Spontaneous-curvature theory of clathrin-coated membranes

The morphological role of ligand inhibitors in blocking receptor- and clathrin-mediated endocytosis

Cells often internalize particles through endocytic pathways that involve the binding between cell receptors and particle ligands, which drives the cell membrane to wrap the particle into a delivery vesicle. Previous findings showed that receptor-mediated endocytosis is impossible for spherical particles smaller than a minimum size because of the energy barrier created by membrane bending. In this study, we investigate the morphological role of ligand inhibitors in blocking endocytosis, inspired by antibodies that inhibit virus ligands to prevent infection. While ligand inhibitors have the obvious effect of reducing the driving force due to adhesion, they also have a nontrivial (morphological) impact on the entropic and elastic energy of the system. We determine the necessary conditions for endocytosis by considering the additional energy barrier due to the membrane bending to wrap the inhibiting protrusions. We find that inhibitors increase the minimum radius previously reported, depending on their density and size. In addition, we extend this result to the case of clathrin-mediated endocytosis, which is the most common pathway for virus entry. The assembly of a clathrin coat with a spontaneous curvature increases the energy barrier and sets a maximum particle size (in agreement with experimental observations on spherical particles). Our investigation suggests that morphological considerations can inform the optimal design of neutralizing viral antibodies and new strategies for targeted nanomedicine.

Unfolding of Tryptophanoctyl Ester and Elastic Deformation of Host Micelles via RR'3 N+ ⋅⋅⋅π Interaction: Conceivable Relevance to Wrapping Process of Receptor Mediated Endocytosis

The interfacial properties of the mixed amphiphiles are modified by a stronger cation-π interaction between the quaternary ammonium head group of CTAB and the π-face of TROE, compared to the tyrosine analogue (TYOE). This eventually triggers a morphology transition through elastic deformation of the spherical micelles of CTAB to cylindrical/wormlike micelles. The unfolding of TROE and the molecular interactions in the nanoenvironment have been recognized by NMR spectroscopy and the physical characteristics of the entangled wormlike micelles are investigated by high resolution transmission electron microscopy (HRTEM), whereas the complex fluidic feature is examined by dynamic rheological measurements. Morphology tuning of the soft nanoaggregates of zwitterionic dodecylphosphocholine by the tryptophan analogue via choline-π interaction has unique biological consequences and we consider the significance of such interactions in facilitating endocytosis of a virion/nano particle(NP) in terms of a quantitative model. The implication in future research on drug development strategies is discussed.

Dynamic interplay between cell membrane tension and clathrin-mediated endocytosis

Deformability of the plasma membrane, the outermost surface of metazoan cells, allows cells to be dynamic, mobile and flexible. Factors that affect this deformability, such as tension on the membrane, can regulate a myriad of cellular functions, including membrane resealing, cell motility, polarisation, shape maintenance, membrane area control and endocytic vesicle trafficking. This review focuses on mechanoregulation of clathrin-mediated endocytosis (CME). We first delineate the origins of cell membrane tension and the factors that yield to its spatial and temporal fluctuations within cells. We then review the recent literature demonstrating that tension on the membrane is a fast-acting and reversible regulator of CME. Finally, we discuss tension-based regulation of endocytic clathrin coat formation during physiological processes.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

Shape selection and mis-assembly in viral capsid formation by elastic frustration

The successful assembly of a closed protein shell (or capsid) is a key step in the replication of viruses and in the production of artificial viral cages for bio/nanotechnological applications. During self-assembly, the favorable binding energy competes with the energetic cost of the growing edge and the elastic stresses generated due to the curvature of the capsid. As a result, incomplete structures such as open caps, cylindrical or ribbon-shaped shells may emerge, preventing the successful replication of viruses. Using elasticity theory and coarse-grained simulations, we analyze the conditions required for these processes to occur and their significance for empty virus self-assembly. We find that the outcome of the assembly can be recast into a universal phase diagram showing that viruses with high mechanical resistance cannot be self-assembled directly as spherical structures. The results of our study justify the need of a maturation step and suggest promising routes to hinder viral infections by inducing mis-assembly.

