Molecular Mechanism of Cytokinesis.

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Actin turnover protects the cytokinetic contractile ring from structural instability.

In common with other actomyosin contractile cellular machineries, actin turnover is required for normal function of the cytokinetic contractile ring. Cofilin is an actin-binding protein contributing to turnover by severing actin filaments, required for cytokinesis by many organisms. In fission yeast cofilin mutants, contractile rings suffer bridging instabilities in which segments of the ring peel away from the plasma membrane, forming straight bridges whose ends remain attached to the membrane. The origin of bridging instability is unclear. Here, we used molecularly explicit simulations of contractile rings to examine the role of cofilin. Simulations reproduced the experimentally observed cycles of bridging and reassembly during constriction, and the occurrence of bridging in ring segments with low density of the myosin II protein Myo2. The lack of cofilin severing produced ∼2-fold longer filaments and, consequently, ∼2-fold higher ring tensions. Simulations identified bridging as originating in the boosted ring tension, which increased centripetal forces that detached actin from Myo2, which was anchoring actin to the membrane. Thus, cofilin serves a critical role in cytokinesis by providing protection from bridging, the principal structural threat to contractile rings.

Myosin turnover controls actomyosin contractile instability.

Actomyosin contractile force produced by myosin II molecules that bind and pull actin filaments is harnessed for diverse functions, from cell division by the cytokinetic contractile ring to morphogenesis driven by supracellular actomyosin networks during development. However, actomyosin contractility is intrinsically unstable to self-reinforcing spatial variations that may destroy the actomyosin architecture if unopposed. How cells control this threat is not established, and while large myosin fluctuations and punctateness are widely reported, the full course of the instability in cells has not been observed. Here, we observed the instability run its full course in isolated cytokinetic contractile rings in cell ghosts where component turnover processes are absent. Unprotected by turnover, myosin II merged hierarchically into aggregates with increasing amounts of myosin and increasing separation, up to a maximum separation. Molecularly explicit simulations reproduced the hierarchical aggregation which precipitated tension loss and ring fracture and identified the maximum separation as the length of actin filaments mediating mechanical communication between aggregates. In the final simulated dead-end state, aggregates were morphologically quiescent, including asters with polarity-sorted actin, similar to the dead-end state observed in actomyosin systems in vitro. Our results suggest the myosin II turnover time controls actomyosin contractile instability in normal cells, long enough for aggregation to build robust aggregates but sufficiently short to intercept catastrophic hierarchical aggregation and fracture.

Synaptotagmin rings as high-sensitivity regulators of synaptic vesicle docking and fusion.

Synchronous release at neuronal synapses is accomplished by a machinery that senses calcium influx and fuses the synaptic vesicle and plasma membranes to release neurotransmitters. Previous studies suggested the calcium sensor synaptotagmin (Syt) is a facilitator of vesicle docking and both a facilitator and inhibitor of fusion. On phospholipid monolayers, the Syt C2AB domain spontaneously oligomerized into rings that are disassembled by Ca2+, suggesting Syt rings may clamp fusion as membrane-separating "washers" until Ca2+-mediated disassembly triggers fusion and release [J. Wang et al., Proc. Natl. Acad. Sci. U.S.A. 111, 13966-13971 (2014)].). Here, we combined mathematical modeling with experiment to measure the mechanical properties of Syt rings and to test this mechanism. Consistent with experimental results, the model quantitatively recapitulates observed Syt ring-induced dome and volcano shapes on phospholipid monolayers and predicts rings are stabilized by anionic phospholipid bilayers or bulk solution with ATP. The selected ring conformation is highly sensitive to membrane composition and bulk ATP levels, a property that may regulate vesicle docking and fusion in ATP-rich synaptic terminals. We find the Syt molecules hosted by a synaptic vesicle oligomerize into a halo, unbound from the vesicle, but in proximity to sufficiently phosphatidylinositol 4,5-bisphosphate (PIP2)-rich plasma membrane (PM) domains, the PM-bound trans Syt ring conformation is preferred. Thus, the Syt halo serves as landing gear for spatially directed docking at PIP2-rich sites that define the active zones of exocytotic release, positioning the Syt ring to clamp fusion and await calcium. Our results suggest the Syt ring is both a Ca2+-sensitive fusion clamp and a high-fidelity sensor for directed docking.

A hemifused complex is the hub in a network of pathways to membrane fusion.

