Spindle oscillations during asymmetric cell division require a threshold number of active cortical force generators

A cytokinetic ring-driven cell rotation achieves Hertwig's rule in early development

Hertwig's rule states that cells divide along their longest axis, usually driven by forces acting on the mitotic spindle. Here, we show that in contrast to this rule, microtubule-based pulling forces in early Caenorhabditis elegans embryos align the spindle with the short axis of the cell. We combine theory with experiments to reveal that in order to correct this misalignment, inward forces generated by the constricting cytokinetic ring rotate the entire cell until the spindle is aligned with the cell's long axis. Experiments with slightly compressed mouse zygotes indicate that this cytokinetic ring-driven mechanism of ensuring Hertwig's rule is general for cells capable of rotating inside a confining shell, a scenario that applies to early cell divisions of many systems.

Quantification of cell shape, intracellular flows and transport based on DIC object detection and tracking

Computational image analysis combined with label-free imaging has helped maintain its relevance for cell biology, despite the rapid technical improvements in fluorescence microscopy with the molecular specificity of tags. Here, we discuss some computational tools developed in our lab and their application to quantify cell shape, intracellular organelle movement and bead transport in vitro, using differential interference contrast (DIC) microscopy data as inputs. The focus of these methods is image filtering to enhance image gradients, and combining them with segmentation and single particle tracking (SPT). We demonstrate the application of these methods to Escherichia coli cell length estimation and tracking of densely packed lipid granules in Caenorhabditis elegans one-celled embryos, diffusing beads in solutions of different viscosities and kinesin-driven transport on microtubules. These approaches demonstrate how improvements to low-level image analysis methods can help obtain insights through quantitative cellular and subcellular microscopy.

Lis1 slows force-induced detachment of cytoplasmic dynein from microtubules

Lis1 is a key cofactor for the assembly of active cytoplasmic dynein complexes that transport cargo along microtubules. Lis1 binds to the AAA+ ring and stalk of dynein and slows dynein motility, but the underlying mechanism has remained unclear. Using single-molecule imaging and optical trapping assays, we investigated how Lis1 binding affects the motility and force generation of yeast dynein in vitro. We showed that Lis1 slows motility by binding to the AAA+ ring of dynein, not by serving as a roadblock or tethering dynein to microtubules. Lis1 binding also does not affect force generation, but it induces prolonged stalls and reduces the asymmetry in the force-induced detachment of dynein from microtubules. The mutagenesis of the Lis1-binding sites on the dynein stalk partially recovers this asymmetry but does not restore dynein velocity. These results suggest that Lis1-stalk interaction slows the detachment of dynein from microtubules by interfering with the stalk sliding mechanism.

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.

Lack of chromokinesin Klp-19 creates a more rigid midzone and affects force transmission during anaphase in C. elegans

Recent studies have highlighted the significance of the spindle midzone - the region positioned between chromosomes - in ensuring proper chromosome segregation. By combining advanced 3D electron tomography and cutting-edge light microscopy we have discovered a previously unknown role of the regulation of microtubule dynamics within the spindle midzone of C. elegans. Using Fluorescence recovery after photobleaching and a combination of second harmonic generation and two-photon fluorescence microscopy, we found that the length of the antiparallel microtubule overlap zone in the spindle midzone is constant throughout anaphase, and independent of cortical pulling forces as well as the presence of the microtubule bundling protein SPD-1. Further investigations of SPD-1 and the chromokinesin KLP-19 in C. elegans suggest that KLP-19 regulates the overlap length and functions independently of SPD-1. Our data shows that KLP-19 plays an active role in regulating the length and turn-over of microtubules within the midzone as well as the size of the antiparallel overlap region throughout mitosis. Depletion of KLP-19 in mitosis leads to an increase in microtubule length in the spindle midzone, which also leads to increased microtubule - microtubule interaction, thus building up a more robust microtubule network. The spindle is globally stiffer and more stable, which has implications for the transmission of forces within the spindle affecting chromosome segregation dynamics. Our data shows that by localizing KLP-19 to the spindle midzone in anaphase microtubule dynamics can be locally controlled allowing the formation of a functional midzone.

A germline-specific role for unconventional components of the γ-tubulin complex in Caenorhabditis elegans

The γ-tubulin complex (γTuC) is a widely conserved microtubule nucleator, but some of its components, namely GCP4, GCP5 and GCP6 (also known as TUBGCP4, TUBGCP5 and TUBGCP6, respectively), have not been detected in Caenorhabditis elegans. Here, we identified two γTuC-associated proteins in C. elegans, GTAP-1 and GTAP-2, for which apparent orthologs were detected only in the genus Caenorhabditis. GTAP-1 and GTAP-2 were found to localize at centrosomes and the plasma membrane of the germline, and their centrosomal localization was interdependent. In early C. elegans embryos, whereas the conserved γTuC component MZT-1 (also known as MOZART1 and MZT1) was essential for the localization of centrosomal γ-tubulin, depletion of GTAP-1 and/or GTAP-2 caused up to 50% reduction of centrosomal γ-tubulin and precocious disassembly of spindle poles during mitotic telophase. In the adult germline, GTAP-1 and GTAP-2 contributed to efficient recruitment of the γTuC to the plasma membrane. Depletion of GTAP-1, but not of GTAP-2, severely disrupted both the microtubule array and the honeycomb-like structure of the adult germline. We propose that GTAP-1 and GTAP-2 are unconventional components of the γTuC that contribute to the organization of both centrosomal and non-centrosomal microtubules by targeting the γTuC to specific subcellular sites in a tissue-specific manner.

A central helical hairpin in SPD-5 enables centrosome strength and assembly

Centrosomes organize microtubules for mitotic spindle assembly and positioning. Forces mediated by these microtubules create tensile stresses on pericentriolar material (PCM), the outermost layer of centrosomes. How PCM resists these stresses is unclear at the molecular level. Here, we use cross-linking mass spectrometry (XL-MS) to map interactions underlying multimerization of SPD-5, an essential PCM scaffold component in C. elegans . We identified an interaction hotspot in an alpha helical hairpin motif in SPD-5 (a.a. 541-677). XL-MS data, ab initio structural predictions, and mass photometry suggest that this region dimerizes to form a tetrameric coiled-coil. Mutating a helical section (a.a. 610-640) or a single residue (R592) inhibited PCM assembly in embryos. This phenotype was rescued by eliminating microtubule pulling forces, revealing that PCM assembly and material strength are interrelated. We propose that interactions mediated by the helical hairpin strongly bond SPD-5 molecules to each other, thus enabling PCM to assemble fully and withstand stresses generated by microtubules.