Entry modes of ellipsoidal nanoparticles on a membrane during clathrin-mediated endocytosis

The membrane wrapping and internalization of nanoparticles, such as viruses and drug nanocarriers, through clathrin-mediated endocytosis (CME) are vitally important for intracellular transport. During CME, the shape of the particle plays crucial roles in the determination of particle-membrane interactions, but much of the previous work has been focused on spherical particles. In this work, we develop a stochastic model to study the CME of ellipsoidal particles. In our model, the deformation of the membrane and wrapping of the nanoparticles are driven by the accumulation of clathrin lattices, which is stimulated by the ligand-receptor interactions. Using our model, we systematically investigate the effect of particle shape (ellipsoids with different aspect ratios) on the CME. Our results show three entry modes: tip-first, tilted, and laying-down modes, used by ellipsoidal nanoparticles for internalization depending on the aspect ratio. Certain ellipsoids are able to take multiple entry modes for internalization. Interestingly, the prolate ellipsoid with an aspect ratio of 0.42 can be internalized with a significantly reduced number of ligand-receptor bonds. Particles which can be internalized with fewer bonds are excellent candidates for transcellular drug delivery. Moreover, our results demonstrate that internalization of ellipsoids with intermediate aspect ratios is easier than that of particles with low and high aspect ratios. Our model and simulations provide critical mechanistic insights into CME of ellipsoidal particles, and represent a viable platform for optimal design of nanoparticles for targeted drug delivery applications.

Structure and Assembly of Clathrin Cages

The unusual structure of clathrin, combined with its ability to assemble and disassemble rapidly in cells provides a model system for us to learn about the ways in which proteins can contribute mechanically to a functioning cell. In this article, we discuss the structural properties of clathrin cages and the triskelions which assemble to form them. The function of clathrin depends on the structure of these triskelions and the interactions they make both with each other during assembly and with the adaptor protein network that drives coated vesicle formation. The atomic resolution structure of clathrin domains has been revealed by X-ray crystallography while scattering studies have enabled the shape of a triskelion in solution to be deduced. Cryo-electron microscopy maps have shown the secondary structure of entire cages, how individual triskelion legs are arranged to form a cage and enabled some bound adaptor proteins to be located. Cage formation itself is energetically finely balanced and requires specific interactions between triskelion legs to be productive, as biochemical studies and in silico modeling have shown. Theoretical, structural and cell biological investigations over many years have contributed to our knowledge of clathrin structure and assembly. It now remains to determine the precise nature of the interactions which occur between clathrin triskelions, light chain and heavy chain and the adaptor protein network.

Mechanics and Buckling of Biopolymeric Shells and Cell Nuclei

We study a Brownian dynamics simulation model of a biopolymeric shell deformed by axial forces exerted at opposing poles. The model exhibits two distinct, linear force-extension regimes, with the response to small tensions governed by linear elasticity and the response to large tensions governed by an effective spring constant that scales with radius as R^-0.25. When extended beyond the initial linear elastic regime, the shell undergoes a hysteretic, temperature-dependent buckling transition. We experimentally observe this buckling transition by stretching and imaging the lamina of isolated cell nuclei. Furthermore, the interior contents of the shell can alter mechanical response and buckling, which we show by simulating a model for the nucleus that quantitatively agrees with our micromanipulation experiments stretching individual nuclei.

Shape transitions during clathrin-induced endocytosis

Endocytosis is among the most common transport mechanisms which cells employ to receive macromolecules, the so-called cargo, from its extra cellular environment. Clathrin-mediated endocytosis (CME), in particular, involves the cytoplasmic protein clathrin which induces formation and internalization of clathrin-coated membrane buds that contain extra-cellular cargo. Decades of experimental work have established that the morphology of the clathrin coat evolves with time and induces its curvature on the membrane bud; but energetics of the process remain unclear. Recent experiments by Avinoam et al. [Science 348, 1369 (2015)SCIEAS0036-807510.1126/science.aaa9555] reported that the area of the clathrin coat remains fixed while its curvature increases with time and also the clathrin molecules in the coat turn over rapidly. We show that these observations challenge existing models of coated membrane bud formation. We analyze their data to bring out certain features consistent with the underlying lattice structure of the coat. We hypothesize that membrane curvature inhibits clathrin deposition and propose a kinetic model that explains the area distribution of clathrin coats. We also show that their data on shape evolution of the coated membrane bud can be approximately understood from simple geometric considerations. However, the energetics of the coat formation which controls the kinetics of the process remains a puzzle.

