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Plasma Membrane—Cortical Cytoskeleton Interactions: A Cell Biology Approach with Biophysical Considerations

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Abstract

From a biophysical standpoint, the interface between the cell membrane and the cytoskeleton is an intriguing site where a “two‐dimensional fluid” interacts with an exceedingly complex three‐dimensional protein meshwork. The membrane is a key regulator of the cytoskeleton, which not only provides docking sites for cytoskeletal elements through transmembrane proteins, lipid binding‐based, and electrostatic interactions, but also serves as the source of the signaling events and molecules that control cytoskeletal organization and remolding. Conversely, the cytoskeleton is a key determinant of the biophysical and biochemical properties of the membrane, including its shape, tension, movement, composition, as well as the mobility, partitioning, and recycling of its constituents. From a cell biological standpoint, the membrane‐cytoskeleton interplay underlies—as a central executor and/or regulator—a multitude of complex processes including chemical and mechanical signal transduction, motility/migration, endo‐/exo‐/phagocytosis, and other forms of membrane traffic, cell‐cell, and cell‐matrix adhesion. The aim of this article is to provide an overview of the tight structural and functional coupling between the membrane and the cytoskeleton. As biophysical approaches, both theoretical and experimental, proved to be instrumental for our understanding of the membrane/cytoskeleton interplay, this review will “oscillate” between the cell biological phenomena and the corresponding biophysical principles and considerations. After describing the types of connections between the membrane and the cytoskeleton, we will focus on a few key physical parameters and processes (force generation, curvature, tension, and surface charge) and will discuss how these contribute to a variety of fundamental cell biological functions. © 2013 American Physiological Society. Compr Physiol 3:1231‐1281, 2013.

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Figure 1. Figure 1.

The two‐dimensional spectrin‐based membrane skeleton of red cells and its relationship to the three‐dimensional actin cytoskeleton. The triple α‐helical coiled‐coil structure of spectrin repeats is shown in the magnified box. Spectrin is linked to the membrane by three mechanisms (i) the pleckstrin homology (PH) domain in β‐spectrin directly binds to anionic lipids of the inner leaflet. (ii) A variety of transmembrane proteins (including the anion exchanger (AE), and the Rhesus factor (Rh) bind to ankyrin, which interacts with α‐spectrin. (iii) Transmembrane proteins also associate with another adapter complex, containing adducin, which directly or through various other connectors (4.1, 4.2, p55, and dematin) link spectrin to the components of the actin skeleton, including actin, tropomyosin, and tropomodulin. Further abbreviations: GPA, GPB, and GPC glycophorin A, B, and C, respectively; GLUT 1, glucose transporter 1; RhAG, Rh‐associated glycoprotein. Reproduced, with permission, from ().

Figure 2. Figure 2.

The fence‐and‐picket model of membrane organization and the three‐tiered mesoscale model of the plasma membrane. (A) The undercoat structure of the cytoplasmic surface of the plasma membrane. Rapid‐freeze, deep‐etch electron microscopy was performed in normal rat kidney fibroblasts (a) and fetal rat skin keratocytes (b). Note the clathrin‐coated pits (arrows), a caveola (*), and the dense meshwork of fibers of the cortical actin skeleton. The latter is thought to be the structural basis of the corralled movement of membrane proteins; the fibers likely correspond to the fences limiting the diffusion of transmembrane proteins. Bar 100 nm, and in the inset: 50 nm. Reproduced, with permission, from (). (B) The fence‐and‐picket model: the membrane skeleton (MSK) forms fences that enclose membrane compartments. Within these sectors membrane components perform random walk (the zigzag lines indicate trajectories). Transmembrane proteins are anchored to the fence (pickets); a, b, and c represent side, bottom, and top views, respectively. (C) The three‐tiered mesoscale model of the membrane. The first tier corresponds to the fences and pickets formed by the membrane skeleton. The second and third tiers correspond to lipid rafts and dynamic protein complexes, respectively. B and C are reproduced, with permission, from ().

Figure 3. Figure 3.

Cytoskeleton‐controlled diffusion of the scavenger receptor CD36 in human macrophages. The movement of antibody‐labeled CD36 molecules on the cells surface was followed by particle tracking. Two measures were used to define trajectory types: the first classified trajectory shape based on the degree of anisotropy of the scatter of particle positions along a trajectory, while the second extracted diffusion types using a moment scaling spectrum analysis of particle displacements. Trajectories, shown in (A), were classified as linear, isotropic confined, isotropic unconfined, and undetermined (B). More than 25% of the trajectories corresponded to a linear path, and more than 75% of the particles followed linear or otherwise confined routes. A linear trajectory as monitored by Qdot‐labeled CD36 is shown in C. The trajectory was reconstructed based on a movie with 1184 frames taken in 18.9 s (the time is color coded). Scale bar 200 nm. The histogram shows the distribution of receptor positions across the width of the linear trajectory. These findings indicate the presence of preformed diffusion pathways in the membrane. Adapted, with permission, from ().

