Elastic properties of biological membranes influenced by attached proteins

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.

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.

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.

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.

Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells

The impact of the intrinsic curvature of in-plane orientationally ordered curved flexible nematic molecules attached to closed 3D flexible shells was studied numerically. A Helfrich-Landau-de Gennes-type mesoscopic approach was adopted where the flexible shell's curvature field and in-plane nematic field are coupled and concomitantly determined in the process of free energy minimisation. We demonstrate that this coupling has the potential to generate a rich diversity of qualitatively new shapes of closed 3D nematic shells and the corresponding specific in-plane orientational ordering textures, which strongly depend on the shell's volume-to-surface area ratio, so far not predicted in mesoscopic-type numerical studies of 3D shapes of closed flexible nematic shells.

A Monte Carlo study of giant vesicle morphologies in nonequilibrium environments

It is known that giant vesicles undergo dynamic morphological changes when exposed to a detergent. The solubilization process may take multiple pathways. In this work, we identify lipid vesicle shape dynamics before the solubilization of 1,2-dioleoyl-sn-glycero-3-phosphocholine giant vesicles with Triton X-100 (TR) detergent. The violent lipid vesicle dynamics was observed with laser confocal scanning microscopy and was qualitatively explained via a numerical simulation. A three-dimensional Monte Carlo scheme was constructed that emulated the nonequilibrium conditions at the beginning stages of solubilization, accounting for a gradual addition of TR detergent molecules into the lipid bilayers. We suggest that the main driving factor for morphology change in lipid vesicles is the associative tendency of the TR molecules, which induces spontaneous curvature of the detergent inclusions, an intrinsic consequence of their molecular shape. The majority of the observed lipid vesicle shapes in the experiments were found to correspond very well to the numerically calculated shapes in the phase space of possible solutions. The results give an insight into the early stages of lipid vesicle solubilization by amphiphilic molecules, which is nonequilibrium in nature and very difficult to study.

Membrane shape remodeling by protein crowding

The steric repulsion between proteins on biological membranes is one of the most generic mechanisms that cause membrane shape changes. We present a minimal model in which a spontaneous curvature is induced by asymmetric protein crowding. Our results show that the interplay between the induced spontaneous curvature and the membrane tension determines the energy-minimizing shapes, which describes the wide range of experimentally observed membrane shapes, i.e., flat membranes, spherical vesicles, elongated tubular protrusions, and pearling structures. Moreover, the model gives precise predictions on how membrane shape changes by protein crowding can be tuned by controlling the protein size, the density of proteins, and the size of the crowded domain.

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.

Additional contributions to elastic energy of lipid membranes: Tilt-curvature coupling and curvature gradient

Lipid bilayer membranes under biologically relevant conditions are flexible thin laterally fluid films consisting of two unimolecular layers (monolayers) each about 2 nm thick. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape. The classical Helfrich theory considers the membrane as an elastic two-dimensional (2D) film, which has no particular internal structure. However, various local membrane heterogeneities can result in a lipids tilt relative to the membrane surface normal. On the basis of the classical elasticity theory of 3D bodies, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)10.1007/s101890070003] derived the most general energy functional, taking into account the tilt and lipid monolayer curvature. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)10.1063/1.4990404] showed that Hamm and Kozlov's derivation was incomplete because the tilt-curvature coupling term had been missed. However, the energy functional derived by Terzi and Deserno appeared to be unstable, thereby being invalid for applications that require minimizations of the overall energy of deformations. Here, we derive a stable elastic energy functional, showing that the squared gradient of the curvature was missed in both of these works. This change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability. We also consider the influence of the prestress terms on the stability of the energy functional, and we show that it should be considered small and the effective Gaussian curvature should be neglected because of the stability requirements. We further generalize the theory, including the stretching-compressing deformation modes, and we provide the geometrical interpretation of the terms that were previously missed by Hamm and Kozlov. The physical consequences of the new terms are analyzed in the case of a membrane-mediated interaction of two amphipathic peptides located in the same monolayer. We also provide the expression for director fluctuations, comparing it with that obtained by Terzi and Deserno.

