Complexity of the tensegrity structure for dynamic energy and force distribution of cytoskeleton during cell spreading

Cytoskeleton plays important roles in intracellular force equilibrium and extracellular force transmission from/to attaching substrate through focal adhesions (FAs). Numerical simulations of intracellular force distribution to describe dynamic cell behaviors are still limited. The tensegrity structure comprises tension-supporting cables and compression-supporting struts that represent the actin filament and microtubule respectively, and has many features consistent with living cells. To simulate the dynamics of intracellular force distribution and total stored energy during cell spreading, the present study employed different complexities of the tensegrity structures by using octahedron tensegrity (OT) and cuboctahedron tensegrity (COT). The spreading was simulated by assigning specific connection nodes for radial displacement and attachment to substrate to form FAs. The traction force on each FA was estimated by summarizing the force carried in sounding cytoskeletal elements. The OT structure consisted of 24 cables and 6 struts and had limitations soon after the beginning of spreading by declining energy stored in struts indicating the abolishment of compression in microtubules. The COT structure, double the amount of cables and struts than the OT structure, provided sufficient spreading area and expressed similar features with documented cell behaviors. The traction force pointed inward on peripheral FAs in the spread out COT structure. The complex structure in COT provided further investigation of various FA number during different spreading stages. Before the middle phase of spreading (half of maximum spreading area), cell attachment with 8 FAs obtained minimized cytoskeletal energy. The maximum number of 12 FAs in the COT structure was required to achieve further spreading. The stored energy in actin filaments increased as cells spread out, while the energy stored in microtubules increased at initial spreading, peaked in middle phase, and then declined as cells reached maximum spreading. The dynamic flows of energy in struts imply that microtubules contribute to structure stabilization.     

Molecular friction in an actomyosin molecular machine

In muscle contraction, it has been widely recognized that a binding state exists between myosin and actin in the presence of Mg-ATP. To estimate the magnitude of binding strength, I introduce a concept of frictional phenomena which occurs between two sliding bodies in contact each other. In such cases, the sliding speed can be formulated as a function of the actin-myosin bond strength. In order to validate this, the present theory is applied for the two movement assay systems with no external load; one movement assay of Phalloidin Rhodamine bound F-actin on a myosin coated hydrophobic cover glass and another assay of myosin coated beads along actin cables of Nitella. If a coefficient of 0.005 is applied to the kinetic friction, 1pN for the sliding force per cross-bridge and 10 microns sec-1 for the sliding speed, it is found that the bond strength between actin and one myosin head is about 200 pN in the contracting state.     

Attachment conditions control actin filament buckling and the production of forces

Actin polymerization is the driving force for a large number of cellular processes. Formation of lamellipodia and filopodia at the leading edge of motile cells requires actin polymerization induced mechanical deformation of the plasma membrane. To generate different types of membrane protrusions, the mechanical properties of actin filaments can be constrained by interacting proteins. A striking example of such constraint is the buckling of actin filaments generated in vitro by the cooperative effect of a processive actin nucleating factor (formin) and a molecular motor (myosin II). We developed a physical model based on equations for an elastic rod that accounts for actin filament buckling. Both ends of the rod were maintained in a fixed position in space and we considered three sets of boundary conditions. The model qualitatively and quantitatively reproduces the shape distribution of actin filaments. We found that actin polymerization counterpoises a force in the range 0.4-1.6 pN for moderate end-to-end distance (approximately 1 microm) and could be as large as 10 pN for shorter distances. If the actin rod attachment includes a spring, we discovered that the stiffness must be in the range 0.1-1.2 pN/nm to account for the observed buckling.     

Antenna Mechanism of Length Control of Actin Cables

Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This “antenna mechanism” involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. We compute the probability distribution of cable lengths as a function of several experimentally tuneable parameters such as the formin-binding affinity of Smy1 and the concentration of myosin motors delivering Smy1. These results provide testable predictions of the antenna mechanism of actin-cable length control.     

Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape

Microtubules are long, proteinaceous filaments that perform structural functions in eukaryotic cells by defining cellular shape and serving as tracks for intracellular motor proteins. We report the first accurate measurements of the flexural rigidity of microtubules. By analyzing the thermally driven fluctuations in their shape, we estimated the mean flexural rigidity of taxol-stabilized microtubules to be 2.2 x 10(-23) Nm2 (with 6.4% uncertainty) for seven unlabeled microtubules and 2.1 x 10(-23) Nm2 (with 4.7% uncertainty) for eight rhodamine-labeled microtubules. These values are similar to earlier, less precise estimates of microtubule bending stiffness obtained by modeling flagellar motion. A similar analysis on seven rhodamine-phalloidin- labeled actin filaments gave a flexural rigidity of 7.3 x 10(-26) Nm2 (with 6% uncertainty), consistent with previously reported results. The flexural rigidity of these microtubules corresponds to a persistence length of 5,200 microns showing that a microtubule is rigid over cellular dimensions. By contrast, the persistence length of an actin filament is only approximately 17.7 microns, perhaps explaining why actin filaments within cells are usually cross-linked into bundles. The greater flexural rigidity of a microtubule compared to an actin filament mainly derives from the former's larger cross-section. If tubulin were homogeneous and isotropic, then the microtubule's Young's modulus would be approximately 1.2 GPa, similar to Plexiglas and rigid plastics. Microtubules are expected to be almost inextensible: the compliance of cells is due primarily to filament bending or sliding between filaments rather than the stretching of the filaments themselves.     

A Highlights from MBoC Selection: Myosin Vs organize actin cables in fission yeast

Myosin V motors are believed to contribute to cell polarization by carrying cargoes along actin tracks. In Schizosaccharomyces pombe, Myosin Vs transport secretory vesicles along actin cables, which are dynamic actin bundles assembled by the formin For3 at cell poles. How these flexible structures are able to extend longitudinally in the cell through the dense cytoplasm is unknown. Here we show that in myosin V (myo52 myo51) null cells, actin cables are curled, bundled, and fail to extend into the cell interior. They also exhibit reduced retrograde flow, suggesting that formin-mediated actin assembly is impaired. Myo52 may contribute to actin cable organization by delivering actin regulators to cell poles, as myoV∆ defects are partially suppressed by diverting cargoes toward cell tips onto microtubules with a kinesin 7–Myo52 tail chimera. In addition, Myo52 motor activity may pull on cables to provide the tension necessary for their extension and efficient assembly, as artificially tethering actin cables to the nuclear envelope via a Myo52 motor domain restores actin cable extension and retrograde flow in myoV mutants. Together these in vivo data reveal elements of a self-organizing system in which the motors shape their own tracks by transporting cargoes and exerting physical pulling forces.     

Microtubule tips redirect actin assembly

In fission yeast, a protein complex that rides on the plus end of growing microtubules regulates establishment of new sites of actin cable assembly, necessary for cell growth, from one to both ends of the rod-shaped cells. Martin et al. describe a direct molecular link between the microtubule tip complex and the formin for3p, the nucleator for assembly of actin cables, which is necessary for this regulatory switch.     

Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules

Unexplained length-dependence of flexural rigidity and Young's modulus of microtubules is studied using an orthotropic elastic shell model. It is showed that vibration frequencies and buckling load predicted by the accurate orthotropic shell model are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is this inaccuracy of the isotropic beam model used by all previous researchers that leads to reported lower flexural rigidity and Young's modulus for shorter microtubules. In particular, much lower shear modulus and circumferential Young's modulus, which only weaken flexural rigidity of shorter microtubules, are responsible for the observed length-dependence of the flexural rigidity. These results confirm that longitudinal Young's modulus of microtubules is length-independent, and the observed length-dependence of the flexural rigidity and Young's modulus is a result of strongly anisotropic elastic properties of microtubules which have a length-dependent weakening effect on flexural rigidity of shorter microtubules.     

Preparation of bead-tailed actin filaments: estimation of the torque produced by the sliding force in an in vitro motility assay.

By coating covalently the surface of a polystyrene bead (diameter = 1 micron) with gelsolin, we have succeeded in attaching the bead selectively at the barbed end of an actin filament and forming a 1:1 bead-actin filament complex. On a layer of heavy meromyosin on a nitrocellulose-coated coverglass, this bead-actin filament complex slid smoothly, trailing the bead at its end. Therefore we called this preparation "bead-tailed" actin filaments. The sliding velocity was indistinguishable from that of nonbeaded filaments. With use of this system, we tried to detect the axial rotation (rotation around the filament axis) in a sliding actin filament. Although a single bead at the tail end did not serve as the marker for the axial rotation, we occasionally found another bead bound to the tail bead. In this case, the orientation of the bead-aggregate could be followed continuously with a video monitor while the filament was sliding over heavy meromyosin. We observed that actin filaments slid over distances of many tens of micrometers without showing a complete turn of the bead-aggregates. On the basis of the calculation of rotational friction drag on the bead-aggregate, we estimate that the rotational component of the sliding force and the torque produced on a sliding actin filament (length < or = 10 microns) did not accumulate > 1 pN and 5 pN.nm, respectively. In the present system of randomly oriented heavy meromyosin lying on a nitrocellulose film without an external load.     

