High Membrane Tension Research Articles

Fission of double-membrane tubes under tension

The division of a cellular compartment culminates with the scission of a highly constricted membrane neck. Scission requires lipid rearrangements, topology changes, and transient formation of nonbilayer intermediate structures driven by curvature stress. Often, a side effect of this stress is pore formation, which may lead to content leakage and thus breaching of the membrane barrier function. In single-membrane systems, leakage is avoided through the formation of a hemifusion (HF) intermediate, whose structure is still a subject of debate. The consequences of curvature stress have not been explored in double-membrane systems, such as the mitochondrion. Here, we combine experimental and theoretical approaches to study neck constriction and scission driven by tension in biomimetic lipid systems, namely single- and double-membrane nanotubes (sNTs and dNTs), respectively. In sNTs, constriction by high tension gives rise to a metastable HF intermediate (seen as stalk or worm-like micelle), whereas poration is universally slower in a simple neck. In dNTs, high membrane tension causes sequential rupture of each membrane. In contrast, low tension leads to the HF of both membranes, which may lead to a leaky fusion pathway, or may progress to further fusion of the two membranes along a number of transformation pathways. These findings provide a new mechanistic basis for fundamental cellular processes.

Cell-intrinsic mechanical regulation of plasma membrane accumulation at the cytokinetic furrow

Cytokinesis is the process where the mother cell's cytoplasm separates into daughter cells. This is driven by an actomyosin contractile ring that produces cortical contractility and drives cleavage furrow ingression, resulting in the formation of a thin intercellular bridge. While cytoskeletal reorganization during cytokinesis has been extensively studied, less is known about the spatiotemporal dynamics of the plasma membrane. Here, we image and model plasma membrane lipid and protein dynamics on the cell surface during leukemia cell cytokinesis. We reveal an extensive accumulation and folding of the plasma membrane at the cleavage furrow and the intercellular bridge, accompanied by a depletion and unfolding of the plasma membrane at the cell poles. These membrane dynamics are caused by two actomyosin-driven biophysical mechanisms: the radial constriction of the cleavage furrow causes local compression of the apparent cell surface area and accumulation of the plasma membrane at the furrow, while actomyosin cortical flows drag the plasma membrane toward the cell division plane as the furrow ingresses. The magnitude of these effects depends on the plasma membrane fluidity, cortex adhesion, and cortical contractility. Overall, our work reveals cell-intrinsic mechanical regulation of plasma membrane accumulation at the cleavage furrow that is likely to generate localized differences in membrane tension across the cytokinetic cell. This may locally alter endocytosis, exocytosis, and mechanotransduction, while also serving as a self-protecting mechanism against cytokinesis failures that arise from high membrane tension at the intercellular bridge.

Effective cell membrane tension protects red blood cells against malaria invasion.

A critical step in how malaria parasites invade red blood cells (RBCs) is the wrapping of the membrane around the egg-shaped merozoites. Recent experiments have revealed that RBCs can be protected from malaria invasion by high membrane tension. While cellular and biochemical aspects of parasite actomyosin motor forces during the malaria invasion have been well studied, the important role of the biophysical forces induced by the RBC membrane-cytoskeleton composite has not yet been fully understood. In this study, we use a theoretical model for lipid bilayer mechanics, cytoskeleton deformation, and membrane-merozoite interactions to systematically investigate the influence of effective RBC membrane tension, which includes contributions from the lipid bilayer tension, spontaneous tension, interfacial tension, and the resistance of cytoskeleton against shear deformation on the progression of membrane wrapping during the process of malaria invasion. Our model reveals that this effective membrane tension creates a wrapping energy barrier for a complete merozoite entry. We calculate the tension threshold required to impede the malaria invasion. We find that the tension threshold is a nonmonotonic function of spontaneous tension and undergoes a sharp transition from large to small values as the magnitude of interfacial tension increases. We also predict that the physical properties of the RBC cytoskeleton layer-particularly the resting length of the cytoskeleton-play key roles in specifying the degree of the membrane wrapping. We also found that the shear energy of cytoskeleton deformation diverges at the full wrapping state, suggesting the local disassembly of the cytoskeleton is required to complete the merozoite entry. Additionally, using our theoretical framework, we predict the landscape of myosin-mediated forces and the physical properties of the RBC membrane in regulating successful malaria invasion. Our findings on the crucial role of RBC membrane tension in inhibiting malaria invasion can have implications for developing novel antimalarial therapeutic or vaccine-based strategies.

