The many faces of membrane tension: Challenges across systems and scales

Biophysical insights into the impact of lateral electric field stimulation to cellular microenvironment: Implications for bioelectronic medicine applications

In the last few decades, electrical stimulation devices have been clinically used for a wide spectrum of applications, ranging from deep brain stimulation to drug and gene delivery. Despite such clinical relevance, the impact of electrical stimulation on the cellular biophysical processes has not been explored significantly. We report here the analytical results to develop quantitative biophysical insights into the influence of lateral electric field stimulation on bioelectric stresses in the intercellular/extracellular region and the membrane tension. In developing quantitative insights, we solved Laplace equation with appropriate boundary conditions in an azimuthally asymmetric system with a single cell. The magnitude of the stresses increases with the electric field strength in a parabolic manner. In case of cell without surface charges, the intracellular stress field is predicted to have both compressive and tensile regions with a maximum of 2 μPa, while a maximum tensile stress of 20 μPa in extracellular region could be predicted, at field strength of 300 V/m. While considering surface charges, the magnitude of extracellular normal and shear stresses at the cell membrane is an order of magnitude higher when compared to without surface charges. Based on the variation of shear stress tensors at cell membrane, the critical field strength for membrane rupture was found to be 5.3 kV/mm and 20 kV/mm for a cell without and with surface charges respectively. The impact of the bioelectric stresses on the mechanotransduction induced cytoskeletal reorganization and stress driven cellular signalling modulation were substantiated using quantitative results from the study.

Effect of membrane tension on pore formation induced by antimicrobial peptides and other membrane-active peptides

Membrane tension plays an important role in various aspects of the dynamics and functions of cells. Here, we review recent studies of the effect of membrane tension on pore formation in lipid bilayers and pore formation induced by membrane-active peptides (MAPs) including antimicrobial peptides (AMPs). For this purpose, the micropipette aspiration method using a patch of cell membrane/lipid bilayers and a giant unilamellar vesicle (GUV)/a total cell, and the application of osmotic pressure (Π) to suspensions of large unilamellar vesicles (LUVs) have been used. However, these conventional methods have some drawbacks for the investigation of the effect of membrane tension on the actions of MAPs such as AMPs. Recently, to overcome these drawbacks, a new Π method using GUVs has been developed. Here, we focus on this Π method as a new technique for revealing the effect of membrane tension on the MAPs-induced pore formation. Firstly, we review studies of the effect of membrane tension on pore formation in lipid bilayers as determined by conventional methods. Secondly, after a brief review of studies of the effect of Π on LUVs, we describe the estimation of membrane tension in GUVs induced by Π and the Π-induced pore formation. Thirdly, after a review of the effect of membrane tension on the MAPs-induced pore formation as obtained by the conventional methods, we describe an application of the Π method to studies of the effect of membrane tension on AMP-induced pore formation. Finally, we discuss the advantages of the Π method over conventional methods and consider future perspectives.

Targeting ELOVL6 to disrupt c-MYC driven lipid metabolism in pancreatic cancer enhances chemosensitivity

Pancreatic ductal adenocarcinoma (PDAC) is a lethal cancer with a 12% survival rate, highlighting the need for novel therapies. c-MYC overexpression, driven by upstream mutations and amplifications, reprograms tumor metabolism and promotes proliferation, migration and metastasis. This study identifies ELOVL6, a fatty acid elongase regulated by c-MYC, as a potential therapeutic target. Using PDAC mouse models and cell lines, we show that c-MYC directly upregulates ELOVL6 during tumor progression. Genetic or chemical inhibition of ELOVL6 reduces proliferation and migration by altering fatty acid composition, affecting membrane rigidity, permeability and pinocytosis. These changes increase Abraxane uptake and show a synergistic effect when combined with ELOVL6 inhibition in vitro. In vivo, ELOVL6 interference significantly suppresses tumor growth and improves Abraxane response, prolonging survival. These findings position ELOVL6 as a promising target for improving PDAC treatment outcomes.

RhoA regulates oligodendrocyte differentiation and myelination by orchestrating cortical and membrane tension

Timely differentiation and myelin formation by oligodendrocytes are essential for the physiological functioning of the central nervous system (CNS). While the Rho GTPase RhoA has been hinted as a negative regulator of myelin sheath formation, the precise in vivo mechanisms have remained elusive. Here we show that RhoA controls the timing and progression of myelination by oligodendrocytes through a fine-tuned balance between cortical tension, membrane tension and cell shape. Using a conditional mouse model, we observe that Rhoa ablation results in the acceleration of myelination driven by hastened differentiation and facilitated through membrane expansion induced by changes in MLCII activity and in F-actin redistribution and turnover within the cell. These findings reveal RhoA as a central molecular integrator of alterations in actin cytoskeleton, actomyosin contractility and membrane tension underlying precise morphogenesis of oligodendrocytes and normal myelination of the CNS.