A morphological model of vertebral trabecular bone

In their micro-structures, typical natural cellular materials such as vertebral trabecular bone have a network of doubly tapered struts, thickening near the strut joints. However, past analytical models for vertebral trabecular bone do not take account of the effect of strut taper on the mechanical properties.This paper presents an analytical cell model comprised of doubly tapered struts to predict the global mechanical properties of vertebral trabecular bone. The predicted results for male, female, and both sexes fit the experimental data well. By considering several strut taper geometries, it is shown that the horizontal Young's modulus and the horizontal uniaxial collapse stress are, in some cases, approximately 1.8- and 2.2-fold higher, respectively, than those of the uniform strut model. This finding illustrates the importance of increased trabecular thickening near the strut joints (i) for improving the accuracy of calculating the mechanical properties and (ii) for the effective treatment of aged bone using drug therapy. It also highlights the need to combine trabecular architecture measurements with information about the morphology near the strut joints.     

Regulation of a formin complex by the microtubule plus end protein tea1p

The plus ends of microtubules have been speculated to regulate the actin cytoskeleton for the proper positioning of sites of cell polarization and cytokinesis. In the fission yeast Schizosaccharomyces pombe, interphase microtubules and the kelch repeat protein tea1p regulate polarized cell growth. Here, we show that tea1p is directly deposited at cell tips by microtubule plus ends. Tea1p associates in large "polarisome" complexes with bud6p and for3p, a formin that assembles actin cables. Tea1p also interacts in a separate complex with the CLIP-170 protein tip1p, a microtubule plus end-binding protein that anchors tea1p to the microtubule plus end. Localization experiments suggest that tea1p and bud6p regulate formin distribution and actin cable assembly. Although single mutants still polarize, for3Deltabud6Deltatea1Delta triple-mutant cells lack polarity, indicating that these proteins contribute overlapping functions in cell polarization. Thus, these experiments begin to elucidate how microtubules contribute to the proper spatial regulation of actin assembly and polarized cell growth.     

The ultrastructure of polygonal networks in chick embryonic cells in vitro

Polygonal networks in cultured chick endoderm cells are ordered arrays of actin microfilaments situated just beneath the dorsal cell surface. Each strut is formed from a bundle of microfilaments and 5-7 bundles intersect at each node. Dense bodies are seen in nodes and some struts. At its periphery the network is attached to the substrate at the termini of long radial struts. Most of the network is resistant to detergent extraction. Sliding microfilaments can explain the observed behaviour of networks in live cells.     

Actin-organelle interaction: association with chloroplast in arabidopsis leaf mesophyll cells.

The role of the cytoskeleton in the regulation of chloroplast motility and positioning has been investigated by studying: (1) structural relationship of actin microfilaments, microtubules, and chloroplasts in cryofixed and freeze-substituted leaf cells of Arabidopsis; and (2) the effects of anti-actin (Latrunculin B; LAT-B) and anti-microtubule (Oryzalin) drugs on intracellular distribution of chloroplasts. Immunolabeling of leaf cells with two plant-actin specific antibodies, which react equivalently with all the expressed Arabidopsis actins, revealed two arrangements of actin microfilaments: longitudinal arrays of thick actin bundles and randomly oriented thin actin filaments that extended from the bundles. Chloroplasts were either aligned along the actin bundles or closely associated with the fine filaments. Baskets of actin microfilaments were also observed around the chloroplasts. The leaf cells labeled with an anti-tubulin antibody showed dense transverse arrays of cortical microtubules that exhibited no apparent association with chloroplasts. The application of LAT-B severely disrupted actin filaments and their association with chloroplasts. In addition, LAT-B induced aberrant aggregation of chloroplasts in the mesophyll and bundle sheath cells. Double labeling of LAT-B treated cells with anti-actin and anti-tubulin antibodies revealed that the microtubules in these cells were unaffected. Moreover, depolymerization of microtubules with Oryzalin did not affect the distribution of chloroplasts. These results provide evidence for the involvement of actin, but not tubulin, in the movement and positioning of chloroplasts in leaf cells. We propose that using motor molecules, some chloroplasts migrate along the actin cables directly, while others are pulled along the cables by the fine actin filaments. The baskets of microfilaments may anchor the chloroplasts during streaming and allow control over proper three-dimensional orientation to light.     

