Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation

Dynamins combine mechano-constriction and membrane remodeling to enable two-step mitochondrial fission via a 'snap-through' instability

Mitochondrial fission is controlled by dynamin proteins, the dysregulation of which is correlated with diverse diseases. Fission dynamins are GTP hydrolysis-driven mechanoenzymes that self-oligomerize into helical structures that constrict membrane to achieve fission, but details are not well understood. However, dynamins can also remodel membranes by inducing negative Gaussian curvature, the type of curvature required for completion of fission. Here, we examine how these drastically different mechanisms synergistically exert their influences on a membrane, via a mechanical model calibrated with small-angle X-ray scattering structural data. We find that free dynamin can trigger a "snap-through instability" that enforces a shape transition from an oligomer-confined cylindrical membrane to a drastically narrower catenoid-shaped neck within the spontaneous hemi-fission regime, in a manner that depends critically on the length of the confined tube. These results indicate how the combination of dynamin assembly, and paradoxically disassembly, can lead to diverse pathways to scission.

Revealing the Structural Intricacies of Biomembrane-Interfaced Emulsions with Small- and Ultra-Small-Angle Neutron Scattering

Utilizing cell membranes from diverse cell types for biointerfacing has demonstrated significant advantages in enhancing colloidal stability and incorporating biological properties, tailored specifically for various biomedical applications. However, the structures of these materials, particularly emulsions interfaced with red blood cell (RBC) or platelet (PLT) membranes, remain an underexplored area. This study systematically employs small- and ultra-small-angle neutron scattering (SANS and USANS) with contrast variation to investigate the structure of emulsions containing perfluorohexane within RBC (RBC/PFH) and PLT membranes (PLT/PFH). The findings reveal that the scattering length density of RBC and PLT membranes is 1.5 × 10-6 Å-2, similar to 30% (w/w) deuterium oxide. Using this solvent as a cell membrane-matching medium, estimated droplet diameters are 770 nm (RBC/PFH) and 1.5 µm (PLT/PFH), based on polydispersed sphere model fitting. Intriguingly, calculated patterns and invariant analysis reveal native droplet architectures featuring entirely liquid PFH cores, differing significantly from the observed bubble-droplet core system in electron microscopy. This highlights the advantage of SANS and USANS in differentiating genuine colloidal structures in complex dispersions. In summary, this work underscores the pivotal role of SANS and USANS in characterizing biointerfaced colloids and in uncovering novel colloidal structures with significant potential for biomedical applications and clinical translation.

Comparing Multifunctional Viral and Eukaryotic Proteins for Generating Scission Necks in Membranes

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is M2 viroporin, a proton pump from the influenza A virus that is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging small-angle X-ray scattering structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemifission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.

Dynamic mechanisms for membrane skeleton transitions

The plasma membrane and the underlying skeleton form a protective barrier for eukaryotic cells. The molecules forming this complex composite material constantly rearrange under mechanical stress to confer this protective capacity. One of those molecules, spectrin, is ubiquitous in the membrane skeleton and primarily located proximal to the inner leaflet of the plasma membrane and engages in protein-lipid interactions via a set of membrane-anchoring domains. Spectrin is linked by short actin filaments and its conformation varies in different types of cells. In this work, we developed a generalized network model for the membrane skeleton integrated with myosin contractility and membrane mechanics to investigate the response of the spectrin meshwork to mechanical loading. We observed that the force generated by membrane bending is important to maintain a smooth skeletal structure. This suggests that the membrane is not just supported by the skeleton, but has an active contribution to the stability of the cell structure. We found that spectrin and myosin turnover are necessary for the transition between stress and rest states in the skeleton. Our model reveals that the actin-spectrin meshwork dynamics are balanced by the membrane forces with area constraint and volume restriction promoting the stability of the membrane skeleton. Furthermore, we showed that cell attachment to the substrate promotes shape stabilization. Thus, our proposed model gives insight into the shared mechanisms of the membrane skeleton associated with myosin and membrane that can be tested in different types of cells.

