Compressive forces stabilize microtubules in living cells.

Microtubules are cytoskeleton components with unique mechanical and dynamic properties. They are rigid polymers that alternate phases of growth and shrinkage. Nonetheless, the cells can display a subset of stable microtubules, but it is unclear whether microtubule dynamics and mechanical properties are related. Recent in vitro studies suggest that microtubules have mechano-responsive properties, being able to stabilize their lattice by self-repair on physical damage. Here we study how microtubules respond to cycles of compressive forces in living cells and find that microtubules become distorted, less dynamic and more stable. This mechano-stabilization depends on CLASP2, which relocates from the end to the deformed shaft of microtubules. This process seems to be instrumental for cell migration in confined spaces. Overall, these results demonstrate that microtubules in living cells have mechano-responsive properties that allow them to resist and even counteract the forces to which they are subjected, being a central mediator of cellular mechano-responses.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes.

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Rounding Out the Understanding of ACD Toxicity with the Discovery of Cyclic Forms of Actin Oligomers.

Actin is an essential element of both innate and adaptive immune systems and can aid in motility and translocation of bacterial pathogens, making it an attractive target for bacterial toxins. Pathogenic Vibrio and Aeromonas genera deliver actin cross-linking domain (ACD) toxin into the cytoplasm of the host cell to poison actin regulation and promptly induce cell rounding. At early stages of toxicity, ACD covalently cross-links actin monomers into oligomers (AOs) that bind through multivalent interactions and potently inhibit several families of actin assembly proteins. At advanced toxicity stages, we found that the terminal protomers of linear AOs can get linked together by ACD to produce cyclic AOs. When tested against formins and Ena/VASP, linear and cyclic AOs exhibit similar inhibitory potential, which for the cyclic AOs is reduced in the presence of profilin. In coarse-grained molecular dynamics simulations, profilin and WH2-motif binding sites on actin subunits remain exposed in modeled AOs of both geometries. We speculate, therefore, that the reduced toxicity of cyclic AOs is due to their reduced configurational entropy. A characteristic feature of cyclic AOs is that, in contrast to the linear forms, they cannot be straightened to form filaments (e.g., through stabilization by cofilin), which makes them less susceptible to neutralization by the host cell.

Insights into Actin Polymerization and Nucleation Using a Coarse-Grained Model.

We studied actin filament polymerization and nucleation with molecular dynamics simulations and a previously established coarse-grained model having each residue represented by a single interaction site located at the Cα atom. We approximate each actin protein as a fully or partially rigid unit to identify the equilibrium structural ensemble of interprotein complexes. Monomers in the F-actin configuration bound to both barbed and pointed ends of a short F-actin filament at the anticipated locations for polymerization. Binding at both ends occurred with similar affinity. Contacts between residues of the incoming subunit and the short filament were consistent with expectation from models based on crystallography, x-ray diffraction, and cryo-electron microscopy. Binding at the barbed and pointed end also occurred at an angle with respect to the polymerizable bound structure, and the angle range depended on the flexibility of the D-loop. Additional barbed end bound states were seen when the incoming subunit was in the G-actin form. Consistent with an activation barrier for pointed end polymerization, G-actin did not bind at an F-actin pointed end. In all cases, binding at the barbed end also occurred in a configuration similar to the antiparallel (lower) dimer. Individual monomers bound each other in a short-pitch helix complex in addition to other configurations, with several of them apparently nonproductive for polymerization. Simulations with multiple monomers in the F-actin form show assembly into filaments as well as transient aggregates at the barbed end. We discuss the implications of these observations on the kinetic pathway of actin filament nucleation and polymerization and possibilities for future improvements of the coarse-grained model.

Disentangling loosening from softening: insights into primary cell wall structure.

How cell wall elasticity, plasticity, and time-dependent extension (creep) relate to one another, to plant cell wall structure and to cell growth remain unsettled topics. To examine these issues without the complexities of living tissues, we treated cell-free strips of onion epidermal walls with various enzymes and other agents to assess which polysaccharides bear mechanical forces in-plane and out-of-plane of the cell wall. This information is critical for integrating concepts of wall structure, wall material properties, tissue mechanics and mechanisms of cell growth. With atomic force microscopy we also monitored real-time changes in the wall surface during treatments. Driselase, a potent cocktail of wall-degrading enzymes, removed cellulose microfibrils in superficial lamellae sequentially, layer-by-layer, and softened the wall (reduced its mechanical stiffness), yet did not induce wall loosening (creep). In contrast Cel12A, a bifunctional xyloglucanase/cellulase, induced creep with only subtle changes in wall appearance. Both Driselase and Cel12A increased the tensile compliance, but differently for elastic and plastic components. Homogalacturonan solubilization by pectate lyase and calcium chelation greatly increased the indentation compliance without changing tensile compliances. Acidic buffer induced rapid cell wall creep via endogenous α-expansins, with negligible effects on wall compliances. We conclude that these various wall properties are not tightly coupled and therefore reflect distinctive aspects of wall structure. Cross-lamellate networks of cellulose microfibrils influenced creep and tensile stiffness whereas homogalacturonan influenced indentation mechanics. This information is crucial for constructing realistic molecular models that define how wall mechanics and growth depend on primary cell wall structure.