Multivalent coiled-coil interactions enable full-scale centrosome assembly and strength

During mitotic spindle assembly, microtubules generate tensile stresses on pericentriolar material (PCM), the outermost layer of centrosomes. The molecular interactions that enable PCM to assemble rapidly and resist external forces are unknown. Here we use cross-linking mass spectrometry to identify interactions underlying supramolecular assembly of SPD-5, the main PCM scaffold protein in C. elegans . Crosslinks map primarily to alpha helices within the phospho-regulated region (PReM), a long C-terminal coiled-coil, and a series of four N-terminal coiled-coils. PLK-1 phosphorylation of SPD-5 creates new homotypic contacts, including two between PReM and the CM2-like domain, and eliminates numerous contacts in disordered linker regions, thus favoring coiled-coil-specific interactions. Mutations within these interacting regions cause PCM assembly defects that are partly rescued by eliminating microtubule-mediated forces. Thus, PCM assembly and strength are interdependent. In vitro , self-assembly of SPD-5 scales with coiled-coil content, although there is a defined hierarchy of association. We propose that multivalent interactions among coiled-coil regions of SPD-5 build the PCM scaffold and contribute sufficient strength to resist microtubule-mediated forces.

Dynamics of a spherical self-propelled tracer in a polymeric medium: interplay of self-propulsion, stickiness, and crowding

We employ computer simulations to study the dynamics of a self-propelled spherical tracer particle in a viscoelastic medium, made of a long polymer chain. Here, the interplay between viscoelasticity, stickiness, and activity (self-propulsion) brings additional complexity to the tracer dynamics. Our simulations show that on increasing the stickiness of the tracer particle to the polymer beads, the dynamics of the tracer particle slows down as it gets stuck to the polymer chain and moves along with it. But with increasing self-propulsion velocity, the dynamics gets enhanced. In the case of increasing stickiness as well as activity, the non-Gaussian parameter (NGP) exhibits non-monotonic behavior, which also shows up in the re-scaled self part of the van-Hove function. Non-Gaussianity results owing to the enhanced binding events and the sticky motion of the tracer along with the chain with increasing stickiness. On the other hand, with increasing activity, initially non-Gaussianity increases as the tracer moves through the heterogeneous polymeric environment but for higher activity, the tracer escapes resulting in a negative NGP. For higher values of stickiness, the trapping time distributions of the passive tracer particle broaden and have long tails. On the other hand, for a given stickiness with increasing self-propulsion force, the trapping time distributions become narrower and have short tails. We believe that our current simulation study will be helpful in elucidating the complex motion of activity-driven probes in viscoelastic media.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

In Silico Studies of Active Probe Dynamics in Crowded Media

Active systems are made of agents, each of which takes energy from the environment and converts it to directed motion. Therefore, by construction, these systems function out of equilibrium and cannot be described using equilibrium statistical mechanics. Though the most studied aspect has been the collective motion of active particles, the motion at the individual particle level in crowded media is also of prime importance. Examples include the motion of bacteria in hydrogels, single cell migration as a way to search for food or escape from toxic agents, and synthetic active agents transporting through soft crowded media. This review presents an overview of our understanding of single active probe dynamics in crowded media from computer simulations. The active probe is a Janus or a dumbbell-shaped particle, and the medium is made of crowders that are either sticky or repulsive to the probe and could be frozen or mobile. The density and the topology of the crowders also play an important role. We hope our in silico studies will help to elucidate the mechanism of activity-driven transport in crowded media in general and design nanomachines for targeted delivery.

Delineating mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

The nematode (roundworm) Caenorhabditis elegans is one of the most popular animal models for the study of developmental biology, as its invariant development and transparent body enable in toto cellular-resolution fluorescence microscopy imaging of developmental processes at 1-min intervals. This has led to the development of various computational tools for the systematic and automated analysis of imaging data to delineate the molecular and cellular processes throughout the embryogenesis of C. elegans, such as those associated with cell lineage, cell migration, cell morphology, and gene activity. In this review, we first introduce C. elegans embryogenesis and the development of techniques for tracking cell lineage and reconstructing cell morphology during this process. We then contrast the developmental modes of C. elegans and the customized technologies used for studying them with the ones of other animal models, highlighting its advantage for studying embryogenesis with exceptional spatial and temporal resolution. This is followed by an examination of the physical models that have been devised—based on accurate determinations of developmental processes afforded by analyses of imaging data—to interpret the early embryonic development of C. elegans from subcellular to intercellular levels of multiple cells, which focus on two key processes: cell polarization and morphogenesis. We subsequently discuss how quantitative data-based theoretical modeling has improved our understanding of the mechanisms of C. elegans embryogenesis. We conclude by summarizing the challenges associated with the acquisition of C. elegans embryogenesis data, the construction of algorithms to analyze them, and the theoretical interpretation.

A coarse-grained approach to model the dynamics of the actomyosin cortex

Background

The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions.

Results

Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin.

Conclusions

We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell cortex.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12915-022-01279-2).

Chemically symmetric and asymmetric self-driven rigid dumbbells in a 2D polymer gel

We employ computer simulations to unveil the translational and rotational dynamics of self-driven chemically symmetric and asymmetric rigid dumbbells in a two-dimensional polymer gel. Our results show that the activity or the self-propulsion always enhances the dynamics of the dumbbells. Making the self-propelled dumbbell chemically asymmetric leads to further enhancement in dynamics. Additionally, the direction of self-propulsion is a key factor for chemically asymmetric dumbbells, where self-propulsion towards the non-sticky half of the dumbbell results in faster translational and rotational dynamics compared to the case with the self-propulsion towards the sticky half of the dumbbell. Our analyses show that both the symmetric and asymmetric passive rigid dumbbells get trapped inside the mesh of the polymer gel, but the chemical asymmetry always facilitates the mesh to mesh motion of the dumbbell and it is even more pronounced when the dumbbell is self-propelled. This results in multiple peaks in the van Hove function with increasing self-propulsion. In a nutshell, we believe that our in silico study can guide researchers to design efficient artificial microswimmers possessing potential applications in site-specific delivery.