Intrinsic capability of budding yeast cofilin to promote turnover of tropomyosin-bound actin filaments

The ability of actin filaments to function in cell morphogenesis and motility is closely coupled to their dynamic properties. Yeast cells contain two prominent actin structures, cables and patches, both of which are rapidly assembled and disassembled. Although genetic studies have shown that rapid actin turnover in patches and cables depends on cofilin, how cofilin might control cable disassembly remains unclear, because tropomyosin, a component of actin cables, is thought to protect actin filaments against the depolymerizing activity of ADF/cofilin. We have identified cofilin as a yeast tropomyosin (Tpm1) binding protein through Tpm1 affinity column and mass spectrometry. Using a variety of assays, we show that yeast cofilin can efficiently depolymerize and sever yeast actin filaments decorated with either Tpm1 or mouse tropomyosins TM1 and TM4. Our results suggest that yeast cofilin has the intrinsic ability to promote actin cable turnover, and that the severing activity may rely on its ability to bind Tpm1.     

Tubulin and actin in paired nonneoplastic and spontaneously transformed neoplastic cell lines in vitro: fluorescent antibody studies.

Pairs of nonneoplastic and spontaneously transformed neoplastic cells were derived from rat, mouse and hamster embryos. The neoplastic cells of each pair had poorly spread cellular morphology, grew in agarose in vitro and produced invasive sarcomas in vivo; the nonneoplastic cells exhibited none of these properties. The distribution of microtubules and microfilament bundles (stress fibers or actin cables) was examined in five such paired lines and in 3T3 and SV40-transformed 3T3 cells by indirect immunofluorescent microscopy of fixed cells treated with rabbit antibody prepared against bovine brain tubulin or guinea pig smooth muscle actin, respectively. Actin cables in all the neoplastic cells appeared thinner and more sparse than in the paired nonneoplastic cells. These differences were also observed in living cells with polarization microscopy. In contrast, microtubules appeared similar in neoplastic and nonneoplastic cells, both in areas of thin peripheral lamellar cytoplasm which allowed a clear visualization of fine, curving microtubules and in regions of thick, central endoplasm which obsecured individual microtubules. In fact, the main morphological difference between neoplastic and nonneoplastic cells was the relative amount of lamellar cytoplasm or endoplasm, rather than the appearance of microtubles in either region. Thus the distinctive growth properties and retracted cellular morphology of neoplastic cells in this study did not correlate with decreased or disorganized microtubules, but with thin and sparse actin cables.     

Behavior of mitochondria, microtubules, and actin in the triangular yeastTrigonopsis variabilis

Summary Dimorphic yeastTrigonopsis variabilis is a unique species that can form either an ellipsoidal or a triangular cell depending upon nutritional conditions. This fluorescence microscopic study was intended to correlate morphological changes of mitochondria in the triangular cells with the distribution of the cytoskeleton. In addition, unique features in the behavior of the cytoskeleton were also examined during triangular cell formation. In log-phase cells stained with 4,6-diamidino-2-phenylindole, mitochondrial nucleoids appeared as a string of beads throughout the vegetative growth. The profile of mitochondria stained by 3,3-dihexyloxacarbocyanine iodide showed a network corresponding to the fluorescence images of mitochondrial nucleoids in both mother and daughter cells. Cell-cycle-dependent fragmentation of mitochondria was not discerned. As the culture reached stationary phase, a network of mitochondria gradually changed to form unique rings that were located near the angles of triangular cells. When examined by immunofluorescence microscopy with anti-tubulin antibody, microtubules were found to be well developed along the sides of cells in the cytoplasm ofT. variabilis interphase cells. Although distributions of microtubules and mitochondria are different during cell cycle as a whole, cytoplasmic microtubules frequently extended along a part of the mitochondria in budded cells, suggesting correlation of microtubules and mitochondria. Rhodamine-phalloidin staining revealed both actin patches and cables. Actin cables elongated from mother cells into the buds and showed close proximity to mitochondria, although complete overlapping of both structures was rare. Moreover, actin patches localized on the mitochondrial network at a frequency of 65%. These results suggested that actin cables and patches, as well as microtubules, participated in the distribution of mitochondria. The localization of actin patches separated towards opposite ends at a bud tip when the bud grew to medium size. The unique localization of actin patches is responsible for bi-directional growth of the bud, forming triangular cells.     