Figure 4. Figure 4.

The intramembrane movement of a transmembrane protein (E‐cadherin). Panel I: E‐cadherin can either be tethered to the cytoskeleton or corralled within cytoskeleton‐delimited fences (A). Experiments using optical tweezers as shown in A can differentiate between these modes. Using trapping forces of ≈1 pN, tethered molecules can only be dragged along to the extent allowed by the stretching of the cytoskeletal anchors. Corralled molecules move freely within compartments delimited by the fences, and smaller forces (0.05‐0.1 pN) might be sufficient to drag them through the fence. Panel II: single molecular tracking of wild‐type (WT) E‐cadherin and various E‐cadherin mutants. Catenin minus lacks the α‐catenin (a cytoskeletal linker) binding site, short‐tailed lacks almost the entire cytosolic tail, whereas in fusion E‐cadherin is covalently linked to α‐catenin. Fusion represents one extreme with strongly limited diffusion, whereas short tailed is the most diffusible species. III: interpretation of the results shown in II. Fusion is tightly linked to the cytoskeleton. WT exists in various subpopulations: it can be linked to the cytoskeleton, may be linked to α‐catenin but not to the actin network or may be free of α‐catenin, resembling catenin minus. The least restricted is short tailed, which moves relatively freely not only within but also across the fences. (A, B, C, and D represent the four mobility states.) Adapted, with permission, from ().

Figure 5. Figure 5.

Summary of cytoskeletal proteins that are regulated or localized by polyphosphoinositides. Proteins marked in blue are activated or localized at the plasma membrane by PIP2 or PIP3; those denoted in red are inhibited by PIP2.

Figure 6. Figure 6.

Deformation of phospholipid vesicles by polymerization of encapsulated actin or tubulin. (A) Shape change of giant unilamellar vesicle formed by 50:50 wt. ratio of dimyristoylphosphatidylcholine cardiolipin after polymerization of 200 μmol/L actin within the vesicle interior. Adapted, with permission, from (). Scale bar: 100 μm. (B) Various morphologies of vesicles composed of 40% dioleoylphosphatidylserine and 60% dioleoylphosphatidylcholine (DOPC) after polymerization of 2.5 mg/mL encapsulated tubulin. Scale bar: 10 μm. (C) Protrusion of initially spherical vesicle by single microtubule polymerization. Reproduced, with permission, from (). Long axis of the vesicle is 15 microns.

Figure 7. Figure 7.

The linear treadmilling (LIT) model. (A) Electron tomography of the lamellipodium. (a) Tomogram section of the cytoskeleton within the keratocyte lamellipodium. The blue rings indicate intersections of overlapping filaments, whereas the red rings mark putative filament branch points. (The arrows indicate typical examples). (b) Model constructed from the tomogram. The green lines correspond to actin filaments, the blue spheres label filament intersections at overlaps, while the red ones indicate putative branch points. In this particular image 320 overlaps and 4 branch points were identified. Based on such findings the authors suggest that the predominant arrangement of filaments in the lamellipodium is linear (nonbranching), and the previously reported excessive branching might have been due to the misinterpretation of the frequent crossovers of linear filaments. Reproduced, with permission, from (). (B) The putative arrangement and role of the actin nucleation machinery in the context of the LIT model. (a) The tethered nucleation/elongation model. Actin is nucleated under the membrane by WAVE‐mediated activation of the Arp2/3 complex in a nonbranching manner. The Arp2/3 complex remains at the pointed end and treadmills with the filament. The plus end grows under the membrane while it remains tethered to WAVE and ENA‐VASP (which may replace WAVE). The structure can be stabilized by short actin cross‐linkers at the membrane and by longer ones (such as filamin) deeper in the lamellipodium. The latter cross‐links filaments at the intersecting regions. At the forming filopodia filaments are extensively bundled, while actin nucleation at the tip is mediated by the collaborative action of ENA‐VASP and formins. (b) and (c) show the boxes labeled in (a) with higher resolution. Reproduced, with permission, from ().

Figure 8. Figure 8.

