Extensional flow of erythrocyte membrane from cell body to elastic tether. II. Experiment

Mechanotransduction through membrane tension: It's all about propagation?

Over the past 25 years, membrane tension has emerged as a primary mechanical factor influencing cell behavior. Although supporting evidences are accumulating, the integration of this parameter in the lifecycle of cells, organs, and tissues is complex. The plasma membrane is envisioned as a bilayer continuum acting as a 2D fluid. However, it possesses almost infinite combinations of proteins, lipids, and glycans that establish interactions with the extracellular or intracellular environments. This results in a tridimensional composite material with non-trivial dynamics and physics, and the task of integrating membrane mechanics and cellular outcome is a daunting chore for biologists. In light of the most recent discoveries, we aim in this review to provide non-specialist readers some tips on how to solve this conundrum.

Inside-out regulation of E-cadherin conformation and adhesion

Cadherin cell-cell adhesion proteins play key roles in tissue morphogenesis and wound healing. Cadherin ectodomains bind in two conformations, X-dimers and strand-swap dimers, with different adhesive properties. However, the mechanisms by which cells regulate ectodomain conformation are unknown. Cadherin intracellular regions associate with several actin-binding proteins including vinculin, which are believed to tune cell-cell adhesion by remodeling the actin cytoskeleton. Here, we show at the single-molecule level, that vinculin association with the cadherin cytoplasmic region allosterically converts weak X-dimers into strong strand-swap dimers and that this process is mediated by myosin II-dependent changes in cytoskeletal tension. We also show that in epithelial cells, ∼70% of apical cadherins exist as strand-swap dimers while the remaining form X-dimers, providing two cadherin pools with different adhesive properties. Our results demonstrate the inside-out regulation of cadherin conformation and establish a mechanistic role for vinculin in this process.

Numerical Simulations of Red-Blood Cells in Fluid Flow: A Discrete Multiphysics Study

In this paper, we present a methodological study of modelling red blood cells (RBCs) in shear-induced flows based on the discrete multiphysics (DMP) approach. The DMP is an alternative approach from traditional multiphysics based on meshless particle-based methods. The proposed technique has been successful in modelling multiphysics and multi-phase problems with large interfacial deformations such as those in biological systems. In this study, we present the proposed method and introduce an accurate geometrical representation of the RBC. The results were validated against available data in the literature. We further illustrate that the proposed method is capable of modelling the rupture of the RBC membrane with minimum computational difficulty.

The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

Red Blood Cells: Tethering, Vesiculation, and Disease in Micro-Vascular Flow

The red blood cell has become implicated in the progression of a range of diseases; mechanisms by which red cells are involved appear to include the transport of inflammatory species via red cell-derived vesicles. We review this role of RBCs in diseases such as diabetes mellitus, sickle cell anemia, polycythemia vera, central retinal vein occlusion, Gaucher disease, atherosclerosis, and myeloproliferative neoplasms. We propose a possibly unifying, and novel, paradigm for the inducement of RBC vesiculation during vascular flow of red cells adhered to the vascular endothelium as well as to the red pulp of the spleen. Indeed, we review the evidence for this hypothesis that links physiological conditions favoring both vesiculation and enhanced RBC adhesion and demonstrate the veracity of this hypothesis by way of a specific example occurring in splenic flow which we argue has various renderings in a wide range of vascular flows, in particular microvascular flows. We provide a mechanistic basis for membrane loss and the formation of lysed red blood cells in the spleen that may mediate their turnover. Our detailed explanation for this example also makes clear what features of red cell deformability are involved in the vesiculation process and hence require quantification and a new form of quantitative indexing.

Tethering, evagination, and vesiculation via cell-cell interactions in microvascular flow

Vesiculation is a ubiquitous process undergone by most cell types and serves a variety of vital cell functions; vesiculation from erythrocytes, in particular, is a well-known example and constitutes a self-protection mechanism against premature clearance, inter alia. Herein, we explore a paradigm that red blood cell derived vesicles may form within the microvascular, in intense shear flow, where cells become adhered to either other cells or the extracellular matrix, by forming tethers or an evagination. Adherence may be enhanced, or caused, by diseased states or chemical anomalies as are discussed herein. The mechanisms for such processes are detailed via numerical simulations that are patterned directly from video-recorded cell microflow within the splenic venous sinus (MacDonald et al. 1987), as included, e.g., as Supplementary Material. The mechanisms uncovered highlight the necessity of accounting for remodeling of the erythrocyte's membrane skeleton and, specifically, for the time scales associated with that process that is an integral part of cell deformation. In this way, the analysis provides pointed, and vital, insights into the notion of what the, often used phrase, cell deformability actually entails in a more holistic manner. The analysis also details what data are required to make further quantitative descriptions possible and suggests experimental pathways for acquiring such.