Bud-neck scaffolding as a possible driving force in ESCRT-induced membrane budding

Membrane budding is essential for processes such as protein sorting and transport. Recent experimental results with ESCRT proteins reveal a novel budding mechanism, with proteins emerging in bud necks but separated from the entire bud surface. Using an elastic model, we show that ESCRT protein shapes are sufficient to spontaneously create experimentally observed structures, with protein-membrane interactions leading to protein scaffolds in bud-neck regions. Furthermore, the model reproduces experimentally observed budding directions and bud sizes. Finally, our results reveal that membrane-mediated sorting has the capability of creating structures more complicated than previously assumed.

On the modeling of endocytosis in yeast

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Results of experiments on endocytosis in yeast show general agreement that 1) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it, and 2) the large-scale membrane deformation is tubular in shape. In contrast, there are three competing proposals for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: 1) initiation, where clathrin interacts with the membrane via adaptor proteins; 2) elongation, where the membrane is then further deformed by polymerizing actin filaments; and 3) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed.

Nonuniform growth and topological defects in the shaping of elastic sheets

We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified. With this connection, we study the problem of choosing an optimal pattern of growth for a prescribed developable surface, finding a fundamental trade-off between optimal design and the accuracy of the resulting shape which can be quantified by the length along which an edge should be identified.

AP2 hemicomplexes contribute independently to synaptic vesicle endocytosis

The clathrin adaptor complex AP2 is thought to be an obligate heterotetramer. We identify null mutations in the α subunit of AP2 in the nematode Caenorhabditis elegans. α-adaptin mutants are viable and the remaining μ2/β hemicomplex retains some function. Conversely, in μ2 mutants, the alpha/sigma2 hemicomplex is localized and is partially functional. α-μ2 double mutants disrupt both halves of the complex and are lethal. The lethality can be rescued by expression of AP2 components in the skin, which allowed us to evaluate the requirement for AP2 subunits at synapses. Mutations in either α or μ2 subunits alone reduce the number of synaptic vesicles by about 30%; however, simultaneous loss of both α and μ2 subunits leads to a 70% reduction in synaptic vesicles and the presence of large vacuoles. These data suggest that AP2 may function as two partially independent hemicomplexes. DOI:http://dx.doi.org/10.7554/eLife.00190.001.

Kinematics, material symmetry, and energy densities for lipid bilayers with spontaneous curvature

Continuum mechanical tools are used to describe the deformation, energy density, and material symmetry of a lipid bilayer with spontaneous curvature. In contrast to conventional approaches in which lipid bilayers are modeled by material surfaces, here we rely on a three-dimensional approach in which a lipid bilayer is modeling by a shell-like body with finite thickness. In this setting, the interface between the leaflets of a lipid bilayer is assumed to coincide with the mid-surface of the corresponding shell-like body. The three-dimensional deformation gradient is found to involve the curvature tensors of the mid-surface in the spontaneous and the deformed states, the deformation gradient of the mid-surface, and the transverse deformation. Attention is also given to the coherency of the leaflets and to the area compatibility of the closed lipid bilayers (i.e., vesicles). A hyperelastic constitutive theory for lipid bilayers in the liquid phase is developed. In combination, the requirements of frame indifference and material symmetry yield a representation for the energy density of a lipid bilayer. This representation shows that three scalar invariants suffice to describe the constitutive response of a lipid bilayer exhibiting in-plane fluidity and transverse isotropy. In addition to exploring the geometrical and physical properties of these invariants, fundamental constitutively associated kinematical quantities are emphasized. On this basis, the effect on the energy density of assuming that the lipid bilayer is incompressible is considered. Lastly, a dimension reduction argument is used to extract an areal energy density per unit area from the three-dimensional energy density. This step explains the origin of spontaneous curvature in the areal energy density. Importantly, along with a standard contribution associated with the natural curvature of the lipid bilayer, our analysis indicates that constitutive asymmetry between the leaflets of the lipid bilayer gives rise to a secondary contribution to the spontaneous curvature.

