Contractile ring composition dictates kinetics of in silico contractility.

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.

Spherical spindle shape promotes perpendicular cortical orientation by preventing isometric cortical pulling on both spindle poles during C. elegans female meiosis.

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.

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics.

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link 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' cross-linking versus motoring activities. Because 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 or coarse graining and unbinding dynamics, and although 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, 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 tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.

Unite to divide - how models and biological experimentation have come together to reveal mechanisms of cytokinesis.

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.

Micron-scale supramolecular myosin arrays help mediate cytoskeletal assembly at mature adherens junctions.

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.

Novel cytokinetic ring components drive negative feedback in cortical contractility.

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 (germinal center kinase-1) and CCM-3 (cerebral cavernous malformations-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 nonmuscle 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 results suggest that GCK-1 and CCM-3 regulate cortical actomyosin contractility via negative feedback. These findings have implications for the molecular and cellular mechanisms of cerebral cavernous malformation pathologies.

Cross-linkers both drive and brake cytoskeletal remodeling and furrowing in cytokinesis.

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.

Autosomal Trisomy and Triploidy Are Corrected During Female Meiosis in Caenorhabditis elegans.

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.

A novel chromosome segregation mechanism during female meiosis.

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.

The asymmetry of female meiosis reduces the frequency of inheritance of unpaired chromosomes.

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.

Dynactin-dependent cortical dynein and spherical spindle shape correlate temporally with meiotic spindle rotation in Caenorhabditis elegans.

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.

Katanin maintains meiotic metaphase chromosome alignment and spindle structure in vivo and has multiple effects on microtubules in vitro.

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.