Cytoskeletal structure in the lamellipodium and Arp2/3‐mediated actin branch formation in vivo and in vitro. I: electron microscopic pictures of the actin network in the lamellipodium of Xenopus keratocytes. In (a), the meshwork was stabilized with polyethylene glycol and phalloidin to prevent actin depolymerization from the pointed end. In (b), unprotected extraction was performed in the absence of these F‐actin‐stabilizing drugs. Note the dense meshwork in the membrane‐adjacent zone of the lamellipodium, which remains nearly intact even without protection against pointed end depolymerization. In contrast, at the rear of the lamellipodium (>1 μm from the membrane), there is substantial reduction in the network after unprotected extraction. This suggests that in the peripheral zone of the lamellipodium pointed filament ends are capped (presumably by Arp2/3, see II). (c) shows the enlarged image of the boxed area in (b). Bar 1 μm. II: immunogold labeling of the Arp2/3 complex in the lamellipodium. Xenopus keratocytes were briefly treated with the barbed end capper cytochalasin D (to reduce the density of the meshwork), extracted in the presence of phalloidin, fixed and immuno‐labeled with a primary antibody against the p21 component of the Arp2/3 complex, and a gold‐conjugated secondary antibody. The gold particles are highlighted with yellow. Actin filaments exhibited multiple branching, and the Arp2/3 complex localized at or near the branching points. Adapted, with permission, from (). III: In vitro formation of actin branches in the presence of the Arp2/3 complex. (A) Electron micrograph of the purified Arp2/3 complex shows globular particles of 10 × 14 nm. In the presence of purified Arp2/3, gelsolin‐capped actin filaments form numerous end‐to‐side branches with a 70º angle (B and C). Linear filaments are periodically decorated with the purified Arp2/3 complex (D). Reproduced, with permission, from (). IV: direct evidence of branch formation by the Arp2/3 complex in vitro. ADP‐actin was polymerized and labeled by Alexa‐green phalloidin. Subsequently, ATP‐actin monomers, Arp2/3 complex, and the Arp2/3‐activating WA domain of WASP were added to prepolymerized green actin, and further polymerization was monitored with rhodamine (red)‐phalloidin. As the “fresh” red labeling shows, monomers were added both at the barbed end and to the sites of existing filaments. Reproduced, with permission, from ().

Figure 9. Figure 9.

The dendritic nucleation/actin treadmilling (DNAT) model for membrane protrusion. The key feature of the model is the generation of daughter filaments sprouting out in a 70o angle at the side of preexistent mother filaments, as induced by the activated Arp2/3 complex. In addition to the major structural characteristics, the model also shows the various signaling steps leading to the activation of the Arp2/3 complex (1‐4), the mechanism of filament elongation, and capping associated with membrane expansion (5‐8), and the various processes that ensure and regulate the continuous recycling of actin monomers (9‐12). Several important aspects of the model are discussed in the text. Reproduced, with permission, from ().

Figure 10. Figure 10.

The original Brownian Ratchet (BR) model and the corresponding force‐velocity (F‐V) relationship for edge protrusion during actin polymerization. The actin filament polymerizes against the membrane, which has a diffusion constant D, and which is acted upon by a load, f. The conditional probability of the association of a monomer with the polymer (provided the gap between the membrane and the polymer tip is sufficiently large) is α, whereas that of the dissociation is β. The gap size should be at least δ, which is half the length of the actin monomer, considering the “staggered” growth of the actin filament. The y axis shows the speed of the polymerization ratchet (v), as a function of the dimensionless load force (ω). The solid line is based on the assumption that β → 0, whereas the dashed line depicts the F‐V relationship as calculated according to equation (5), that is, when monomer association and dissociation are much slower than the diffusion. Reproduced, with permission, from ().

Figure 11. Figure 11.

The Elastic Brownian Ratchet (EBR) model. (A) According to the EBR model, the thermal fluctuations of the “free” filament end (rather than that of the membrane) generate the gap (δ) between the tip of the filaments and the membrane. The moving portion of the filament (with a length of l) is anchored to a rigid base, that is, a cross‐linked portion of the actin meshwork. In addition, the filament end is not perpendicular to the membrane but impinges on it in an angle of θ. (B) The mechanical equivalent of the EBR model. The fluctuating filaments is modeled by a spring with a spring constant κ, which has an equilibrium position at a distance y from the membrane. The deviation from the equilibrium is denoted by x. Reproduced, with permission, from ().

Figure 12. Figure 12.

Lamellipodial protrusion according to the EBR model. (A) Lamellipodial actin is modeled as a biorthogonal array of filaments, oriented at angle θ to the membrane normal. The system pushes the membrane against a load force f. The force‐velocity curve was calculated for a hypothetical lamellipodium, containing 5000 filaments acting on a membrane area of 5 μm × 0.2 μm, and at a local monomer concentration of 45 μmol/L. Reproduced, with permission, from ().

Figure 13. Figure 13.

Clamped filament elongation (CFE)/end‐tracking motor (ETM) Model. (A) According to the actoclampin hypothesis, the membrane is directly linked to the polymerization machinery through a “clamp,” whose affinity for actin is dynamically modulated, and which contains or is associated with a membrane‐tethering domain. (B) In the CFT/EMT model, the actoclampin system pushes the membrane as a “three‐stroke” engine through a “Load‐Lock‐Fire” mechanism. The central features of the model are that (i) there is enough space between the membrane and the actin‐associated region of the clamp for monomers to be added to the clamped filament; (ii) the affinity of the clamp changes according to the hydrolysis of the actin‐associated adenine nucleotide (high affinity for actin‐ATP, low affinity for actin‐ADP+Pi or actin‐ADP); and (iii) the clamp translocates from the low‐affinity penultimate actin subunits to the high affinity, ultimate actin subunits. For further details, see the figure and the text. Reproduced, with permission, from ().