A physical mechanism of TANGO1-mediated bulky cargo export

The endoplasmic reticulum (ER)-resident protein TANGO1 assembles into a ring around ER exit sites (ERES), and links procollagens in the ER lumen to COPII machinery, tethers, and ER-Golgi intermediate compartment (ERGIC) in the cytoplasm (Raote et al., 2018). Here, we present a theoretical approach to investigate the physical mechanisms of TANGO1 ring assembly and how COPII polymerization, membrane tension, and force facilitate the formation of a transport intermediate for procollagen export. Our results indicate that a TANGO1 ring, by acting as a linactant, stabilizes the open neck of a nascent COPII bud. Elongation of such a bud into a transport intermediate commensurate with bulky procollagens is then facilitated by two complementary mechanisms: (i) by relieving membrane tension, possibly by TANGO1-mediated fusion of retrograde ERGIC membranes and (ii) by force application. Altogether, our theoretical approach identifies key biophysical events in TANGO1-driven procollagen export.

Magneto-mechanical actuation of barium-hexaferrite nanoplatelets for the disruption of phospholipid membranes

HYPOTHESIS

The magneto-mechanical actuation (MMA) of magnetic nanoparticles with a low-frequency alternating magnetic field (AMF) can be used to destroy cancer cells. So far, MMA was tested on different cells using different nanoparticles and different field characteristics, which makes comparisons and any generalizations about the results of MMA difficult. In this paper we propose the use of giant unilamellar vesicles (GUVs) as a simple model system to study the effect of MMA on a closed lipid bilayer membrane, i.e., a basic building block of any cell.

EXPERIMENTS

The GUVs were exposed to barium-hexaferrite nanoplatelets (NPLs, ~50 nm wide and 3 nm thick) with unique magnetic properties dominated by a permanent magnetic moment that is perpendicular to the platelet, at different concentrations (1-50 µg/mL) and pH values (4.2-7.4) of the aqueous suspension. The GUVs were observed with an optical microscope while being exposed to a uniaxial AMF (3-100 Hz, 2.2-10.6 mT).

FINDINGS

When the NPLs were electrostatically attached to the GUV membranes, the MMA induced cyclic fluctuations of the GUVs' shape corresponding to the AMF frequency at the low NPL concentration (1 µm/mL), whereas the GUVs were bursting at the higher concentration (10 µg/mL). Theoretical considerations suggested that the bursting of the GUVs is a consequence of the local action of an assembly of several NPLs, rather than a collective effect of all the absorbed NPLs.

Protein Recruitment through Indirect Mechanochemical Interactions

Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Inception Mechanisms of Tunneling Nanotubes

Tunneling nanotubes (TNTs) are thin membranous tubes that interconnect cells, representing a novel route of cell-to-cell communication and spreading of pathogens. TNTs form between many cell types, yet their inception mechanisms remain elusive. We review in this study general concepts related to the formation and stability of membranous tubular structures with a focus on a deviatoric elasticity model of membrane nanodomains. We review experimental evidence that tubular structures initiate from local membrane bending facilitated by laterally distributed proteins or anisotropic membrane nanodomains. We further discuss the numerical results of several theoretical and simulation models of nanodomain segregation suggesting the mechanisms of TNT inception and stability. We discuss the coupling of nanodomain segregation with the action of protruding cytoskeletal forces, which are mostly provided in eukaryotic cells by the polymerization of f-actin, and review recent inception mechanisms of TNTs in relation to motor proteins.