Stochastic model of clathrin-coated pit assembly

In recent years, fluorescence microscopy has enabled researchers to observe the dynamics of clathrin-coated pit (CCP) assembly in real time. The assembly dynamics of CCPs shows striking heterogeneity. Some CCPs are long-lived (productive CCPs); they bind cargo and grow in size to form clathrin-coated vesicles. In contrast, other CCPs (abortive CCPs) are relatively short-lived and disassemble well before reaching vesicle size. Within both populations there is significant variance in CCP lifetime. We propose a stochastic biophysical model that links these observations with the energetics of CCPs and kinetics of their assembly. We show that without cargo, CCP assembly faces a high energy barrier that is difficult to overcome. As a consequence, CCPs without cargo are almost always abortive. We suggest a mechanism by which cargo binding stabilizes CCPs and facilitates their growth. The lifetime distribution of abortive pits calculated from our model agrees well with published experimental data. We also estimate the lifetimes of productive CCPs and show that the stochastic nature of CCP assembly plays a crucial role in causing their observed wide distribution.

The generation of curved clathrin coats from flat plaques

Flat clathrin lattices or 'plaques' are commonly believed to be the precursors to clathrin-coated buds and vesicles. The sequence of steps carrying the flat hexagonal lattice into a highly curved polyhedral cage with exactly 12 pentagons remains elusive, however, and the large numbers of disrupted interclathrin connections in previously proposed conversion pathways make these scenarios rather unlikely. The recent notion that clathrin can make controlled small conformational transitions opens new avenues. Simulations with a self-assembling clathrin model suggest that localized conformational changes in a plaque can create sufficiently strong stresses for a dome-like fragment to break apart. The released fragment, which is strongly curved but still hexagonal, may subsequently grow into a cage by recruiting free triskelia from the cytoplasm, thus building all 12 pentagonal faces without recourse to complex topological changes. The critical assembly concentration in a slightly acidic in vitro solution is used to estimate the binding energy of a cage at 25-40 k(B) T/clathrin.

Membrane Curvature Induced by Sugar and Polymer Solutions

We monitor the effect of transversal membrane asymmetry on the morphology of giant uni-lamellar vesicles in sugar and polymer solutions. The shapes of fluid lipid vesicles are governed by the bending elasticity of their membrane which is characterized by the bending modulus and the spontaneous curvature of the bilayer. We present a recently developed technique for the measurement of the spontaneous curvature using quantitative phase contrast microscopy. Different mechanisms for elastic membrane asymmetry and the role of the bending energy concept for the morphology of cellular organelles are discussed.

Size-dependent endocytosis of gold nanoparticles studied by three-dimensional mapping of plasmonic scattering images

Background

Understanding the endocytosis process of gold nanoparticles (AuNPs) is important for the drug delivery and photodynamic therapy applications. The endocytosis in living cells is usually studied by fluorescent microscopy. The fluorescent labeling suffers from photobleaching. Besides, quantitative estimation of the cellular uptake is not easy. In this paper, the size-dependent endocytosis of AuNPs was investigated by using plasmonic scattering images without any labeling.

Results

The scattering images of AuNPs and the vesicles were mapped by using an optical sectioning microscopy with dark-field illumination. AuNPs have large optical scatterings at 550-600 nm wavelengths due to localized surface plasmon resonances. Using an enhanced contrast between yellow and blue CCD images, AuNPs can be well distinguished from cellular organelles. The tracking of AuNPs coated with aptamers for surface mucin glycoprotein shows that AuNPs attached to extracellular matrix and moved towards center of the cell. Most 75-nm-AuNPs moved to the top of cells, while many 45-nm-AuNPs entered cells through endocytosis and accumulated in endocytic vesicles. The amounts of cellular uptake decreased with the increase of particle size.

Conclusions

We quantitatively studied the endocytosis of AuNPs with different sizes in various cancer cells. The plasmonic scattering images confirm the size-dependent endocytosis of AuNPs. The 45-nm-AuNP is better for drug delivery due to its higher uptake rate. On the other hand, large AuNPs are immobilized on the cell membrane. They can be used to reconstruct the cell morphology.

Modeling membrane deformations and lipid demixing upon protein-membrane interaction: the BAR dimer adsorption

