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Constriction kinetics of the cytokinetic ring are expected to depend on dynamic adjustment of contractile ring composition, but the impact of ring component abundance dynamics on ring constriction is understudied. Computational models generally assume that contractile networks maintain constant total amounts of components, which is not always true. To test how compositional dynamics affect constriction kinetics, we first measured F-actin, non-muscle myosin II, septin, and anillin during Caenorhabditis elegans zygotic mitosis. A custom microfluidic device that positioned the cell with the division plane parallel to a light sheet allowed even illumination of the cytokinetic ring. Measured component abundances were implemented in a three-dimensional agent-based model of a membrane-associated contractile ring. With constant network component amounts, constriction completed with biologically unrealistic kinetics. However, imposing the measured changes in component quantities allowed this model to elicit realistic constriction kinetics. Simulated networks were more sensitive to changes in motor and filament amounts than those of crosslinkers and tethers. Our findings highlight the importance of network composition for actomyosin contraction kinetics.

Epithelial cells assemble specialized actomyosin structures at E-Cadherin–based cell–cell junctions, and the force exerted drives cell shape change during morphogenesis. The mechanisms that build this supramolecular actomyosin structure remain unclear. We used ZO-knockdown MDCK cells, which assemble a robust, polarized, and highly organized actomyosin cytoskeleton at the zonula adherens, combining genetic and pharmacologic approaches with superresolution microscopy to define molecular machines required. To our surprise, inhibiting individual actin assembly pathways (Arp2/3, formins, or Ena/VASP) did not prevent or delay assembly of this polarized actomyosin structure. Instead, as junctions matured, micron-scale supramolecular myosin arrays assembled, with aligned stacks of myosin filaments adjacent to the apical membrane, overlying disorganized actin filaments. This suggested that myosin arrays might bundle actin at mature junctions. Consistent with this idea, inhibiting ROCK or myosin ATPase disrupted myosin localization/organization and prevented actin bundling and polarization. We obtained similar results in Caco-2 cells. These results suggest a novel role for myosin self-assembly, helping drive actin organization to facilitate cell shape change.

Actomyosin cortical contractility drives many cell shape changes including cytokinetic furrowing. While positive regulation of contractility is well characterized, counterbalancing negative regulation and mechanical brakes are less well understood. The small GTPase RhoA is a central regulator, activating cortical actomyosin contractility during cytokinesis and other events. Here we report how two novel cytokinetic ring components, GCK-1 and CCM-3, participate in a negative feedback loop among RhoA and its cytoskeletal effectors to inhibit contractility. GCK-1 and CCM-3 are recruited by active RhoA and anillin to the cytokinetic ring, where they in turn limit RhoA activity and contractility. This is evidenced by increased RhoA activity, anillin and non-muscle myosin II in the cytokinetic ring, and faster cytokinetic furrowing, following depletion of GCK-1 or CCM-3. GCK-1 or CCM-3 depletion also reduced RGA-3 levels in pulses, and increased baseline RhoA activity and pulsed contractility during zygote polarization. Together, our findings suggest that GCK-1 and CCM-3 regulate cortical actomyosin contractility via negative feedback.SummaryNovel cytokinetic ring proteins, the Ste20 family kinase GCK-1 and its heterodimeric cofactor Cerebral Cavernous Malformations-3, close a negative feedback loop involving the RhoA GAP RGA-3/4, RhoA, and its cytoskeletal effector anillin to limit actomyosin contractility in cytokinesis and during polarization of the C. elegans zygote.

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, crosslink, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is non-muscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and crosslink actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions including how the number of NMMII subunits affects dynamics, and what affects the relative contribution of ensembles’ crosslinking versus motoring activities. Since biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization/coarse-graining and unbinding dynamics, and while general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse-graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model (PCM) previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse-graining, though connectivity was still markedly reduced for this ensemble type with coarse-graining. Together our results reveal substantial trade-offs associated with the process of coarse-graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.STATEMENT OF SIGNIFICANCEAgent-based simulations of contractile networks allow us to explore the mechanics of actomyosin contractility, which drives many cell shape changes including cytokinesis, the final step of cell division. Such simulations should be able to predict the mechanics and dynamics of non-muscle contractility, however recent work has highlighted a lack of consensus on how to best model the non-muscle myosin II. These ensembles of approximately 32 motors are the key components responsible for driving contractility. Here, we explored different methods for modeling non-muscle myosin II ensembles within the context of contractile actomyosin networks. We show that the level of coarse-graining and the choice of unbinding model used to model motor unbinding under load indeed has profound effects on contractile network dynamics.