Tubulation pattern of membrane vesicles coated with biofilaments

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged in which an array of such tubes grows spontaneously from vesicles coated with bioactive cytoskeletal filaments (e.g., FtsZ, microtubule) in the presence GTP or ATP. We show how a soft vesicle deforms as a result of the interplay between its topology, local curvature, and the forces due to filament bundles. We present results from dynamically triangulated Monte Carlo simulations of a closed membrane vesicle coated with a nematic field (the filaments), and we show how the intrinsic curvature of the filaments and their bundling interactions drive membrane tubulation. We predict interesting patterns consisting of a large number of nematic defects that accompany tubulation. A common theme emerges: defect locations on vesicle surfaces are hot spots of membrane deformation activity, which could be useful for vesicle origami. Although our equilibrium model is not applicable to the nonequilibrium shape dynamics exhibited by active microtubule-coated vesicles, we show that some of the features, such as the size-dependent vesicle shape and the number of tubes, can still be understood from our equilibrium model.

S-Palmitoylation Sorts Membrane Cargo for Anterograde Transport in the Golgi

While retrograde cargo selection in the Golgi is known to depend on specific signals, it is unknown whether anterograde cargo is sorted, and anterograde signals have not been identified. We suggest here that S-palmitoylation of anterograde cargo at the Golgi membrane interface is an anterograde signal and that it results in concentration in curved regions at the Golgi rims by simple physical chemistry. The rate of transport across the Golgi of two S-palmitoylated membrane proteins is controlled by S-palmitoylation. The bulk of S-palmitoylated proteins in the Golgi behave analogously, as revealed by click chemistry-based fluorescence and electron microscopy. These palmitoylated cargos concentrate in the most highly curved regions of the Golgi membranes, including the fenestrated perimeters of cisternae and associated vesicles. A palmitoylated transmembrane domain behaves similarly in model systems.

Surface deformation during an action potential in pearled cells

Electric pulses in biological cells (action potentials) have been reported to be accompanied by a propagating cell-surface deformation with a nanoscale amplitude. Typically, this cell surface is covered by external layers of polymer material (extracellular matrix, cell wall material, etc.). It was recently demonstrated in excitable plant cells (Chara braunii) that the rigid external layer (cell wall) hinders the underlying deformation. When the cell membrane was separated from the cell wall by osmosis, a mechanical deformation, in the micrometer range, was observed upon excitation of the cell. The underlying mechanism of this mechanical pulse has, to date, remained elusive. Herein we report that Chara cells can undergo a pearling instability, and when the pearled fragments were excited even larger and more regular cell shape changes were observed (∼10-100μm in amplitude). These transient cellular deformations were captured by a curvature model that is based on three parameters: surface tension, bending rigidity, and pressure difference across the surface. In this paper these parameters are extracted by curve-fitting to the experimental cellular shapes at rest and during excitation. This is a necessary step to identify the mechanical parameters that change during an action potential.

Pulling Membrane Nanotubes from Giant Unilamellar Vesicles

The reshaping of the cell membrane is an integral part of many cellular phenomena, such as endocytosis, trafficking, the formation of filopodia, etc. Many different proteins associate with curved membranes because of their ability to sense or induce membrane curvature. Typically, these processes involve a multitude of proteins making them too complex to study quantitatively in the cell. We describe a protocol to reconstitute a curved membrane in vitro, mimicking a curved cellular structure, such as the endocytic neck. A giant unilamellar vesicle (GUV) is used as a model of a cell membrane, whose internal pressure and surface tension are controlled with micropipette aspiration. Applying a point pulling force on the GUV using optical tweezers creates a nanotube of high curvature connected to a flat membrane. This method has traditionally been used to measure the fundamental mechanical properties of lipid membranes, such as bending rigidity. In recent years, it has been expanded to study how proteins interact with membrane curvature and the way they affect the shape and the mechanics of membranes. A system combining micromanipulation, microinjection, optical tweezers, and confocal microscopy allows measurement of membrane curvature, membrane tension, and the surface density of proteins, concurrently. From these measurements, many important mechanical and morphological properties of the protein-membrane system can be inferred. In addition, we lay out a protocol of creating GUVs in the presence of physiological salt concentration, and a method of quantifying the surface density of proteins on the membrane from fluorescence intensities of labeled proteins and lipids.