We use a self-consistent mean-field theory, designed to investigate membrane reshaping and lipid demixing upon interaction with proteins, to explore BAR domains interacting with large patches of lipid membranes of heterogeneous compositions. The computational model includes contributions to the system free energy from electrostatic interactions and elastic energies of the membrane, as well as salt and lipid mixing entropies. The results from our simulation of a single adsorbing Amphiphysin BAR dimer indicate that it is capable of stabilizing a significantly curved membrane. However, we predict that such deformations will occur only for membrane patches that have the inherent propensity for high curvature, reflected in the tendency to create local distortions that closely match the curvature of the BAR dimer itself. Such favorable preconditioning for BAR-membrane interaction may be the result of perturbations such as local lipid demixing induced by the interaction, or of a prior insertion of the BAR domain's amphiphatic N-helix. From our simulations it appears that local segregation of charged lipids under the influence of the BAR dimer cannot produce high enough asymmetry between bilayer leaflets to induce significant bending. In the absence of additional energy contributions that favor membrane asymmetry, the membrane will remain nearly flat upon single BAR dimer adsorption, relative to the undulation expected from thermal fluctuations. Thus, we conclude that the N-helix insertions have a critical mechanistic role in the local perturbation and curving of the membrane, which is then stabilized by the electrostatic interaction with the BAR dimer. We discuss how these results can be used to estimate the tendency of BARs to bend membranes in terms of a spatially nonisotropic spontaneous curvature.

Architecture of clathrin fullerene cages reflects a geometric constraint--the head-to-tail exclusion rule--and a preference for asymmetry

Fullerene cages have n trivalent vertices, 12 pentagonal faces, and (n-20)/2 hexagonal faces. The smallest cage in which all of the pentagons are surrounded by hexagons and thus isolated from each other has 60 vertices and is shaped like a soccer ball. The protein clathrin self-assembles into fullerene cages of a variety of sizes and shapes, including smaller ones with adjacent pentagons as well as larger ones, but the variety is limited. To explain the range of clathrin architecture and how these fullerene cages self-assemble, we proposed a hypothesis, the "head-to-tail exclusion rule" (the "Rule"). Of the 5769 small clathrin cage isomers with n< or =60 vertices and adjacent pentagons, the Rule permits just 15, three identified in 1976 and 12 others. A "weak version" of the Rule permits another 99. Based on cryo-electron tomography, Cheng et al. reported six raw clathrin fullerene cages. One was among the three identified in 1976. Here, (1) we identify the remaining five. (2) Four are new and are among the 12 others permitted by the Rule. (3) One, also new, is among the 99 weak version cages. (4) Of particular note, none of the remaining 5565 excluded cages has been identified. These findings provide powerful experimental confirmation of the Rule and the principle on which it is based. (5) Surprisingly, the newly identified clathrin cages are among the least symmetric of those permitted. (6) By devising a method for counting assembly paths, (7) we show that asymmetric cages can be assembled by larger numbers of paths, thus providing a kinetic explanation for the prevalence of asymmetric cages. (8) Finally, we show that operation during cage growth of the Rule greatly increases the likelihood of producing a closed fullerene cage, specifically one of those permitted, but efficient assembly still appears to require internal remodeling.

Size-dependent cellular uptake and expulsion of single-walled carbon nanotubes: single particle tracking and a generic uptake model for nanoparticles

The cellular uptake and expulsion rates of length-fractionated single-walled carbon nanotubes (SWNT) from 130 to 660 nm in NIH-3T3 cells were measured via single particle tracking of their intrinsic photoluminescence. We develop a quantitative model to correlate endocytosis rate with nanoparticle geometry that accurately describes this data set and also literature results for Au nanoparticles. The model asserts that nanoparticles cluster on the cell membrane to form a size sufficient to generate a large enough enthalpic contribution via receptor ligand interactions to overcome the elastic energy and entropic barriers associated with vesicle formation. Interestingly, the endocytosis rate constant of SWNT (10(-3) min(-1)) is found to be nearly 1000 times that of Au nanoparticles (10(-6) min(-1)) but the recycling (exocytosis) rate constants are similar in magnitude (10(-4) to 10(-3) min(-1)) for poly(d,l-lactide-co-glycolide), SWNT, and Au nanoparticles across distinct cell lines. The total uptake of both SWNT and Au nanoparticles is maximal at a common radius of 25 nm when scaled using an effective capture dimension for membrane diffusion. The ability to understand and predict the cellular uptake of nanoparticles quantitatively should find utility in designing nanosystems with controlled toxicity, efficacy, and functionality.