Meiotic spindles are positioned perpendicular to the oocyte cortex to facilitate segregation of chromosomes into a large egg and a tiny polar body. In C. elegans, spindles are initially ellipsoid and parallel to the cortex before shortening to a spherical shape and rotating to the perpendicular orientation by dynein-driven cortical pulling. The mechanistic connection between spindle shape and rotation has remained elusive. Here we used mutants of the microtubule-severing protein katanin to manipulate spindle shape without eliminating cortical pulling. In a katanin mutant, spindles remained ellipsoid, had pointed poles and became trapped in either a diagonal or a parallel orientation. Results indicated that astral microtubules emanating from both spindle poles initially engage in cortical pulling until microtubules emanating from one pole detach from the cortex allowing pivoting of the spindle. The lower viscous drag experienced by spherical spindles prevented recapture of the cortex by astral microtubules emanating from the detached pole. In addition, maximizing contact between pole dynein and cortical dynein stabilizes round poles in a perpendicular orientation. Spherical spindle shape can thus promote perpendicular orientation by two distinct mechanisms.

Meiotic spindles are positioned perpendicular to the oocyte cortex to facilitate segregation of chromosomes into a large egg and a tiny polar body. In C. elegans, spindles are initially ellipsoid and parallel to the cortex before shortening to a near-spherical shape with flattened poles and then rotating to the perpendicular orientation by dynein-driven cortical pulling. The mechanistic connection between spindle shape and rotation has remained elusive. Here, we have used three different genetic backgrounds to manipulate spindle shape without eliminating dynein-dependent movement or dynein localization. Ellipsoid spindles with flattened or pointed poles became trapped in either a diagonal or a parallel orientation. Mathematical models that recapitulated the shape dependence of rotation indicated that the lower viscous drag experienced by spherical spindles prevented recapture of the cortex by astral microtubules emanating from the pole pivoting away from the cortex. In addition, maximizing contact between pole dynein and cortical dynein stabilizes flattened poles in a perpendicular orientation, and spindle rigidity prevents spindle bending that can lock both poles at the cortex. Spindle shape can thus promote perpendicular orientation by three distinct mechanisms.

Meiotic spindles are positioned perpendicular to the oocyte cortex to facilitate segregation of chromosomes into a large egg and a tiny polar body. In C. elegans, spindles are initially ellipsoid and parallel to the cortex before shortening to a near spherical shape with flattened poles and then rotating to the perpendicular orientation by dynein-driven cortical pulling. The mechanistic connection between spindle shape and rotation has remained elusive. Here we used three different genetic backgrounds to manipulate spindle shape without eliminating dynein-dependent movement or dynein localization. Ellipsoid spindles with flattened or pointed poles became trapped in either a diagonal or a parallel orientation. Mathematical models that recapitulated the shape dependence of rotation indicated that the lower viscous drag experienced by spherical spindles prevented recapture of the cortex by astral microtubules emanating from the pole pivoting away from the cortex. In addition, maximizing contact between pole dynein and cortical dynein stabilizes flattened poles in a perpendicular orientation and spindle rigidity prevents spindle bending that can lock both poles at the cortex. Spindle shape can thus promote perpendicular orientation by three distinct mechanisms.

Cytokinesis is the fundamental and ancient cellular process by which one cell physically divides into two. Cytokinesis in animal and fungal cells is achieved by contraction of an actomyosin cytoskeletal ring assembled in the cell cortex, typically at the cell equator. Cytokinesis is essential for the development of fertilized eggs into multicellular organisms and for homeostatic replenishment of cells. Correct execution of cytokinesis is also necessary for genome stability and the evasion of diseases including cancer. Cytokinesis has fascinated scientists for well over a century, but its speed and dynamics make experiments challenging to perform and interpret. The presence of redundant mechanisms is also a challenge to understand cytokinesis, leaving many fundamental questions unresolved. For example, how does a disordered cytoskeletal network transform into a coherent ring? What are the long-distance effects of localized contractility? Here, we provide a general introduction to ‘modeling for biologists’, and review how agent-based modeling and continuum mechanics modeling have helped to address these questions.