Membrane fusion is a critical step for many essential processes, from neurotransmission to fertilization. For over 40 years, protein-free fusion driven by calcium or other cationic species has provided a simplified model of biological fusion, but the mechanisms remain poorly understood. Cation-mediated membrane fusion and permeation are essential in their own right to drug delivery strategies based on cell-penetrating peptides or cation-bearing lipid nanoparticles. Experimental studies suggest calcium drives anionic membranes to a hemifused intermediate that constitutes a hub in a network of pathways, but the pathway selection mechanism is unknown. Here we develop a mathematical model that identifies the network hub as a highly dynamic hemifusion complex. Multivalent cations drive expansion of this high-tension hemifusion interface between interacting vesicles during a brief transient. The fate of this interface determines the outcome, either fusion, dead-end hemifusion, or vesicle lysis. The model reproduces the unexplained finding that calcium-driven fusion of vesicles with planar membranes typically stalls at hemifusion, and we show the equilibrated hemifused state is a novel lens-shaped complex. Thus, membrane fusion kinetics follow a stochastic trajectory within a network of pathways, with outcome weightings set by a hemifused complex intermediate.

Three membrane fusion pore families determine the pathway to pore dilation.

During exocytosis secretory vesicles fuse with a target membrane and release neurotransmitters, hormones, or other bioactive molecules through a membrane fusion pore. The initially small pore may subsequently dilate for full contents release, as commonly observed in amperometric traces. The size, shape, and evolution of the pore is critical to the course of contents release, but exact fusion pore solutions accounting for membrane tension and bending energy constraints have not been available. Here, we obtained exact solutions for fusion pores between two membranes. We find three families: a narrow pore, a wide pore, and an intermediate tether-like pore. For high tensions these are close to the catenoidal and tether solutions recently reported for freely hinged membrane boundaries. We suggest membrane fusion initially generates a stable narrow pore, and the dilation pathway is a transition to the stable wide pore family. The unstable intermediate pore is the transition state that sets the energy barrier for this dilation pathway. Pore dilation is mechanosensitive, as the energy barrier is lowered by increased membrane tension. Finally, we study fusion pores in nanodiscs, powerful systems for the study of individual pores. We show that nanodiscs stabilize fusion pores by locking them into the narrow pore family.

Entropic forces drive self-organization and membrane fusion by SNARE proteins.

SNARE proteins are the core of the cell's fusion machinery and mediate virtually all known intracellular membrane fusion reactions on which exocytosis and trafficking depend. Fusion is catalyzed when vesicle-associated v-SNAREs form trans-SNARE complexes ("SNAREpins") with target membrane-associated t-SNAREs, a zippering-like process releasing ∼65 kT per SNAREpin. Fusion requires several SNAREpins, but how they cooperate is unknown and reports of the number required vary widely. To capture the collective behavior on the long timescales of fusion, we developed a highly coarse-grained model that retains key biophysical SNARE properties such as the zippering energy landscape and the surface charge distribution. In simulations the ∼65-kT zippering energy was almost entirely dissipated, with fully assembled SNARE motifs but uncomplexed linker domains. The SNAREpins self-organized into a circular cluster at the fusion site, driven by entropic forces that originate in steric-electrostatic interactions among SNAREpins and membranes. Cooperative entropic forces expanded the cluster and pulled the membranes together at the center point with high force. We find that there is no critical number of SNAREs required for fusion, but instead the fusion rate increases rapidly with the number of SNAREpins due to increasing entropic forces. We hypothesize that this principle finds physiological use to boost fusion rates to meet the demanding timescales of neurotransmission, exploiting the large number of v-SNAREs available in synaptic vesicles. Once in an unfettered cluster, we estimate ≥15 SNAREpins are required for fusion within the ∼1-ms timescale of neurotransmitter release.

Convective Nozaki-Bekki holes in a long cavity OCT laser.

We show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts are seeded by appearance of Nozaki-Bekki holes, characterised by the zero field amplitude and π phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model.

The fission yeast cytokinetic contractile ring regulates septum shape and closure.

