Formation and maintenance of tubular membrane projections require mechanical force, but their elongation and shortening do not require additional force

Living cells develop their own characteristic shapes depending on their physiological functions, and their morphologies are based on the mechanical characteristics of the cytoskeleton and of membranes. To investigate the role of lipid membranes in morphogenesis, we constructed a simple system that can manipulate liposomes and measure the forces required to transform their shapes. Two polystyrene beads (1 microm in diameter) were encapsulated in giant liposomes and were manipulated using double-beam laser tweezers. Without any specific interaction between the lipid membrane and beads, mechanical forces could be applied to the liposome membrane from the inside. Spherical liposomes transformed into a lemon shape with increasing tension, and tubular membrane projections were subsequently generated in the tips at either end. This process is similar to the liposomal transformation caused by elongation of encapsulated cytoskeletons. In the elongation stage of lemon-shaped liposomes, the force required for the transformation became larger as the end-to-end length increased. Just before the tubular membrane was generated, the force reached the maximum strength (approximately 11 pN). However, immediately after the tubular membrane developed, the force suddenly decreased and was maintained at a constant strength (approximately 4 pN) that was independent of further tube elongation or shortening, even though there was no excess membrane reservoir as occurs in living cells. When the tube length was shortened to approximately 2 microm, the liposome reversed to a lemon shape and the force temporarily increased (to approximately 7 pN). These results indicate that the simple application of mechanical force is sufficient to form a protrusion in a membrane, that a critical force and length is needed to form and to maintain the protrusion, and suggest that the lipid bilayer itself has the ability to buffer the membrane tension.     

Spreading dynamics of biomimetic actin cortices

Reconstituted systems mimicking cells are interesting tools for understanding the details of cell behavior. Here, we use an experimental system that mimics cellular actin cortices, namely liposomes developing an actin shell close to their inner membrane, and we study their dynamics of spreading. We show that depending on the morphology of the actin shell inside the liposome, spreading dynamics is either reminiscent of a bare liposome (in the case of a sparse actin shell) or of a cell (in the case of a continuous actin shell). We use a mechanical model that qualitatively accounts for the shape of the experimental curves. From the data on spreading dynamics, we extract characteristic times that are consistent with mechanical estimates. The mechanical characterization of such stripped-down experimental systems paves the way for a more complex design closer to a cell. We report here the first step in building an artificial cell and studying its mechanics.     

Reconstitution of an Actin Cortex Inside a Liposome

The composite and versatile structure of the cytoskeleton confers complex mechanical properties on cells. Actin filaments sustain the cell membrane and their dynamics insure cell shape changes. For example, the lamellipodium moves by actin polymerization, a mechanism that has been studied using simplified experimental systems. Much less is known about the actin cortex, a shell-like structure underneath the membrane that contracts for cell movement. We have designed an experimental system that mimicks the cell cortex by allowing actin polymerization to nucleate and assemble at the inner membrane of a liposome. Actin shell growth can be triggered inside the liposome, which offers a useful system for a controlled study. The observed actin shell thickness and estimated mesh size of the actin structure are in good agreement with cellular data. Such a system paves the way for a thorough characterization of cortical dynamics and mechanics.     

Cracking up: symmetry breaking in cellular systems

The shape of animal cells is, to a large extent, determined by the cortical actin network that underlies the cell membrane. Because of the presence of myosin motors, the actin cortex is under tension, and local relaxation of this tension can result in cortical flows that lead to deformation and polarization of the cell. Cortex relaxation is often regulated by polarizing signals, but the cortex can also rupture and relax spontaneously. A similar tension-induced polarization is observed in actin gels growing around beads, and we propose that a common mechanism governs actin gel rupture in both systems.     