Evolutionary divergence of anaphase spindle mechanics in nematode embryos constrained by antagonistic pulling and viscous forces

Cellular functions like cell division are remarkably conserved across phyla. However the evolutionary principles of cellular organization that drive it are less well explored. Thus, an essential question remains: to what extent cellular parameters evolve without altering the basic function they sustain? Here we have observed 6 different nematode species for which the mitotic spindle is positioned asymmetrically during the first embryonic division. Whereas the C. elegans spindle undergoes oscillations during its displacement, the spindle elongates without oscillations in other species. We asked which evolutionary changes in biophysical parameters could explain differences in spindle motion while maintaining a constant output. Using laser microsurgery of the spindle we revealed that all species are subjected to cortical pulling forces, of varying magnitudes. Using a viscoelastic model to fit the recoil trajectories and with an independent measurement of cytoplasmic viscosity, we extracted the values of cytoplasmic drag, cortical pulling forces and spindle elasticity for all species. We found large variations in cytoplasmic viscosity whereas cortical pulling forces and elasticity were often more constrained. In agreement with previous simulations, we found that increased viscosity correlates with decreased oscillation speeds across species. However, the absence of oscillations despite low viscosity in some species, can only be explained by smaller pulling forces. Consequently, we find that spindle mobility across the species analyzed here is characterized by a tradeoff between cytoplasmic viscosity and pulling forces normalized by the size of the embryo. Our work provides a framework for understanding mechanical constraints on evolutionary diversification of spindle mobility.

Stochastic model of T Cell repolarization during target elimination (II)

Cytotoxic T lymphocytes (T cells) and natural killer cells form a tight contact, the immunological synapse (IS), with target cells, where they release their lytic granules containing perforin/granzyme and cytokine-containing vesicles. During this process the cell repolarizes and moves the microtubule organizing center (MTOC) toward the IS. In the first part of our work we developed a computational model for the molecular-motor-driven motion of the microtubule cytoskeleton during T cell polarization and analyzed the effects of cortical-sliding and capture-shrinkage mechanisms. Here we use this model to analyze the dynamics of the MTOC repositioning in situations in which 1) the IS is in an arbitrary position with respect to the initial position of the MTOC and 2) the T cell has two IS at two arbitrary positions. In the case of one IS, we found that the initial position determines which mechanism is dominant and that the time of repositioning does not rise monotonously with the MTOC-IS distance. In the case of two IS, we observe several scenarios that have also been reported experimentally: the MTOC alternates stochastically (but with a well-defined average transition time) between the two IS; it wiggles in between the two IS without transiting to one of the two; or it is at some point pulled to one of the two IS and stays there. Our model allows one to predict which scenario emerges in dependency of the mechanisms in action and the number of dyneins present. We report that the presence of capture-shrinkage mechanism in at least one IS is necessary to assure the transitions in every cell configuration. Moreover, the frequency of transitions does not decrease with the distance between the two IS and is the highest when both mechanisms are present in both IS.

Spatial and Temporal Scaling of Microtubules and Mitotic Spindles

During cell division, the mitotic spindle, a macromolecular structure primarily comprised of microtubules, drives chromosome alignment and partitioning between daughter cells. Mitotic spindles can sense cellular dimensions in order to adapt their length and mass to cell size. This scaling capacity is particularly remarkable during early embryo cleavage when cells divide rapidly in the absence of cell growth, thus leading to a reduction of cell volume at each division. Although mitotic spindle size scaling can occur over an order of magnitude in early embryos, in many species the duration of mitosis is relatively short, constant throughout early development and independent of cell size. Therefore, a key challenge for cells during embryo cleavage is not only to assemble a spindle of proper size, but also to do it in an appropriate time window which is compatible with embryo development. How spatial and temporal scaling of the mitotic spindle is achieved and coordinated with the duration of mitosis remains elusive. In this review, we will focus on the mechanisms that support mitotic spindle spatial and temporal scaling over a wide range of cell sizes and cellular contexts. We will present current models and propose alternative mechanisms allowing cells to spatially and temporally coordinate microtubule and mitotic spindle assembly.

Novel mechanism for oscillations in catchbonded motor-filament complexes

Generation of mechanical oscillations is ubiquitous to a wide variety of intracellular processes ranging from activity of muscle fibres to oscillations of the mitotic spindle. The activity of motors plays a vital role in maintaining the integrity of the mitotic spindle structure and in generating spontaneous oscillations. While the structural features and properties of the individual motors are well characterized, their implications on the functional behaviour of motor-filament complexes is more involved. We show that force-induced allosteric deformations in dynein, which results in catchbonding behaviour, provide a generic mechanism to generate spontaneous oscillations in motor-cytoskeletal filament complexes. The resultant phase diagram of such motor-filament systems - characterized by force-induced allosteric deformations - exhibits bistability and sustained limit cycle oscillations in biologically relevant regimes, such as for catchbonded dynein. The results reported here elucidate the central role of this mechanism in fashioning a distinctive stability behaviour and oscillations in motor-filament complexes, such as mitotic spindles.

EFA6 in Axon Regeneration, as a Microtubule Regulator and as a Guanine Nucleotide Exchange Factor

Axon regeneration after injury is a conserved biological process that involves a large number of molecular pathways, including rapid calcium influx at injury sites, retrograde injury signaling, epigenetic transition, transcriptional reprogramming, polarized transport, and cytoskeleton reorganization. Despite the numerous efforts devoted to understanding the underlying cellular and molecular mechanisms of axon regeneration, the search continues for effective target molecules for improving axon regeneration. Although there have been significant historical efforts towards characterizing pro-regenerative factors involved in axon regeneration, the pursuit of intrinsic inhibitors is relatively recent. EFA6 (exchange factor for ARF6) has been demonstrated to inhibit axon regeneration in different organisms. EFA6 inhibition could be a promising therapeutic strategy to promote axon regeneration and functional recovery after axon injury. This review summarizes the inhibitory role on axon regeneration through regulating microtubule dynamics and through affecting ARF6 (ADP-ribosylation factor 6) GTPase-mediated integrin transport.

The coordination of spindle-positioning forces during the asymmetric division of the Caenorhabditis elegans zygote

In Caenorhabditis elegans zygote, astral microtubules generate forces essential to position the mitotic spindle, by pushing against and pulling from the cortex. Measuring microtubule dynamics there, we revealed the presence of two populations, corresponding to pulling and pushing events. It offers a unique opportunity to study, under physiological conditions, the variations of both spindle-positioning forces along space and time. We propose a threefold control of pulling force, by polarity, spindle position and mitotic progression. We showed that the sole anteroposterior asymmetry in dynein on-rate, encoding pulling force imbalance, is sufficient to cause posterior spindle displacement. The positional regulation, reflecting the number of microtubule contacts in the posterior-most region, reinforces this imbalance only in late anaphase. Furthermore, we exhibited the first direct proof that dynein processivity increases along mitosis. It reflects the temporal control of pulling forces, which strengthens at anaphase onset following mitotic progression and independently from chromatid separation. In contrast, the pushing force remains constant and symmetric and contributes to maintaining the spindle at the cell centre during metaphase.