Flexural rigidity of individual microtubules measured by a buckling force with optical traps

We used direct buckling force measurements with optical traps to determine the flexural rigidity of individual microtubules bound to polystyrene beads. To optimize the accuracy of the measurement, we used two optical traps and antibody-coated beads to manipulate each microtubule. We then applied a new analytical model assuming nonaxial buckling. Paclitaxel-stabilized microtubules were polymerized from purified tubulin, and the average microtubule rigidity was calculated as 2.0 x 10(-24) Nm2 using this novel microtubule buckling system. This value was not dependent on microtubule length. We also measured the rigidity of paclitaxel-free microtubules, and obtained the value of 7.9 x 10(-24) Nm2, which is nearly four times that measured for paclitaxel-stabilized microtubules.     

Actin cable distribution and dynamics arising from cross-linking,motor pulling,and filament turnover

The growth of fission yeast relies on the polymerization of actin filaments nucleated by formin For3p, which localizes at tip cortical sites. These actin filaments bundle to form actin cables that span the cell and guide the movement of vesicles toward the cell tips. A big challenge is to develop a quantitative understanding of these cellular actin structures. We used computer simulations to study the spatial and dynamical properties of actin cables. We simulated individual actin filaments as semiflexible polymers in three dimensions composed of beads connected with springs. Polymerization out of For3p cortical sites, bundling by cross-linkers, pulling by type V myosin, and severing by cofilin are simulated as growth, cross-linking, pulling, and turnover of the semiflexible polymers. With the foregoing mechanisms, the model generates actin cable structures and dynamics similar to those observed in live-cell experiments. Our simulations reproduce the particular actin cable structures in myoVΔ cells and predict the effect of increased myosin V pulling. Increasing cross-linking parameters generates thicker actin cables. It also leads to antiparallel and parallel phases with straight or curved cables, consistent with observations of cells overexpressing α-actinin. Finally, the model predicts that clustering of formins at cell tips promotes actin cable formation.     

Formation of actin filament bundles in the ring canals of developing Drosophila follicles

Growing the intracellular bridges that connect nurse cells with each o ther and to the developing oocyte is vital for egg development. These ring canals increase from 0.5 microns in diameter at stage 2 to 10 microns in diameter at stage 11. Thin sections cut horizontally as you would cut a bagel, show that there is a layer of circumferentially oriented actin filaments attached to the plasma membrane at the periphery of each canal. By decoration with subfragment 1 of myosin we find actin filaments of mixed polarities in the ring such as found in the "contractile ring" formed during cytokinesis. In vertical sections through the canal the actin filaments appear as dense dots. At stage 2 there are 82 actin filaments in the ring, by stage 6 there are 717 and by stage 10 there are 726. Taking into account the diameter, this indicates that there is 170 microns of actin filaments/canal at stage 2 (pi x 0.5 microns x 82), 14,000 microns at stage 9 and approximately 23,000 microns at stage 11 or one inch of actin filament! The density of actin filaments remains unchanged throughout development. What is particularly striking is that by stages 4-5, the ring of actin filaments has achieved its maximum thickness, even though the diameter has not yet increased significantly. Thereafter, the diameter increases. Throughout development, stages 2-11, the canal length also increases. Although the density (number of actin filaments/micron2) through a canal remains constant from stage 5 on, the actin filaments appear as a net of interconnected bundles. Further information on this net of bundles comes from studying mutant animals that lack kelch, a protein located in the ring canal that has homology to the actin binding protein, scruin. In this mutant, the actin filaments form normally but individual bundles that comprise the fibers of the net are not bound tightly together. Some bundles enter into the ring canal lumen but do not completely occlude the lumen. all these observations lay the groundwork for our understanding of how a noncontractile ring increases in thickness, diameter, and length during development.