Trisomy and triploidy, defined as the presence of a third copy of one or all chromosomes, respectively, are deleterious in many species including humans. Previous studies have demonstrated that Caenorhabditis elegans with a third copy of the X chromosome are viable and fertile. However, the extra X chromosome was shown to preferentially segregate into the first polar body during oocyte meiosis to produce a higher frequency of euploid offspring than would be generated by random segregation. Here, we demonstrate that extra autosomes are preferentially eliminated by triploid C. elegans and trisomy IV C. elegans. Live imaging of anaphase-lagging chromosomes and analysis of REC-8 staining of metaphase II spindles revealed that, in triploids, some univalent chromosomes do not lose cohesion and preferentially segregate intact into the first polar body during anaphase I, whereas other autosomes segregate chromatids equationally at anaphase I and eliminate some of the resulting single chromatids during anaphase II. We also demonstrate asymmetry in the anaphase spindle, which may contribute to the asymmetric segregation. This study reveals a pathway that allows aneuploid parents to produce euploid offspring at higher than random frequency.

Cell shape changes such as cytokinesis are driven by the actomyosin contractile cytoskeleton. The molecular rearrangements that bring about contractility in nonmuscle cells are currently debated. Specifically, both filament sliding by myosin motors, as well as cytoskeletal cross-linking by myosins and nonmotor cross-linkers, are thought to promote contractility. Here we examined how the abundance of motor and nonmotor cross-linkers affects the speed of cytokinetic furrowing. We built a minimal model to simulate contractile dynamics in the Caenorhabditis elegans zygote cytokinetic ring. This model predicted that intermediate levels of nonmotor cross-linkers are ideal for contractility; in vivo, intermediate levels of the scaffold protein anillin allowed maximal contraction speed. Our model also demonstrated a nonlinear relationship between the abundance of motor ensembles and contraction speed. In vivo, thorough depletion of nonmuscle myosin II delayed furrow initiation, slowed F-actin alignment, and reduced maximum contraction speed, but partial depletion allowed faster-than-expected kinetics. Thus, cytokinetic ring closure is promoted by moderate levels of both motor and nonmotor cross-linkers but attenuated by an over-abundance of motor and nonmotor cross-linkers. Together, our findings extend the growing appreciation for the roles of cross-linkers in cytokinesis and reveal that they not only drive but also brake cytoskeletal remodeling.

Cytokinesis and other cell shape changes are driven by the actomyosin contractile cytoskeleton. The molecular rearrangements that bring about contractility in non-muscle cells are currently debated. Specifically, both filament sliding by myosin motors, as well as cytoskeletal crosslinking by myosins and non-motor crosslinkers, are thought to promote contractility. Here, we examined how the abundance of motor and non-motor crosslinkers controls the speed of cytokinetic furrowing. We built a minimal model to simulate the contractile dynamics of the C. elegans zygote cytokinetic ring. This model predicted that intermediate levels of non-motor crosslinkers would allow maximal contraction speed, which we found to be the case for the scaffold protein anillin, in vivo. Our model also demonstrated a non-linear relationship between the abundance of motor ensembles and contraction speed. In vivo, thorough depletion of non-muscle myosin II delayed furrow initiation, slowed F-actin alignment, and reduced maximum contraction speed, but partial depletion allowed faster-than-expected kinetics. Thus, both motor and non-motor crosslinkers promote cytokinetic ring closure when present at low levels, but act as a brake when present at higher levels. Together, our findings extend the growing appreciation for the roles of crosslinkers, but reveal that they not only drive but also brake cytoskeletal remodeling.

Trisomy and triploidy, defined as the presence of a third copy of one or all chromosomes, respectively, are deleterious in many species including humans. Previous studies have demonstrated that Caenorhabditis elegans with a third copy of the X chromosome are viable and fertile. However, the extra X chromosome was shown to preferentially segregate into the first polar body during oocyte meiosis to produce a higher frequency of euploid offspring than would be generated by random segregation. Here, we demonstrate that extra autosomes are preferentially eliminated by triploid C. elegans and trisomy IV C. elegans. Live imaging of anaphase-lagging chromosomes and analysis of REC-8 staining of metaphase II spindles revealed that, in triploids, some univalent chromosomes do not lose cohesion and preferentially segregate intact into the first polar body during anaphase I, whereas other autosomes segregate chromatids equationally at anaphase I and eliminate some of the resulting single chromatids during anaphase II. We also demonstrate asymmetry in the anaphase spindle, which may contribute to the asymmetric segregation. This study reveals a pathway that allows aneuploid parents to produce euploid offspring at higher than random frequency.