Figure 14. Figure 14.

Hypothetical actin polymerization motors involved in clamped filament elongation. (A) According to the end‐tracking stepping motor model, the clamp has a regulated affinity for F‐actin through an F‐actin‐binding region (FAB). This domain translocates to the ultimate actin subunits as they get incorporated in the filament. (B) According to the direct transfer end‐trapping motor model, the tracking protein has a G‐actin binding region (GAB) as well, which captures the monomer (or the G‐actin‐profilin complex, as shown here). This step reduces the affinity of the GAB on the adjacent actin polymer. The FAB region helps localize the GAB to the filament end. Reproduced, with permission, from Dickinson ().

Figure 15. Figure 15.

Measurement of the lamellipodial stalling force in migrating cells. (A) Experimental setup to measure the stalling force. The cantilever of the atomic force microscope was placed in front of a migrating keratocyte. The lamellipodium deflects the cantilever. Measuring the deflection and knowing the spring constant of the cantilever, the force exerted on the lamellipodium can be calculated. Monitoring the movement of the lamellipodium, the stalling force (at which the lamellipodial protrusion is prevented) can be determined. (B) Visualization of the interaction between the lamellipodium and the cantilever. The keratocyte was fixed shortly after making contact with the cantilever and stained with labeled phalloidin. At the site of contact, the cantilever caused an indentation in the lamellipodium (boxed area), while the adjacent regions of the lamellipodium continued to move forward. (C) Deflection (force)‐time curve for the moving keratocytes. (D) The gray box shown in C is magnified. Note that upon initial contact, there is a sharp deflection, which peaks after a few seconds when the lamellipodium stalls (shaded area). Subsequently, the lamellipodium escapes (sneaks around) the cantilever and the deflection falls to zero. This phase is followed by a second rise, when the cell body (that continues to move) hits the probe. Adapted, with permission, from ().

Figure 16. Figure 16.

Force‐velocity relationships. (A) Typical atomic force microscopy recording showing cantilever deflection as a function of time in the fish keratocyte lamellipodium, determined as described in Figure . (B) Force‐velocity relationship of the lamellipodium obtained from the experiments shown in A. Reproduced, with permission, from Prass M. et al. J Cell Biol. 2006, 174(6):767‐72 (). (C) Force‐velocity relationship derived from the theoretical considerations of the filament end‐tracking motor model (Fig. 13). The monomer transfer/edge advancement steps is assumed to be a function of a force (F)‐dependent rate constant (kt = kt0 eFd/kBT, where d = 2.7 nm). The numbers beside the curves indicate various ratios between the baseline transfer rate constant (kt0) and the monomer binding rate. At small compressive forces the force‐independent monomer binding step is slower than the force‐dependent transfer/advancement step and, therefore, filament elongation is force independent. At larger forces, the advancement step becomes rate limiting, and ultimately no elongation occurs. The experimental data shown in B are compatible with the end‐tracking motor model, whereas they do not correspond well to the predictions of the original BR model (shown on the graph as well). Reproduced, with permission, from ().

Figure 17. Figure 17.

Membrane curvature. (A) The membrane is a two‐dimensional surface in a three‐dimensional space, and to characterize its curvature in a vicinity of a given point on it, two principal planes can be defined that are perpendicular to the surface and each other and have some other special properties (Euler's theorem). The intersections of these planes with the surface define two perpendicular arcs with radii R1 and R2, and the reciprocals of these are the principal curvatures. Reproduced, with permission, from (). (B) Basic curved shapes. These shapes are characterized and distinguished by their principal curvatures (c1 and c2), their total curvature J (defined as the sum of the principal curvatures) and their Gaussian curvature K, (defined as the product of the principal curvatures). Adapted, with permission, from ().

Figure 18. Figure 18.

Various mechanisms underlying membrane curvature formation. Curvature can be generated by (A) asymmetric lipid distribution; (B) intrinsic shape of transmembrane proteins or their complexes; (C) pushing or pulling the membrane by polymerization of cytoskeletal filaments or by cytoskeletal motors; (D) scaffolding, and (E) insertion of amphipathic helices. Further explanation can be found in the text. Reproduced, with permission, from ().

Figure 19. Figure 19.

BAR domain proteins. BAR domains are composed of a symmetric arrangement of two triple helices. Various BAR domains can be classified into different families and possess characteristic curvatures. They bend the membrane as scaffolds but may also contain amphipathic helices. Reproduced, with permission, from ().

Figure 20. Figure 20.

The structure of the filopodium. The formation of the filopodium requires the coordinated function of various cytoskeletal and membrane‐shaping proteins. The core of the filopodium is composed of cross‐linked (bundled), nonbranching actin filaments, the growth of which is brought about by leaky capper nucleators such as ENA‐VASP and linear actin polymerization machines such as formins, localized at the tip. I‐BAR and N‐BAR proteins participate in the formation of negative and positive curvatures at the filopodium tip and base, respectively.