A geometric principle may guide self-assembly of fullerene cages from clathrin triskelia and from carbon atoms

Clathrin triskelia and carbon atoms alike self-assemble into a limited selection of fullerene cages (with n three connected vertices, 3n/2 edges, 12 pentagonal faces, and (n-20)/2 hexagonal faces). We show that a geometric constraint-exclusion of head-to-tail dihedral angle discrepancies (DADs)-explains this limited selection as well as successful assembly into such closed cages in the first place. An edge running from a pentagon to a hexagon has a DAD, since the dihedral angles about the edge broaden from its pentagon (tail) end to its hexagon (head) end. Of the 21 configurations of a central face and surrounding faces, six have such DAD vectors arranged head-to-tail. Of the 5770 mathematically possible fullerene cages for n <or= 60, excluding those with any of the six configurations leaves just 15 cages plus buckminsterfullerene (n = 60), among them the known clathrin cages. Of the 216,739 mathematically possible cages for 60 < n <or= 84, just the 50 that obey the isolated-pentagon rule, among them known carbon cages, pass. The absence of likely fullerenes for some n (30,34,46,48,52-58,62-68) explains the abundance of certain cages, including buckminsterfullerene. These principles also suggest a "probable roads" path to self-assembly in place of pentagon-road and fullerene-road hypotheses.

The physical basis for the head-to-tail rule that excludes most fullerene cages from self-assembly

In the companion article, we proposed that fullerene cages with head-to-tail dihedral angle discrepancies do not self-assemble. Here we show why. If an edge abuts a pentagon at one end and a hexagon at the other, the dihedral angle about the edge increases, producing a dihedral angle discrepancy (DAD) vector. The DADs about all five/six edges of a central pentagonal/hexagonal face are determined by the identities-pentagon or hexagon-of its five/six surrounding faces. Each "Ring"-central face plus specific surrounding faces-may have zero, two, or four edges with DAD. In most Rings, the nonplanarity induced by DADs is shared among surrounding faces. However, in a Ring that has DADs arranged head of one to tail of another, the nonplanarity cannot be shared, so some surrounding faces would be especially nonplanar. Because the head-to-tail exclusion rule is an implicit geometric constraint, the rule may operate either by imposing a kinetic barrier that prevents assembly of certain Rings or by imposing an energy cost that makes those Rings unlikely to last in an equilibrium circumstance. Since Rings with head-to-tail DADs would be unlikely to self-assemble or last, fullerene cages with those Rings would be unlikely to self-assemble.

Shape transitions in lipid membranes and protein mediated vesicle fusion and fission

In the cell, the plasma membrane is often densely decorated by transmembrane proteins. The morphology and dynamics of the membrane are strongly influenced by the presence of proteins. In this paper, we use a coarse-grained model to explore the composite membrane-protein system and develop a simulation methodology based on thermodynamic integration to examine free energy changes during membrane shape transitions. The authors show that a critical concentration of conical membrane proteins or proteins with nonzero spontaneous curvature can drive the formation of small vesicles. The driving force of vesicle budding stems from the preference of proteins to gather in regions of high curvature. A sufficiently high concentration of proteins therefore can influence the topology of the membrane. The biological significance of our results is discussed.

Crystalline Protein Domains and Lipid Bilayer Vesicle Shape Transformations

Cellular membranes can take on a variety of shapes to assist biological processes including endocytosis. Membrane-associated protein domains provide a possible mechanism for determining membrane curvature. We study the effect of tethered streptavidin protein crystals on the curvature of giant unilamellar vesicles (GUVs) using confocal, fluorescence, and differential interference contrast microscopy. Above a critical protein concentration, streptavidin domains align and percolate as they form, deforming GUVs into prolate spheroidal shapes in a size-dependent fashion. We propose a mechanism for this shape transformation based on domain growth and jamming. Osmotic deflation of streptavidin-coated GUVs reveals that the relatively rigid streptavidin protein domains resist membrane bending. Moreover, in contrast to highly curved protein domains that facilitate membrane budding, the relatively flat streptavidin domains prevent membrane budding under high osmotic stress. Thus, crystalline streptavidin domains are shown to have a stabilizing effect on lipid membranes. Our study gives insight into the mechanism for protein-mediated stabilization of cellular membranes.