Membrane stretch as the mechanism of activation of PIEZO1 ion channels in chondrocytes

Osteoarthritis is a chronic disease that can be initiated by altered joint loading or injury of the cartilage. The mechanically sensitive PIEZO ion channels have been shown to transduce injurious levels of biomechanical strain in articular chondrocytes and mediate cell death. However, the mechanisms of channel gating in response to high cellular deformation and the strain thresholds for activating PIEZO channels remain unclear. We coupled studies of single-cell compression using atomic force microscopy (AFM) with finite element modeling (FEM) to identify the biophysical mechanisms of PIEZO-mediated calcium (Ca2+) signaling in chondrocytes. We showed that PIEZO1 and PIEZO2 are needed for initiating Ca2+ signaling at moderately high levels of cellular deformation, but at the highest strains, PIEZO1 functions independently of PIEZO2. Biophysical factors that increase apparent chondrocyte membrane tension, including hypoosmotic prestrain, high compression magnitudes, and low deformation rates, also increased PIEZO1-driven Ca2+ signaling. Combined AFM/FEM studies showed that 50% of chondrocytes exhibit Ca2+ signaling at 80 to 85% nominal cell compression, corresponding to a threshold of apparent membrane finite principal strain of E = 1.31, which represents a membrane stretch ratio (λ) of 1.9. Both intracellular and extracellular Ca2+ are necessary for the PIEZO1-mediated Ca2+ signaling response to compression. Our results suggest that PIEZO1-induced signaling drives chondrocyte mechanical injury due to high membrane tension, and this threshold can be altered by factors that influence membrane prestress, such as cartilage hypoosmolarity, secondary to proteoglycan loss. These findings suggest that modulating PIEZO1 activation or downstream signaling may offer avenues for the prevention or treatment of osteoarthritis.

A novel force transduction pathway from a tension sensor to the gate in the mechano-gating of MscL channel.

The bacterial mechanosensitive channel of large conductance MscL is activated exclusively by increased tension in the membrane bilayer. Despite many proposed models for MscL opening, its precise mechano-gating mechanism, particularly how the received force at the tension sensor transmits to the gate remains incomplete. Previous studies have shown that along with amphipathic N-terminus located near the cytoplasmic surface of the membrane, Phe78 residue near the outer surface also acts as a "tension sensor," while Gly22 is a central constituent of the "hydrophobic gate." Present study focused on elucidating the force transmission mechanism from the sensor Phe78 in the outer transmembrane helix (TM2) to the gate in the inner transmembrane helix (TM1) of MscL by applying the patch clamp and molecular dynamics (MD) simulations to the wild type MscL channel and its single mutants at the sensor (F78N), the gate (G22N) and their combination (G22N/F78N) double mutant. F78N MscL resulted in a severe loss-of-function, while G22N MscL caused a gain-of-function channel exhibiting spontaneous openings at the resting membrane tension. We initially speculated that the spontaneous opening in G22N mutant might occur without tension acting on Phe78 residue. To test this hypothesis, we examined the (G22N/F78N) double mutant, which unexpectedly exhibited neither spontaneous activity nor activity by a relatively high membrane tension. To understand the underlying mechanism, we conducted MD simulations and analyzed the force transduction pathway. Results showed that the mutation at the tension sensor (F78N) in TM2 caused decreased interaction of this residue not only with lipids, but also with a group of amino acids (Ile32-Leu36-Ile40) in the neighboring TM1 helix, which resulted in an inefficient force transmission to the gate-constituting amino acids on TM1. This change also induced a slight tilting of TM1 towards the membrane plane and decreased the size of the channel pore at the gate, which seems to be the major mechanism for the inhibition of spontaneous opening of the double mutant channel. More importantly, the newly identified interaction between the TM2 (Phe78) and adjacent TM1 (Ile32-Leu36-Ile40) helices seems to be an essential force transmitting mechanism for the stretch-dependent activation of MscL given that substitution of any one of these four amino acids with Asn resulted in severe loss-of-function MscL as reported in our previous work.

The Effect of the Nanoparticle Shape on T Cell Activation.