Quantifying the contribution of actin networks to the elastic strength of fibroblasts

The structural models created to understand the cytoskeletal mechanics of cells in suspension are described here. Suspended cells can be deformed by well-defined surface stresses in an Optical Stretcher [Guck, J., Ananthakrishnan, R., Mahmood, H., Moon, T.J., Cunningham, C.C., K?s, J., 2001. The optical stretcher: a novel laser tool to micromanipulate cells. Biophys. J. 81(2), 767-784], a two-beam optical trap designed for the contact-free deformation of cells. Suspended cells have a well-defined cytoskeleton, displaying a radially symmetric actin cortical network underlying the cell membrane with no actin stress fibers, and microtubules and intermediate filaments in the interior. Based on experimental data using suspended fibroblasts, we create two structural models: a thick shell actin cortex model that describes cell deformation for a localized stress distribution on these cells and a three-layered model that considers the entire cytoskeleton when a broad stress distribution is applied. Applying the models to data, we obtain a (actin) cortical shear moduli G of approximately 220 Pa for normal fibroblasts and approximately 185 Pa for malignantly transformed fibroblasts. Additionally, modeling the cortex as a transiently crosslinked isotropic actin network, we show that actin and its crosslinkers must be co-localized into a tight shell to achieve these cortical strengths. The similar moduli values and cortical actin and crosslinker densities but different deformabilities of the normal and cancerous cells suggest that a cell's structural strength is not solely determined by cytoskeletal composition but equally importantly by (actin) cytoskeletal architecture via differing cortical thicknesses. We also find that although the interior structural elements (microtubules, nucleus) contribute to the deformed cell's exact shape via their loose coupling to the cortex, it is the outer actin cortical shell (and its thickness) that mainly determines the cell's structural response.     

Actin polymerization or myosin contraction: two ways to build up cortical tension for symmetry breaking

Cells use complex biochemical pathways to drive shape changes for polarization and movement. One of these pathways is the self-assembly of actin filaments and myosin motors that together produce the forces and tensions that drive cell shape changes. Whereas the role of actin and myosin motors in cell polarization is clear, the exact mechanism of how the cortex, a thin shell of actin that is underneath the plasma membrane, can drive cell shape changes is still an open question. Here, we address this issue using biomimetic systems: the actin cortex is reconstituted on liposome membranes, in an ‘outside geometry’. The actin shell is either grown from an activator of actin polymerization immobilized at the membrane by a biotin–streptavidin link, or built by simple adsorption of biotinylated actin filaments to the membrane, in the presence or absence of myosin motors. We show that tension in the actin network can be induced either by active actin polymerization on the membrane via the Arp2/3 complex or by myosin II filament pulling activity. Symmetry breaking and spontaneous polarization occur above a critical tension that opens up a crack in the actin shell. We show that this critical tension is reached by growing branched networks, nucleated by the Arp2/3 complex, in a concentration window of capping protein that limits actin filament growth and by a sufficient number of motors that pull on actin filaments. Our study provides the groundwork to understanding the physical mechanisms at work during polarization prior to cell shape modifications.     

Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets.

Many nonadherent cells exist as spheres in suspension and when sucked into pipets, deform continuously like liquids within the fixed surface area limitation of a plasma membrane envelope. After release, these cells eventually recover their spherical form. Consequently, pipet aspiration test provides a useful method to assay the apparent viscosity of such cells. For this purpose, we have analyzed the inertialess flow of a liquid-like model cell into a tube at constant suction pressure. The cell is modeled as a uniform liquid core encapsulated by a distinct cortical shell. The method of analysis employs a variational approach that minimizes errors in boundary conditions defined by the equations of motion for the cortical shell where the trial functions are exact solutions for the flow field inside the liquid core. For the particular case of an anisotropic liquid cortex with persistent tension, we have determined universal predictions for flow rate scaled by the ratio of excess pressure (above the threshold established by the cortical tension) and core viscosity which is the reciprocal of the dynamic resistance to entry. The results depend on pipet to cell size ratio and a parameter that characterizes the ratio of viscous flow resistance in the cortex to that inside the cytoplasmic core. The rate of entry increases markedly as the pipet size approaches the outer segment diameter of the cell. Viscous dissipation in the cortex strongly influences the entry flow resistance for small tube sizes but has little effect for large tubes. This indicates that with sufficient experimental resolution, measurement of cell entry flow with different-size pipets could establish both the cortex to cell dissipation ratio as well as the apparent viscosity of the cytoplasmic core.     