Two modes of PRC1-mediated mechanical resistance to kinesin-driven microtubule network disruption

The proper organization of the microtubule-based spindle during cell division requires the collective activity of many different proteins. These include non-motor microtubule-associated proteins (MAPs), whose functions include crosslinking microtubules to regulate filament sliding rates and assemble microtubule arrays. One such protein is PRC1, an essential MAP that has been shown to preferentially crosslink overlapping antiparallel microtubules at the spindle midzone. PRC1 has been proposed to act as a molecular brake, but insight into the mechanism of how PRC1 molecules function cooperatively to resist motor-driven microtubule sliding and to allow for the formation of stable midzone overlaps remains unclear. Here, we employ a modified microtubule gliding assay to rupture PRC1-mediated microtubule pairs using surface-bound kinesins. We discovered that PRC1 crosslinks always reduce bundled filament sliding velocities relative to single-microtubule gliding rates and do so via two distinct emergent modes of mechanical resistance to motor-driven sliding. We term these behaviors braking and coasting, where braking events exhibit substantially slowed microtubule sliding compared to coasting events. Strikingly, braking behavior requires the formation of two distinct high-density clusters of PRC1 molecules near microtubule tips. Our results suggest a cooperative mechanism for PRC1 accumulation when under mechanical load that leads to a unique state of enhanced resistance to filament sliding and provides insight into collective protein ensemble behavior in regulating the mechanics of spindle assembly.

Polar relaxation by dynein-mediated removal of cortical myosin II

Nearly six decades ago, Lewis Wolpert proposed the relaxation of the polar cell cortex by the radial arrays of astral microtubules as a mechanism for cleavage furrow induction. While this mechanism has remained controversial, recent work has provided evidence for polar relaxation by astral microtubules, although its molecular mechanisms remain elusive. Here, using C. elegans embryos, we show that polar relaxation is achieved through dynein-mediated removal of myosin II from the polar cortexes. Mutants that position centrosomes closer to the polar cortex accelerated furrow induction, whereas suppression of dynein activity delayed furrowing. We show that dynein-mediated removal of myosin II from the polar cortexes triggers a bidirectional cortical flow toward the cell equator, which induces the assembly of the actomyosin contractile ring. These results provide a molecular mechanism for the aster-dependent polar relaxation, which works in parallel with equatorial stimulation to promote robust cytokinesis.

The first steps in the life of a worm: Themes and variations in asymmetric division in C. elegans and other nematodes

Starting with Boveri in the 1870s, microscopic investigation of early embryogenesis in a broad swath of nematode species revealed the central role of asymmetric cell division in embryonic axis specification, blastomere positioning, and cell fate specification. Notably, across the class Chromadorea, a conserved theme emerges-asymmetry is first established in the zygote and specifies its asymmetric division, giving rise to an anterior somatic daughter cell and a posterior germline daughter cell. Beginning in the 1980s, the emergence of Caenorhabditis elegans as a model organism saw the advent of genetic tools that enabled rapid progress in our understanding of the molecular mechanisms underlying asymmetric division, in many cases defining key paradigms that turn out to regulate asymmetric division in a wide range of systems. Yet, the consequence of this focus on C. elegans came at the expense of exploring the extant diversity of developmental variation exhibited across nematode species. Given the resurgent interest in evolutionary studies facilitated in part by new tools, here we revisit the diversity in this asymmetric first division, juxtaposing molecular insight into mechanisms of symmetry-breaking, spindle positioning and fate specification, with a consideration of plasticity and variability within and between species. In the process, we hope to highlight questions of evolutionary forces and molecular variation that may have shaped the extant diversity of developmental mechanisms observed across Nematoda.

CentTracker: a trainable, machine-learning-based tool for large-scale analyses of Caenorhabditis elegans germline stem cell mitosis

Investigating the complex interactions between stem cells and their native environment requires an efficient means to image them in situ. Caenorhabditis elegans germline stem cells (GSCs) are distinctly accessible for intravital imaging; however, long-term image acquisition and analysis of dividing GSCs can be technically challenging. Here we present a systematic investigation into the technical factors impacting GSC physiology during live imaging and provide an optimized method for monitoring GSC mitosis under minimally disruptive conditions. We describe CentTracker, an automated and generalizable image analysis tool that uses machine learning to pair mitotic centrosomes and that can extract a variety of mitotic parameters rapidly from large-scale data sets. We employ CentTracker to assess a range of mitotic features in a large GSC data set. We observe spatial clustering of mitoses within the germline tissue but no evidence that subpopulations with distinct mitotic profiles exist within the stem cell pool. We further find biases in GSC spindle orientation relative to the germline’s distal–proximal axis and thus the niche. The technical and analytical tools provided herein pave the way for large-scale screening studies of multiple mitotic processes in GSCs dividing in situ, in an intact tissue, in a living animal, under seemingly physiological conditions.

Quantifying Intracellular Particle Flows by DIC Object Tracking

Label-free imaging techniques such as differential interference contrast (DIC) allow the observation of cells and large subcellular structures in their native, unperturbed states with minimal exposure to light. The development of robust computational image-analysis routines is vital to quantitative label-free imaging. The reliability of quantitative analysis of time-series microscopy data based on single-particle tracking relies on accurately detecting objects as distinct from the background, i.e., segmentation. Typical approaches to segmenting DIC images either involve converting images to those resembling phase contrast, mimicking the optics of DIC object formation, or using the morphological properties of objects. Here, we describe MATLAB based, single-particle tracking tool with a GUI for mobility analysis of objects from in vitro and in vivo DIC time-series microscopy. The tool integrates contrast enhancement with multiple modified Gaussian filters, automated threshold detection for segmentation and minimal distance-based two-dimensional single-particle tracking. We compare the relative performance of multiple filters and demonstrate the utility of the tool for DIC object tracking (DICOT). We quantify subcellular dynamics of a time series of Caenorhabditis elegans embryos in the one-celled stage by detecting birefringent yolk granules in the cytoplasm with high precision. The resulting two-dimensional map of oscillatory dynamics of granules quantifies the cytoplasmic flows driven by anaphasic spindle oscillations. The frequency of oscillations across the anterior-posterior (A-P) and transverse axes of the embryo correspond well with the reported frequency of spindle oscillations. We validate the quantitative accuracy of our method by tracking the in vitro diffusive mobility of micron-sized beads in glycerol solutions. Estimates of the diffusion coefficients of the granules are used to measure the viscosity of a dilution series of glycerol. Thus, our computational method is likely to be useful for both intracellular mobility and in vitro microrheology.