Closed membrane shapes with attached BAR domains subject to external force of actin filaments

Membrane deformations induced by attached BAR superfamily domains could trigger or facilitate the growth of plasma membrane protrusions. The BAR domain family consists of BAR, F-BAR and I-BAR domains, each enforcing a different local curvature when attached to the membrane surface. Our theoretical study mainly focuses on the role of I-BAR in the membrane tubular deformations generated or stabilised by actin filaments. The influence of the area density of membrane attached BAR domains and their intrinsic curvature on the closed membrane shapes (vesicles) was investigated numerically. We derived an analytical approximative expression for the critical relative area density of BARs at which the membrane tubular protrusions on vesicles are most prominent. We have shown that the BARs with a higher intrinsic curvature induce thinner and longer cylindrical protrusions. The average orientation of the membrane attached BARs is altered when the vesicle shape is subjected to external force of growing actin rod-like structure inside a vesicle. The average orientation angle of membrane attached BARs may indicate whether the actin filaments are just stabilising the protrusion or generating it by stretching the vesicle.

Phenomenology based multiscale models as tools to understand cell membrane and organelle morphologies

An intriguing question in cell biology is "how do cells regulate their shape?" It is commonly believed that the observed cellular morphologies are a result of the complex interaction among the lipid molecules (constituting the cell membrane), and with a number of other macromolecules, such as proteins. It is also believed that the common biophysical processes essential for the functioning of a cell also play an important role in cellular morphogenesis. At the cellular scale-where typical dimensions are in the order of micrometers-the effects arising from the molecular scale can either be modeled as equilibrium or non-equilibrium processes. In this chapter, we discuss the dynamically triangulated Monte Carlo technique to model and simulate membrane morphologies at the cellular scale, which in turn can be used to investigate several questions related to shape regulation in cells. In particular, we focus on two specific problems within the framework of isotropic and anisotropic elasticity theories: namely, (i) the origin of complex, physiologically relevant, membrane shapes due to the interaction of the membrane with curvature remodeling proteins, and (ii) the genesis of steady state cellular shapes due to the action of non-equilibrium forces that are generated by the fission and fusion of transport vesicles and by the binding and unbinding of proteins from the parent membrane.

Effects of magnetic cobalt ferrite nanoparticles on biological and artificial lipid membranes

Background

The purpose of this work is to provide experimental evidence on the interactions of suspended nanoparticles with artificial or biological membranes and to assess the possibility of suspended nanoparticles interacting with the lipid component of biological membranes.

Methods

1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid vesicles and human red blood cells were incubated in suspensions of magnetic bare cobalt ferrite (CoFe₂O₄) or citric acid (CA)-adsorbed CoFe₂O₄ nanoparticles dispersed in phosphate-buffered saline and glucose solution. The stability of POPC giant unilamellar vesicles after incubation in the tested nanoparticle suspensions was assessed by phase-contrast light microscopy and analyzed with computer-aided imaging. Structural changes in the POPC multilamellar vesicles were assessed by small angle X-ray scattering, and the shape transformation of red blood cells after incubation in tested suspensions of nanoparticles was observed using scanning electron microscopy and sedimentation, agglutination, and hemolysis assays.

Results

Artificial lipid membranes were disturbed more by CA-adsorbed CoFe₂O₄ nanoparticle suspensions than by bare CoFe₂O₄ nanoparticle suspensions. CA-adsorbed CoFe₂O₄-CA nanoparticles caused more significant shape transformation in red blood cells than bare CoFe₂O₄ nanoparticles.

Conclusion

Consistent with their smaller sized agglomerates, CA-adsorbed CoFe₂O₄ nanoparticles demonstrate more pronounced effects on artificial and biological membranes. Larger agglomerates of nanoparticles were confirmed to be reactive against lipid membranes and thus not acceptable for use with red blood cells. This finding is significant with respect to the efficient and safe application of nanoparticles as medicinal agents.

