex, a major kinetochore MT-binding component. Phosphorylation at multiple residues of its Hec1 subunit may tune kinetochore–MT binding affinity for diverse mitotic functions, but molecular details of such phosphoregulation remain elusive. Using quantitative analyses of mitotic progression in mammalian cells, we show that Hec1 phosphorylation provides graded control of kinetochore–MT affinity. In contrast, modeling the kinetochore interface with repetitive MT binding sites predicts a switchlike response. To reconcile these findings, we hypothesize that interactions between NDC80 complexes and MTs are not constrained, i.e., the NDC80 complexes can alternate their binding between adjacent kinetochore MTs. Experiments using cells with phosphomimetic Hec1 mutants corroborate predictions of such a model but not of the repetitive sites model. We propose that accurate regulation of kinetochore–MT affinity is driven by incremental phosphorylation of an NDC80 molecular “lawn,” in which the NDC80–MT bonds reorganize dynamically in response to the number and stability of MT attachments.

Forces due to curving protofilaments in microtubules

Microtubules consist of 13 protofilaments arranged in the form of a cylinder. The protofilaments are composed of longitudinally attached tubulin dimers that can exist in either a less curved state [GTP-bound tubulin (T)] or a more curved state [GDP-bound tubulin (D)]. Hydrolysis of T into D leaves the straight and laterally attached protofilaments of the microtubule in a mechanically stressed state, thus leading to their unzipping. The elastic energy in the unzipping protofilaments can be harnessed by a force transducer such as the Dam1-kinetochore ring complex in order to exert pulling force on chromosomes during cell division. In the present paper we develop a simple continuum model to obtain this pulling force as a function of the mechanical properties of protofilaments and the size of the Dam1-kinetochore ring. We also extend this model to investigate the role played by the T subunits found at the plus end of the microtubule (the T cap) on the mechanical stability of microtubules.

Highly Transient Molecular Interactions Underlie the Stability of Kinetochore-Microtubule Attachment During Cell Division

Chromosome segregation during mitosis is mediated by spindle microtubules that attach to chromosomal kinetochores with strong yet labile links. The exact molecular composition of the kinetochore-microtubule interface is not known but microtubules are thought to bind to kinetochores via the specialized microtubule-binding sites, which contain multiple microtubule-binding proteins. During prometaphase the lifetime of microtubule attachments is short but in metaphase it increases 3-fold, presumably owing to dephosphorylation of the microtubule-binding proteins that increases their affinity. Here, we use mathematical modeling to examine in quantitative and systematic manner the general relationships between the molecular properties of microtubule-binding proteins and the resulting stability of microtubule attachment to the protein-containing kinetochore site. We show that when the protein connections are stochastic, the physiological rate of microtubule turnover is achieved only if these molecular interactions are very transient, each lasting fraction of a second. This "microscopic" time is almost four orders of magnitude shorter than the characteristic time of kinetochore-microtubule attachment. Cooperativity of the microtubule-binding events further increases the disparity of these time scales. Furthermore, for all values of kinetic parameters the microtubule stability is very sensitive to the minor changes in the molecular constants. Such sensitivity of the lifetime of microtubule attachment to the kinetics and cooperativity of molecular interactions at the microtubule-binding site may hinder the accurate regulation of kinetochore-microtubule stability during mitotic progression, and it necessitates detailed experimental examination of the microtubule-binding properties of kinetochore-localized proteins.

Filament depolymerization can explain chromosome pulling during bacterial mitosis

Chromosome segregation is fundamental to all cells, but the force-generating mechanisms underlying chromosome translocation in bacteria remain mysterious. Caulobacter crescentus utilizes a depolymerization-driven process in which a ParA protein structure elongates from the new cell pole, binds to a ParB-decorated chromosome, and then retracts via disassembly, pulling the chromosome across the cell. This poses the question of how a depolymerizing structure can robustly pull the chromosome that disassembles it. We perform Brownian dynamics simulations with a simple, physically consistent model of the ParABS system. The simulations suggest that the mechanism of translocation is “self-diffusiophoretic”: by disassembling ParA, ParB generates a ParA concentration gradient so that the ParA concentration is higher in front of the chromosome than behind it. Since the chromosome is attracted to ParA via ParB, it moves up the ParA gradient and across the cell. We find that translocation is most robust when ParB binds side-on to ParA filaments. In this case, robust translocation occurs over a wide parameter range and is controlled by a single dimensionless quantity: the product of the rate of ParA disassembly and a characteristic relaxation time of the chromosome. This time scale measures the time it takes for the chromosome to recover its average shape after it is has been pulled. Our results suggest explanations for observed phenomena such as segregation failure, filament-length-dependent translocation velocity, and chromosomal compaction.