Membrane mechanics dictate axonal pearls-on-a-string morphology and function

Axons are ultrathin membrane cables that are specialized for the conduction of action potentials. Although their diameter is variable along their length, how their morphology is determined is unclear. Here, we demonstrate that unmyelinated axons of the mouse central nervous system have nonsynaptic, nanoscopic varicosities ~200 nm in diameter repeatedly along their length interspersed with a thin cable ~60 nm in diameter like pearls-on-a-string. In silico modeling suggests that this axon nanopearling can be explained by membrane mechanical properties. Treatments disrupting membrane properties, such as hyper- or hypotonic solutions, cholesterol removal and nonmuscle myosin II inhibition, alter axon nanopearling, confirming the role of membrane mechanics in determining axon morphology. Furthermore, neuronal activity modulates plasma membrane cholesterol concentration, leading to changes in axon nanopearls and causing slowing of action potential conduction velocity. These data reveal that biophysical forces dictate axon morphology and function, and modulation of membrane mechanics likely underlies unmyelinated axonal plasticity.

Programmable Lipid Bilayer Tension-Control Apparatus for Quantitative Mechanobiology

The biological membrane is not just a platform for information processing but also a field of mechanics. The lipid bilayer that constitutes the membrane is an elastic body, generating stress upon deformation, while the membrane protein embedded therein deforms the bilayer through structural changes. Among membrane-protein interplays, various channel species act as tension-current converters for signal transduction, serving as elementary processes in mechanobiology. However, in situ studies in chaotically complex cell membranes are challenging, and characterizing the tension dependency of mechanosensitive channels remains semiquantitative owing to technical limitations. Here, we developed a programmable membrane tension-control apparatus on a lipid bilayer system. This synthetic membrane system [contact bubble bilayer (CBB)] uses pressure to drive bilayer tension changes via the Young-Laplace principle, whereas absolute bilayer tension is monitored in real-time through image analysis of the bubble geometry via the Young principle. Consequently, the mechanical nature of the system permits the implementation of closed-loop feedback control of bilayer tension (tension-clamp CBB), maintaining a constant tension for minutes and allowing stepwise tension changes within a hundred milliseconds in the tension range of 0.8 to 15 mN·m-1. We verified the system performance by examining the single-channel behavior of tension-dependent KcsA and TREK-1 potassium channels under scheduled tension time courses prescribed via visual interfaces. The result revealed steady-state activity and dynamic responses to the step tension changes, which are essential to the biophysical characterization of the channels. The apparatus explores a frontier for quantitative mechanobiology studies and promotes the development of a tension-operating experimental robot.

Shape of the membrane neck around a hole during plasma membrane repair

Plasma membrane damage and rupture occurs frequently in cells, and holes must be sealed rapidly to ensure homeostasis and cell survival. The membrane repair machinery is known to involve recruitment of curvature-inducing annexin proteins, but the connection between membrane remodeling and hole closure is poorly described. The induction of curvature by repair proteins leads to the possible formation of a membrane neck around the hole as a key intermediate structure before sealing. We formulate a theoretical model of equilibrium neck shapes to examine the potential connection to a repair mechanism. Using variational calculus, the shape equations for the membrane near a hole are formulated and solved numerically. The system is described under a condition of fixed area, and a shooting approach is applied to fulfill the boundary conditions at the free membrane edge. A state diagram of neck shapes is produced describing the variation in neck morphology with respect to the membrane area. Two distinct types of necks are predicted, one with conformations curved beyond π existing at positive excess area, whereas flat neck conformations (curved below π) have negative excess area. The results indicate that in cells, the supply of additional membrane area and a change in edge tension is linked to the formation of narrow and curved necks. Such necks may be susceptible to passive or actively induced membrane fission as a possible mechanism for hole sealing during membrane repair in cells.

Lipid osmosis, membrane tension, and other mechanochemical driving forces of lipid flow

Nonvesicular lipid transport among different membranes or membrane domains plays crucial roles in lipid homeostasis and organelle biogenesis. However, the forces that drive such lipid transport are not well understood. We propose that lipids tend to flow towards the membrane area with a higher membrane protein density in a process termed lipid osmosis. This process lowers the membrane tension in the area, resulting in a membrane tension difference called osmotic membrane tension. We examine the thermodynamic basis and experimental evidence of lipid osmosis and osmotic membrane tension. We predict that lipid osmosis can drive bulk lipid flows between different membrane regions through lipid transfer proteins, scramblases, or similar barriers that selectively pass lipids but not membrane proteins. We also speculate on the biological functions of lipid osmosis. Finally, we explore other driving forces for lipid transfer and describe potential methods and systems to further test our theory.