The mechanism of extracellular ligand nano-geometry in ex vivo T cell activation for immunotherapy remains elusive. Herein, the authors demonstrate large aspect ratio (AR) of gold nanorods (AuNRs) conjugated on cell culture substrate enhancing both murine and human T cell activation through the nanoscale anisotropic presentation of stimulatory ligands (anti-CD3(αCD3) and anti-CD28(αCD28) antibodies). AuNRs with large AR bearing αCD3 and αCD28 antibodies significantly promote T cell expansion and key cytokine secretion including interleukin-2 (IL-2), interferon-gamma (IFN-γ), and tumor necrosis factor-alpha (TNF-α). High membrane tension observed in large AR AuNRs regulates actin filament and focal adhesion assembly and develops maturation-related morphological features in T cells such as membrane ruffle formation, cell spreading, and large T cell receptor (TCR) cluster formation. Anisotropic stimulatory ligand presentation promotes differentiation of naïve CD8+ T cells toward the effector phenotype inducing CD137 expression upon co-culture with human cervical carcinoma. The findings suggest the importance of manipulating extracellular ligand nano-geometry in optimizing T cell behaviors to enhance therapeutic outcomes.

Single-molecule manipulation of macromolecules on GUV or SUV membranes using optical tweezers

Despite their wide applications in soluble macromolecules, optical tweezers have rarely been used to characterize the dynamics of membrane proteins, mainly due to the lack of model membranes compatible with optical trapping. Here, we examined optical trapping and mechanical properties of two potential model membranes, giant and small unilamellar vesicles (GUVs and SUVs, respectively) for studies of membrane protein dynamics. We found that optical tweezers can stably trap GUVs containing iodixanol with controlled membrane tension. The trapped GUVs with high membrane tension can serve as a force sensor to accurately detect reversible folding of a DNA hairpin or membrane binding of synaptotagmin-1 C2AB domain attached to the GUV. We also observed that SUVs are rigid enough to resist large pulling forces and are suitable for detecting protein conformational changes induced by force. Our methodologies may facilitate single-molecule manipulation studies of membrane proteins using optical tweezers.

Mechanical Effect on Gene Transfection Based on Dielectric Elastomer Actuator.

Gene transfection has been widely applied in genome function and gene therapy. Although many efforts have been focused on designing carrier materials and transfection methods, the influence of mechanical stimulation on gene transfection efficiency has rarely been studied. Herein, dielectric elastomer actuator (DEA)-based stimulation bioreactors are designed to generate tensile and contractile stress on cells simultaneously. With the example of the EGFP transfection, cells with high membrane tension in the stretching stimulation regions had lower transfection efficiency, while the transfection efficiency of cells in the compressing regions tended to increase. Besides, the duty cycle and loading frequency of the applied stress on cells were also important factors that affect gene transfection efficiency. Furthermore, the pathways of cell endocytosis with the effect of mechanical stimulation were explored on the mechanism for the change of EGFP transfection efficiency. This design of the DEA-based bioreactor, as a strategy to study gene transfection efficiency, could be helpful for developing efficient transfection methods.

Competing pathways for the invagination of clathrin-coated membranes.

Clathrin-mediated endocytosis is the major pathway by which eukaryotic cells take up extracellular material, but it is still elusive which physical pathways are being taken during membrane invagination. From a continuum point of view, it can be driven by increases in coat stiffness, preferred curvature or line tension. Here we develop a comprehensive theoretical framework that can be solved analytically and that predicts the consequences of these different scenarios. We find that for the case of increasing stiffness or preferred curvature, curvature will be acquired gradually with growth, while for increasing line tension, the lattice must have grown to a certain size before a flat-to-curved transition can occur. At low membrane tension, the critical value for coat stiffness is 30 kBT, for preferred curvature it is 200 nm, and for line tension it is 6 pN. For high membrane tension, critical coat stiffness is 150 kBT and critical preferred curvature is 70 nm. In the mixed case when a coat with finite rigidity but increasing line tension is considered, a cup-to-sphere transition can occur for a line tension of 6 pN. The flat-to-curved and the cup-to-sphere transitions driven by line tension are both suppressed by high membrane tension.

Mechanomodulation of Lipid Membranes by Weakly Aggregating Silver Nanoparticles.