Figure 21. Figure 21.

Measurement of membrane tension. A probe such as a bead in an optical trap or a magnetic particle is attached to the outer surface of the cell membrane. A force ft is applied to the probe sufficient to pull out a membrane tether. The tether, with a radius Rt is separated from the cytoskeleton to which the rest of the plasma membrane is attached. The force required to pull such a tether depends on both the bending constant and the tension of the membrane.

Figure 22. Figure 22.

Surface charge and the components of the surface potential. The distribution of differentially mobile layers of ions in the vicinity of a charged particle (or the negatively charged inner leaflet of the membrane) and the corresponding components of the surface potential are shown. Modified from Life Science Leader http://www.bioresearchonline.com/article.mvc/Automated‐Protein‐Characterization‐With‐The‐M‐0002. Reprinted, with permission, from Malvern Instruments Ltd., www.malvern.com.



Figure 1.

The two‐dimensional spectrin‐based membrane skeleton of red cells and its relationship to the three‐dimensional actin cytoskeleton. The triple α‐helical coiled‐coil structure of spectrin repeats is shown in the magnified box. Spectrin is linked to the membrane by three mechanisms (i) the pleckstrin homology (PH) domain in β‐spectrin directly binds to anionic lipids of the inner leaflet. (ii) A variety of transmembrane proteins (including the anion exchanger (AE), and the Rhesus factor (Rh) bind to ankyrin, which interacts with α‐spectrin. (iii) Transmembrane proteins also associate with another adapter complex, containing adducin, which directly or through various other connectors (4.1, 4.2, p55, and dematin) link spectrin to the components of the actin skeleton, including actin, tropomyosin, and tropomodulin. Further abbreviations: GPA, GPB, and GPC glycophorin A, B, and C, respectively; GLUT 1, glucose transporter 1; RhAG, Rh‐associated glycoprotein. Reproduced, with permission, from ().



Figure 2.

The fence‐and‐picket model of membrane organization and the three‐tiered mesoscale model of the plasma membrane. (A) The undercoat structure of the cytoplasmic surface of the plasma membrane. Rapid‐freeze, deep‐etch electron microscopy was performed in normal rat kidney fibroblasts (a) and fetal rat skin keratocytes (b). Note the clathrin‐coated pits (arrows), a caveola (*), and the dense meshwork of fibers of the cortical actin skeleton. The latter is thought to be the structural basis of the corralled movement of membrane proteins; the fibers likely correspond to the fences limiting the diffusion of transmembrane proteins. Bar 100 nm, and in the inset: 50 nm. Reproduced, with permission, from (). (B) The fence‐and‐picket model: the membrane skeleton (MSK) forms fences that enclose membrane compartments. Within these sectors membrane components perform random walk (the zigzag lines indicate trajectories). Transmembrane proteins are anchored to the fence (pickets); a, b, and c represent side, bottom, and top views, respectively. (C) The three‐tiered mesoscale model of the membrane. The first tier corresponds to the fences and pickets formed by the membrane skeleton. The second and third tiers correspond to lipid rafts and dynamic protein complexes, respectively. B and C are reproduced, with permission, from ().



Figure 3.

Cytoskeleton‐controlled diffusion of the scavenger receptor CD36 in human macrophages. The movement of antibody‐labeled CD36 molecules on the cells surface was followed by particle tracking. Two measures were used to define trajectory types: the first classified trajectory shape based on the degree of anisotropy of the scatter of particle positions along a trajectory, while the second extracted diffusion types using a moment scaling spectrum analysis of particle displacements. Trajectories, shown in (A), were classified as linear, isotropic confined, isotropic unconfined, and undetermined (B). More than 25% of the trajectories corresponded to a linear path, and more than 75% of the particles followed linear or otherwise confined routes. A linear trajectory as monitored by Qdot‐labeled CD36 is shown in C. The trajectory was reconstructed based on a movie with 1184 frames taken in 18.9 s (the time is color coded). Scale bar 200 nm. The histogram shows the distribution of receptor positions across the width of the linear trajectory. These findings indicate the presence of preformed diffusion pathways in the membrane. Adapted, with permission, from ().



Figure 4.

The intramembrane movement of a transmembrane protein (E‐cadherin). Panel I: E‐cadherin can either be tethered to the cytoskeleton or corralled within cytoskeleton‐delimited fences (A). Experiments using optical tweezers as shown in A can differentiate between these modes. Using trapping forces of ≈1 pN, tethered molecules can only be dragged along to the extent allowed by the stretching of the cytoskeletal anchors. Corralled molecules move freely within compartments delimited by the fences, and smaller forces (0.05‐0.1 pN) might be sufficient to drag them through the fence. Panel II: single molecular tracking of wild‐type (WT) E‐cadherin and various E‐cadherin mutants. Catenin minus lacks the α‐catenin (a cytoskeletal linker) binding site, short‐tailed lacks almost the entire cytosolic tail, whereas in fusion E‐cadherin is covalently linked to α‐catenin. Fusion represents one extreme with strongly limited diffusion, whereas short tailed is the most diffusible species. III: interpretation of the results shown in II. Fusion is tightly linked to the cytoskeleton. WT exists in various subpopulations: it can be linked to the cytoskeleton, may be linked to α‐catenin but not to the actin network or may be free of α‐catenin, resembling catenin minus. The least restricted is short tailed, which moves relatively freely not only within but also across the fences. (A, B, C, and D represent the four mobility states.) Adapted, with permission, from ().