Cell membrane biophysics with optical tweezers

Membrane elastic properties play important roles in regulating cell shape, motility, division and differentiation. Here I review optical tweezer (OT) investigations of membrane surface tension and bending modulus, emphasizing didactic aspects and insights provided for cell biology. OT measurements employ membrane-attached microspheres to extract long cylindrical nanotubes named tethers. The Helfrich-Canham theory yields elastic parameters in terms of tether radius and equilibrium extraction force. It assumes initial point-like microsphere attachment and no cytoskeleton content within tethers. Experimental force-displacement curves reveal violations of those assumptions, and I discuss proposed explanations of such discrepancies, as well as recommended OT protocols. Measurements of elastic parameters for predominant cell types in the central nervous system yield correlations between their values and cell function. Micro-rheology OT experiments extend these correlations to viscoelastic parameters. The results agree with a quasi-universal phenomenological scaling law and are interpreted in terms of the soft glass rheology model. Spontaneously-generated cell nanotube protrusions are also briefly reviewed, emphasizing common features with tethers. Filopodia as well as tunneling nanotubes (TNT), which connect distant cells and allow transfers between their cytoplasms, are discussed, including OT tether pulling from TNTs which mediate communication among bacteria, even of different species. Pathogens, including bacteria, viruses and prions, opportunistically exploit TNTs for cell-to-cell transmission of infection, indicating that TNTs have an ancient evolutionary origin.

Membrane tension: A challenging but universal physical parameter in cell biology

The plasma membrane separates the interior of cells from the outside environment. The membrane tension, defined as the force per unit length acting on a cross-section of membrane, regulates many vital biological processes. In this review, we summarize the first historical findings and the latest advances, showing membrane tension as an important physical parameter in cell biology. We also discuss how this parameter must be better integrated and we propose experimental approaches for key unanswered questions.

Measuring Force-Induced Dissociation Kinetics of Protein Complexes Using Single-Molecule Atomic Force Microscopy

Proteins respond to mechanical force by undergoing conformational changes and altering the kinetics of their interactions. However, the biophysical relationship between mechanical force and the lifetime of protein complexes is not completely understood. In this chapter, we provide a step-by-step tutorial on characterizing the force-dependent regulation of protein interactions using in vitro and in vivo single-molecule force clamp measurements with an atomic force microscope (AFM). While we focus on the force-induced dissociation of E-cadherins, a critical cell-cell adhesion protein, the approaches described here can be readily adapted to study other protein complexes. We begin this chapter by providing a brief overview of theoretical models that describe force-dependent kinetics of biomolecular interactions. Next, we present step-by-step methods for measuring the response of single receptor-ligand bonds to tensile force in vitro. Finally, we describe methods for quantifying the mechanical response of single protein complexes on the surface of living cells. We describe general protocols for conducting such measurements, including sample preparation, AFM force clamp measurements, and data analysis. We also highlight critical limitations in current technologies and discuss solutions to these challenges.

Membrane mechanical properties of synthetic asymmetric phospholipid vesicles

Synthetic lipid vesicles have served as important model systems to study cellular membrane biology. Research has shown that the mechanical properties of bilayer membranes significantly affects their biological behavior. The properties of a lipid bilayer are governed by lipid acyl chain length, headgroup type, and the presence of membrane proteins. However, few studies have explored how membrane architecture, in particular trans-bilayer lipid asymmetry, influences membrane mechanical properties. In this study, we investigated the effects of lipid bilayer architecture (i.e. asymmetry) on the mechanical properties of biological membranes. This was achieved using a customized micropipette aspiration system and a novel microfluidic technique previously developed by our team for building asymmetric phospholipid vesicles with tailored bilayer architecture. We found that the bending modulus and area expansion modulus of the synthetic asymmetric bilayers were up to 50% larger than the values acquired for symmetric bilayers. This was caused by the dissimilar lipid distribution in each leaflet of the bilayer for the asymmetric membrane. To the best of our knowledge, this is the first report on the impact of trans-bilayer asymmetry on the area expansion modulus of synthetic bilayer membranes. Since the mechanical properties of bilayer membranes play an important role in numerous cellular processes, these results have significant implications for membrane biology studies.