During cytokinesis, fission yeast and other fungi and bacteria grow a septum that divides the cell in two. In fission yeast closure of the circular septum hole by the ß-glucan synthases (Bgs) and other glucan synthases in the plasma membrane is tightly coupled to constriction of an actomyosin contractile ring attached to the membrane. It is unknown how septum growth is coordinated over scales of several microns to maintain septum circularity. Here, we documented the shapes of ingrowing septum edges by measuring the roughness of the edges, a measure of the deviation from circularity. The roughness was small, with spatial correlations indicative of spatially coordinated growth. We hypothesized that Bgs-mediated septum growth is mechanosensitive and coupled to contractile ring tension. A mathematical model showed that ring tension then generates almost circular septum edges by adjusting growth rates in a curvature-dependent fashion. The model reproduced experimental roughness statistics and showed that septum synthesis sets the mean closure rate. Our results suggest that the fission yeast cytokinetic ring tension does not set the constriction rate but regulates septum closure by suppressing roughness produced by inherently stochastic molecular growth processes.

A mechanical-biochemical feedback loop regulates remodeling in the actin cytoskeleton.

Cytoskeletal actin assemblies transmit mechanical stresses that molecular sensors transduce into biochemical signals to trigger cytoskeletal remodeling and other downstream events. How mechanical and biochemical signaling cooperate to orchestrate complex remodeling tasks has not been elucidated. Here, we studied remodeling of contractile actomyosin stress fibers. When fibers spontaneously fractured, they recoiled and disassembled actin synchronously. The disassembly rate was accelerated more than twofold above the resting value, but only when contraction increased the actin density to a threshold value following a time delay. A mathematical model explained this as originating in the increased overlap of actin filaments produced by myosin II-driven contraction. Above a threshold overlap, this mechanical signal is transduced into accelerated disassembly by a mechanism that may sense overlap directly or through associated elastic stresses. This biochemical response lowers the actin density, overlap, and stresses. The model showed that this feedback mechanism, together with rapid stress transmission along the actin bundle, spatiotemporally synchronizes actin disassembly and fiber contraction. Similar actin remodeling kinetics occurred in expanding or contracting intact stress fibers but over much longer timescales. The model accurately described these kinetics, with an almost identical value of the threshold overlap that accelerates disassembly. Finally, we measured resting stress fibers, for which the model predicts constant actin overlap that balances disassembly and assembly. The overlap was indeed regulated, with a value close to that predicted. Our results suggest that coordinated mechanical and biochemical signaling enables extended actomyosin assemblies to adapt dynamically to the mechanical stresses they convey and direct their own remodeling.

Cholesterol Increases the Openness of SNARE-Mediated Flickering Fusion Pores.

Flickering of fusion pores during exocytotic release of hormones and neurotransmitters is well documented, but without assays that use biochemically defined components and measure single-pore dynamics, the mechanisms remain poorly understood. We used total internal reflection fluorescence microscopy to quantify fusion-pore dynamics in vitro and to separate the roles of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins and lipid bilayer properties. When small unilamellar vesicles bearing neuronal v-SNAREs fused with planar bilayers reconstituted with cognate t-SNARES, lipid and soluble cargo transfer rates were severely reduced, suggesting that pores flickered. From the lipid release times we computed pore openness, the fraction of time the pore is open, which increased dramatically with cholesterol. For most lipid compositions tested, SNARE-mediated and nonspecifically nucleated pores had similar openness, suggesting that pore flickering was controlled by lipid bilayer properties. However, with physiological cholesterol levels, SNAREs substantially increased the fraction of fully open pores and fusion was so accelerated that there was insufficient time to recruit t-SNAREs to the fusion site, consistent with t-SNAREs being preclustered by cholesterol into functional docking and fusion platforms. Our results suggest that cholesterol opens pores directly by reducing the fusion-pore bending energy, and indirectly by concentrating several SNAREs into individual fusion events.

A fast, single-vesicle fusion assay mimics physiological SNARE requirements.

Almost all known intracellular fusion reactions are driven by formation of trans-SNARE complexes through pairing of vesicle-associated v-SNAREs with complementary t-SNAREs on target membranes. However, the number of SNARE complexes required for fusion is unknown, and there is controversy about whether additional proteins are required to explain the fast fusion which can occur in cells. Here we show that single vesicles containing the synaptic/exocytic v-SNAREs VAMP/synaptobrevin fuse rapidly with planar, supported bilayers containing the synaptic/exocytic t-SNAREs syntaxin-SNAP25. Fusion rates decreased dramatically when the number of externally oriented v-SNAREs per vesicle was reduced below 5-10, directly establishing this as the minimum number required for rapid fusion. Docking-to-fusion delay time distributions were consistent with a requirement that 5-11 t-SNAREs be recruited to achieve fusion, closely matching the v-SNARE requirement.