Caenorhabditis elegans bivalents are positioned between dense bundles of microtubules within female meiotic spindles. Rapid inactivation of katanin after meiotic spindle assembly causes loss of organized microtubule bundles and displacement of bivalents from the metaphase plate. Purified katanin can preferentially sever at intersections between microtubules., Assembly of Caenorhabditis elegans female meiotic spindles requires both MEI-1 and MEI-2 subunits of the microtubule-severing ATPase katanin. Strong loss-of-function mutants assemble apolar intersecting microtubule arrays, whereas weaker mutants assemble bipolar meiotic spindles that are longer than wild type. To determine whether katanin is also required for spindle maintenance, we monitored metaphase I spindles after a fast-acting mei-1(ts) mutant was shifted to a nonpermissive temperature. Within 4 min of temperature shift, bivalents moved off the metaphase plate, and microtubule bundles within the spindle lengthened and developed a high degree of curvature. Spindles eventually lost bipolar structure. Immunofluorescence of embryos fixed at increasing temperature indicated that MEI-1 was lost from spindle microtubules before loss of ASPM-1, indicating that MEI-1 and ASPM-1 act independently at spindle poles. We quantified the microtubule-severing activity of purified MEI-1/MEI-2 complexes corresponding to six different point mutations and found a linear relationship between microtubule disassembly rate and meiotic spindle length. Previous work showed that katanin is required for severing at points where two microtubules intersect in vivo. We show that purified MEI-1/MEI-2 complexes preferentially sever at intersections between two microtubules and directly bundle microtubules in vitro. These activities could promote parallel/antiparallel microtubule organization in meiotic spindles.

During conventional anaphase A, chromosomes move outward toward spindle poles. Caenorhabditis elegans meiotic spindle poles move inward toward chromosomes to achieve the same end., In a wide range of eukaryotes, chromosome segregation occurs through anaphase A, in which chromosomes move toward stationary spindle poles, anaphase B, in which chromosomes move at the same velocity as outwardly moving spindle poles, or both. In contrast, Caenorhabditis elegans female meiotic spindles initially shorten in the pole-to-pole axis such that spindle poles contact the outer kinetochore before the start of anaphase chromosome separation. Once the spindle pole-to-kinetochore contact has been made, the homologues of a 4-μm-long bivalent begin to separate. The spindle shortens an additional 0.5 μm until the chromosomes are embedded in the spindle poles. Chromosomes then separate at the same velocity as the spindle poles in an anaphase B–like movement. We conclude that the majority of meiotic chromosome movement is caused by shortening of the spindle to bring poles in contact with the chromosomes, followed by separation of chromosome-bound poles by outward sliding.

Cytoplasmic dynein accumulates on the cortex of Caenorhabditis elegans female meiotic spindles just before they rotate in a dynein-dependent manner. These spindles also shorten to a spherical shape that might reduce the drag that opposes cortical pulling by dynein., Oocyte meiotic spindles orient with one pole juxtaposed to the cortex to facilitate extrusion of chromosomes into polar bodies. In Caenorhabditis elegans, these acentriolar spindles initially orient parallel to the cortex and then rotate to the perpendicular orientation. To understand the mechanism of spindle rotation, we characterized events that correlated temporally with rotation, including shortening of the spindle in the pole-to pole axis, which resulted in a nearly spherical spindle at rotation. By analyzing large spindles of polyploid C. elegans and a related nematode species, we found that spindle rotation initiated at a defined spherical shape rather than at a defined spindle length. In addition, dynein accumulated on the cortex just before rotation, and microtubules grew from the spindle with plus ends outward during rotation. Dynactin depletion prevented accumulation of dynein on the cortex and prevented spindle rotation independently of effects on spindle shape. These results support a cortical pulling model in which spindle shape might facilitate rotation because a sphere can rotate without deforming the adjacent elastic cytoplasm. We also present evidence that activation of spindle rotation is promoted by dephosphorylation of the basic domain of p150 dynactin.