Direct observations of the mechanical behaviors of the cytoskeleton in living fibroblasts

Cytoskeletal proteins tagged with green fluorescent protein were used to directly visualize the mechanical role of the cytoskeleton in determining cell shape. Rat embryo (REF 52) fibroblasts were deformed using glass needles either uncoated for purely physical manipulations, or coated with laminin to induce attachment to the cell surface. Cells responded to uncoated probes in accordance with a three-layer model in which a highly elastic nucleus is surrounded by cytoplasmic microtubules that behave as a jelly-like viscoelastic fluid. The third, outermost cortical layer is an elastic shell under sustained tension. Adhesive, laminin-coated needles caused focal recruitment of actin filaments to the contacted surface region and increased the cortical layer stiffness. This direct visualization of actin recruitment confirms a widely postulated model for mechanical connections between extracellular matrix proteins and the actin cytoskeleton. Cells tethered to laminin-treated needles strongly resisted elongation by actively contracting. Whether using uncoated probes to apply simple deformations or laminin-coated probes to induce surface-to-cytoskeleton interaction we observed that experimentally applied forces produced exclusively local responses by both the actin and microtubule cytoskeleton. This local accomodation and dissipation of force is inconsistent with the proposal that cellular tensegrity determines cell shape.     

One-dimensional steady continuum model of retraction of pseudopod in leukocytes

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.     

Cortical Mechanics and Meiosis II Completion in Mammalian Oocytes Are Mediated by Myosin-II and Ezrin-Radixin-Moesin (ERM) Proteins

Cell division is inherently mechanical, with cell mechanics being a critical determinant governing the cell shape changes that accompany progression through the cell cycle. The mechanical properties of symmetrically dividing mitotic cells have been well characterized, whereas the contribution of cellular mechanics to the strikingly asymmetric divisions of female meiosis is very poorly understood. Progression of the mammalian oocyte through meiosis involves remodeling of the cortex and proper orientation of the meiotic spindle, and thus we hypothesized that cortical tension and stiffness would change through meiotic maturation and fertilization to facilitate and/or direct cellular remodeling. This work shows that tension in mouse oocytes drops about sixfold during meiotic maturation from prophase I to metaphase II and then increases ∼1.6-fold upon fertilization. The metaphase II egg is polarized, with tension differing ∼2.5-fold between the cortex over the meiotic spindle and the opposite cortex, suggesting that meiotic maturation is accompanied by assembly of a cortical domain with stiffer mechanics as part of the process to achieve asymmetric cytokinesis. We further demonstrate that actin, myosin-II, and the ERM (Ezrin/Radixin/Moesin) family of proteins are enriched in complementary cortical domains and mediate cellular mechanics in mammalian eggs. Manipulation of actin, myosin-II, and ERM function alters tension levels and also is associated with dramatic spindle abnormalities with completion of meiosis II after fertilization. Thus, myosin-II and ERM proteins modulate mechanical properties in oocytes, contributing to cell polarity and to completion of meiosis.     

Research on the mechanism of interaction between actin and membrane lipids

Using an in vitro system involving pure actin and liposomes, we have established that actin may interact with membrane lipids without any intermediate proteins, and that the mechanism of interaction depends upon the concentration of divalent cation. In the absence of divalent cation, actin increases membrane permeability. Low concentrations (1 mM) of divalent cation potentialize this interaction. In the presence of high divalent cation concentration, actin deposits on the surface of liposomes in a crystalline organization and reduces the membrane microviscosity as shown by the polarization of fluorescence of the DPH probe. We propose that actin interacts with lipids by hydrophobic association which is facilitated by initial electrostatic binding.     

Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex

Diffusion of lipids and proteins within the cell membrane is essential for numerous membrane-dependent processes including signaling and molecular interactions. It is assumed that the membrane-associated cytoskeleton modulates lateral diffusion. Here, we use a minimal actin cortex to directly study proposed effects of an actin meshwork on the diffusion in a well-defined system. The lateral diffusion of a lipid and a protein probe at varying densities of membrane-bound actin was characterized by fluorescence correlation spectroscopy (FCS). A clear correlation of actin density and reduction in mobility was observed for both the lipid and the protein probe. At high actin densities, the effect on the protein probe was ∼3.5-fold stronger compared to the lipid. Moreover, addition of myosin filaments, which contract the actin mesh, allowed switching between fast and slow diffusion in the minimal system. Spot variation FCS was in accordance with a model of fast microscopic diffusion and slower macroscopic diffusion. Complementing Monte Carlo simulations support the analysis of the experimental FCS data. Our results suggest a stronger interaction of the actin mesh with the larger protein probe compared to the lipid. This might point toward a mechanism where cortical actin controls membrane diffusion in a strong size-dependent manner.     