Bending a membrane: how clathrin affects budding

Receptor-mediated endocytosis of ligands, such as transferrin and LDL, is suppressed when clathrin synthesis is blocked by RNA interference in HeLa cells. We have found that domains containing the adapter complex 2 (AP2)-coated vesicle adapter and the endocytic accessory proteins CALM (clathrin assembly lymphoid myeloid leukemia protein), epsin, and eps15/eps15R (EGF receptor pathway substrate 15-related) nevertheless persist at the plasma membrane. They are similar in size and number to those seen in clathrin-expressing cells. Here we characterize these membrane domains by fluorescence and electron microscopy in detail. Fluorescence recovery after photobleaching measurements suggest that the exchange between membrane-bound and free cytosolic AP2 molecules is not significantly influenced by the depletion of clathrin. The AP2 membrane domains are dispersed upon interfering with protein-protein interactions that involve the alpha appendage domain of AP2. Electron microscopy of cellular cortices revealed that the AP2 membrane domains lack any curvature, suggesting that clathrin is essential for driving coated pit invagination. A model for coated vesicle formation, incorporating a mechanism commonly referred to as a "Brownian ratchet," is consistent with our observations.

Membrane curvature and mechanisms of dynamic cell membrane remodelling

Membrane curvature is no longer seen as a passive consequence of cellular activity but an active means to create membrane domains and to organize centres for membrane trafficking. Curvature can be dynamically modulated by changes in lipid composition, the oligomerization of curvature scaffolding proteins and the reversible insertion of protein regions that act like wedges in membranes. There is an interplay between curvature-generating and curvature-sensing proteins during vesicle budding. This is seen during vesicle budding and in the formation of microenvironments. On a larger scale, membrane curvature is a prime player in growth, division and movement.

Mechanics of receptor-mediated endocytosis

Most viruses and bioparticles endocytosed by cells have characteristic sizes in the range of tens to hundreds of nanometers. The process of viruses entering and leaving animal cells is mediated by the binding interaction between ligand molecules on the viral capid and their receptor molecules on the cell membrane. How does the size of a bioparticle affect receptor-mediated endocytosis? Here, we study how a cell membrane containing diffusive mobile receptors wraps around a ligand-coated cylindrical or spherical particle. It is shown that particles in the size range of tens to hundreds of nanometers can enter or exit cells via wrapping even in the absence of clathrin or caveolin coats, and an optimal particles size exists for the smallest wrapping time. This model can also be extended to include the effect of clathrin coat. The results seem to show broad agreement with experimental observations.

Theoretical model for the formation of caveolae and similar membrane invaginations

We study a physical model for the formation of bud-like invaginations on fluid lipid membranes under tension, and apply this model to caveolae formation. We demonstrate that budding can be driven by membrane-bound proteins, provided that they exert asymmetric forces on the membrane that give rise to bending moments. In particular, caveolae formation does not necessarily require forces to be applied by the cytoskeleton. Our theoretical model is able to explain several features observed experimentally in caveolae, where proteins in the caveolin family are known to play a crucial role in the formation of caveolae buds. These include 1), the formation of caveolae buds with sizes in the 100-nm range and 2), that certain N- and C-termini deletion mutants result in vesicles that are an order-of-magnitude larger. Finally, we discuss the possible origin of the morphological striations that are observed on the surfaces of the caveolae.

Budding of crystalline domains in fluid membranes

Crystalline domains embedded in fluid membrane vesicles are studied by Monte Carlo simulations of dynamically triangulated surfaces and by scaling arguments. A budding transition from a caplike state to a budded shape is observed for increasing spontaneous curvature C0 of the crystalline domain as well as increasing line tension lambda. The location of the budding transition is determined as a function of C0, lambda, and the radius R(A) of the crystalline domain. In contrast to previous theoretical predictions, it is found that budding occurs at a value of the spontaneous curvature C0, that is always a decreasing function of the domain size R(A). Several characteristic scaling regimes are predicted. The distribution of five- and sevenfold disclinations as the budding transition is approached is determined, and the dynamics of the generation of defects is studied.

Interactions between proteins bound to biomembranes

We study a physical model for the interaction between general inclusions bound to fluid membranes that possess finite tension gamma, as well as the usual bending rigidity kappa. We are motivated by an interest in proteins bound to cell membranes that apply forces to these membranes, due to either entropic or direct chemical interactions. We find an exact analytic solution for the repulsive interaction between two similar circularly symmetric inclusions. This repulsion extends over length scales approximately sqrt[kappa/gamma] and contrasts with the membrane-mediated contact attraction for similar inclusions on tensionless membranes. For noncircularly symmetric inclusions we study the small, algebraically long-ranged, attractive contribution to the force that arises. We discuss the relevance of our results to biological phenomena, such as the budding of caveolae from cell membranes and the striations that are observed on their coats. These, and other, "gnarly buds" may prove fascinating to study further.