Trisomy, the presence of a third copy of one chromosome, is deleterious and results in inviable or defective progeny if passed through the germ line. Random segregation of an extra chromosome is predicted to result in a high frequency of trisomic offspring from a trisomic parent. Caenorhabditis elegans with trisomy of the X chromosome, however, have far fewer trisomic offspring than expected. We found that the extra X chromosome was preferentially eliminated during anaphase I of female meiosis. We utilized a mutant with a specific defect in pairing of the X chromosome as a model to investigate the apparent bias against univalent inheritance. First, univalents lagged during anaphase I and their movement was biased toward the cortex and future polar body. Second, late-lagging univalents were frequently captured by the ingressing polar body contractile ring. The asymmetry of female meiosis can thus partially correct pre-existing trisomy. DOI: http://dx.doi.org/10.7554/eLife.06056.001, eLife digest Inside cells, DNA is found packaged into structures called chromosomes. Most human and animal cells contain two sets of chromosomes, one inherited from each parent. Chromosomes from one set pair up with the equivalent chromosome from the other set. However, egg and sperm cells only contain one copy of each chromosome, so that when the egg is fertilized, the resulting cell again has two sets of chromosomes. If there are either more or fewer than two copies of a chromosome in the fertilized cell, this can cause birth defects and conditions such as Down syndrome. An egg cell develops from a cell called an oocyte via a process called meiosis. The oocyte first duplicates its DNA so that it contains four copies of each chromosome. The oocyte then divides, and the resulting cells divide again, to produce four cells that each contains one copy of each chromosome. Only one of these cells is an egg cell: the other three are called polar bodies, and these normally self-destruct. The tiny roundworm C. elegans is a model organism used to study meiosis. Worms can be hermaphrodites or males; the hermaphrodites normally have a pair of ‘X’ sex chromosomes. However, sometimes problems with meiosis can produce hermaphrodite worms with three X chromosomes in each of their cells. In these cells, two of the X chromosomes pair with each other as normal, and one X chromosome remains unpaired. Cortes et al. examined meiosis in mutant worms that had an extra copy of the X chromosome by marking all the chromosomes with a fluorescent tag. This allowed the movement of the chromosomes to be tracked through images taken using a microscope. This revealed that an unpaired X chromosome moves more slowly than a normal paired set. Furthermore, the unpaired chromosomes tend to move toward the region of the oocyte that will develop into a polar body. Thus, when the oocyte divides, the unpaired chromosomes are placed in the polar body and eliminated. This mechanism improves the chance that the correct number of chromosomes will end up in the egg cell. Women with three X chromosomes are often fertile and in most cases produce normal offspring. Further work is needed to see whether human oocytes remove extra chromosomes by a mechanism similar to that seen in the roundworms. DOI: http://dx.doi.org/10.7554/eLife.06056.002

A subset of medulloblastomas, the most common brain tumor in children, is hypothesized to originate from granule neuron precursors (GNPs) in which the sonic hedgehog (SHH) pathway is over-activated. MXD3, a basic helix-look-helix zipper transcription factor of the MAD family, has been reported to be upregulated during postnatal cerebellar development and to promote GNP proliferation and MYCN expression. Mxd3 is upregulated in mouse models of medulloblastoma as well as in human medulloblastomas. Therefore, we hypothesize that MXD3 plays a role in the cellular events that lead to medulloblastoma biogenesis. In agreement with its proliferative role in GNPs, MXD3 knock-down in DAOY cells resulted in decreased proliferation. Sustained overexpression of MXD3 resulted in decreased cell numbers due to increased apoptosis and cell cycle arrest. Structure-function analysis revealed that the Sin3 interacting domain, the basic domain, and binding to E-boxes are essential for this activity. Microarray-based expression analysis indicated up-regulation of 84 genes and down-regulation of 47 genes. Potential direct MXD3 target genes were identified by ChIP-chip. Our results suggest that MXD3 is necessary for DAOY medulloblastoma cell proliferation. However, increased level and/or duration of MXD3 expression ultimately reduces cell numbers via increased cell death and cell cycle arrest.