Reliable chromosome segregation is crucial to all dividing cells. In some bacteria, segregation has been found to occur in a rather counterintuitive way: the chromosome attaches to a filament bundle and erodes it by causing depolymerization of the filaments. Moreover, unlike eukaryotic cells, bacteria do not use molecular motors and/or macromolecular tethers to position their chromosomes. This raises the general question of how depolymerizing filaments alone can continuously and robustly pull cargo as the filaments themselves are falling apart. In this work, we introduce the first quantitative physical model for depolymerization-driven translocation in a many-filament system. Our simulations of this model suggest a novel underlying mechanism for robust translocation, namely self-diffusiophoresis, motion of an object in a self-generated concentration gradient in a viscous environment. In this case, the cargo generates and sustains a concentration gradient of filaments by inducing them to depolymerize. We demonstrate that our model agrees well with existing experimental observations such as segregation failure, filament-length-dependent translocation velocity, and chromosomal compaction. In addition, we make several predictions–including predictions for the specific modes by which the chromosome binds to the filament structure and triggers its disassembly–that can be tested experimentally.

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.

The Dam1 ring binds to the E-hook of tubulin and diffuses along the microtubule

There has been much effort in recent years aimed at understanding the molecular mechanism by which the Dam1 kinetochore complex is able to couple microtubule depolymerization to poleward movement. Both a biased diffusion and a forced walk model have been proposed, and several key functional aspects of Dam1-microtubule binding are disputed. Here, we investigate the elements involved in tubulin-Dam1 complex interactions and directly visualize Dam1 rings on microtubules in order to infer their dynamic behavior on the microtubule lattice and its likely relevance at the kinetochore. We find that the Dam1 complex has a preference for native tubulin over tubulin that is lacking its acidic C-terminal tail. Statistical mechanical analysis of images of Dam1 rings on microtubules, applied to both the distance between rings and the tilt angle of the rings with respect to the microtubule axis, supports a diffusive ring model. We also present a cryo-EM reconstruction of the Dam1 ring, likely the relevant assembly form of the complex for energy coupling during microtubule depolymerization in budding yeast. The present studies constitute a significant step forward by linking structural and biochemical observations toward a comprehensive understanding of the Dam1 complex.

Kinetochore-microtubule interactions: steps towards bi-orientation

Eukaryotic cells segregate their chromosomes accurately to opposite poles during mitosis, which is necessary for maintenance of their genetic integrity. This process mainly relies on the forces generated by kinetochore-microtubule (KT-MT) attachment. During prometaphase, the KT initially interacts with a single MT extending from a spindle pole and then moves towards a spindle pole. Subsequently, MTs from the other spindle pole also interact with the KT. Eventually, one sister KT becomes attached to MTs from one pole while the other sister to those from the other pole (sister KT bi-orientation). If sister KTs interact with MTs with aberrant orientation, this must be corrected to attain proper bi-orientation (error correction) before the anaphase is initiated. Here, I discuss how KTs initially interact with MTs and how this interaction develops into bi-orientation; both processes are fundamentally crucial for proper chromosome segregation in the subsequent anaphase.

Kinetochores' gripping feat: conformational wave or biased diffusion?

Climbing up a cliff while the rope unravels underneath your fingers does not sound like a well-planned adventure. Yet chromosomes face a similar challenge during each cell division. Their alignment and accurate segregation depends on staying attached to the assembling and disassembling tips of microtubule fibers. This coupling is mediated by kinetochores, intricate machines that attach chromosomes to an ever-changing microtubule substrate. Two models for kinetochore-microtubule coupling were proposed a quarter century ago: conformational wave and biased diffusion. These models differ in their predictions for how coupling is performed and regulated. The availability of purified kinetochore proteins has enabled biochemical and biophysical analyses of the kinetochore-microtubule interface. Here, we discuss what these studies reveal about the contributions of each model.