Silver nanoparticles (AgNPs) have wide-ranging applications, including as additives in consumer products and in medical diagnostics and therapy. Therefore, understanding how AgNPs interact with biological systems is important for ascertaining any potential health risks due to the likelihood of high levels of human exposure. Besides any severe, acute effects, it is desirable to understand more subtle interactions that could lead to milder, chronic health impacts. Nanoparticles are small enough to be able to enter biological cells and interfere with their internal biochemistry. The initial contact between the nanoparticle and cell is at the plasma membrane. To gain fundamental mechanistic insight into AgNP-membrane interactions, we investigate these phenomena in minimal model systems using a wide range of biophysical approaches applied to lipid vesicles. We find a strong dependence on the medium composition, where colloidally stable AgNPs in a glucose buffer have a negligible effect on the membrane. However, at physiological salt concentrations, the AgNPs start to weakly aggregate and sporadic but significant membrane perturbation events are observed. Under these latter conditions, transient poration and structural remodeling of some vesicle membranes are observed. We observe that the fluidity of giant vesicle membranes universally decreases by an average of 16% across all vesicles. However, we observe a small population of vesicles that display a significant change in their mechanical properties with lower bending rigidity and higher membrane tension. Therefore, we argue that the isolated occurrences of membrane perturbation by AgNPs are due to low-probability mechanomodulation by AgNP aggregation at the membrane.

Connecting the Dots between Mechanosensitive Channel Abundance, Osmotic Shock, and Survival at Single-Cell Resolution.

Rapid changes in extracellular osmolarity are one of many insults microbial cells face on a daily basis. To protect against such shocks, Escherichia coli and other microbes express several types of transmembrane channels that open and close in response to changes in membrane tension. In E. coli, one of the most abundant channels is the mechanosensitive channel of large conductance (MscL). While this channel has been heavily characterized through structural methods, electrophysiology, and theoretical modeling, our understanding of its physiological role in preventing cell death by alleviating high membrane tension remains tenuous. In this work, we examine the contribution of MscL alone to cell survival after osmotic shock at single-cell resolution using quantitative fluorescence microscopy. We conducted these experiments in an E. coli strain which is lacking all mechanosensitive channel genes save for MscL, whose expression was tuned across 3 orders of magnitude through modifications of the Shine-Dalgarno sequence. While theoretical models suggest that only a few MscL channels would be needed to alleviate even large changes in osmotic pressure, we find that between 500 and 700 channels per cell are needed to convey upwards of 80% survival. This number agrees with the average MscL copy number measured in wild-type E. coli cells through proteomic studies and quantitative Western blotting. Furthermore, we observed zero survival events in cells with fewer than ∼100 channels per cell. This work opens new questions concerning the contribution of other mechanosensitive channels to survival, as well as regulation of their activity.IMPORTANCE Mechanosensitive (MS) channels are transmembrane protein complexes which open and close in response to changes in membrane tension as a result of osmotic shock. Despite extensive biophysical characterization, the contribution of these channels to cell survival remains largely unknown. In this work, we used quantitative video microscopy to measure the abundance of a single species of MS channel in single cells, followed by their survival after a large osmotic shock. We observed total death of the population with fewer than ∼100 channels per cell and determined that approximately 500 to 700 channels were needed for 80% survival. The number of channels we found to confer nearly full survival is consistent with the counts of the numbers of channels in wild-type cells in several earlier studies. These results prompt further studies to dissect the contribution of other channel species to survival.

The ERM family member Merlin is required for endometrial gland morphogenesis

Disruption of endometrial gland formation or function can cause female infertility. Formation of endometrial glands via tubulogenesis of luminal epithelial cells requires the establishment and maintenance of cell polarity and cell adhesion. The FERM domain-containing protein Merlin coordinates epithelial cell polarity and cell adhesion and is critical for epithelial tissue function in the skin and kidney. We now demonstrate a requirement for Merlin in endometrial gland development. Conditional deletion of Merlin in the endometrium results in female infertility caused by the absence of gland formation. Interestingly, we observed glandular epithelial markers within discrete groups of cells in the Merlin-deficient luminal epithelium. Wnt signaling, a pathway necessary for endometrial gland development is maintained in Merlin-deficient endometrium, suggesting the glandular fate program is active. Instead, we observe increased levels of apical actin and markers indicative of high membrane tension on the basal surface of the Merlin-deficient luminal epithelium. These findings suggest that the structural integrity of the luminal epithelium during gland formation is required for appropriate endometrial tubulogenesis and tissue function. Moreover, our work implicates Merlin-dependent regulation of mechanical tension in the proper formation of endometrial gland architecture and function.