Figure 5.

Summary of cytoskeletal proteins that are regulated or localized by polyphosphoinositides. Proteins marked in blue are activated or localized at the plasma membrane by PIP2 or PIP3; those denoted in red are inhibited by PIP2.



Figure 6.

Deformation of phospholipid vesicles by polymerization of encapsulated actin or tubulin. (A) Shape change of giant unilamellar vesicle formed by 50:50 wt. ratio of dimyristoylphosphatidylcholine cardiolipin after polymerization of 200 μmol/L actin within the vesicle interior. Adapted, with permission, from (). Scale bar: 100 μm. (B) Various morphologies of vesicles composed of 40% dioleoylphosphatidylserine and 60% dioleoylphosphatidylcholine (DOPC) after polymerization of 2.5 mg/mL encapsulated tubulin. Scale bar: 10 μm. (C) Protrusion of initially spherical vesicle by single microtubule polymerization. Reproduced, with permission, from (). Long axis of the vesicle is 15 microns.



Figure 7.

The linear treadmilling (LIT) model. (A) Electron tomography of the lamellipodium. (a) Tomogram section of the cytoskeleton within the keratocyte lamellipodium. The blue rings indicate intersections of overlapping filaments, whereas the red rings mark putative filament branch points. (The arrows indicate typical examples). (b) Model constructed from the tomogram. The green lines correspond to actin filaments, the blue spheres label filament intersections at overlaps, while the red ones indicate putative branch points. In this particular image 320 overlaps and 4 branch points were identified. Based on such findings the authors suggest that the predominant arrangement of filaments in the lamellipodium is linear (nonbranching), and the previously reported excessive branching might have been due to the misinterpretation of the frequent crossovers of linear filaments. Reproduced, with permission, from (). (B) The putative arrangement and role of the actin nucleation machinery in the context of the LIT model. (a) The tethered nucleation/elongation model. Actin is nucleated under the membrane by WAVE‐mediated activation of the Arp2/3 complex in a nonbranching manner. The Arp2/3 complex remains at the pointed end and treadmills with the filament. The plus end grows under the membrane while it remains tethered to WAVE and ENA‐VASP (which may replace WAVE). The structure can be stabilized by short actin cross‐linkers at the membrane and by longer ones (such as filamin) deeper in the lamellipodium. The latter cross‐links filaments at the intersecting regions. At the forming filopodia filaments are extensively bundled, while actin nucleation at the tip is mediated by the collaborative action of ENA‐VASP and formins. (b) and (c) show the boxes labeled in (a) with higher resolution. Reproduced, with permission, from ().



Figure 8.

Cytoskeletal structure in the lamellipodium and Arp2/3‐mediated actin branch formation in vivo and in vitro. I: electron microscopic pictures of the actin network in the lamellipodium of Xenopus keratocytes. In (a), the meshwork was stabilized with polyethylene glycol and phalloidin to prevent actin depolymerization from the pointed end. In (b), unprotected extraction was performed in the absence of these F‐actin‐stabilizing drugs. Note the dense meshwork in the membrane‐adjacent zone of the lamellipodium, which remains nearly intact even without protection against pointed end depolymerization. In contrast, at the rear of the lamellipodium (>1 μm from the membrane), there is substantial reduction in the network after unprotected extraction. This suggests that in the peripheral zone of the lamellipodium pointed filament ends are capped (presumably by Arp2/3, see II). (c) shows the enlarged image of the boxed area in (b). Bar 1 μm. II: immunogold labeling of the Arp2/3 complex in the lamellipodium. Xenopus keratocytes were briefly treated with the barbed end capper cytochalasin D (to reduce the density of the meshwork), extracted in the presence of phalloidin, fixed and immuno‐labeled with a primary antibody against the p21 component of the Arp2/3 complex, and a gold‐conjugated secondary antibody. The gold particles are highlighted with yellow. Actin filaments exhibited multiple branching, and the Arp2/3 complex localized at or near the branching points. Adapted, with permission, from (). III: In vitro formation of actin branches in the presence of the Arp2/3 complex. (A) Electron micrograph of the purified Arp2/3 complex shows globular particles of 10 × 14 nm. In the presence of purified Arp2/3, gelsolin‐capped actin filaments form numerous end‐to‐side branches with a 70º angle (B and C). Linear filaments are periodically decorated with the purified Arp2/3 complex (D). Reproduced, with permission, from (). IV: direct evidence of branch formation by the Arp2/3 complex in vitro. ADP‐actin was polymerized and labeled by Alexa‐green phalloidin. Subsequently, ATP‐actin monomers, Arp2/3 complex, and the Arp2/3‐activating WA domain of WASP were added to prepolymerized green actin, and further polymerization was monitored with rhodamine (red)‐phalloidin. As the “fresh” red labeling shows, monomers were added both at the barbed end and to the sites of existing filaments. Reproduced, with permission, from ().