Lipid osmosis, membrane tension, and other mechanochemical driving forces of lipid flow

Nonvesicular lipid transport among different membranes or membrane domains plays crucial roles in lipid homeostasis and organelle biogenesis. However, the forces that drive such lipid transport are not well understood. We propose that lipids tend to flow towards the membrane area with a higher membrane protein density in a process termed lipid osmosis. This process lowers the membrane tension in the area, resulting in a membrane tension difference called osmotic membrane tension. We examine the thermodynamic basis and experimental evidence of lipid osmosis and osmotic membrane tension. We predict that lipid osmosis can drive bulk lipid flows between different membrane regions through lipid transfer proteins, scramblases, or other similar barriers that selectively pass lipids but not membrane proteins. We also speculate on the biological functions of lipid osmosis. Finally, we explore other driving forces for lipid transfer and describe potential methods and systems to further test our theory.

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.

Estimation of negative membrane tension in lipid bilayers and its effect on antimicrobial peptide magainin 2-induced pore formation

Positive membrane tension in the stretched plasma membrane of cells and in the stretched lipid bilayer of vesicles has been well analyzed quantitatively, whereas there is limited quantitative information on negative membrane tension in compressed plasma membranes and lipid bilayers. Here, we examined negative membrane tension quantitatively. First, we developed a theory to describe negative membrane tension by analyzing the free energy of lipid bilayers to obtain a theoretical equation for negative membrane tension. This allowed us to obtain an equation describing the negative membrane tension (σosm) for giant unilamellar vesicles (GUVs) in hypertonic solutions due to negative osmotic pressure (Π). Then, we experimentally estimated the negative membrane tension for GUVs in hypertonic solutions by measuring the rate constant (kr) of rupture of the GUVs induced by the constant tension (σex) due to an external force as a function of σex. We found that larger σex values were required to induce the rupture of GUVs under negative Π compared with GUVs in isotonic solution and quantitatively determined the negative membrane tension induced by Π (σosm) by the difference between these σex values. At small negative Π, the experimental values of negative σosm agree with their theoretical values within experimental error, but as negative Π increases, the deviation increases. Negative tension increased the stability of GUVs because higher tensions were required for GUV rupture, and the rate constant of antimicrobial peptide magainin 2-induced pore formation decreased.

Asymmetric Lipid Bilayers and Potassium Channels Embedded Therein in the Contact Bubble Bilayer

Cell membranes are highly intricate systems comprising numerous lipid species and membrane proteins, where channel proteins, lipid molecules, and lipid bilayers, as continuous elastic fabric, collectively engage in multi-modal interplays. Owing to the complexity of the native cell membrane, studying the elementary processes of channel-membrane interactions necessitates a bottom-up approach starting from forming simplified synthetic membranes. This is the rationale for establishing an in vitro membrane reconstitution system consisting of a lipid bilayer with a defined lipid composition and a channel molecule. Recent technological advancements have facilitated the development of asymmetric membranes, and the contact bubble bilayer (CBB) method allows single-channel current recordings under arbitrary lipid compositions in asymmetric bilayers. Here, we present an experimental protocol for the formation of asymmetric membranes using the CBB method. The KcsA potassium channel is a prototypical model channel with huge structural and functional information and thus serves as a reporter of membrane actions on the embedded channels. We demonstrate specific interactions of anionic lipids in the inner leaflet. Considering that the local lipid composition varies steadily in cell membranes, we `present a novel lipid perfusion technique that allows rapidly changing the lipid composition while monitoring the single-channel behavior. Finally, we demonstrate a leaflet perfusion method for modifying the composition of individual leaflets. These techniques with custom synthetic membranes allow for variable experiments, providing crucial insights into channel-membrane interplay in cell membranes.

Membrane Tension Inhibits Lipid Mixing by Increasing the Hemifusion Stalk Energy

Fusion of biological membranes is fundamental in various physiological events. The fusion process involves several intermediate stages with energy barriers that are tightly dependent on the mechanical and physical properties of the system, one of which is membrane tension. As previously established, the late stages of fusion, including hemifusion diaphragm and pore expansions, are favored by membrane tension. However, a current understanding of how the energy barrier of earlier fusion stages is affected by membrane tension is lacking. Here, we apply a newly developed experimental approach combining micropipette-aspirated giant unilamellar vesicles and optically trapped membrane-coated beads, revealing that membrane tension inhibits lipid mixing. We show that lipid mixing is 6 times slower under a tension of 0.12 mN/m compared with tension-free membranes. Furthermore, using continuum elastic theory, we calculate the dependence of the hemifusion stalk formation energy on membrane tension and intermembrane distance and find the increase in the corresponding energy barrier to be 1.6 kBT in our setting, which can explain the increase in lipid mixing time delay. Finally, we show that tension can be a significant factor in the stalk energy if the pre-fusion intermembrane distance is on the order of several nanometers, while for membranes that are tightly docked, tension has a negligible effect.