Lamellipodium tip actin barbed ends serve as a force sensor.

Cells change direction of migration by sensing rigidity of environment and traction force, yet its underlying mechanism is unclear. Here, we show that tip actin barbed ends serve as an active "force sensor" at the leading edge. We established a method to visualize intracellular single-molecule fluorescent actin through an elastic culture substrate. We found that immediately after cell edge stretch, actin assembly increased specifically at the lamellipodium tip. The rate of actin assembly increased with increasing stretch speed. Furthermore, tip actin polymerization remained elevated at the subsequent hold step, which was accompanied by a decrease in the load on the tip barbed ends. Stretch-induced tip actin polymerization was still observed without either the WAVE complex or Ena/VASP proteins. The observed relationships between forces and tip actin polymerization are consistent with a force-velocity relationship as predicted by the Brownian ratchet mechanism. Stretch caused extra membrane protrusion with respect to the stretched substrate and increased local tip polymerization by >5% of total cellular actin in 30 s. Our data reveal that augmentation of lamellipodium tip actin assembly is directly coupled to the load decrease, which may serve as a force sensor for directed cell protrusion.

Convection-Induced Biased Distribution of Actin Probes in Live Cells.

Fluorescent markers that bind endogenous target proteins are frequently employed for quantitative live-cell imaging. To visualize the actin cytoskeleton in live cells, several actin-binding probes have been widely used. Among them, Lifeact is the most popular probe with ideal properties, including fast exchangeable binding kinetics. Because of its fast kinetics, Lifeact is generally believed to distribute evenly throughout cellular actin structures. In this study, however, we demonstrate misdistribution of Lifeact toward the rear of lamellipodia where actin filaments continuously move inward along the retrograde flow. Similarly, phalloidin showed biased misdistribution toward the rear of lamellipodia in live cells. We show evidence of convection-induced misdistribution of actin probes by both experimental data and physical models. Our findings warn about the potential error arising from the use of target-binding probes in quantitative live imaging.

Exploration and stabilization of Ras1 mating zone: A mechanism with positive and negative feedbacks.

In mating fission yeast cells, sensing and response to extracellular pheromone concentrations occurs through an exploratory Cdc42 patch that stochastically samples the cell cortex before stabilizing towards a mating partner. Active Ras1 (Ras1-GTP), an upstream regulator of Cdc42, and Gap1, the GTPase-activating protein for Ras1, localize at the patch. We developed a reaction-diffusion model of Ras1 patch appearance and disappearance with a positive feedback by a Guanine nucleotide Exchange Factor (GEF) and Gap1 inhibition. The model is based on new estimates of Ras1-GDP, Ras1-GTP and Gap1 diffusion coefficients and rates of cytoplasmic exchange studied by FRAP. The model reproduces exploratory patch behavior and lack of Ras1 patch in cells lacking Gap1. Transition to a stable patch can occur by change of Gap1 rates constants or local increase of the positive feedback rate constants. The model predicts that the patch size and number of patches depend on the strength of positive and negative feedbacks. Measurements of Ras1 patch size and number in cells overexpressing the Ras1 GEF or Gap1 are consistent with the model.

Spontaneous Cdc42 polarization independent of GDI-mediated extraction and actin-based trafficking.

The small Rho-family GTPase Cdc42 is critical for cell polarization and polarizes spontaneously in absence of upstream spatial cues. Spontaneous polarization is thought to require dynamic Cdc42 recycling through Guanine nucleotide Dissociation Inhibitor (GDI)-mediated membrane extraction and vesicle trafficking. Here, we describe a functional fluorescent Cdc42 allele in fission yeast, which demonstrates Cdc42 dynamics and polarization independent of these pathways. Furthermore, an engineered Cdc42 allele targeted to the membrane independently of these recycling pathways by an amphipathic helix is viable and polarizes spontaneously to multiple sites in fission and budding yeasts. We show that Cdc42 is highly mobile at the membrane and accumulates at sites of activity, where it displays slower mobility. By contrast, a near-immobile transmembrane domain-containing Cdc42 allele supports viability and polarized activity, but does not accumulate at sites of activity. We propose that Cdc42 activation, enhanced by positive feedback, leads to its local accumulation by capture of fast-diffusing inactive molecules.