Regulated changes in material properties underlie centrosome disassembly during mitotic exit

Centrosomes must resist microtubule-mediated forces for mitotic chromosome segregation. During mitotic exit, however, centrosomes are deformed and fractured by those same forces, which is a key step in centrosome disassembly. How the functional material properties of centrosomes change throughout the cell cycle, and how they are molecularly tuned, remain unknown. Here, we used optically induced flow perturbations to determine the molecular basis of centrosome strength and ductility in C. elegans embryos. We found that both properties declined sharply at anaphase onset, long before natural disassembly. This mechanical transition required PP2A phosphatase and correlated with inactivation of PLK-1 (Polo kinase) and SPD-2 (Cep192). In vitro, PLK-1 and SPD-2 directly protected centrosome scaffolds from force-induced disassembly. Our results suggest that, before anaphase, PLK-1 and SPD-2 respectively confer strength and ductility to the centrosome scaffold so that it can resist microtubule-pulling forces. In anaphase, centrosomes lose PLK-1 and SPD-2 and transition to a weak, brittle state that enables force-mediated centrosome disassembly.

Going with the flow: insights from Caenorhabditis elegans zygote polarization

Cell polarity is the asymmetric distribution of cellular components along a defined axis. Polarity relies on complex signalling networks between conserved patterning proteins, including the PAR (partitioning defective) proteins, which become segregated in response to upstream symmetry breaking cues. Although the mechanisms that drive the asymmetric localization of these proteins are dependent upon cell type and context, in many cases the regulation of actomyosin cytoskeleton dynamics is central to the transport, recruitment and/or stabilization of these polarity effectors into defined subcellular domains. The transport or advection of PAR proteins by an actomyosin flow was first observed in the Caenorhabditis elegans zygote more than a decade ago. Since then a multifaceted approach, using molecular methods, high-throughput screens, and biophysical and computational models, has revealed further aspects of this flow and how polarity regulators respond to and modulate it. Here, we review recent findings on the interplay between actomyosin flow and the PAR patterning networks in the polarization of the C. elegans zygote. We also discuss how these discoveries and developed methods are shaping our understanding of other flow-dependent polarizing systems. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

Translational and rotational dynamics of a self-propelled Janus probe in crowded environments

We computationally investigate the dynamics of a self-propelled Janus probe in crowded environments. The crowding is caused by the presence of viscoelastic polymers or non-viscoelastic disconnected monomers. Our simulations show that the translational as well as rotational mean square displacements have a distinctive three-step growth for fixed values of self-propulsion force, and steadily increase with self-propulsion, irrespective of the nature of the crowder. On the other hand, in the absence of crowders, the rotational dynamics of the Janus probe is independent of self-propulsion force. On replacing the repulsive polymers with sticky ones, translational and rotational mean square displacements of the Janus probe show a sharp drop. Since different faces of a Janus particle interact differently with the environment, we show that the direction of self-propulsion also affects its dynamics. The ratio of long-time translational and rotational diffusivities of the self-propelled probe with a fixed self-propulsion, when plotted against the area fraction of the crowders, passes through a minimum and at higher area fraction merges to its value in the absence of the crowder. This points towards the decoupling of the translational and rotational dynamics of the self-propelled probe at an intermediate area fraction of the crowders. However, such translational-rotational decoupling is absent for passive probes.

Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution

The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.

Mechanochemical Crosstalk Produces Cell-Intrinsic Patterning of the Cortex to Orient the Mitotic Spindle

Proliferating animal cells are able to orient their mitotic spindles along their interphase cell axis, setting up the axis of cell division, despite rounding up as they enter mitosis. This has previously been attributed to molecular memory and, more specifically, to the maintenance of adhesions and retraction fibers in mitosis [1-6], which are thought to act as local cues that pattern cortical Gαi, LGN, and nuclear mitotic apparatus protein (NuMA) [3, 7-18]. This cortical machinery then recruits and activates Dynein motors, which pull on astral microtubules to position the mitotic spindle. Here, we reveal a dynamic two-way crosstalk between the spindle and cortical motor complexes that depends on a Ran-guanosine triphosphate (GTP) signal [12], which is sufficient to drive continuous monopolar spindle motion independently of adhesive cues in flattened human cells in culture. Building on previous work [1, 12, 19-23], we implemented a physical model of the system that recapitulates the observed spindle-cortex interactions. Strikingly, when this model was used to study spindle dynamics in cells entering mitosis, the chromatin-based signal was found to preferentially clear force generators from the short cell axis, so that cortical motors pulling on astral microtubules align bipolar spindles with the interphase long cell axis, without requiring a fixed cue or a physical memory of interphase shape. Thus, our analysis shows that the ability of chromatin to pattern the cortex during the process of mitotic rounding is sufficient to translate interphase shape into a cortical pattern that can be read by the spindle, which then guides the axis of cell division.

The Generation of Dynein Networks by Multi-Layered Regulation and Their Implication in Cell Division

Cytoplasmic dynein-1 (hereafter referred to as dynein) is a major microtubule-based motor critical for cell division. Dynein is essential for the formation and positioning of the mitotic spindle as well as the transport of various cargos in the cell. A striking feature of dynein is that, despite having a wide variety of functions, the catalytic subunit is coded in a single gene. To perform various cellular activities, there seem to be different types of dynein that share a common catalytic subunit. In this review, we will refer to the different kinds of dynein as “dyneins.” This review attempts to classify the mechanisms underlying the emergence of multiple dyneins into four layers. Inside a cell, multiple dyneins generated through the multi-layered regulations interact with each other to form a network of dyneins. These dynein networks may be responsible for the accurate regulation of cellular activities, including cell division. How these networks function inside a cell, with a focus on the early embryogenesis of Caenorhabditis elegans embryos, is discussed, as well as future directions for the integration of our understanding of molecular layering to understand the totality of dynein’s function in living cells.

Dynein Harnesses Active Fluctuations of Microtubules for Faster Movement

The cytoskeleton forms a dynamic network that generates fluctuations larger than thermal agitation of the cytoplasm¹. Here, we tested whether dynein, a minus-end-directed microtubule (MT) motor², can harness energy from these fluctuations using optical trapping in vitro. We show that dynein forms an asymmetric slip bond with MTs, where its detachment rate increases more slowly under hindering forces than assisting forces. This asymmetry enables dynein to generate unidirectional motility towards the minus-end from force fluctuations. Consistent with our model, oscillatory forces exerted by the trap drive dynein stepping without net force and ATP. Dynein is capable of ratcheting towards the minus-end even when the net force is in the plus-end direction. With ATP, force oscillations increase the velocity and stall force of dynein as it transports cargos and glides MTs. Therefore, dynein is a mechanical ratchet that rectifies cytoskeletal fluctuations to move faster and resists higher forces along MTs.