Influence of nanoparticle-membrane electrostatic interactions on membrane fluidity and bending elasticity

The aim of this work is to investigate the effect of electrostatic interactions between the nanoparticles and the membrane lipids on altering the physical properties of the liposomal membrane such as fluidity and bending elasticity. For this purpose, we have used nanoparticles and lipids with different surface charges. Positively charged iron oxide (γ-Fe2O3) nanoparticles, neutral and negatively charged cobalt ferrite (CoFe2O4) nanoparticles were encapsulated in neutral lipid 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine and negatively charged 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine lipid mixture. Membrane fluidity was assessed through the anisotropy measurements using the fluorescent probe 1,6-diphenyl-1,3,5-hexatriene. Though the interaction of both the types of nanoparticles reduced the membrane fluidity, the results were more pronounced in the negatively charged liposomes encapsulated with positively charged iron oxide nanoparticles due to strong electrostatic attractions. X-ray photoelectron spectroscopy results also confirmed the presence of significant quantity of positively charged iron oxide nanoparticles in negatively charged liposomes. Through thermally induced shape fluctuation measurements of the giant liposomes, a considerable reduction in the bending elasticity modulus was observed for cobalt ferrite nanoparticles. The experimental results were supported by the simulation studies using modified Langevin-Poisson-Boltzmann model.

Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation

The shapes of cell membranes are largely regulated by membrane-associated, curvature-active proteins. Herein, we use a numerical model of the membrane, recently developed by us, with elongated membrane inclusions possessing spontaneous directional curvatures that could be different along, and perpendicular to, the membrane's long axis. We show that, due to membrane-mediated interactions, these curvature-inducing membrane-nematogens can aggregate spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these protein lattices. Furthermore, the elastic properties of the tubes, such as their compressional stiffness and persistence length, are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes.

Interaction between dipolar lipid headgroups and charged nanoparticles mediated by water dipoles and ions

In this work, a theoretical model describing the interaction between a positively or negatively charged nanoparticle and neutral zwitterionic lipid bilayers is presented. It is shown that in the close vicinity of the positively charged nanoparticle, the zwitterionic lipid headgroups are less extended in the direction perpendicular to the membrane surface, while in the vicinity of the negatively charged nanoparticle, the headgroups are more extended. This result coincides with the calculated increase in the osmotic pressure between the zwitterionic lipid surface and positively charged nanoparticle and the decrease of osmotic pressure between the zwitterionic lipid surface and the negatively charged nanoparticle. Our theoretical predictions agree well with the experimentally determined fluidity of a lipid bilayer membrane in contact with positively or negatively charged nanoparticles. The prospective significance of the present work is mainly to contribute to better understanding of the interactions of charged nanoparticles with a zwitterionic lipid bilayer, which may be important in the efficient design of the lipid/nanoparticle nanostructures (like liposomes with encapsulated nanoparticles), which have diverse biomedical applications, including targeted therapy (drug delivery) and imaging of cancer cells.

Membrane sculpting by F-BAR domains studied by molecular dynamics simulations

Interplay between cellular membranes and their peripheral proteins drives many processes in eukaryotic cells. Proteins of the Bin/Amphiphysin/Rvs (BAR) domain family, in particular, play a role in cellular morphogenesis, for example curving planar membranes into tubular membranes. However, it is still unclear how F-BAR domain proteins act on membranes. Electron microscopy revealed that, in vitro, F-BAR proteins form regular lattices on cylindrically deformed membrane surfaces. Using all-atom and coarse-grained (CG) molecular dynamics simulations, we show that such lattices, indeed, induce tubes of observed radii. A 250 ns all-atom simulation reveals that F-BAR domain curves membranes via the so-called scaffolding mechanism. Plasticity of the F-BAR domain permits conformational change in response to membrane interaction, via partial unwinding of the domains 3-helix bundle structure. A CG simulation covering more than 350 µs provides a dynamic picture of membrane tubulation by lattices of F-BAR domains. A series of CG simulations identified the optimal lattice type for membrane sculpting, which matches closely the lattices seen through cryo-electron microscopy.