Model of turnover kinetics in the lamellipodium: implications of slow- and fast- diffusing capping protein and Arp2/3 complex.

Cell protrusion through polymerization of actin filaments at the leading edge of motile cells may be influenced by spatial gradients of diffuse actin and regulators. Here we study the distribution of two of the most important regulators, capping protein and Arp2/3 complex, which regulate actin polymerization in the lamellipodium through capping and nucleation of free barbed ends. We modeled their kinetics using data from prior single molecule microscopy experiments on XTC cells. These experiments have provided evidence for a broad distribution of diffusion coefficients of both capping protein and Arp2/3 complex. The slowly diffusing proteins appear as extended 'clouds' while proteins bound to the actin filament network appear as speckles that undergo retrograde flow. Speckle appearance and disappearance events correspond to assembly and dissociation from the actin filament network and speckle lifetimes correspond to the dissociation rate. The slowly diffusing capping protein could represent severed capped actin filament fragments or membrane-bound capping protein. Prior evidence suggests that slowly diffusing Apr2/3 complex associates with the membrane. We use the measured rates and estimates of diffusion coefficients of capping protein and Arp2/3 complex in a Monte Carlo simulation that includes particles in association with a filament network and diffuse in the cytoplasm. We consider two separate pools of diffuse proteins, representing fast and slowly diffusing species. We find a steady state with concentration gradients involving a balance of diffusive flow of fast and slow species with retrograde flow. We show that simulations of FRAP are consistent with prior experiments performed on different cell types. We provide estimates for the ratio of bound to diffuse complexes and calculate conditions where Arp2/3 complex recycling by diffusion may become limiting. We discuss the implications of slowly diffusing populations and suggest experiments to distinguish among mechanisms that influence long range transport.

Dynamic network morphology and tension buildup in a 3D model of cytokinetic ring assembly.

During fission yeast cytokinesis, actin filaments nucleated by cortical formin Cdc12 are captured by myosin motors bound to a band of cortical nodes and bundled by cross-linking proteins. The myosin motors exert forces on the actin filaments, resulting in a net pulling of the nodes into a contractile ring, while cross-linking interactions help align actin filaments and nodes into a single bundle. We used these mechanisms in a three-dimensional computational model of contractile ring assembly, with semiflexible actin filaments growing from formins at cortical nodes, capturing of filaments by neighboring nodes, and cross-linking among filaments through attractive interactions. The model was used to predict profiles of actin filament density at the cell cortex, morphologies of condensing node-filament networks, and regimes of cortical tension by varying the node pulling force and strength of cross-linking among actin filaments. Results show that cross-linking interactions can lead to confinement of actin filaments at the simulated cortical boundary. We show that the ring-formation region in parameter space lies close to regions leading to clumps, meshworks or double rings, and stars/cables. Since boundaries between regions are not sharp, transient structures that resemble clumps, stars, and meshworks can appear in the process of ring assembly. These results are consistent with prior experiments with mutations in actin-filament turnover regulators, myosin motor activity, and changes in the concentration of cross-linkers that alter the morphology of the condensing network. Transient star shapes appear in some simulations, and these morphologies offer an explanation for star structures observed in prior experimental images. Finally, we quantify tension along actin filaments and forces on nodes during ring assembly and show that the mechanisms describing ring assembly can also drive ring constriction once the ring is formed.

Model of fission yeast cell shape driven by membrane-bound growth factors and the cytoskeleton.

Fission yeast serves as a model for how cellular polarization machinery consisting of signaling molecules and the actin and microtubule cytoskeleton regulates cell shape. In this work, we develop mathematical models to investigate how these cells maintain a tubular shape of approximately constant diameter. Many studies identify active Cdc42, found in a cap at the inner membrane of growing cell tips, as an important regulator of local cell wall remodeling, likely through control of exocyst tethering and the targeting of other polarity-enhancing structures. First, we show that a computational model with Cdc42-dependent local cell wall remodeling under turgor pressure predicts a relationship between spatial extent of growth signal and cell diameter that is in agreement with prior experiments. Second, we model the consequences of feedback between cell shape and distribution of Cdc42 growth signal at cell tips. We show that stability of cell diameter over successive cell divisions places restrictions on their mutual dependence. We argue that simple models where the spatial extent of the tip growth signal relies solely on geometrical alignment of confined microtubules might lead to unstable width regulation. Third, we study a computational model that combines a growth signal distributed over a characteristic length scale (as, for example, by a reaction-diffusion mechanism) with an axis-sensing microtubules system that places landmarks at positions where microtubule tips touch the cortex. A two-dimensional implementation of this model leads to stable cell diameter for a wide range of parameters. Changes to the parameters of this model reproduce straight, bent, and bulged cell shapes, and we discuss how this model is consistent with other observed cell shapes in mutants. Our work provides an initial quantitative framework for understanding the regulation of cell shape in fission yeast, and a scaffold for understanding this process on a more molecular level in the future.