Collective effects of yeast cytoplasmic dynein based microtubule transport

Teams of cortically anchored dyneins pulling at microtubules (MTs) are known to be essential for aster, spindle and nuclear positioning during cell division and fertilization. While the single-molecule basis of dynein processivity is now better understood, the effect of increasing numbers of motors on transport is not clear. Here, we examine the collective transport properties of a Saccharomyces cerevisiae cytoplasmic dynein fragment, widely used as a minimal model, by a combination of quantitative MT gliding assays and stochastic simulations. We find both MT lengths and motor densities qualitatively affect the degree of randomness of MT transport. However, the directionality and velocity of MTs increase above a threshold number of motors (N) interacting with a filament. To better understand this behavior, we simulate a gliding assay based on a model of uniformly distributed immobilized motors transporting semi-flexible MTs. Each dynein dimer is modeled as an effective stochastic stepper with asymmetric force dependent detachment dynamics, based on single-molecule experiments. Simulations predict increasing numbers of motors (N) result in a threshold dependent transition in directionality and transport velocity and a monotonic decrease in effective diffusivity. Thus both experiment and theory show qualitative agreement in the emergence of coordination in transport above a threshold number of motor heads. We hypothesize that the phase-transition like property of this dynein could play a role in vivo during yeast mitosis, when this dynein localizes to the cortex and pulls astral MTs of increasing length, resulting in correct positioning and orientation of the nucleus at the bud-neck.

Measuring the Elastic Properties of Living Cells

Cell's elasticity is an integrative parameter summarizing the biophysical outcome of many known and unknown cellular processes. This includes intracellular signaling, cytoskeletal activity, changes of cell volume and morphology, and many others. Not only intracellular processes defines a cell's elasticity but also environmental factors like their biochemical and biophysical surrounding. Therefore, cell mechanics represents a comprehensive variable of life. A cell in its standard conditions shows variabilities of biochemical and biophysical processes resulting in a certain range of cell's elasticity. Changes of the standard conditions, endogenously or exogenously induced, are frequently paralleled by changes of cell elasticity. Therefore cell elasticity could serve as parameter to characterize different states of a cell. Atomic force microscopy (AFM) combines high spatial resolution with very high force sensitivity and allows investigating mechanical properties of living cells under physiological conditions. However, elastic moduli reported in the literature showed a large variability, sometimes by an order of magnitude (or even more) for the same cell type assessed in different labs. Clearly, a prerequisite for the use of cell elasticity to describe the actual cell status is a standardized procedure that allows obtaining comparable values of a cell independent from the instrument, from the lab and operator. Biologically derived variations of elasticity could not be reduced due to the nature of living cells but technically and methodologically derived variations could be minimized by a standardized procedure.This chapter provides a Standardized Nanomechanical AFM Procedure (SNAP) that reduces strongly the variability of results obtained on soft samples and living cells by a reliable method to calibrate AFM cantilevers.

The polarity-induced force imbalance in Caenorhabditis elegans embryos is caused by asymmetric binding rates of dynein to the cortex

During asymmetric cell division, the molecular motor dynein generates cortical pulling forces that position the spindle to reflect polarity and adequately distribute cell fate determinants. In Caenorhabditis elegans embryos, despite a measured anteroposterior force imbalance, antibody staining failed to reveal dynein enrichment at the posterior cortex, suggesting a transient localization there. Dynein accumulates at the microtubule plus ends, in an EBP-2EB-dependent manner. This accumulation, although not transporting dynein, contributes modestly to cortical forces. Most dyneins may instead diffuse to the cortex. Tracking of cortical dynein revealed two motions: one directed and the other diffusive-like, corresponding to force-generating events. Surprisingly, while dynein is not polarized at the plus ends or in the cytoplasm, diffusive-like tracks were more frequently found at the embryo posterior tip, where the forces are higher. This asymmetry depends on GPR-1/2LGN and LIN-5NuMA, which are enriched there. In csnk-1(RNAi) embryos, the inverse distribution of these proteins coincides with an increased frequency of diffusive-like tracks anteriorly. Importantly, dynein cortical residence time is always symmetric. We propose that the dynein-binding rate at the posterior cortex is increased, causing the polarity-reflecting force imbalance. This mechanism of control supplements the regulation of mitotic progression through the nonpolarized dynein detachment rate.

Microtubule Feedback and LET-99-Dependent Control of Pulling Forces Ensure Robust Spindle Position

During asymmetric division of the Caenorhabditis elegans zygote, to properly distribute cell fate determinants, the mitotic spindle is asymmetrically localized by a combination of centering and cortical-pulling microtubule-mediated forces, the dynamics of the latter being regulated by mitotic progression. Here, we show a, to our knowledge, novel and additional regulation of these forces by spindle position itself. For that, we observed the onset of transverse spindle oscillations, which reflects the burst of anaphase pulling forces. After delaying anaphase onset, we found that the position at which the spindle starts to oscillate was unchanged compared to control embryos and uncorrelated to anaphase onset. In mapping the cortical microtubule dynamics, we measured a steep increase in microtubule contact density after the posterior centrosome reached the critical position of 70% of embryo length, strongly suggesting the presence of a positional switch for spindle oscillations. Expanding a previous model based on a force-generator temporal control, we implemented this positional switch and observed that the large increase in microtubule density accounted for the pulling force burst. Thus, we propose that the spindle position influences the cortical availability of microtubules on which the active force generators, controlled by cell cycle progression, can pull. Importantly, we found that this positional control relies on the polarity-dependent LET-99 cortical band, the boundary of which could be probed by microtubules. This dual positional and temporal control well accounted for our observation that the oscillation onset position resists changes in cellular geometry and moderate variations in the active force generator number. Finally, our model suggests that spindle position at mitosis end is more sensitive to the polarity factor LET-99, which restricts the region of active force generators to a posterior-most region, than to microtubule number or force generator number/activity. Overall, we show that robustness in spindle positioning originates in cell mechanics rather than biochemical networks.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

The Scribble Cell Polarity Module in the Regulation of Cell Signaling in Tissue Development and Tumorigenesis

The Scribble cell polarity module, comprising Scribbled (Scrib), Discs-large (Dlg) and Lethal-2-giant larvae (Lgl), has a tumor suppressive role in mammalian epithelial cancers. The Scribble module proteins play key functions in the establishment and maintenance of different modes of cell polarity, as well as in the control of tissue growth, differentiation and directed cell migration, and therefore are major regulators of tissue development and homeostasis. Whilst molecular details are known regarding the roles of Scribble module proteins in cell polarity regulation, their precise mode of action in the regulation of other key cellular processes remains enigmatic. An accumulating body of evidence indicates that Scribble module proteins play scaffolding roles in the control of various signaling pathways, which are linked to the control of tissue growth, differentiation and cell migration. Multiple Scrib, Dlg and Lgl interacting proteins have been discovered, which are involved in diverse processes, however many function in the regulation of cellular signaling. Herein, we review the components of the Scrib, Dlg and Lgl protein interactomes, and focus on the mechanism by which they regulate cellular signaling pathways in metazoans, and how their disruption leads to cancer.