Erythrocytes' surface properties and stiffness predict survival and functional decline in ALS patients

Erythrocytes play a fundamental role in oxygen delivery to tissues and binding to inflammatory mediators. Evidences suggest that dysregulated erythrocyte function could contribute to the pathophysiology of several neurodegenerative diseases. We aimed to evaluate changes in morphological, biomechanical, and biophysical properties of erythrocytes from amyotrophic lateral sclerosis (ALS) patients, as new areas of study in this disease. Blood samples were collected from ALS patients, comparing with healthy volunteers. Erythrocytes were assessed using atomic force microscopy (AFM) and zeta potential analysis. The patients' motor and respiratory functions were evaluated using the revised ALS Functional Rating Scale (ALSFRS-R) and percentage of forced vital capacity (%FVC). Patient survival was also assessed. Erythrocyte surface roughness was significantly smoother in ALS patients, and this parameter was a predictor of faster decline in ALSFRS-R scores. ALS patients exhibited higher erythrocyte stiffness, as indicated by reduced AFM tip penetration depth, which predicted a faster ALSFRS-R score and respiratory subscore decay. A lower negative charge on the erythrocyte membrane was predictor of a faster ALSFRS-R and FVC decline. Additionally, a larger erythrocyte surface area was an independent predictor of lower survival. These changes in morphological and biophysical membrane properties of ALS patients' erythrocytes, lead to increased cell stiffness and morphological variations. We speculate that these changes might precipitate motoneurons dysfunction and accelerate disease progression. Further studies should explore the molecular alterations related to these observations. Our findings may contribute to dissect the complex interplay between respiratory function, tissue hypoxia, progression rate, and survival in ALS.

Comparing multifunctional viral and eukaryotic proteins for generating scission necks in membranes

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is the M2 viroporin, a proton pump from the influenza A virus which is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging Small-Angle X-ray Scattering (SAXS) structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemi-fission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.

Piezo1 Regulation Involves Lipid Domains and the Cytoskeleton and Is Favored by the Stomatocyte-Discocyte-Echinocyte Transformation

Piezo1 is a mechanosensitive ion channel required for various biological processes, but its regulation remains poorly understood. Here, we used erythrocytes to address this question since they display Piezo1 clusters, a strong and dynamic cytoskeleton and three types of submicrometric lipid domains, respectively enriched in cholesterol, GM1 ganglioside/cholesterol and sphingomyelin/cholesterol. We revealed that Piezo1 clusters were present in both the rim and the dimple erythrocyte regions. Upon Piezo1 chemical activation by Yoda1, the Piezo1 cluster proportion mainly increased in the dimple area. This increase was accompanied by Ca2+ influx and a rise in echinocytes, in GM1/cholesterol-enriched domains in the dimple and in cholesterol-enriched domains in the rim. Conversely, the effects of Piezo1 activation were abrogated upon membrane cholesterol depletion. Furthermore, upon Piezo1-independent Ca2+ influx, the above changes were not observed. In healthy donors with a high echinocyte proportion, Ca2+ influx, lipid domains and Piezo1 fluorescence were high even at resting state, whereas the cytoskeleton membrane occupancy was lower. Accordingly, upon decreases in cytoskeleton membrane occupancy and stiffness in erythrocytes from patients with hereditary spherocytosis, Piezo1 fluorescence was increased. Altogether, we showed that Piezo1 was differentially controlled by lipid domains and the cytoskeleton and was favored by the stomatocyte-discocyte-echinocyte transformation.

How Cell-Penetrating Peptides Behave Differently from Pore-Forming Peptides: Structure and Stability of Induced Transmembrane Pores

Peptide-induced transmembrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell-penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions, and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore-forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small-angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that although AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

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.

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.

How cell penetrating peptides behave differently from pore forming peptides: structure and stability of induced transmembrane pores

Peptide induced trans-membrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that whereas AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

Molecular Resolution Mapping of Erythrocyte Cytoskeleton by Ultrastructure Expansion Single-Molecule Localization Microscopy

The combination of expansion microscopy and single-molecule localization microscopy has the potential to approach the molecular resolution. However, this combination meets challenges due to the hydrogel shrinkage in the presence of imaging buffer. Here, a method of ultrastructure expansion single-molecule localization microscopy (U-ExSMLM) based on skillfully adhering the gel onto poly-l-lysine (pLL)-coated coverslip is developed to prevent lateral shrinkage of the hydrogel. U-ExSMLM is then applied to dissect the membrane cytoskeleton organization of human erythrocytes at molecular resolution. The resolved nanoscale spatial distributions of cytoskeleton proteins, including the N/C-termini of β-spectrin, protein 4.1, and tropomodulin, show good agreement with the acknowledged model of erythrocyte cytoskeleton structure, demonstrating the reliability of U-ExSMLM. Furthermore, the concentration of pLL is adjusted to preserve the physiological biconcave morphology of erythrocytes, and it is found that the spectrin cytoskeleton in the dimple regions has lower density and larger length than that in the rim regions, which provides the direct evidence for cytoskeleton asymmetry in human erythrocytes. Therefore, the integrated method offers future opportunities to study the ultrastructure of membrane cytoskeleton at molecular resolution.