Figure 9.

The dendritic nucleation/actin treadmilling (DNAT) model for membrane protrusion. The key feature of the model is the generation of daughter filaments sprouting out in a 70o angle at the side of preexistent mother filaments, as induced by the activated Arp2/3 complex. In addition to the major structural characteristics, the model also shows the various signaling steps leading to the activation of the Arp2/3 complex (1‐4), the mechanism of filament elongation, and capping associated with membrane expansion (5‐8), and the various processes that ensure and regulate the continuous recycling of actin monomers (9‐12). Several important aspects of the model are discussed in the text. Reproduced, with permission, from ().



Figure 10.

The original Brownian Ratchet (BR) model and the corresponding force‐velocity (F‐V) relationship for edge protrusion during actin polymerization. The actin filament polymerizes against the membrane, which has a diffusion constant D, and which is acted upon by a load, f. The conditional probability of the association of a monomer with the polymer (provided the gap between the membrane and the polymer tip is sufficiently large) is α, whereas that of the dissociation is β. The gap size should be at least δ, which is half the length of the actin monomer, considering the “staggered” growth of the actin filament. The y axis shows the speed of the polymerization ratchet (v), as a function of the dimensionless load force (ω). The solid line is based on the assumption that β → 0, whereas the dashed line depicts the F‐V relationship as calculated according to equation (5), that is, when monomer association and dissociation are much slower than the diffusion. Reproduced, with permission, from ().



Figure 11.

The Elastic Brownian Ratchet (EBR) model. (A) According to the EBR model, the thermal fluctuations of the “free” filament end (rather than that of the membrane) generate the gap (δ) between the tip of the filaments and the membrane. The moving portion of the filament (with a length of l) is anchored to a rigid base, that is, a cross‐linked portion of the actin meshwork. In addition, the filament end is not perpendicular to the membrane but impinges on it in an angle of θ. (B) The mechanical equivalent of the EBR model. The fluctuating filaments is modeled by a spring with a spring constant κ, which has an equilibrium position at a distance y from the membrane. The deviation from the equilibrium is denoted by x. Reproduced, with permission, from ().



Figure 12.

Lamellipodial protrusion according to the EBR model. (A) Lamellipodial actin is modeled as a biorthogonal array of filaments, oriented at angle θ to the membrane normal. The system pushes the membrane against a load force f. The force‐velocity curve was calculated for a hypothetical lamellipodium, containing 5000 filaments acting on a membrane area of 5 μm × 0.2 μm, and at a local monomer concentration of 45 μmol/L. Reproduced, with permission, from ().



Figure 13.

Clamped filament elongation (CFE)/end‐tracking motor (ETM) Model. (A) According to the actoclampin hypothesis, the membrane is directly linked to the polymerization machinery through a “clamp,” whose affinity for actin is dynamically modulated, and which contains or is associated with a membrane‐tethering domain. (B) In the CFT/EMT model, the actoclampin system pushes the membrane as a “three‐stroke” engine through a “Load‐Lock‐Fire” mechanism. The central features of the model are that (i) there is enough space between the membrane and the actin‐associated region of the clamp for monomers to be added to the clamped filament; (ii) the affinity of the clamp changes according to the hydrolysis of the actin‐associated adenine nucleotide (high affinity for actin‐ATP, low affinity for actin‐ADP+Pi or actin‐ADP); and (iii) the clamp translocates from the low‐affinity penultimate actin subunits to the high affinity, ultimate actin subunits. For further details, see the figure and the text. Reproduced, with permission, from ().



Figure 14.

Hypothetical actin polymerization motors involved in clamped filament elongation. (A) According to the end‐tracking stepping motor model, the clamp has a regulated affinity for F‐actin through an F‐actin‐binding region (FAB). This domain translocates to the ultimate actin subunits as they get incorporated in the filament. (B) According to the direct transfer end‐trapping motor model, the tracking protein has a G‐actin binding region (GAB) as well, which captures the monomer (or the G‐actin‐profilin complex, as shown here). This step reduces the affinity of the GAB on the adjacent actin polymer. The FAB region helps localize the GAB to the filament end. Reproduced, with permission, from Dickinson ().



Figure 15.