Energetics of clathrin basket assembly

A minimal thermodynamic model is used to study the in vitro equilibrium assembly of reconstituted clathrin baskets. The model contains parameters accounting for i) the combined bending and flexing rigidities of triskelion legs and hubs, ii) the intrinsic curvature of an isolated triskelion, and iii) the free energy changes associated with interactions between legs of neighboring triskelions. Analytical expressions for basket size distributions are derived, and published size distribution data (Zaremba S, Keen JH. J Cell Biol 1983;97: 1339-1347) are then used to provide estimates for net total basket assembly energies. Results suggest that energies involved in adding triskelions to partially formed clathrin lattices are small (of the order of kBT), in accord with the notion that lattice remodeling during basket formation occurs as a result of thermodynamic fluctuations. In addition, analysis of data showing the effects of assembly proteins (APs) on basket size indicates that the binding of APs increases the intrinsic curvature of an elemental triskelial subunit, the stabilizing energy of leg interactions, and the effective leg/hub rigidity. Values of effective triskelial rigidity determined in this investigation are similar to those estimated by previous analysis of shape fluctuations of isolated triskelia.

Endocytosis switch controlled by transmembrane osmotic pressure and phospholipid number asymmetry

The dynamics of endocytosis in living K562 cells was investigated after the osmotic pressure of the external medium was decreased and the transmembrane phospholipid number asymmetry was increased. When the external pressure was decreased by a factor of 0.54, a sudden inhibition of endocytosis was observed. Under these conditions, the endocytosis suddenly recovered after the phospholipid number asymmetry was increased. The phospholipid asymmetry was generated by the addition of exogenous phosphatidylserine, which is translocated by the endogenous flippase activity to the inner layer of the membrane. The recovery of endocytosis is thus consistent with the view that the phospholipid number asymmetry can act as a budding force for endocytosis. Moreover, we quantitatively predict both the inhibition and recovery of endocytosis as first-order phase transitions, using a general model that assumes the existence of a transmembrane surface tension asymmetry as the budding driving force. In this model, the tension asymmetry is considered to be elastically generated by the activity of phospholipid pumping. We finally propose that cells may trigger genetic transcription responses after the internalization of cytokine-receptor complexes, which could be controlled by variations in the cytosolic or external pressure.

Amplitude hierarchy of vesicle shapes

Shapes of fluid lipid vesicles are governed by the bending elasticity of their membrane as described by the Area-Difference-Elasticity (ADE) model. These shapes can be quantified using a suitable modal representation of the vesicle contour. Prolate vesicles are characterized by a hierarchy in their shape amplitudes. Experimentally, we find an ordering of the amplitudes with mode number both in large (100 nm) as well as giant (10 μm) unilamellar vesicles. Mean shapes are found only within the small energetically stable region of the prolate phase. Our study demonstrates that bending energy concepts may be quantitatively used on cellular length scales ranging from the size of organelles to the plasma membrane.

Human proteolipid protein (PLP) mediates winding and adhesion of phospholipid membranes but prevents their fusion

Proteolipid protein (PLP or lipophilin) is a highly conserved, strongly hydrophobic, integral membrane protein, and is the major protein component of central nervous system myelin. Although PLP has been implicated in many functions, its in vivo role is still uncertain. Here, we report the investigation of PLP's putative adhesive function using purified PLP and reconstituted phospholipid vesicles made of either 100% phosphatidylcholine (PC), or a mixture of 92% PC and 8% phosphatidylserine (PS), by weight. PLP-induced changes in the phospholipid bilayer surfaces were directly examined by transmission electron microscopy. We found that upon the introduction of PLP, larger lipid vesicles became smaller and unilamellar. At the PLP:lipid molar ratio of 1:20, vesicle membranes rolled onto themselves forming 'croissant'-like structures that subsequently adhered to each other. The phenomena of PLP-induced bilayer rolling and adhesion were dependent on the concentration of PLP and the period of incubation, but were independent of the presence of calcium and types of phospholipids (PC or PC:PS). Furthermore, the presence of PLP in the lipid bilayers prevented the fusion of membranes. These findings show that PLP can induce membrane 'winding' while preventing the fusion of adjacent lipid bilayers. Hence, our data provide direct evidence for PLP's suspected function of membrane adhesion, and also suggest that PLP could potentially play a role in the formation of the myelin sheath.