Piezo1 as a force-through-membrane sensor in red blood cells

Piezo1 is the stretch activated Ca2+ channel in red blood cells that mediates homeostatic volume control. Here, we study the organization of Piezo1 in red blood cells using a combination of super-resolution microscopy techniques and electron microscopy. Piezo1 adopts a non-uniform distribution on the red blood cell surface, with a bias toward the biconcave 'dimple'. Trajectories of diffusing Piezo1 molecules, which exhibit confined Brownian diffusion on short timescales and hopping on long timescales, also reflect a bias toward the dimple. This bias can be explained by 'curvature coupling' between the intrinsic curvature of the Piezo dome and the curvature of the red blood cell membrane. Piezo1 does not form clusters with itself, nor does it colocalize with F-actin, Spectrin, or the Gardos channel. Thus, Piezo1 exhibits the properties of a force-through-membrane sensor of curvature and lateral tension in the red blood cell.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

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

Our understanding of the role of membrane tension in the field of membrane biophysics is rapidly evolving from a passive construct to an active player in a variety of cellular phenomena. Membrane tension has been shown to be a key regulator of many cellular processes ranging including trafficking, ion channel activation, and the invasion of red blood cells by malaria parasites. Recent experimental advances in cells, including the development of a fluorescent tension reporter, have shown that membrane tension is heterogeneous. In this mini-review, I summarize the recent advances in membrane tension measurements and discuss the contributions from different cellular constituents such as the cortical cytoskeleton. Then, I will explore how these different complexities can be considered in biophysical models of different scales. Finally, I will elaborate on the need for iterations between models and experiments as technologies in both fields advance to enable us to obtain critical insights into the physiological role of membrane tension as a critical component of mechanotransduction.

Membrane Localization of Piezo1 in the Context of Its Role in the Regulation of Red Blood Cell Volume

Piezo1 is a membrane nonspecific cation channel involved in red blood cells (RBCs) in the regulation of their volume. Recently, it was shown that it is distributed on the RBC membrane in a nonuniform manner. Here it is shown that it is possible to interpret the lateral distribution of Piezo1 molecules on RBC membrane by the curvature dependent Piezo1—bilayer interaction which is the consequence of the mismatch between the intrinsic principal curvatures of the Piezo1 trimer and the principal curvatures of the membrane at Piezo1′s location but without its presence. This result supports the previously proposed model for the role of Piezo1 in the regulation of RBC volume.

RBC membrane biomechanics and Plasmodium falciparum invasion: probing beyond ligand-receptor interactions

A critical step in malaria blood-stage infections is the invasion of red blood cells (RBCs) by merozoite forms of the Plasmodium parasite. Much progress has been made in defining the parasite ligands and host receptors that mediate this critical step. However, less well understood are the RBC biophysical determinants that influence parasite invasion. In this review we explore how Plasmodium falciparum merozoites interact with the RBC membrane during invasion to modulate RBC deformability and facilitate invasion. We further highlight RBC biomechanics-related polymorphisms that might have been selected for in human populations due to their ability to reduce parasite invasion. Such an understanding will reveal the translational potential of targeting host pathways affecting RBC biomechanical properties for the treatment of malaria.

Nanoscale Dynamics of Actin Filaments in the Red Blood Cell Membrane Skeleton

Red blood cell (RBC) shape and deformability are supported by a planar network of short actin filament (F-actin) nodes (∼37 nm length, 15–18 subunits) interconnected by long spectrin strands at the inner surface of the plasma membrane. Spectrin-F-actin network structure underlies quantitative modeling of forces controlling RBC shape, membrane curvature, and deformation, yet the nanoscale organization and dynamics of the F-actin nodes in situ are not well understood. We examined F-actin distribution and dynamics in RBCs using fluorescent-phalloidin labeling of F-actin imaged by multiple microscopy modalities. Total internal reflection fluorescence and Zeiss Airyscan confocal microscopy demonstrate that F-actin is concentrated in multiple brightly stained F-actin foci ∼200–300 nm apart interspersed with dimmer F-actin staining regions. Single molecule stochastic optical reconstruction microscopy imaging of Alexa 647-phalloidin-labeled F-actin and computational analysis also indicates an irregular, nonrandom distribution of F-actin nodes. Treatment of RBCs with latrunculin A and cytochalasin D indicates that F-actin foci distribution depends on actin polymerization, while live cell imaging reveals dynamic local motions of F-actin foci, with lateral movements, appearance and disappearance. Regulation of F-actin node distribution and dynamics via actin assembly/disassembly pathways and/or via local extension and retraction of spectrin strands may provide a new mechanism to control spectrin-F-actin network connectivity, RBC shape, and membrane deformability.

Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.

Multimodal imaging reveals membrane skeleton reorganisation during reticulocyte maturation and differences in dimple and rim regions of mature erythrocytes

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Multimodal microscopies reveal dynamic changes in erythrocyte membrane skeleton architecture.

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Reticulocytes have 30% more surface area than mature erythrocytes but only slightly lower skeletal meshwork coverage.

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The spectrin-based skeleton reorganises during reticulocyte maturation.

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Inhomogeneity within the erythrocyte’s membrane skeleton underpins its biconcave disc shape.

The red blood cell (RBC) is remarkable in its ability to deform as it passages through the vasculature. Its deformability derives from a spectrin-actin protein network that supports the cell membrane and provides strength and flexibility, however questions remain regarding the assembly and maintenance of the skeletal network. Using scanning electron microscopy (SEM) and atomic force microscopy (AFM) we have examined the nanoscale architecture of the cytoplasmic side of membrane discs prepared from reticulocytes and mature RBCs. Immunofluorescence microscopy was used to probe the distribution of spectrin and other membrane skeleton proteins. We found that the cell surface area decreases by up to 30% and the spectrin-actin network increases in density by approximately 20% as the reticulocyte matures. By contrast, the inter-junctional distance and junctional density increase only by 3–4% and 5–9%, respectively. This suggests that the maturation-associated reduction in surface area is accompanied by an increase in spectrin self-association to form higher order oligomers. We also examined the mature RBC membrane in the edge (rim) and face (dimple) regions of mature RBCs and found the rim contains about 1.5% more junctional complexes compared to the dimple region. A 2% increase in band 4.1 density in the rim supports these structural measurements.

Mechanics of cup-shaped caveolae

Caveolae are cell membrane invaginations of defined lipid and protein composition that flatten with increasing membrane tension. Super-resolution light microscopy and electron microscopy have revealed that caveolae can take a variety of cuplike shapes. We show here that, for the range in membrane tension relevant for cell membranes, the competition between membrane tension and membrane bending yields caveolae with cuplike shapes similar to those observed experimentally. We find that the caveola shape and its sensitivity to changes in membrane tension can depend strongly on the caveola spontaneous curvature and on the size of caveola domains. Our results suggest that heterogeneity in caveola shape produces a staggered response of caveolae to mechanical perturbations of the cell membrane, which may facilitate regulation of membrane tension over the wide range of scales thought to be relevant for cell membranes.

Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces

In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson–Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces’ nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO₂ nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO₂ nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

Surface model of the human red blood cell simulating changes in membrane curvature under strain

We present mathematical simulations of shapes of red blood cells (RBCs) and their cytoskeleton when they are subjected to linear strain. The cell surface is described by a previously reported quartic equation in three dimensional (3D) Cartesian space. Using recently available functions in Mathematica to triangularize the surfaces we computed four types of curvature of the membrane. We also mapped changes in mesh-triangle area and curvatures as the RBCs were distorted. The highly deformable red blood cell (erythrocyte; RBC) responds to mechanically imposed shape changes with enhanced glycolytic flux and cation transport. Such morphological changes are produced experimentally by suspending the cells in a gelatin gel, which is then elongated or compressed in a custom apparatus inside an NMR spectrometer. A key observation is the extent to which the maximum and minimum Principal Curvatures are localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. Changes on the nanometre to micro-meter scale of curvature, suggest activation of only a subset of the intrinsic mechanosensitive cation channels, Piezo1, during experiments carried out with controlled distortions, which persist for many hours. This finding is relevant to a proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. However, if the curvature that gates Piezo1 is at a very fine length scale, then membrane tension will determine local curvature; so, curvatures as computed here (in contrast to much finer surface irregularities) may not influence Piezo1 activity. Nevertheless, our analytical methods can be extended address these new mechanistic proposals. The geometrical reorganization of the simulated cytoskeleton informs ideas about the mechanism of concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.