Tumor suppressor APC is an attenuator of spindle-pulling forces during C. elegans asymmetric cell division

The adenomatous polyposis coli (APC) tumor suppressor has dual functions in Wnt/β-catenin signaling and accurate chromosome segregation and is frequently mutated in colorectal cancers. Although APC contributes to proper cell division, the underlying mechanisms remain poorly understood. Here we show that Caenorhabditis elegans APR-1/APC is an attenuator of the pulling forces acting on the mitotic spindle. During asymmetric cell division of the C. elegans zygote, a LIN-5/NuMA protein complex localizes dynein to the cell cortex to generate pulling forces on astral microtubules that position the mitotic spindle. We found that APR-1 localizes to the anterior cell cortex in a Par-aPKC polarity-dependent manner and suppresses anterior centrosome movements. Our combined cell biological and mathematical analyses support the conclusion that cortical APR-1 reduces force generation by stabilizing microtubule plus-ends at the cell cortex. Furthermore, APR-1 functions in coordination with LIN-5 phosphorylation to attenuate spindle-pulling forces. Our results document a physical basis for the attenuation of spindle-pulling force, which may be generally used in asymmetric cell division and, when disrupted, potentially contributes to division defects in cancer.

Evolution of mitotic spindle behavior during the first asymmetric embryonic division of nematodes

Asymmetric cell division is essential to generate cellular diversity. In many animal cells, the cleavage plane lies perpendicular to the mitotic spindle, and it is the spindle positioning that dictates the size of the daughter cells. Although some properties of spindle positioning are conserved between distantly related model species and different cell types, little is known of the evolutionary robustness of the mechanisms underlying this event. We recorded the first embryonic division of 42 species of nematodes closely related to Caenorhabditis elegans, which is an excellent model system to study the biophysical properties of asymmetric spindle positioning. Our recordings, corresponding to 128 strains from 27 Caenorhabditis and 15 non-Caenorhabditis species (accessible at http://www.ens-lyon.fr/LBMC/NematodeCell/videos/), constitute a powerful collection of subcellular phenotypes to study the evolution of various cellular processes across species. In the present work, we analyzed our collection to the study of asymmetric spindle positioning. Although all the strains underwent an asymmetric first cell division, they exhibited large intra- and inter-species variations in the degree of cell asymmetry and in several parameters controlling spindle movement, including spindle oscillation, elongation, and displacement. Notably, these parameters changed frequently during evolution with no apparent directionality in the species phylogeny, with the exception of spindle transverse oscillations, which were an evolutionary innovation at the base of the Caenorhabditis genus. These changes were also unrelated to evolutionary variations in embryo size. Importantly, spindle elongation, displacement, and oscillation each evolved independently. This finding contrasts starkly with expectations based on C. elegans studies and reveals previously unrecognized evolutionary changes in spindle mechanics. Collectively, these data demonstrate that, while the essential process of asymmetric cell division has been conserved over the course of nematode evolution, the underlying spindle movement parameters can combine in various ways. Like other developmental processes, asymmetric cell division is subject to system drift.

Physical Limits on the Precision of Mitotic Spindle Positioning by Microtubule Pushing forces: Mechanics of mitotic spindle positioning

Tissues are shaped and patterned by mechanical and chemical processes. A key mechanical process is the positioning of the mitotic spindle, which determines the size and location of the daughter cells within the tissue. Recent force and position-fluctuation measurements indicate that pushing forces, mediated by the polymerization of astral microtubules against- the cell cortex, maintain the mitotic spindle at the cell center in Caenorhabditis elegans embryos. The magnitude of the centering forces suggests that the physical limit on the accuracy and precision of this centering mechanism is determined by the number of pushing microtubules rather than by thermally driven fluctuations. In cells that divide asymmetrically, anti-centering, pulling forces generated by cortically located dyneins, in conjunction with microtubule depolymerization, oppose the pushing forces to drive spindle displacements away from the center. Thus, a balance of centering pushing forces and anti-centering pulling forces localize the mitotic spindles within dividing C. elegans cells.

Bidirectional motion of filaments: the role of motor proteins and passive cross linkers

In eukaryotic cells, motor proteins (MPs) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules forms whose stability and dynamics under the influence of MPs have been studied extensively. Although passive cross linkers (PCLs) are known to provide structural stability to a filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on filamentous overlap remain largely unexplored. Here, we formulate and characterize a model to study this, using linear stability analysis and numerical integration. In the presence of PCLs, we find dynamic phase transitions with changing activity exhibiting regimes of stable partial overlap with or without oscillations, instability towards complete overlap, and stable limit cycle oscillations that emerge via a supercritical Hopf bifurcation characterized by an oscillation frequency determined by the MP and PCL parameters. We show that the overlap dynamics and stability depend crucially on whether both the filaments of an overlapping pair are movable or one is immobilized, having potential implications for in vivo and in vitro studies.

An Emergence Framework of Carcinogenesis

Experimental paradigms provide the framework for the understanding of cancer, and drive research and treatment, but are rarely considered by clinicians. The somatic mutation theory (SMT), in which cancer is considered a genetic disease, has been the predominant traditional model of cancer for over 50 years. More recently, alternative theories have been proposed, such as tissue organization field theory (TOFT), evolutionary models, and inflammatory models. Key concepts within the various models have led to them being difficult to reconcile. Progressively, it has been recognized that biological systems cannot be fully explained by the physicochemical properties of their constituent parts. There is an increasing call for a 'systems' approach. Incorporating the concepts of 'emergence', 'systems', 'thermodynamics', and 'chaos', a single integrated framework for carcinogenesis has been developed, enabling existing theories to become compatible as alternative mechanisms, facilitating the integration of bioinformatics and providing a structure in which translational research can flow from both 'benchtop to bedside' and 'bedside to benchtop'. In this review, a basic understanding of the key concepts of 'emergence', 'systems', 'system levels', 'complexity', 'thermodynamics', 'entropy', 'chaos', and 'fractals' is provided. Non-linear mathematical equations are included where possible to demonstrate compatibility with bioinformatics. Twelve principles that define the 'emergence framework of carcinogenesis' are developed, with principles 1-10 encapsulating the key concepts upon which the framework is built and their application to carcinogenesis. Principle 11 relates the framework to cancer progression. Principle 12 relates to the application of the framework to translational research. The 'emergence framework of carcinogenesis' collates current paradigms, concepts, and evidence around carcinogenesis into a single framework that incorporates previously incompatible viewpoints and ideas. Any researcher, scientist, or clinician involved in research, treatment, or prevention of cancer can employ this framework.