Unfertilized sea urchin eggs contain a discrete cortical shell of actin that is subdivided into two organizational states

Changes in the distribution and organizational state of actin in the cortex of echinoderm eggs are believed to be important events following fertilization. To examine the initial distribution and form of actin in unfertilized eggs, we have adapted immunogold-labeling procedures for use with eggs of Strongylocentrotus purpuratus. Using these procedures, as well as fluorescence microscopy, we have revealed a discrete 1-micron-thick concentrated shell of actin in the unfertilized egg cortex. This actin is located in the short surface projections of unfertilized eggs and around the cortical granules in a manner that suggests it is associated with the cortical granule surface. The actin in the short surface projections appears to be organized into filaments. However, most if not all of the actin surrounding the cortical granules is organized in a form that does not bind phalloidin, even though it is accessible to actin antibody. The lack of phalloidin binding is consistent with either the presence of nonfilamentous actin associated with the cortical granules or the masking of actin-filament phalloidin-binding sites by some cellular actin-binding component. In addition to the concentrated shell of actin found in the cortex, actin was also found to be concentrated in the nuclei of unfertilized eggs.     

Unexpected Membrane Dynamics Unveiled by Membrane Nanotube Extrusion

In cell mechanics, distinguishing the respective roles of the plasma membrane and of the cytoskeleton is a challenge. The difference in the behavior of cellular and pure lipid membranes is usually attributed to the presence of the cytoskeleton as explored by membrane nanotube extrusion. Here we revisit this prevalent picture by unveiling unexpected force responses of plasma membrane spheres devoid of cytoskeleton and synthetic liposomes. We show that a tiny variation in the content of synthetic membranes does not affect their static mechanical properties, but is enough to reproduce the dynamic behavior of their cellular counterparts. This effect is attributed to an amplified intramembrane friction. Reconstituted actin cortices inside liposomes induce an additional, but not dominant, contribution to the effective membrane friction. Our work underlines the necessity of a careful consideration of the role of membrane proteins on cell membrane rheology in addition to the role of the cytoskeleton.     

Enveloped viruses as model membrane systems: microviscosity of vesicular stomatitis virus and host cell membranes.

The fluorescence probe 1,6-diphenyl-1,3,5-hexatriene was used to study and compare the dynamic properties of the hydrophobic region of vesicular stomatitis virus grown on L-929 cells, plasma membrane of L-929 cells prepared by two different methods, liposomes prepared from virus lipids and plasma membrane lipids, and intact L-929 cells. The rate of penetration of the probe into the hydrophobic region of the lipid bilayer was found to be much faster in the lipid vesicle bilayer as compared with the intact membrane, but in all cases the fluorescence anisotropy was constant with time. The L-cell plasma membranes, the vesicles prepared from the lipids derived from the plasma membranes, and intact cells are found to have much lower microviscosity values than the virus or virus lipid vesicles throughout a wide range of temperatures. The microviscosity of plasma membrane and plasma membrane lipid vesicles was found to depend on the procedure for plasma membrane preparation as the membranes prepared by different methods had different microviscosities. The intact virus and liposomes prepared from the virus lipids were found to have very similar microviscosity values. Plasma membrane and liposomes prepared from plasma membrane lipids also had similar microviscosity values. Factors affecting microviscosity in natural membranes and artificially mixed lipid membranes are discussed.     

Determinants of Fluidlike Behavior and Effective Viscosity in Cross-Linked Actin Networks

The actin cortex has a well-documented ability to rapidly remodel and flow while maintaining long-range connectivity, but how this is achieved remains poorly understood. Here, we use computer simulations to explore how stress relaxation in cross-linked actin networks subjected to extensional stress depends on the interplay between network architecture and turnover. We characterize a regime in which a network response is nonaffine and stress relaxation is governed by the continuous dissipation of elastic energy via cyclic formation, elongation, and turnover of tension-bearing elements. Within this regime, for a wide range of network parameters, we observe a constant deformation (creep) rate that is linearly proportional to the rate of filament turnover, leading to a constant effective viscosity that is inversely proportional to turnover rate. Significantly, we observe a biphasic dependence of the creep rate on applied stress: below a critical stress threshold, the creep rate increases linearly with applied stress; above that threshold, the creep rate becomes independent of applied stress. We show that this biphasic stress dependence can be understood in terms of the nonlinear force-extension behavior of individual force-transmitting network elements. These results have important implications for understanding the origins and control of viscous flows both in the cortex of living cells and in other polymer networks.     