Force transduction by the microtubule-bound Dam1 ring

The coupling between the depolymerization of microtubules (MTs) and the motion of the Dam1 ring complex is now thought to play an important role in the generation of forces during mitosis. Our current understanding of this motion is based on a number of detailed computational models. Although these models realize possible mechanisms for force transduction, they can be extended by variation of any of a large number of poorly measured parameters and there is no clear strategy for determining how they might be distinguished experimentally. Here we seek to identify and analyze two distinct mechanisms present in the computational models. In the first, the splayed protofilaments at the end of the depolymerizing MT physically prevent the Dam1 ring from falling off the end, and in the other, an attractive binding secures the ring to the microtubule. Based on this analysis, we discuss how to distinguish between competing models that seek to explain how the Dam1 ring stays on the MT. We propose novel experimental approaches that could resolve these models for the first time, either by changing the diffusion constant of the Dam1 ring (e.g., by tethering a long polymer to it) or by using a time-varying load.

The perpetual movements of anaphase

One of the most extraordinary events in the lifetime of a cell is the coordinated separation of sister chromatids during cell division. This is truly the essence of the entire mitotic process and the reason for the most profound morphological changes in cytoskeleton and nuclear organization that a cell may ever experience. It all occurs within a very short time window known as "anaphase", as if the cell had spent the rest of its existence getting ready for this moment in an ultimate act of survival. And there is a good reason for this: no space for mistakes. Problems in the distribution of chromosomes during cell division have been correlated with aneuploidy, a common feature observed in cancers and several birth defects, and the main cause of spontaneous abortion in humans. In this paper, we critically review the mechanisms of anaphase chromosome motion that resisted the scrutiny of more than 100 years of research, as part of a tribute to the pioneering work of Miguel Mota.

Structure-function insights into the yeast Dam1 kinetochore complex

Faithful segregation of genetic material during cell division requires the dynamic but robust attachment of chromosomes to spindle microtubules during all stages of mitosis. This regulated attachment occurs at kinetochores, which are complex protein organelles that are essential for cell survival and genome integrity. In budding yeast, in which a single microtubule attaches per kinetochore, a heterodecamer known as the Dam1 complex (or DASH complex) is required for proper chromosome segregation. Recent years have seen a burst of structural and biophysical data concerning this interesting complex, which has caught the attention of the mitosis research field. In vitro, the Dam1 complex interacts directly with tubulin and self-assembles into ring structures around the microtubule surface. The ring is capable of tracking with depolymerizing ends, and a model has been proposed whereby the circular geometry of the oligomeric Dam1 complex allows it to couple the depolymerization of microtubules to processive chromosome movement in the absence of any additional energy source. Although it is attractive and simple, several important aspects of this model remain controversial. Additionally, the generality of the Dam1 mechanism has been questioned owing to the fact that there are no obvious Dam1 homologs beyond fungi. In this Commentary, we discuss recent structure-function studies of this intriguing complex.

The Dam1 ring binds microtubules strongly enough to be a processive as well as energy-efficient coupler for chromosome motion

Accurate chromosome segregation during mitotic division of budding yeast depends on the multiprotein kinetochore complex, Dam1 (also known as DASH). Purified Dam1 heterodecamers encircle microtubules (MTs) to form rings that can function as "couplers," molecular devices that transduce energy from MT disassembly into the motion of a cargo. Here we show that MT depolymerization develops a force against a Dam1 ring that is sixfold larger than the force exerted on a coupler that binds only one side of an MT. Wild-type rings slow depolymerization fourfold, but rings that include a mutant Dam1p with truncated C terminus slow depolymerization less, consistent with the idea that this tail is part of a strong bond between rings and MTs. A molecular-mechanical model for Dam1-MT interaction predicts that binding between this flexible tail and the MT wall should cause a Dam1 ring to wobble, and Fourier analysis of moving, ring-attached beads corroborates this prediction. Comparison of the forces generated against wild-type and mutant complexes confirms the importance of tight Dam1-MT association for processive cargo movement under load.

An integrated mechanobiochemical feedback mechanism describes chromosome motility from prometaphase to anaphase in mitosis

During mitosis, chromosomes undergo a series of movements while being end-on attached to the kinetochore microtubules (KMTs) from spindle poles. The mechanism underlying such movements and their physiological functions remains elusive. We describe a mechanobiochemical feedback model of chromosome motility. The key ingredient is a feedback mechanism between the local chemical reactions that control the dynamics of KMTs and the mechanical state of the chromosome via tension-sensitive proteins localized at the kinetochores. This model can recapitulate all of the essential and distinct features of chromosome motilities from prometaphase to anaphase in a coherent manner. We further show that this feedback mechanism provides robust and precise means of guiding the chromosome to the cell equator regardless of the initial conditions and uncertainty in velocity. Predictions of our model can be tested experimentally.