Two populations of cytoplasmic dynein contribute to spindle positioning in C. elegans embryos

The position of the mitotic spindle is tightly controlled in animal cells as it determines the plane and orientation of cell division. Contacts between cytoplasmic dynein and astral microtubules (MTs) at the cell cortex generate pulling forces that position the spindle. An evolutionarily conserved Gα-GPR-1/2Pins/LGN-LIN-5Mud/NuMA cortical complex interacts with dynein and is required for pulling force generation, but the dynamics of this process remain unclear. In this study, by fluorescently labeling endogenous proteins in Caenorhabditis elegans embryos, we show that dynein exists in two distinct cortical populations. One population directly depends on LIN-5, whereas the other is concentrated at MT plus ends and depends on end-binding (EB) proteins. Knockout mutants lacking all EBs are viable and fertile and display normal pulling forces and spindle positioning. However, EB protein-dependent dynein plus end tracking was found to contribute to force generation in embryos with a partially perturbed dynein function, indicating the existence of two mechanisms that together create a highly robust force-generating system.

Antagonistic Behaviors of NMY-1 and NMY-2 Maintain Ring Channels in the C. elegans Gonad

Contractile rings play critical roles in a number of biological processes, including oogenesis, wound healing, and cytokinesis. In many cases, the activity of motor proteins such as nonmuscle myosins is required for appropriate constriction of these contractile rings. In the gonad of the nematode worm Caenorhabditis elegans, ring channels are a specialized form of contractile ring that are maintained at a constant diameter before oogenesis. We propose a model of ring channel maintenance that explicitly incorporates force generation by motor proteins that can act normally or tangentially to the ring channel opening. We find that both modes of force generation are needed to maintain the ring channels. We demonstrate experimentally that the type II myosins NMY-1 and NMY-2 antagonize each other in the ring channels by producing force in perpendicular directions: the experimental depletion of NMY-1/theoretical decrease in orthogonal force allows premature ring constriction and cellularization, whereas the experimental depletion of NMY-2/theoretical decrease in tangential force opens the ring channels and prevents cellularization. Together, our experimental and theoretical results show that both forces, mediated by NMY-1 and NMY-2, are crucial for maintaining the appropriate ring channel diameter and dynamics throughout the gonad.

Dynein is regulated by the stability of its microtubule track

How dynein motors accurately move cargoes is an important question. In budding yeast, dynein moves the mitotic spindle to the predetermined site of cytokinesis by pulling on astral microtubules. In this study, using high-resolution imaging in living cells, we discover that spindle movement is regulated by changes in microtubule plus-end dynamics that occur when dynein generates force. Mutants that increase plus-end stability increase the frequency and duration of spindle movements, causing positioning errors. We find that dynein plays a primary role in regulating microtubule dynamics by destabilizing microtubules. In contrast, the dynactin complex counteracts dynein and stabilizes microtubules through a mechanism involving the shoulder subcomplex and the cytoskeletal-associated protein glycine-rich domain of Nip100/p150^glued Our results support a model in which dynein destabilizes its microtubule substrate by using its motility to deplete dynactin from the plus end. We propose that interplay among dynein, dynactin, and the stability of the microtubule substrate creates a mechanism that regulates accurate spindle positioning.

Spindle orientation: a question of complex positioning

The direction in which a cell divides is determined by the orientation of its mitotic spindle at metaphase. Spindle orientation is therefore important for a wide range of developmental processes, ranging from germline stem cell division to epithelial tissue homeostasis and regeneration. In multiple cell types in multiple animals, spindle orientation is controlled by a conserved biological machine that mediates a pulling force on astral microtubules. Restricting the localization of this machine to only specific regions of the cortex can thus determine how the mitotic spindle is oriented. As we review here, recent findings based on studies in tunicate, worm, fly and vertebrate cells have revealed that the mechanisms for mediating this restriction are surprisingly diverse.

Asymmetric Cell Division in the One-Cell C. elegans Embryo: Multiple Steps to Generate Cell Size Asymmetry

The first division of the one-cell C. elegans embryo has been a fundamental model in deciphering the mechanisms underlying asymmetric cell division. Polarization of the one-cell zygote is induced by a signal from the sperm centrosome and results in the asymmetric distribution of PAR proteins. Multiple mechanisms then maintain PAR polarity until the end of the first division. Once asymmetrically localized, PAR proteins control several essential aspects of asymmetric division, including the position of the mitotic spindle along the polarity axis. Coordination of the spindle and cytokinetic furrow positions is the next essential step to ensure proper asymmetric division. In this chapter, I review the different mechanisms underlying these successive steps of asymmetric division. Work from the last 30 years has revealed the existence of multiple and redundant regulatory pathways which ensure division robustness. Besides the essential role of PAR proteins, this work also emphasizes the importance of both microtubules and actomyosin throughout the different steps of asymmetric division.

The Mitotic Spindle in the One-Cell C. elegans Embryo Is Positioned with High Precision and Stability

Precise positioning of the mitotic spindle is important for specifying the plane of cell division, which in turn determines how the cytoplasmic contents of the mother cell are partitioned into the daughter cells, and how the daughters are positioned within the tissue. During metaphase in the early Caenorhabditis elegans embryo, the spindle is aligned and centered on the anterior-posterior axis by a microtubule-dependent machinery that exerts restoring forces when the spindle is displaced from the center. To investigate the accuracy and stability of centering, we tracked the position and orientation of the mitotic spindle during the first cell division with high temporal and spatial resolution. We found that the precision is remarkably high: the cell-to-cell variation in the transverse position of the center of the spindle during metaphase, as measured by the standard deviation, was only 1.5% of the length of the short axis of the cell. Spindle position is also very stable: the standard deviation of the fluctuations in transverse spindle position during metaphase was only 0.5% of the short axis of the cell. Assuming that stability is limited by fluctuations in the number of independent motor elements such as microtubules or dyneins underlying the centering machinery, we infer that the number is ∼1000, consistent with the several thousand of astral microtubules in these cells. Astral microtubules grow out from the two spindle poles, make contact with the cell cortex, and then shrink back shortly thereafter. The high stability of centering can be accounted for quantitatively if, while making contact with the cortex, the astral microtubules buckle as they exert compressive, pushing forces. We thus propose that the large number of microtubules in the asters provides a highly precise mechanism for positioning the spindle during metaphase while assembly is completed before the onset of anaphase.