Formation of Tethers from Spreading Cellular Aggregates

Membrane tubes are commonly extruded from cells and vesicles when a point-like force is applied on the membrane. We report here the unexpected formation of membrane tubes from lymph node cancer prostate (LNCaP) cell aggregates in the absence of external applied forces. The spreading of LNCaP aggregates deposited on adhesive glass substrates coated with fibronectin is very limited because cell-cell adhesion is stronger than cell-substrate adhesion. Some cells on the aggregate periphery are very motile and try to escape from the aggregate, leading to the formation of membrane tubes. Tethered networks and exchange of cargos between cells were observed as well. Growth of the tubes is followed by either tube retraction or tube rupture. Hence, even very cohesive cells are successful in escaping aggregates, which may lead to epithelial mesenchymal transition and tumor metastasis. We interpret the dynamics of formation and retraction of tubes in the framework of membrane mechanics.

Complex instability of axially compressed tubular lipid membrane with controlled spontaneous curvature

Tubular lipid membranes (TLMs) are formed by an external pulling force from artificial or biological bilayer vesicles and can be subsequently stabilized by incorporating proteins or amphiphilic polymers into the lipid bilayer. The arising spontaneous curvature of the lipid sheet allows switching off the pulling force without TLM destabilization. However, here we show that during this process two different thermal fluctuation modes drastically increase their amplitudes making fluctuations of the TLM much greater than its radius. Due to the system's proximity to the critical fluctuation point, a weak axial compressive force is sufficient to destabilize the TLM. Its absolute value is shown to be much smaller than that of the pulling force required for the initial lipid nanotube formation. Induced complex instability was studied in the frame of Landau phase transition theory. The process involves two consecutive second-order phase transitions and leads to the tube deformation combining annular corrugation with completely unconventional chiral buckling.

Axonal transport: how high microtubule density can compensate for boundary effects in small-caliber axons

Long-distance intracellular axonal transport is predominantly microtubule-based, and its impairment is linked to neurodegeneration. In this study, we present theoretical arguments that suggest that near the axon boundaries (walls), the effective viscosity can become large enough to impede cargo transport in small (but not large) caliber axons. Our theoretical analysis suggests that this opposition to motion increases rapidly as the cargo approaches the wall. We find that having parallel microtubules close enough together to enable a cargo to simultaneously engage motors on more than one microtubule dramatically enhances motor activity, and thus minimizes the effects of any opposition to transport. Even if microtubules are randomly placed in axons, we find that the higher density of microtubules found in small-caliber axons increases the probability of having parallel microtubules close enough that they can be used simultaneously by motors on a cargo. The boundary effect is not a factor in transport in large-caliber axons where the microtubule density is lower.

Dynamics of red blood cells in microporous membranes

We have performed microfluidic experiments with erythrocytes passing through a network of microchannels of 20-25 μm width and 5 μm of height. Red blood cells (RBCs) were flowing in countercurrent directions through microchannels connected by μm pores. Thereby, we have observed interesting flow dynamics. All pores were blocked by erythrocytes. Some erythrocytes have passed through pores, depending on the channel size and cell elasticity. Many RBCs split into two or more smaller parts. Two types of splits were observed. In one type, the lipid bilayer and spectrin network were cut at the same time. In the second type, the lipid bilayer reconnected, but the part of spectrin network stayed outside the cell forming a rope like structure, which could eventually break. The microporous membrane results in multiple breakups of the cells, which can have various clinical implications, e.g., glomerulus hematuria and anemia of patients undergoing dialysis. The cell breakup procedure is similar to the one observed in the droplet breakage of viscoelastic liquids in confinement.

Tubular membrane formation of binary giant unilamellar vesicles composed of cylinder and inverse-cone-shaped lipids

We have succeeded in controlling tubular membrane formations in binary giant unilamellar vesicles (GUVs) using a simple temperature changing between the homogeneous one-phase region and the two-phase coexistence region. The binary GUV is composed of inverse-cone (bulky hydrocarbon chains and a small headgroup) and cylinder-shaped lipids. When the temperature was set in the two-phase coexistence region, the binary GUV had a spherical shape with solidlike domains. By increasing the temperature to the homogeneous one-phase region, the excess area created by the chain melting of the lipid produced tubes inside the GUV. The tubes had a radius on the micrometer scale and were stable in the one-phase region. When we again decreased the temperature to the two-phase coexisting region, the tubes regressed and the GUVs recovered their phase-separated spherical shape. We infer that the tubular formation was based on the mechanical balance of the vesicle membrane (spontaneous tension) coupled with the asymmetric distribution of the inverse-cone-shaped lipids between the inner and outer leaflets of the vesicle (lipid sorting).

Recent developments in the field of bending rigidity measurements on membranes

This review gives a brief overview of experimental approaches used to assess the bending rigidity of membranes. Emphasis is placed on techniques based on the use of giant unilamellar vesicles. We summarize the effect on the bending rigidity of membranes as a function of membrane composition, presence of various inclusions in the bilayer and molecules and ions in the bathing solutions. Examples for the impact of temperature, cholesterol, some peptides and proteins, sugars and salts are provided and the literature data are discussed critically. Future directions, open questions and possible developments in this research field are also included.