Design Principles for Robust Vesiculation in Clathrin-Mediated Endocytosis

Budding of membranes by protein coats is a universal phenomenon that is critically important in cellular trafficking pathways. Recent experiments have demonstrated that elevated membrane tension inhibits the ability of protein coats to deform membranes into buds. However, the robustness of clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a modified Helfrich model for membrane mechanics and membrane protein interaction, we have investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension and force from actin polymerization on robust bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a snapthrough instability in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to ¯¯snap“ from an open, U-shape to a closed bud. Through systematic analyses of the different parameters contributing to membrane budding, we have identified potential ways of overcoming the energy barrier associated with the instability. For example, increasing the bending rigidity of the coat smooths out this instability, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can induce the transition from an open to a closed bud, bypassing the instability. Finally, a combination of increased coat rigidity and force from actin polymerization ensures robust vesiculation, even at high membrane tensions.

Exploring the inhibitory effect of membrane tension on cell polarization.

Cell polarization toward an attractant is influenced by both physical and chemical factors. Most existing mathematical models are based on reaction-diffusion systems and only focus on the chemical process occurring during cell polarization. However, membrane tension has been shown to act as a long-range inhibitor of cell polarization. Here, we present a cell polarization model incorporating the interplay between Rac GTPase, filamentous actin (F-actin), and cell membrane tension. We further test the predictions of this model by performing single cell measurements of the spontaneous polarization of cancer stem cells (CSCs) and non-stem cancer cells (NSCCs), as the former have lower cell membrane tension. Based on both our model and the experimental results, cell polarization is more sensitive to stimuli under low membrane tension, and high membrane tension improves the robustness and stability of cell polarization such that polarization persists under random perturbations. Furthermore, our simulations are the first to recapitulate the experimental results described by Houk et al., revealing that aspiration (elevation of tension) and release (reduction of tension) result in a decrease in and recovery of the activity of Rac-GTP, respectively, and that the relaxation of tension induces new polarity of the cell body when a cell with the pseudopod-neck-body morphology is severed.

Design principles for robust vesiculation in clathrin-mediated endocytosis

A critical step in cellular-trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension, and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a "snap-through instability" in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to "snap" from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions.

Whole-GUV patch-clamping

Studying how the membrane modulates ion channel and transporter activity is challenging because cells actively regulate membrane properties, whereas existing in vitro systems have limitations, such as residual solvent and unphysiologically high membrane tension. Cell-sized giant unilamellar vesicles (GUVs) would be ideal for in vitro electrophysiology, but efforts to measure the membrane current of intact GUVs have been unsuccessful. In this work, two challenges for obtaining the "whole-GUV" patch-clamp configuration were identified and resolved. First, unless the patch pipette and GUV pressures are precisely matched in the GUV-attached configuration, breaking the patch membrane also ruptures the GUV. Second, GUVs shrink irreversibly because the membrane/glass adhesion creating the high-resistance seal (>1 GΩ) continuously pulls membrane into the pipette. In contrast, for cell-derived giant plasma membrane vesicles (GPMVs), breaking the patch membrane allows the GPMV contents to passivate the pipette surface, thereby dynamically blocking membrane spreading in the whole-GMPV mode. To mimic this dynamic passivation mechanism, beta-casein was encapsulated into GUVs, yielding a stable, high-resistance, whole-GUV configuration for a range of membrane compositions. Specific membrane capacitance measurements confirmed that the membranes were truly solvent-free and that membrane tension could be controlled over a physiological range. Finally, the potential for ion transport studies was tested using the model ion channel, gramicidin, and voltage-clamp fluorometry measurements were performed with a voltage-dependent fluorophore/quencher pair. Whole-GUV patch-clamping allows ion transport and other voltage-dependent processes to be studied while controlling membrane composition, tension, and shape.

The Abscission Checkpoint: Making It to the Final Cut.