Anillin-related Mid1 as an adaptive and multimodal contractile ring anchoring protein: A simulation study.

Cytokinesis of animal and fungi cells depends crucially on the anillin scaffold proteins. Fission yeast anillin-related Mid1 anchors cytokinetic ring precursor nodes to the membrane. However, it is unclear if both of its Pleckstrin Homology (PH) and C2 C-terminal domains bind to the membrane as monomers or dimers, and if one domain plays a dominant role. We studied Mid1 membrane binding with all-atom molecular dynamics near a membrane with yeast-like lipid composition. In simulations with the full C terminal region started away from the membrane, Mid1 binds through the disordered L3 loop of C2 in a vertical orientation, with the PH away from the membrane. However, a configuration with both C2 and PH initially bound to the membrane remains associated with the membrane. Simulations of C2-PH dimers show extensive asymmetric membrane contacts. These multiple modes of binding may reflect Mid1's multiple interactions with membranes, node proteins, and ability to sustain mechanical forces.

Myosin-I Synergizes with Arp2/3 Complex to Enhance Pushing Forces of Branched Actin Networks.

Myosin-Is colocalize with Arp2/3 complex-nucleated actin networks at sites of membrane protrusion and invagination, but the mechanisms by which myosin-I motor activity coordinates with branched actin assembly to generate force are unknown. We mimicked the interplay of these proteins using the "comet tail" bead motility assay, where branched actin networks are nucleated by Arp2/3 complex on the surface of beads coated with myosin-I and the WCA domain of N-WASP. We observed that myosin-I increased bead movement efficiency by thinning actin networks without affecting growth rates. Remarkably, myosin-I triggered symmetry breaking and comet-tail formation in dense networks resistant to spontaneous fracturing. Even with arrested actin assembly, myosin-I alone could break the network. Computational modeling recapitulated these observations suggesting myosin-I acts as a repulsive force shaping the network's architecture and boosting its force-generating capacity. We propose that myosin-I leverages its power stroke to amplify the forces generated by Arp2/3 complex-nucleated actin networks.

Distributed actin turnover in the lamellipodium and FRAP kinetics.

Studies of actin dynamics at the leading edge of motile cells with single-molecule speckle (SiMS) microscopy have shown a broad distribution of EGFP-actin speckle lifetimes and indicated actin polymerization and depolymerization over an extended region. Other experiments using FRAP with the same EGFP-actin as a probe have suggested, by contrast, that polymerization occurs exclusively at the leading edge. We performed FRAP experiments on XTC cells to compare SiMS to FRAP on the same cell type. We used speckle statistics obtained by SiMS to model the steady-state distribution and kinetics of actin in the lamellipodium. We demonstrate that a model with a single diffuse actin species is in good agreement with FRAP experiments. A model including two species of diffuse actin provides an even better agreement. The second species consists of slowly diffusing oligomers that associate to the F-actin network throughout the lamellipodium or break up into monomers after a characteristic time. Our work motivates studies to test the presence and composition of slowly diffusing actin species that may contribute to local remodeling of the actin network and increase the amount of soluble actin.

Image analysis tools to quantify cell shape and protein dynamics near the leading edge.

We present a set of flexible image analysis tools to analyze dynamics of cell shape and protein concentrations near the leading edge of cells adhered to glass coverslips. Plugins for ImageJ streamline common analyses of microscopic images of cells, including the calculation of leading edge speeds, total and average intensities of fluorescent markers, and retrograde flow rate measurements of fluorescent single-molecule speckles. We also provide automated calculations of auto- and cross-correlation functions between velocity and intensity measurements. The application of the methods is illustrated on images of XTC cells.

Molecular viewing of actin polymerizing actions and beyond: combination analysis of single-molecule speckle microscopy with modeling, FRAP and s-FDAP (sequential fluorescence decay after photoactivation).

Live-cell single-molecule imaging is a powerful tool to elucidate the in vivo biochemistry of cytoskeletal proteins. However, it is often somewhat difficult to interpret how a bulk population of the observed molecule might behave as a whole. We review our recent studies in which the combination of image analysis with modeling and bulk kinetics measurements such as FRAP (fluorescence recovery after photobleaching) clarified basic problems in the regulation of actin remodeling pathways.