Actomyosin pulsing rescues embryonic tissue folding from disruption by myosin fluctuations.

During early development, myosin II mechanically reshapes and folds embryo tissue. A muchstudied example is ventral furrow formation in Drosophila, marking the onset of gastrulation. Furrowing is driven by contraction of actomyosin networks on apical cell surfaces, but how the myosin patterning encodes tissue shape is unclear, and elastic models failed to reproduce essential features of experimental cell contraction profiles. The myosin patterning exhibits substantial cell-to-cell fluctuations with pulsatile time-dependence, a striking but unexplained feature of morphogenesis in many organisms. Here, using biophysical modeling we find viscous forces offer the principal resistance to actomyosin-driven apical constriction. In consequence, tissue shape is encoded in the direction-dependent curvature of the myosin patterning which orients an anterior-posterior furrow. Tissue contraction is highly sensitive to cell-to-cell myosin fluctuations, explaining furrowing failure in genetically perturbed embryos whose fluctuations are temporally persistent. In wild-type embryos this disastrous outcome is averted by pulsatile myosin time-dependence, which rescues furrowing by eliminating high frequencies in the fluctuation power spectrum. This low pass filter mechanism may underlie the usage of actomyosin pulsing in diverse morphogenetic processes across many organisms.

Host Cell Membrane Capture by the SARS-CoV-2 Spike Protein Fusion Intermediate.

Cell entry by SARS-CoV-2 is accomplished by the S2 subunit of the spike S protein on the virion surface by capture of the host cell membrane and fusion with the viral envelope. Capture and fusion require the prefusion S2 to transit to its potent fusogenic form, the fusion intermediate (FI). However, the FI structure is unknown, detailed computational models of the FI are unavailable, and the mechanisms and timing of membrane capture and fusion are not established. Here, we constructed a full-length model of the SARS-CoV-2 FI by extrapolating from known SARS-CoV-2 pre- and postfusion structures. In atomistic and coarse-grained molecular dynamics simulations the FI was remarkably flexible and executed giant bending and extensional fluctuations due to three hinges in the C-terminal base. The simulated configurations and their giant fluctuations are quantitatively consistent with SARS-CoV-2 FI configurations measured recently using cryo-electron tomography. Simulations suggested a host cell membrane capture time of ∼2 ms. Isolated fusion peptide simulations identified an N-terminal helix that directed and maintained binding to the membrane but grossly underestimated the binding time, showing that the fusion peptide environment is radically altered when attached to its host fusion protein. The large configurational fluctuations of the FI generated a substantial exploration volume that aided capture of the target membrane, and may set the waiting time for fluctuation-triggered refolding of the FI that draws the viral envelope and host cell membrane together for fusion. These results describe the FI as machinery that uses massive configurational fluctuations for efficient membrane capture and suggest novel potential drug targets.

Evolution of the hemifused intermediate on the pathway to membrane fusion.

The pathway to membrane fusion in synthetic and biological systems is thought to pass through hemifusion, in which the outer leaflets are fused while the inner leaflets engage in a hemifusion diaphragm (HD). Fusion has been proposed to be completed by lysis of the expanded HD that matures from a localized stalklike initial connection. However, the process that establishes the expanded HD is poorly understood. Here we mathematically modeled hemifusion of synthetic vesicles, where hemifusion and fusion are most commonly driven by calcium and membrane tension. The model shows that evolution of the hemifused state is driven by these agents and resisted by interleaflet frictional and tensile stresses. Predicted HD growth rates depend on tension and salt concentration, and agree quantitatively with experimental measurements. For typical conditions, we predict that HDs expand at ~30 µm(2)/s, reaching a final equilibrium area ~7% of the vesicle area. Key model outputs are the evolving HD tension and area during the growth transient, properties that may determine whether HD lysis occurs. Applying the model to numerous published experimental studies that reported fusion, our results are consistent with a final fusion step in which the HD ruptures due to super-lysis HD membrane tensions.

Self-organization of myosin II in reconstituted actomyosin bundles.