Cristae formation is a mechanical buckling event controlled by the inner membrane lipidome

Cristae are high curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous mechanisms for lipids have yet to be elucidated. Here we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the IMM against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. The model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that CL is essential in low oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of CL is dependent on the surrounding lipid and protein components of the IMM.

Membrane mechanics dictate axonal morphology and function

Axons are thought to be ultrathin membrane cables of a relatively uniform diameter, designed to conduct electrical signals, or action potentials. Here, we demonstrate that unmyelinated axons are not simple cylindrical tubes. Rather, axons have nanoscopic boutons repeatedly along their length interspersed with a thin cable with a diameter of ∼60 nm like pearls-on-a-string. These boutons are only ∼200 nm in diameter and do not have synaptic contacts or a cluster of synaptic vesicles, hence non-synaptic. Our in silico modeling suggests that axon pearling can be explained by the mechanical properties of the membrane including the bending modulus and tension. Consistent with modeling predictions, treatments that disrupt these parameters like hyper- or hypo-tonic solutions, cholesterol removal, and non-muscle myosin II inhibition all alter the degree of axon pearling, suggesting that axon morphology is indeed determined by the membrane mechanics. Intriguingly, neuronal activity modulates the cholesterol level of plasma membrane, leading to shrinkage of axon pearls. Consequently, the conduction velocity of action potentials becomes slower. These data reveal that biophysical forces dictate axon morphology and function and that modulation of membrane mechanics likely underlies plasticity of unmyelinated axons.

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. These tubes can be formed due to localized forces acting on the membrane or by the curvature induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare membrane tension and the protein-induced curvature. We also found that the length of the tube undergoes an abrupt transition from a short, dome-shaped membrane to a long cylinder and this transition is characteristic of a snapthrough instability. Finally, we show that the snapthrough instability depends on the different parameters including coat area, bending modulus, and extent of protein-induced curvature. Our findings have implications for tube formation due to BAR-domain proteins in processes such as endocytosis, t-tubule formation in myocytes, and cristae formation in mitochondria.

Nanoscale membrane curvature sorts lipid phases and alters lipid diffusion

The precise spatiotemporal control of nanoscale membrane shape and composition is the result of a complex interplay of individual and collective molecular behaviors. Here, we employed single-molecule localization microscopy and computational simulations to observe single-lipid diffusion and sorting in model membranes with varying compositions, phases, temperatures, and curvatures. Supported lipid bilayers were created over 50-nm-radius nanoparticles to mimic the size of naturally occurring membrane buds, such as endocytic pits and the formation of viral envelopes. The curved membranes recruited liquid-disordered lipid phases while altering the diffusion and sorting of tracer lipids. Disorder-preferring fluorescent lipids sorted to and experienced faster diffusion on the nanoscale curvature only when embedded in a membrane capable of sustaining lipid phase separation at low temperatures. The curvature-induced sorting and faster diffusion even occurred when the sample temperature was above the miscibility temperature of the planar membrane, implying that the nanoscale curvature could induce phase separation in otherwise homogeneous membranes. Further confirmation and understanding of these results are provided by continuum and coarse-grained molecular dynamics simulations with explicit and spontaneous curvature-phase coupling, respectively. The curvature-induced membrane compositional heterogeneity and altered dynamics were achieved only with a coupling of the curvature with a lipid phase separation. These cross-validating results demonstrate the complex interplay of lipid phases, molecular diffusion, and nanoscale membrane curvature that are critical for membrane functionality.

Modelling membrane curvature generation using mechanics and machine learning

The deformation of cellular membranes regulates trafficking processes, such as exocytosis and endocytosis. Classically, the Helfrich continuum model is used to characterize the forces and mechanical parameters that cells tune to accomplish membrane shape changes. While this classical model effectively captures curvature generation, one of the core challenges in using it to approximate a biological process is selecting a set of mechanical parameters (including bending modulus and membrane tension) from a large set of reasonable values. We used the Helfrich model to generate a large synthetic dataset from a random sampling of realistic mechanical parameters and used this dataset to train machine-learning models. These models produced promising results, accurately classifying model behaviour and predicting membrane shape from mechanical parameters. We also note emerging methods in machine learning that can leverage the physical insight of the Helfrich model to improve performance and draw greater insight into how cells control membrane shape change.