Measurement of the lamellipodial stalling force in migrating cells. (A) Experimental setup to measure the stalling force. The cantilever of the atomic force microscope was placed in front of a migrating keratocyte. The lamellipodium deflects the cantilever. Measuring the deflection and knowing the spring constant of the cantilever, the force exerted on the lamellipodium can be calculated. Monitoring the movement of the lamellipodium, the stalling force (at which the lamellipodial protrusion is prevented) can be determined. (B) Visualization of the interaction between the lamellipodium and the cantilever. The keratocyte was fixed shortly after making contact with the cantilever and stained with labeled phalloidin. At the site of contact, the cantilever caused an indentation in the lamellipodium (boxed area), while the adjacent regions of the lamellipodium continued to move forward. (C) Deflection (force)‐time curve for the moving keratocytes. (D) The gray box shown in C is magnified. Note that upon initial contact, there is a sharp deflection, which peaks after a few seconds when the lamellipodium stalls (shaded area). Subsequently, the lamellipodium escapes (sneaks around) the cantilever and the deflection falls to zero. This phase is followed by a second rise, when the cell body (that continues to move) hits the probe. Adapted, with permission, from ().



Figure 16.

Force‐velocity relationships. (A) Typical atomic force microscopy recording showing cantilever deflection as a function of time in the fish keratocyte lamellipodium, determined as described in Figure . (B) Force‐velocity relationship of the lamellipodium obtained from the experiments shown in A. Reproduced, with permission, from Prass M. et al. J Cell Biol. 2006, 174(6):767‐72 (). (C) Force‐velocity relationship derived from the theoretical considerations of the filament end‐tracking motor model (Fig. 13). The monomer transfer/edge advancement steps is assumed to be a function of a force (F)‐dependent rate constant (kt = kt0 eFd/kBT, where d = 2.7 nm). The numbers beside the curves indicate various ratios between the baseline transfer rate constant (kt0) and the monomer binding rate. At small compressive forces the force‐independent monomer binding step is slower than the force‐dependent transfer/advancement step and, therefore, filament elongation is force independent. At larger forces, the advancement step becomes rate limiting, and ultimately no elongation occurs. The experimental data shown in B are compatible with the end‐tracking motor model, whereas they do not correspond well to the predictions of the original BR model (shown on the graph as well). Reproduced, with permission, from ().



Figure 17.

Membrane curvature. (A) The membrane is a two‐dimensional surface in a three‐dimensional space, and to characterize its curvature in a vicinity of a given point on it, two principal planes can be defined that are perpendicular to the surface and each other and have some other special properties (Euler's theorem). The intersections of these planes with the surface define two perpendicular arcs with radii R1 and R2, and the reciprocals of these are the principal curvatures. Reproduced, with permission, from (). (B) Basic curved shapes. These shapes are characterized and distinguished by their principal curvatures (c1 and c2), their total curvature J (defined as the sum of the principal curvatures) and their Gaussian curvature K, (defined as the product of the principal curvatures). Adapted, with permission, from ().



Figure 18.

Various mechanisms underlying membrane curvature formation. Curvature can be generated by (A) asymmetric lipid distribution; (B) intrinsic shape of transmembrane proteins or their complexes; (C) pushing or pulling the membrane by polymerization of cytoskeletal filaments or by cytoskeletal motors; (D) scaffolding, and (E) insertion of amphipathic helices. Further explanation can be found in the text. Reproduced, with permission, from ().



Figure 19.

BAR domain proteins. BAR domains are composed of a symmetric arrangement of two triple helices. Various BAR domains can be classified into different families and possess characteristic curvatures. They bend the membrane as scaffolds but may also contain amphipathic helices. Reproduced, with permission, from ().



Figure 20.

The structure of the filopodium. The formation of the filopodium requires the coordinated function of various cytoskeletal and membrane‐shaping proteins. The core of the filopodium is composed of cross‐linked (bundled), nonbranching actin filaments, the growth of which is brought about by leaky capper nucleators such as ENA‐VASP and linear actin polymerization machines such as formins, localized at the tip. I‐BAR and N‐BAR proteins participate in the formation of negative and positive curvatures at the filopodium tip and base, respectively.



Figure 21.

Measurement of membrane tension. A probe such as a bead in an optical trap or a magnetic particle is attached to the outer surface of the cell membrane. A force ft is applied to the probe sufficient to pull out a membrane tether. The tether, with a radius Rt is separated from the cytoskeleton to which the rest of the plasma membrane is attached. The force required to pull such a tether depends on both the bending constant and the tension of the membrane.



Figure 22.

Surface charge and the components of the surface potential. The distribution of differentially mobile layers of ions in the vicinity of a charged particle (or the negatively charged inner leaflet of the membrane) and the corresponding components of the surface potential are shown. Modified from Life Science Leader http://www.bioresearchonline.com/article.mvc/Automated‐Protein‐Characterization‐With‐The‐M‐0002. Reprinted, with permission, from Malvern Instruments Ltd., www.malvern.com.

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András Kapus, Paul Janmey. Plasma Membrane—Cortical Cytoskeleton Interactions: A Cell Biology Approach with Biophysical Considerations. Compr Physiol 2013, 3: 1231-1281. doi: 10.1002/cphy.c120015