Bending lipid membranes: experiments after W. Helfrich's model

Current description of biomembrane mechanics originates for a large part from W. Helfrich's model. Based on his continuum theory, many experiments have been performed in the past four decades on simplified membranes in order to characterize the mechanical properties of lipid membranes and the contribution of polymers or proteins. The long-term goal was to develop a better understanding of the mechanical properties of cell membranes. In this paper, we will review representative experimental approaches that were developed during this period and the main results that were obtained.

Quantitative optical microscopy and micromanipulation studies on the lipid bilayer membranes of giant unilamellar vesicles

This manuscript discusses basic methodological aspects of optical microscopy and micromanipulation methods to study membranes and reviews methods to generate giant unilamellar vesicles (GUVs). In particular, we focus on the use of fluorescence microscopy and micropipet manipulation techniques to study composition-structure-property materials relationships of free-standing lipid bilayer membranes. Because their size (∼5-100 μm diameter) that is well above the resolution limit of regular light microscopes, GUVs are suitable membrane models for optical microscopy and micromanipulation experimentation. For instance, using different fluorescent reporters, fluorescence microscopy allows strategies to study membrane lateral structure/dynamics at the level of single vesicles of diverse compositions. The micropipet manipulation technique on the other hand, uses Hoffman modulation contrast microscopy and allows studies on the mechanical, thermal, molecular exchange and adhesive-interactive properties of compositionally different membranes under controlled environmental conditions. The goal of this review is to (i) provide a historical perspective for both techniques; (ii) present and discuss some of their most important contributions to our understanding of lipid bilayer membranes; and (iii) outline studies that would utilize both techniques simultaneously on the same vesicle thus bringing the ability to characterize structure and strain responses together with the direct application of well-defined stresses to a single membrane or observe the effects of adhesive spreading. Knowledge gained by these studies has informed several applications of lipid membranes including their use as lung surfactants and drug delivery systems for cancer.

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.

Use the force: membrane tension as an organizer of cell shape and motility

Many cell phenomena that involve shape changes are affected by the intrinsic deformability of the plasma membrane (PM). Far from being a passive participant, the PM is now known to physically, as well as biochemically, influence cell processes ranging from vesicle trafficking to actin assembly. Here we review current understanding of how changes in PM tension regulate cell shape and movement, as well as how cells sense PM tension.

Molecular structure of membrane tethers

Membrane tethers are nanotubes formed by a lipid bilayer. They play important functional roles in cell biology and provide an experimental window on lipid properties. Tethers have been studied extensively in experiments and described by theoretical models, but their molecular structure remains unknown due to their small diameters and dynamic nature. We used molecular dynamics simulations to obtain molecular-level insight into tether formation. Tethers were pulled from single-component lipid bilayers by application of an external force to a lipid patch along the bilayer normal or by lateral compression of a confined bilayer. Tether development under external force proceeded by viscoelastic protrusion followed by viscous lipid flow. Weak forces below a threshold value produced only a protrusion. Larger forces led to a crossover to tether elongation, which was linear at a constant force. Under lateral compression, tethers formed from undulations of unrestrained bilayer area. We characterized in detail the tether structure and its formation process, and obtained the material properties of the membrane. To our knowledge, these results provide the first molecular view of membrane tethers.

Stereocilia membrane deformation: implications for the gating spring and mechanotransduction channel

In hair cells, although mechanotransduction channels have been localized to tips of shorter stereocilia of the mechanically sensitive hair bundle, little is known about how force is transmitted to the channel. Here, we use a biophysical model of the membrane-channel complex to analyze the nature of the gating spring compliance and channel arrangement. We use a triangulated surface model and Monte Carlo simulation to compute the deformation of the membrane under the action of tip link force. We show that depending on the gating spring stiffness, the compliant component of the gating spring arises from either the membrane alone or a combination of the membrane and a tether that connects the channel to the actin cytoskeleton. If a bundle is characterized by relatively soft gating springs, such as those of the bullfrog sacculus, the need for membrane reinforcement by channel tethering then depends on membrane parameters. With stiffer gating springs, such as those from rat outer hair cells, the channel must be tethered for all biophysically realistic parameters of the membrane. We compute the membrane forces (resultants), which depend on membrane tension, bending modulus, and curvature, and show that they can determine the fate of the channel.