Cells assemble a variety of bundled actomyosin structures in the cytoskeleton for activities such as cell-shape regulation, force production, and cytokinesis. Although these linear structures exhibit varied architecture, two common organizational themes are a punctate distribution of myosin II and distinct patterns of actin polarity. The mechanisms that cells use to assemble and maintain these organizational features are poorly understood. To study these, we reconstituted actomyosin bundles in vitro that contained only actin filaments and myosin II. Upon addition of ATP, the bundles contracted and the uniformly distributed myosin spontaneously reorganized into discrete clusters. We developed a mathematical model in which the motion of myosin II filaments is governed by the polarities of the actin filaments with which they interact. The model showed that the assembly of myosins into clusters is driven by their tendency to migrate to locations with zero net actin filament polarity. With no fitting parameters, the predicted distribution of myosin cluster separations was in close agreement with our experiments, including a -3/2 power law decay for intermediate length scales. Thus, without an organizing template or accessory proteins, a minimal bundle of actin and myosin has the inherent capacity to self-organize into a heterogeneous banded structure.

The hemifused state on the pathway to membrane fusion.

Fusion of compartments enclosed by membrane bilayers enables secretion and other vital cellular processes and is widely studied in model synthetic membrane systems. Experiments suggest the fusion pathway passes through a hemifused intermediate where only outer monolayers are fused. Here we show membrane tension and divalent cations drive vesicles to hemifused equilibrium with expanded hemifusion diaphragms (HDs) where inner monolayers engage. Predicted HD sizes agree with recent measurements of Nikolaus et al. [Biophys. J. 98, 1192 (2010).]. The fusion pathway is completed by HD lysis provided HD tension is sufficiently high.

The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores.

All membrane fusion reactions proceed through an initial fusion pore, including calcium-triggered release of neurotransmitters and hormones. Expansion of this small pore to release cargo is energetically costly and regulated by cells, but the mechanisms are poorly understood. Here, we show that the neuronal/exocytic calcium sensor Synaptotagmin-1 (Syt1) promotes expansion of fusion pores induced by SNARE proteins. Pore dilation relied on calcium-induced insertion of the tandem C2 domain hydrophobic loops of Syt1 into the membrane, previously shown to reorient the C2 domain. Mathematical modelling suggests that C2B reorientation rotates a bound SNARE complex so that it exerts force on the membranes in a mechanical lever action that increases the height of the fusion pore, provoking pore dilation to offset the bending energy penalty. We conclude that Syt1 exerts novel non-local calcium-dependent mechanical forces on fusion pores that dilate pores and assist neurotransmitter and hormone release.

Vesicle Shrinking and Enlargement Play Opposing Roles in the Release of Exocytotic Contents.

For decades, two fusion modes were thought to control hormone and transmitter release essential to life; one facilitates release via fusion pore dilation and flattening (full collapse), and the other limits release by closing a narrow fusion pore (kiss-and-run). Using super-resolution stimulated emission depletion (STED) microscopy to visualize fusion modes of dense-core vesicles in neuroendocrine cells, we find that facilitation of release is mediated not by full collapse but by shrink fusion, in which the Ω-profile generated by vesicle fusion shrinks but maintains a large non-dilating pore. We discover that the physiological osmotic pressure of a cell squeezes, but does not dilate, the Ω-profile, which explains why shrink fusion prevails over full collapse. Instead of kiss-and-run, enlarge fusion, in which Ω-profiles grow while maintaining a narrow pore, slows down release. Shrink and enlarge fusion may thus account for diverse hormone and transmitter release kinetics observed in secretory cells, previously interpreted within the full-collapse/kiss-and-run framework.

Recoil after severing reveals stress fiber contraction mechanisms.

Stress fibers are cellular contractile actomyosin machines central to wound healing, shear stress response, and other processes. Contraction mechanisms have been difficult to establish because stress fibers in cultured cells typically exert isometric tension and present little kinetic activity. In a recent study, living cell stress fibers were severed with laser nanoscissors and recoiled several mum over approximately 5 s. We developed a quantitative model of stress fibers based on known components and available structural information suggesting periodic sarcomeric organization similar to striated muscle. The model was applied to the severing assay and compared to the observed recoil. We conclude that the sarcomere force-length relation is similar to that of muscle with two distinct regions on the ascending limb and that substantial external drag forces act on the recoiling fiber corresponding to effective cytosolic viscosity approximately 10(4) times that of water. This may originate from both nonspecific and specific interactions. The model predicts highly nonuniform contraction with caps of collapsed sarcomeres growing at the severed ends. A directly measurable signature of external drag is that cap length and recoil distance increase at intermediate times as t(1/2). The severing data is consistent with this prediction.