Cytokinesis is the final stage of cell division and is concluded by abscission of the intercellular bridge to physically separate the daughter cells. Timing of cytokinetic abscission is monitored by a molecular machinery termed the abscission checkpoint. This machinery delays abscission in cells with persistent chromatin in the intercellular bridge. Recent work has also uncovered its response to high membrane tension, nuclear pore defects, and DNA replication stress. Although it is known that the abscission checkpoint depends on persistent activity of the Aurora B protein kinase, we have only recently begun to understand its molecular basis. We propose here a molecular framework for abscission checkpoint signaling and we discuss outstanding questions relating to its function and physiological relevance.

Membrane Tension Acts Through PLD2 and mTORC2 to Limit Actin Network Assembly During Neutrophil Migration.

For efficient polarity and migration, cells need to regulate the magnitude and spatial distribution of actin assembly. This process is coordinated by reciprocal interactions between the actin cytoskeleton and mechanical forces. Actin polymerization-based protrusion increases tension in the plasma membrane, which in turn acts as a long-range inhibitor of actin assembly. These interactions form a negative feedback circuit that limits the magnitude of membrane tension in neutrophils and prevents expansion of the existing front and the formation of secondary fronts. It has been suggested that the plasma membrane directly inhibits actin assembly by serving as a physical barrier that opposes protrusion. Here we show that efficient control of actin polymerization-based protrusion requires an additional mechanosensory feedback cascade that indirectly links membrane tension with actin assembly. Specifically, elevated membrane tension acts through phospholipase D2 (PLD2) and the mammalian target of rapamycin complex 2 (mTORC2) to limit actin nucleation. In the absence of this pathway, neutrophils exhibit larger leading edges, higher membrane tension, and profoundly defective chemotaxis. Mathematical modeling suggests roles for both the direct (mechanical) and indirect (biochemical via PLD2 and mTORC2) feedback loops in organizing cell polarity and motility—the indirect loop is better suited to enable competition between fronts, whereas the direct loop helps spatially organize actin nucleation for efficient leading edge formation and cell movement. This circuit is essential for polarity, motility, and the control of membrane tension.

Linear and weakly nonlinear global instability of a fluid flow through a collapsible channel

Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim of this paper is to present a variant (obtained via a weighted residual approach) of the averaged one-dimensional model derived by Stewart et al. [“Local and global instabilities of flow in a flexible-walled channel,” Eur. J. Mech. B/Fluids 28, 541–557 (2009)]. The asymptotic expansions for small Reynolds numbers of these two models, compared to the exact solution obtained from the lubrication approach, reveal some quantitative difference, even at higher Reynolds numbers. Qualitatively, the two models give similar results at least at a linear level. It is shown that for relatively low membrane tension (T), there are distinct regions in the (T, R) parameter space where steady bifurcating flows may occur. These flows can also be observed at vanishingly small Reynolds numbers combined with relatively high membrane tension. At sufficiently high T and R, the bifurcating flow is rather time periodic. A weakly nonlinear analysis is then performed in both cases leading to the derivation of evolution equations for the amplitudes of the bifurcating flows. The amplitude equations show that the saddle node bifurcation has a transcritical character while the Hopf bifurcation is either subcritical or supercritical, depending both on the mode number and membrane tension.

Membrane Tension Inhibits Deformation by Coat Proteins in Clathrin-Mediated Endocytosis

In clathrin-mediated endocytosis (CME), clathrin and various adaptor proteins coat a patch of the plasma membrane, which is reshaped to form a budded vesicle. Experimental studies have demonstrated that elevated membrane tension can inhibit bud formation by a clathrin coat. In this study, we investigate the impact of membrane tension on the mechanics of membrane budding by simulating clathrin coats that either grow in area or progressively induce greater curvature. At low membrane tension, progressively increasing the area of a curvature-generating coat causes the membrane to smoothly evolve from a flat to budded morphology, whereas the membrane remains essentially flat at high membrane tensions. Interestingly, at physiologically relevant, intermediate membrane tensions, the shape evolution of the membrane undergoes a snapthrough instability in which increasing coat area causes the membrane to "snap" from an open, U-shaped bud to a closed, $\Omega$-shaped bud. This instability is accompanied by a large energy barrier, which could cause a developing endocytic pit to stall if the binding energy of additional coat is insufficient to overcome this barrier. Similar results were found for a coat of constant area in which the spontaneous curvature progressively increases. Additionally, a pulling force on the bud, simulating a force from actin polymerization, is sufficient to drive a transition from an open to closed bud, overcoming the energy barrier opposing this transition.