A microfabricated magnetic force transducer-microaspiration system for studying membrane mechanics

The application of forces to cell membranes is a powerful method for studying membrane mechanics. To apply controlled dynamic forces on the piconewton scale, we designed and characterized a microfabricated magnetic force transducer (MMFT) consisting of current-carrying gold wires patterned on a sapphire substrate. The experimentally measured forces applied to paramagnetic and ferromagnetic beads as a function of applied current agree well with theoretical models. We used this device to pull tethers from microaspirated giant unilamellar vesicles and measure the threshold force for tether formation. In addition, the interlayer drag coefficient of the membrane was determined from the tether-return velocity under magnetic force-free conditions. At high levels of current, vesicles expanded as a result of local temperature changes. A finite element thermal model of the MMFT provided absolute temperature calibration, allowing determination of the thermal expansivity coefficient of stearoyl-oleoyl-phosphatidycholine vesicles (1.7 ± 0.4 × 10(-3) K(-1)) and characterization of the Joule heating associated with current passing through the device. This effect can be used as a sensitive probe of temperature changes on the microscale. These studies establish the MMFT as an effective tool for applying precise forces to membranes at controlled rates and quantitatively studying membrane mechanical and thermo-mechanical properties.

Temporary increase in plasma membrane tension coordinates the activation of exocytosis and contraction during cell spreading

Cell migration and spreading involve the coordination of membrane trafficking, actomyosin contraction, and modifications to plasma membrane tension and area. The biochemical or biophysical basis for this coordination is however unknown. In this study, we show that during cell spreading, lamellipodia protrusion flattens plasma membrane folds and blebs and, once the plasma membrane area is depleted, there is a temporary increase in membrane tension by over twofold that is followed by activation of exocytosis and myosin contraction. Further, an artificial increase in plasma membrane tension stopped lamellipodia protrusion and activated an exocytotic burst. Subsequent decrease in tension restored spreading with activation of contraction. Conversely, blebbistatin inhibition of actomyosin contraction resulted in an even greater increase in plasma membrane tension and exocytosis activation. This spatiotemporal synchronization indicates that membrane tension is the signal that coordinates membrane trafficking, actomyosin contraction, and plasma membrane area change. We suggest that cells use plasma membrane tension as a global physical parameter to control cell motility.

Mobility in geometrically confined membranes

Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the "membrane size" for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111-3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman-Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion.

Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids

Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations.

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.

Membrane nanotubes induced by aqueous phase separation and stabilized by spontaneous curvature

Tubular membrane structures are widespread in eukaryotic cells, but the mechanisms underlying their formation and stability are not well understood. Previous work has focused on tube extrusion from cells and model membranes under the application of external forces. Here, we present novel membrane/polymer systems, where stable tubes form in the absence of externally applied forces. Solutions of two water-soluble polymers, polyethylene glycol and dextran, were encapsulated in giant lipid vesicles, cell-size model systems. Hypertonic deflation induced phase separation of the enclosed solution. The excess membrane area created during the deflation process was stored in a large number of membrane nanotubes inside the vesicle. The tubes had a diameter below optical resolution and became visible only when fluorescently labeled. The tubes were rather stable: In the absence of external forces, they existed for several days. A theoretical analysis of the shapes of the deflated vesicles reveals that these shapes would be unstable if the membranes had no spontaneous curvature. Using the large separation of length scales between the tube diameter and the overall size of the vesicles, the spontaneous curvature can be calculated and is found to be about -1/(240 nm) for a certain range of polymer concentrations. The nanotubes could also be retracted back into the mother vesicle by increasing the membrane tension via micropipette aspiration of the vesicle. Membrane tubes, which can form and be retracted easily, should be relevant for lipid storage in cells.

Quantifying Membrane Curvature Generation of Drosophila Amphiphysin N-BAR Domains

Biological membrane functions are coupled to membrane curvature, the regulation of which often involves membrane-associated proteins. The membrane-binding N-terminal amphipathic helix-containing BIN/Amphiphysin/Rvs (N-BAR) domain of amphiphysin is implicated in curvature generation and maintenance. Improving the mechanistic understanding of membrane curvature regulation by N-BAR domains requires quantitative experimental characterization. We have measured tube pulling force modulation by the N-BAR domain of Drosophila amphiphysin (DA-N-BAR) bound to tubular membranes pulled from micropipette-aspirated giant vesicles. We observed that fluorescently-labeled DA-N-BAR showed significantly higher protein density on tubules compared to the connected low-curvature vesicle membrane. Furthermore, we found the equilibrium tube pulling force to be systematically dependent on the aqueous solution concentration of DA-N-BAR, thereby providing the first quantitative assessment of spontaneous curvature generation. At sufficiently high protein concentrations, pulled tubes required no external force to maintain mechanical equilibrium, in agreement with the qualitative spontaneous tubulation previously reported for amphiphysin.

