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

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.