To generate organelles, eukaryotic cells sculpt their membranes into compartments, often employing proteins as chaperones, for example, F-BAR domains. The latter induce formation of tubular and vesicular membranes. Functional and structural studies suggest that F-BAR domains sculpt membranes through electrostatic interactions, driving the membrane to match the concave surface of the protein's banana-like shape. Cryo-electron microscopy (cryo-EM) studies provide an average static picture of how F-BAR domains form lattices on the surface of membranes to induce tube formation. Complementing the cryo-EM images, molecular dynamics simulations reported here offer a detailed, dynamic picture of membrane tubulation by a lattice of F-BAR domains and identified lattice types optimally attuned to producing high membrane curvature. The simulations reproduced also a process lasting 350 µs in which lattices of F-BAR domains form a complete tube out of an initially flat membrane. The molecular dynamics study offers, thereby, both a large-scale picture of membrane sculpting by F-BAR domain lattices as well as atomic-level dynamic information about the involvement of the individual F-BAR domain and its interactions with partner F-BAR domains and membrane in the sculpting process.

The role of cholesterol-sphingomyelin membrane nanodomains in the stability of intercellular membrane nanotubes

Intercellular membrane nanotubes (ICNs) are highly curved tubular structures that connect neighboring cells. The stability of these structures depends on the inner cytoskeleton and the cell membrane composition. Yet, due to the difficulty in the extraction of ICNs, the cell membrane composition remains elusive. In the present study, a raft marker, ostreolysin, revealed the enrichment of cholesterol-sphingomyelin membrane nanodomains along ICNs in a T24 (malignant) urothelial cancer cell line. Cholesterol depletion, due to the addition of methyl-β-cyclodextrin, caused the dispersion of cholesterol-sphingomyelin membrane nanodomains and the retraction of ICNs. The depletion of cholesterol also led to cytoskeleton reorganization and to formation of actin stress fibers. Live cell imaging data revealed the possible functional coupling between the change from polygonal to spherical shape, cell separation, and the disconnection of ICNs. The ICN was modeled as an axisymmetric tubular structure, enabling us to investigate the effects of cholesterol content on the ICN curvature. The removal of cholesterol was predicted to reduce the positive spontaneous curvature of the remaining membrane components, increasing their curvature mismatch with the tube curvature. The mechanisms by which the increased curvature mismatch could contribute to the disconnection of ICNs are discussed.

Membrane fission is promoted by insertion of amphipathic helices and is restricted by crescent BAR domains

Shallow hydrophobic insertions and crescent-shaped BAR scaffolds promote membrane curvature. Here, we investigate membrane fission by shallow hydrophobic insertions quantitatively and mechanistically. We provide evidence that membrane insertion of the ENTH domain of epsin leads to liposome vesiculation, and that epsin is required for clathrin-coated vesicle budding in cells. We also show that BAR-domain scaffolds from endophilin, amphiphysin, GRAF, and β2-centaurin limit membrane fission driven by hydrophobic insertions. A quantitative assay for vesiculation reveals an antagonistic relationship between amphipathic helices and scaffolds of N-BAR domains in fission. The extent of vesiculation by these proteins and vesicle size depend on the number and length of amphipathic helices per BAR domain, in accord with theoretical considerations. This fission mechanism gives a new framework for understanding membrane scission in the absence of mechanoenzymes such as dynamin and suggests how Arf and Sar proteins work in vesicle scission.

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.

Attachment of rod-like (BAR) proteins and membrane shape

Previous studies have shown that cellular function depends on rod-like membrane proteins, among them Bin/Amphiphysin/Rvs (BAR) proteins may curve the membrane leading to physiologically important membrane invaginations and membrane protrusions. The membrane shaping induced by BAR proteins has a major role in various biological processes such as cell motility and cell growth. Different models of binding of BAR domains to the lipid bilayer are described. The binding includes hydrophobic insertion loops and electrostatic interactions between basic amino acids at the concave region of the BAR domain and negatively charged lipids. To shed light on the elusive binding dynamics, a novel experiment is proposed to expand the technique of single-molecule AFM for the traction of binding energy of a single BAR domain.