Bi-orienting chromosomes: acrobatics on the mitotic spindle

To maintain their genetic integrity, eukaryotic cells must segregate their chromosomes properly to opposite poles during mitosis. This process mainly depends on the forces generated by microtubules that attach to kinetochores. During prometaphase, kinetochores initially interact with a single microtubule that extends from a spindle pole and then move towards a spindle pole. Subsequently, microtubules that extend from the other spindle pole also interact with kinetochores and, eventually, each sister kinetochore attaches to microtubules that extend from opposite poles (sister kinetochore bi-orientation). If sister kinetochores interact with microtubules in wrong orientation, this must be corrected before the onset of anaphase. Here, I discuss the processes leading to bi-orientation and the mechanisms ensuring this pivotal state that is required for proper chromosome segregation.

Kinetochore-microtubule interactions: the means to the end

Kinetochores are proteinaceous complexes containing dozens of components; they are assembled at centromeric DNA regions and provide the major microtubule attachment site on chromosomes during cell division. Recent studies have defined the kinetochore components comprising the direct interface with spindle microtubules, primarily through structural and functional analysis of the Ndc80 and Dam1 complexes. These studies have facilitated our understanding of how kinetochores remain attached to the end of dynamic microtubules and how proper orientation of a kinetochore-microtubule attachment is promoted on the mitotic spindle. In this article, we review these recent studies and summarize their key findings.

In search of an optimal ring to couple microtubule depolymerization to processive chromosome motions

Mitotic chromosome motions are driven by microtubules (MTs) and associated proteins that couple kinetochores to MT ends. A good coupler should ensure a high stability of attachment, even when the chromosome changes direction or experiences a large opposing force. The optimal coupler is also expected to be efficient in converting the energy of MT depolymerization into chromosome motility. As was shown years ago, a "sleeve"-based, chromosome-associated structure could, in principle, couple MT dynamics to chromosome motion. A recently identified kinetochore complex from yeast, the "Dam1" or "DASH" complex, may function as an encircling coupler in vivo. Some features of the Dam1 ring differ from those of the "sleeve," but whether these differences are significant has not been examined. Here, we analyze theoretically the biomechanical properties of encircling couplers that have properties of the Dam1/DASH complex, such as its large diameter and inward-directed extensions. We demonstrate that, if the coupler is modeled as a wide ring with links that bind the MT wall, its optimal performance is achieved when the linkers are flexible and their binding to tubulin dimers is strong. The diffusive movement of such a coupler is limited, but MT depolymerization can drive its motion via a "forced walk," whose features differ significantly from those of the mechanisms based on biased diffusion. Our analysis identifies key experimental parameters whose values should determine whether the Dam1/DASH ring moves via diffusion or a forced walk.

A mechanobiochemical mechanism for monooriented chromosome oscillation in mitosis

During mitosis, the condensed chromosomes undergo a series of spectacular oscillations after they are captured in an end-on manner by kinetochore microtubules (KMT) emanating from the spindle poles. Such oscillations are commonly attributed to tug-of-war-like mechanisms, where the mechanical force imbalance alone drives the chromosome movement. However, a large portion of the force imbalance upon the chromosome is absorbed by the kinetochore and may not drive chromosome movement directly. Mounting evidence suggests that such resistance by the kinetochores regulates the chemical reactions of KMT plus-end growth and shrinkage, which have been shown as the determinant of the chromosome antipoleward (AP) and poleward movements. Here we incorporate this important regulatory feature, propose a mechanobiochemical feedback mechanism, and apply it to the monooriented chromosome oscillation, the early stage of the series of observed chromosome oscillations. In this model, the mechanical movement of the chromosome and the local biochemical reactions at the attached kinetochore region form a feedback loop that drives the oscillation. The force imbalance exerted on the chromosomes provides a bias (via mechanically sensitive proteins) on the local biochemical reactions controlling the KMT plus-end dynamics, and the movement of the chromosome in turn changes the forces exerted on it through the experimentally supported gradient in AP force. The proposed feedback mechanism can generate oscillatory behavior that depends on the topology of the feedback loop but is largely independent of the detailed molecular mechanism. We suggest potential molecular players, whose perturbation may allow direct experimental tests of the model.