Determinants of Fluidlike Behavior and Effective Viscosity in Cross-Linked Actin Networks

The actin cortex has a well-documented ability to rapidly remodel and flow while maintaining long-range connectivity, but how this is achieved remains poorly understood. Here, we use computer simulations to explore how stress relaxation in cross-linked actin networks subjected to extensional stress depends on the interplay between network architecture and turnover. We characterize a regime in which a network response is nonaffine and stress relaxation is governed by the continuous dissipation of elastic energy via cyclic formation, elongation, and turnover of tension-bearing elements. Within this regime, for a wide range of network parameters, we observe a constant deformation (creep) rate that is linearly proportional to the rate of filament turnover, leading to a constant effective viscosity that is inversely proportional to turnover rate. Significantly, we observe a biphasic dependence of the creep rate on applied stress: below a critical stress threshold, the creep rate increases linearly with applied stress; above that threshold, the creep rate becomes independent of applied stress. We show that this biphasic stress dependence can be understood in terms of the nonlinear force-extension behavior of individual force-transmitting network elements. These results have important implications for understanding the origins and control of viscous flows both in the cortex of living cells and in other polymer networks.     

Interactions between myosin and actin crosslinkers control cytokinesis contractility dynamics and mechanics

INTRODUCTION: Contractile networks are fundamental to many cellular functions, particularly cytokinesis and cell motility. Contractile networks depend on myosin-II mechanochemistry to generate sliding force on the actin polymers. However, to be contractile, the networks must also be crosslinked by crosslinking proteins, and to change the shape of the cell, the network must be linked to the plasma membrane. Discerning how this integrated network operates is essential for understanding cytokinesis contractility and shape control. Here, we analyzed the cytoskeletal network that drives furrow ingression in Dictyostelium. RESULTS: We establish that the actin polymers are assembled into a meshwork and that myosin-II does not assemble into a discrete ring in the Dictyostelium cleavage furrow of adherent cells. We show that myosin-II generates regional mechanics by increasing cleavage furrow stiffness and slows furrow ingression during late cytokinesis as compared to myoII nulls. Actin crosslinkers dynacortin and fimbrin similarly slow furrow ingression and contribute to cell mechanics in a myosin-II-dependent manner. By using FRAP, we show that the actin crosslinkers have slower kinetics in the cleavage furrow cortex than in the pole, that their kinetics differ between wild-type and myoII null cells, and that the protein dynamics of each crosslinker correlate with its impact on cortical mechanics. CONCLUSIONS: These observations suggest that myosin-II along with actin crosslinkers establish local cortical tension and elasticity, allowing for contractility independent of a circumferential cytoskeletal array. Furthermore, myosin-II and actin crosslinkers may influence each other as they modulate the dynamics and mechanics of cell-shape change.     

Physical properties of liposomes and proteoliposomes prepared from Escherichia coli polar lipids

Reconstituted proteoliposomes serve as experimental systems for the study of membrane enzymes. Osmotic shifts and other changes in the solution environment may influence the structures and membrane properties of phospholipid vesicles (including liposomes, proteoliposomes and biological membrane vesicles) and hence the activities of membrane-associated proteins. Polar lipid extracts from Escherichia coli are commonly used in membrane protein reconstitution. The solution environment influenced the phase transition temperature and the diameter of liposomes and proteoliposomes prepared from E. coli polar lipid by extrusion. Liposomes prepared from E. coli polar lipids differed from dioleoylphosphatidylglycerol liposomes in Young's elastic modulus, yield point for solute leakage and structural response to osmotic shifts, the latter indicated by static light scattering spectroscopy. At high concentrations, NaCl caused aggregation of E. coli lipid liposomes that precluded detailed interpretation of light scattering data. Proteoliposomes and liposomes prepared from E. coli polar lipids were similar in size, yield point for solute leakage and structural response to osmotic shifts imposed with sucrose as osmolyte. These results will facilitate studies of bacterial enzymes implicated in osmosensing and of other enzymes that are reconstituted in E. coli lipid vesicles.