Temperature and cholera toxin B are factors that influence formation of membrane nanotubes in RT4 and T24 urothelial cancer cell lines

The growth of membrane nanotubes is crucial for intercellular communication in both normal development and pathological conditions. Therefore, identifying factors that influence their stability and formation are important for both basic research and in development of potential treatments of pathological states. Here we investigate the effect of cholera toxin B (CTB) and temperature on two pathological model systems: urothelial cell line RT4, as a model system of a benign tumor, and urothelial cell line T24, as a model system of a metastatic tumor. In particular, the number of intercellular membrane nanotubes (ICNs; ie, membrane nanotubes that bridge neighboring cells) was counted. In comparison with RT4 cells, we reveal a significantly higher number in the density of ICNs in T24 cells not derived from RT4 without treatments (P = 0.005), after 20 minutes at room temperature (P = 0.0007), and following CTB treatment (P = 0.000025). The binding of CTB to GM1–lipid complexes in membrane exvaginations or tips of membrane nanotubes may reduce the positive spontaneous (intrinsic) curvature of GM1–lipid complexes, which may lead to lipid mediated attractive interactions between CTB–GM1–lipid complexes, their aggregation and consequent formation of enlarged spherical tips of nanotubes. The binding of CTB to GM1 molecules in the outer membrane leaflet of membrane exvaginations and tips of membrane nanotubes may also increase the area difference between the two leaflets and in this way facilitate the growth of membrane nanotubes.

Mechanical stability of membrane nanotubular protrusions influenced by attachment of flexible rod-like proteins

It is indicated that nonhomogeneous lateral distribution of membrane attached and flexible rod-like proteins (MRPs) may stabilize nanotubular membrane protrusions. We have shown that curvature induced accumulation of MRPs in the nanotubular membrane protrusion and the corresponding reduction of the membrane free energy are possible if the decrease of the deviatoric free energy of MRPs in the nanotubular protrusions is large enough to overcome the increase of the free energy due to decrease of configurational entropy in the process of lateral sorting of MRPs. The decrease of isotropic curvature energy of MRPs in the region of membrane protrusion is usually not sufficient for substantial MRPs sorting and consequent stabilization of the nanotubular membrane protrusions.

Diffusion of macromolecules on lipid vesicles

Diffusion of macromolecules on a surface of lipid vesicles of different reduced volume and geometry is investigated. It is assumed that the macromolecules deform the surface of the vesicles by inducing the spontaneous curvature which is proportional to their concentration. We study how nonuniform distribution of macromolecules is reflected in the shape of the vesicles and how the shape of the vesicles influences the diffusion process.

Physical model of contractile ring initiation in dividing cells

We present a physical mechanism to describe initiation of the contractile ring during cell division. The model couples the membrane curvature with the contractile forces produced by protein clusters attached to the membrane. These protein clusters are mobile on the membrane and possess either an isotropic or an anisotropic spontaneous curvature. Our results show that under these conditions the contraction force gives rise to an instability that corresponds in a closed cellular system to the initiation of the contractile ring. We find a quantization of this process at distinct length-scales, which we compare to available data for different types of eukaryote cells.

Possible role of flexible red blood cell membrane nanodomains in the growth and stability of membrane nanotubes

Tubular budding of the erythrocyte membrane may be induced by exogenously added substances. It is shown that tubular budding may be explained by self-assembly of anisotropic membrane nanodomains into larger domains forming nanotubular membrane protrusions. In contrast to some previously reported theories, no direct external mechanical force is needed to explain the observed tubular budding of the bilayer membrane. The mechanism that explains tubular budding may also be responsible for stabilization of the thin tubes that connect cells or cell organelles and which might be important for the transport of matter and information in cellular systems. It is shown that small carrier vesicles (gondolas), transporting enclosed material or the molecules composing their membrane, may travel over long distances along the nanotubes connecting two cells.