Cell membrane tethers generate mechanical force in response to electrical stimulation

Living cells maintain a huge transmembrane electric field across their membranes. This electric field exerts a force on the membrane because the membrane surfaces are highly charged. We have measured electromechanical force generation by cell membranes using optically trapped beads to detach the plasma membrane from the cytoskeleton and form long thin cylinders (tethers). Hyperpolarizing potentials increased and depolarizing potentials decreased the force required to pull a tether. The membrane tether force in response to sinusoidal voltage signals was a function of holding potential, tether diameter, and tether length. Membrane electromechanical force production can occur at speeds exceeding those of ATP-based protein motors. By harnessing the energy in the transmembrane electric field, cell membranes may contribute to processes as diverse as outer hair cell electromotility, ion channel gating, and transport.

The viscoelastic properties of microvilli are dependent upon the cell-surface molecule

We studied at nanometer resolution the viscoelastic properties of microvilli and tethers pulled from myelogenous cells via P-selectin glycoprotein ligand 1 (PSGL-1) and found that in contrast to pure membrane tethers, the viscoelastic properties of microvillus deformations are dependent upon the cell-surface molecule through which load is applied. A laser trap and polymer bead coated with anti-PSGL-1 (KPL-1) were used to apply step loads to microvilli. The lengthening of the microvillus in response to the induced step loads was fitted with a viscoelastic model. The quasi-steady state force on the microvillus at any given length was approximately fourfold lower in cells treated with cytochalasin D or when pulled with concanavalin A-coated rather than KPL-1-coated beads. These data suggest that associations between PSGL-1 and the underlying actin cytoskeleton significantly affect the early stages of leukocyte deformation under flow.

Steady-state electrochemical determination of lipidic nanotube diameter utilizing an artificial cell model

By exploiting the capabilities of steady-state electrochemical measurements, we have measured the inner diameter of a lipid nanotube using Fick's first law of diffusion in conjunction with an imposed linear concentration gradient of electroactive molecules over the length of the nanotube. Fick's law has been used in this way to provide a direct relationship between the nanotube diameter and the measurable experimental parameters Deltai (change in current) and nanotube length. Catechol was used to determine the Deltai attributed to its flux out of the nanotube. Comparing the nanotube diameter as a function of nanotube length revealed that membrane elastic energy was playing an important role in determining the size of the nanotube and was different when the tube was connected to either end of two vesicles or to a vesicle on one end and a pipet tip on the other. We assume that repulsive interaction between neck regions can be used to explain the trends observed. This theoretical approach based on elastic energy considerations provides a qualitative description consistent with experimental data.

Dynamic sorting of lipids and proteins in membrane tubes with a moving phase boundary

Cellular organelle membranes maintain their integrity, global shape, and composition despite vigorous exchange among compartments of lipids and proteins during trafficking and signaling. Organelle homeostasis involves dynamic molecular sorting mechanisms that are far from being understood. In contrast, equilibrium thermodynamics of membrane mixing and sorting, particularly the phase behavior of binary and ternary model membrane mixtures and its coupling to membrane mechanics, is relatively well characterized. Elucidating the continuous turnover of live cell membranes, however, calls for experimental and theoretical membrane models enabling manipulation and investigation of directional mass transport. Here we introduce the phenomenon of curvature-induced domain nucleation and growth in membrane mixtures with fluid phase coexistence. Membrane domains were consistently observed to nucleate precisely at the junction between a strongly curved cylindrical (tube) membrane and a pipette-aspirated giant unilamellar vesicle. This experimental geometry mimics intracellular sorting compartments, because they often show tubular-vesicular membrane regions. Nucleated domains at tube necks were observed to present diffusion barriers to the transport of lipids and proteins. We find that curvature-nucleated domains grow with characteristic parabolic time dependence that is strongly curvature-dependent. We derive an analytical model that reflects the observed growth dynamics. Numerically calculated membrane shapes furthermore allow us to elucidate mechanical details underlying curvature-dependent directed lipid transport. Our observations suggest a novel dynamic membrane sorting principle that may contribute to intracellular protein and lipid sorting and trafficking.