Steps of actin filament branch formation by Arp2/3 complex investigated with coarse-grained molecular dynamics.

The nucleation of actin filament branches by the Arp2/3 complex involves activation through nucleation promotion factors (NPFs), recruitment of actin monomers, and binding of the complex to the side of actin filaments. Because of the large system size and processes that involve flexible regions and diffuse components, simulations of branch formation using all-atom molecular dynamics are challenging. We applied a coarse-grained model that retains amino-acid level information and allows molecular dynamics simulations in implicit solvent, with globular domains represented as rigid bodies and flexible regions allowed to fluctuate. We used recent electron microscopy structures of the inactive Arp2/3 complex bound to NPF domains and to mother actin filament for the activated Arp2/3 complex. We studied interactions of Arp2/3 complex with the activating VCA domain of the NPF Wiskott-Aldrich syndrome protein, actin monomers, and actin filament. We found stable configurations with one or two actin monomers bound along the branch filament direction and with CA domain of VCA associated to the strong and weak binding sites of the Arp2/3 complex, supporting prior structural studies and validating our approach. We reproduced delivery of actin monomers and CA to the Arp2/3 complex under different conditions, providing insight into mechanisms proposed in previous studies. Simulations of active Arp2/3 complex bound to a mother actin filament indicate the contribution of each subunit to the binding. Addition of the C-terminal tail of Arp2/3 complex subunit ArpC2, which is missing in the cryo-EM structure, increased binding affinity, indicating a possible stabilizing role of this tail.

Anillin Related Mid1 as an Adaptive and Multimodal Contractile Ring Anchoring Protein: A Simulation Study.

The organization of the cytokinetic ring at the cell equator of dividing animal and fungi cells depends crucially on the anillin scaffold proteins. In fission yeast, anillin related Mid1 binds to the plasma membrane and helps anchor and organize a medial broad band of cytokinetic nodes, which are the precursors of the contractile ring. Similar to other anillins, Mid1 contains a C terminal globular domain with two potential regions for membrane binding, the Pleckstrin Homology (PH) and C2 domains, and an N terminal intrinsically disordered region that is strongly regulated by phosphorylation. Previous studies have shown that both PH and C2 domains can associate with the membrane, preferring phosphatidylinositol-(4,5)-bisphosphate (PIP 2 ) lipids. However, it is unclear if they can simultaneously bind to the membrane in a way that allows dimerization or oligomerization of Mid1, and if one domain plays a dominant role. To elucidate Mid1's membrane binding mechanism, we used the available structural information of the C terminal region of Mid1 in all-atom molecular dynamics (MD) near a membrane with a lipid composition based on experimental measurements (including PIP 2 lipids). The disordered L3 loop of C2, as well as the PH domain, separately bind the membrane through charged lipid contacts. In simulations with the full C terminal region started away from the membrane, Mid1 binds through the L3 loop and is stabilized in a vertical orientation with the PH domain away from the membrane. However, a configuration with both C2 and PH initially bound to the membrane remains associated with the membrane. These multiple modes of binding may reflect Mid1's multiple interactions with membranes and other node proteins, and ability to sustain mechanical forces.

Design principles of Cdr2 node patterns in fission yeast cells.

Pattern-forming networks have diverse roles in cell biology. Rod-shaped fission yeast cells use pattern formation to control the localization of mitotic signaling proteins and the cytokinetic ring. During interphase, the kinase Cdr2 forms membrane-bound multiprotein complexes termed nodes, which are positioned in the cell middle due in part to the node inhibitor Pom1 enriched at cell tips. Node positioning is important for timely cell cycle progression and positioning of the cytokinetic ring. Here, we combined experimental and modeling approaches to investigate pattern formation by the Pom1-Cdr2 system. We found that Cdr2 nodes accumulate near the nucleus, and Cdr2 undergoes nucleocytoplasmic shuttling when cortical anchoring is reduced. We generated particle-based simulations based on tip inhibition, nuclear positioning, and cortical anchoring. We tested model predictions by investigating Pom1-Cdr2 localization patterns after perturbing each positioning mechanism, including in both anucleate and multinucleated cells. Experiments show that tip inhibition and cortical anchoring alone are sufficient for the assembly and positioning of nodes in the absence of the nucleus, but that the nucleus and Pom1 facilitate the formation of unexpected node patterns in multinucleated cells. These findings have implications for spatial control of cytokinesis by nodes and for spatial patterning in other biological systems.