Probing PIEZO1 Localization upon Activation Using High-Resolution Atomic Force and Confocal Microscopy

PIEZO1 ion channels are activated by mechanical stimuli, triggering intracellular chemical signals. Recent structural studies suggest that plasma membrane tension or local curvature changes modulate PIEZO1 channel gating and activation. However, whether PIEZO1 localization is governed by tension gradients or long-range mechanical perturbations across the cells is still unclear. Here, we probe the nanoscale localization of PIEZO1 on red blood cells (RBCs) at high resolution (∼30 nm), and we report for the first time the existence of submicrometric PIEZO1 clusters in native conditions. Upon interaction with Yoda1, an allosteric modulator, PIEZO1 clusters increase in abundance in regions of higher membrane tension and lower curvature. We further show that PIEZO1 ion channels interact with the spectrin cytoskeleton in both resting and activated states. Our results point toward a strong interplay between plasma membrane tension gradients, curvature, and cytoskeleton association of PIEZO1.

Mechanical Principles Governing the Shapes of Dendritic Spines

Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes-stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.

Volumetric Semantic Instance Segmentation of the Plasma Membrane of HeLa Cells

In this work, an unsupervised volumetric semantic instance segmentation of the plasma membrane of HeLa cells as observed with serial block face scanning electron microscopy is described. The resin background of the images was segmented at different slices of a 3D stack of 518 slices with 8192 × 8192 pixels each. The background was used to create a distance map, which helped identify and rank the cells by their size at each slice. The centroids of the cells detected at different slices were linked to identify them as a single cell that spanned a number of slices. A subset of these cells, i.e., the largest ones and those not close to the edges were selected for further processing. The selected cells were then automatically cropped to smaller regions of interest of 2000 × 2000 × 300 voxels that were treated as cell instances. Then, for each of these volumes, the nucleus was segmented, and the cell was separated from any neighbouring cells through a series of traditional image processing steps that followed the plasma membrane. The segmentation process was repeated for all the regions of interest previously selected. For one cell for which the ground truth was available, the algorithm provided excellent results in Accuracy (AC) and the Jaccard similarity Index (JI): nucleus: JI =0.9665, AC =0.9975, cell including nucleus JI =0.8711, AC =0.9655, cell excluding nucleus JI =0.8094, AC =0.9629. A limitation of the algorithm for the plasma membrane segmentation was the presence of background. In samples with tightly packed cells, this may not be available. When tested for these conditions, the segmentation of the nuclear envelope was still possible. All the code and data were released openly through GitHub, Zenodo and EMPIAR.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types

Tiny membrane-enclosed cellular fragments that can mediate interactions between cells and organisms have recently become a subject of increasing attention. In this work the mechanism of formation of cell membrane nanovesicles (CNVs) was studied experimentally and theoretically. CNVs were isolated by centrifugation and washing of blood cells and observed by optical microscopy and scanning electron microscopy. The shape of the biological membrane in the budding process, as observed in phospholipid vesicles, in erythrocytes and in CNVs, was described by an unifying model. Taking the mean curvature h and the curvature deviator d of the membrane surface as the relevant parameters, the shape and the distribution of membrane constituents were determined theoretically by minimization of membrane free energy. Considering these results and previous results on vesiculation of red blood cells it was interpreted that the budding processes may lead to formation of different types of CNVs as regards the compartment (exo/endovesicles), shape (spherical/tubular/torocytic) and composition (enriched/depleted in particular kinds of molecules). It was concluded that the specificity of pinched off nanovesicles derives from the shape of the membrane constituents and not primarily from their chemical identity, which explains evidences on great heterogeneity of isolated extracellular vesicles with respect to composition.

One of the amazing properties of a biological membrane is the ability to undergo dramatic changes of its shape. It may exhibit very high curvature and thereby enclose nano-sized compartments that pinch off from the mother membrane and become freely moving cellular nanovesicles (CNVs). CNVs externalize the pieces of the cell and make them available to other cells within the same organism or other organisms. Therefore they have been acknowledged as mediators of communication between microorganisms, plants, animals and human. Furthernore, they dwell on the border between living and non-living things. Recent findings report on heterogeneity of the size and composition of CNVs found in isolates from different biological samples. As communication between cells is involved in many physiological and patophysiological processes, it is of importance to understand the mechanisms of CNVs formation and recognize the natural laws that mainly govern them. We point to an unifying mechanism that explains stability of differently shaped and composed CNVs by taking into account that the biological membrane tends to attain the minimum of its relevant energy. Conveniently, the procedure can be described by a mathematical model which allows for transparent comparison between experimentally induced shapes of membrane-enclosed vesicular structures and numerical calculations.