Curvature sensing by the epsin N-terminal homology domain measured on cylindrical lipid membrane tethers

The protein epsin is believed to play important roles in clathrin-mediated endocytosis, including generation of the high membrane curvature necessary for vesicle formation. Here we assess the basis for this hypothesis by systematically quantifying the curvature dependence of the area density of epsin N-terminal homology (ENTH) domain on cylindrical membranes of controlled curvature. In cylindrical tethers pulled from micropipet-aspirated giant unilamellar vesicles, repartitioning of membrane-bound ENTH from vesicles onto highly curved membranes was observed by fluorescence microscopy. First-order thermodynamic theory used to analyze our data yielded the first measurement of Leibler's thermodynamic curvature-composition coupling coefficient to be reported for an endocytic accessory protein. Our results highlight the possibility that epsin contributes to cellular membrane curvature sensing and generation, and we believe that our method will provide useful contributions toward the goal of relating molecular descriptions of interactions to macroscopic membrane remodeling in cells and identifying and characterizing roles for proteins in these processes.

Bending stiffness depends on curvature of ternary lipid mixture tubular membranes

Lipid and protein sorting and trafficking in intracellular pathways maintain cellular function and contribute to organelle homeostasis. Biophysical aspects of membrane shape coupled to sorting have recently received increasing attention. Here we determine membrane tube bending stiffness through measurements of tube radii, and demonstrate that the stiffness of ternary lipid mixtures depends on membrane curvature for a large range of lipid compositions. This observation indicates amplification by curvature of cooperative lipid demixing. We show that curvature-induced demixing increases upon approaching the critical region of a ternary lipid mixture, with qualitative differences along two roughly orthogonal compositional trajectories. Adapting a thermodynamic theory earlier developed by M. Kozlov, we derive an expression that shows the renormalized bending stiffness of an amphiphile mixture membrane tube in contact with a flat reservoir to be a quadratic function of curvature. In this analytical model, the degree of sorting is determined by the ratio of two thermodynamic derivatives. These derivatives are individually interpreted as a driving force and a resistance to curvature sorting. We experimentally show this ratio to vary with composition, and compare the model to sorting by spontaneous curvature. Our results are likely to be relevant to the molecular sorting of membrane components in vivo.

Sorting of lipids and proteins in membrane curvature gradients

The sorting of lipids and proteins in cellular trafficking pathways is a process of central importance in maintaining compartmentalization in eukaryotic cells. However, the mechanisms behind these sorting phenomena are currently far from being understood. Among several mechanistic suggestions, membrane curvature has been invoked as a means to segregate lipids and proteins in cellular sorting centers. To assess this hypothesis, we investigate the sorting of lipid analog dye trace components between highly curved tubular membranes and essentially flat membranes of giant unilamellar vesicles. Our experimental findings indicate that intracellular lipid sorting, contrary to frequent assumptions, is unlikely to occur by lipids fitting into membrane regions of appropriate curvature. This observation is explained in the framework of statistical mechanical lattice models that show that entropy, rather than curvature energy, dominates lipid distribution in the absence of strongly preferential lateral intermolecular interactions. Combined with previous findings of curvature induced phase segregation, we conclude that lipid cooperativity is required to enable efficient sorting. In contrast to lipid analog dyes, the peripheral membrane binding protein Cholera toxin subunit B is effectively curvature-sorted. The sorting of Cholera toxin subunit B is rationalized by statistical models. We discuss the implications of our findings for intracellular sorting mechanisms.

Hair cell bundles: flexoelectric motors of the inner ear

Microvilli (stereocilia) projecting from the apex of hair cells in the inner ear are actively motile structures that feed energy into the vibration of the inner ear and enhance sensitivity to sound. The biophysical mechanism underlying the hair bundle motor is unknown. In this study, we examined a membrane flexoelectric origin for active movements in stereocilia and conclude that it is likely to be an important contributor to mechanical power output by hair bundles. We formulated a realistic biophysical model of stereocilia incorporating stereocilia dimensions, the known flexoelectric coefficient of lipid membranes, mechanical compliance, and fluid drag. Electrical power enters the stereocilia through displacement sensitive ion channels and, due to the small diameter of stereocilia, is converted to useful mechanical power output by flexoelectricity. This motor augments molecular motors associated with the mechanosensitive apparatus itself that have been described previously. The model reveals stereocilia to be highly efficient and fast flexoelectric motors that capture the energy in the extracellular electro-chemical potential of the inner ear to generate mechanical power output. The power analysis provides an explanation for the correlation between stereocilia height and the tonotopic organization of hearing organs. Further, results suggest that flexoelectricity may be essential to the exquisite sensitivity and frequency selectivity of non-mammalian hearing organs at high auditory frequencies, and may contribute to the “cochlear amplifier” in mammals.