Formation and Stability of Lipid Membrane Nanotubes

Membrane-mediated interactions between arc-shaped particles strongly depend on membrane curvature

Besides direct molecular interactions, proteins and nanoparticles embedded in or adsorbed to membranes experience indirect interactions that are mediated by the membranes. Membrane-mediated interactions between curvature-inducing proteins or nanoparticles can lead to assemblies of particles that generate highly curved spherical or tubular membrane shapes, but have mainly been quantified for planar or weakly curved membranes. In this article, we systematically investigate the membrane-mediated interactions of arc-shaped particles adsorbed to a variety of tubular and spherical membrane shapes with coarse-grained modelling and simulations. These arc-shaped particles induce membrane curvature by binding to the membrane with their inner, concave side akin to N-BAR domain proteins. We determine both the pairwise interaction free energy, which includes entropic contributions due to rotational entropy loss at close particle distances, and the pairwise interaction energy without entropic components from particle distributions observed in the simulations. For membrane shapes with small curvature, the membrane-mediated interaction free energies of particle pairs exceed the thermal energy kBT and can lead to particle ordering and aggregation. The interactions strongly decrease with increasing curvature of the membrane shape and are minimal for tubular shapes with membrane curvatures close to the particle curvature.

Membrane nanotubes transform into double-membrane sheets at condensate droplets

Cellular membranes exhibit a multitude of highly curved morphologies such as buds, nanotubes, cisterna-like sheets defining the outlines of organelles. Here, we mimic cell compartmentation using an aqueous two-phase system of dextran and poly(ethylene glycol) encapsulated in giant vesicles. Upon osmotic deflation, the vesicle membrane forms nanotubes, which undergo surprising morphological transformations at the liquid-liquid interfaces inside the vesicles. At these interfaces, the nanotubes transform into cisterna-like double-membrane sheets (DMS) connected to the mother vesicle via short membrane necks. Using super-resolution (stimulated emission depletion) microscopy and theoretical considerations, we construct a morphology diagram predicting the tube-to-sheet transformation, which is driven by a decrease in the free energy. Nanotube knots can prohibit the tube-to-sheet transformation by blocking water influx into the tubes. Because both nanotubes and DMSs are frequently formed by cellular membranes, understanding the formation and transformation between these membrane morphologies provides insight into the origin and evolution of cellular organelles.

Defining permeability of curved membranes in molecular dynamics simulations

Many phospholipid membranes in the cell have a high curvature; for instance, in caveolae, mitochondrial crystae, nanotubes, membrane pearls, small liposomes, or exosomes. Molecular dynamics (MD) simulations are a computational tool to gain insight in the transport behavior at the atomic scale. Membrane permeability is a key kinetic property that might be affected in these highly curved membranes. Unfortunately, the geometry of highly curved membranes creates ambiguity in the permeability value, even with an arbitrarily large factor purely based on geometry, caused by the radial flux not being a constant value in steady state. In this contribution, the ambiguity in permeability for liposomes is countered by providing a new permeability definition. First, the inhomogeneous solubility diffusion model based on the Smoluchowski equation is solved analytically under radial symmetry, from which the entrance and escape permeabilities are defined. Next, the liposome permeability is defined guided by the criterion that a flat and curved membrane should have equal permeability, in case these were to be carved out from an imaginary homogeneous medium. With this criterion, our new definition allows for a fair comparison of flat and curved membranes. The definition is then transferred to the counting method, which is a practical computational approach to derive permeability by counting complete membrane crossings. Finally, the usability of the approach is illustrated with MD simulations of diphosphatidylcholine (DPPC) bilayers, without or with some cholesterol content. Our new liposome permeability definition allows us to compare a spherically shaped membrane with its flat counterpart, thus showcasing how the curvature effect on membrane transport may be assessed.

Stability of Branched Tubular Membrane Structures

We study the energetics and stability of branched tubular membrane structures by computer simulations of a triangulated network model. We find that triple (Y) junctions can be created and stabilized by applying mechanical forces, if the angle between branches is 120°. The same holds for tetrahedral junctions with tetraeder angles. If the wrong angles are enforced, the branches coalesce to a linear structure, a pure tube. After releasing the mechanical force, Y-branched structures remain metastable if one constrains the enclosed volume and the average curvature (the area difference) to a fixed value; tetrahedral junctions however split up into two Y junctions. Somewhat counterintuitively, the energy cost of adding a Y branch is negative in structures with fixed surface area and tube diameter, even if one accounts for the positive contribution of the additional branch end. For fixed average curvature, however, adding a branch also enforces a thinning of tubes, therefore the overall curvature energy cost is positive. Possible implications for the stability of branched networks structures in cells are discussed.

Endosomal lipid signaling reshapes the endoplasmic reticulum to control mitochondrial function

Cells respond to fluctuating nutrient supply by adaptive changes in organelle dynamics and in metabolism. How such changes are orchestrated on a cell-wide scale is unknown. We show that endosomal signaling lipid turnover by MTM1, a phosphatidylinositol 3-phosphate [PI(3)P] 3-phosphatase mutated in X-linked centronuclear myopathy in humans, controls mitochondrial morphology and function by reshaping the endoplasmic reticulum (ER). Starvation-induced endosomal recruitment of MTM1 impairs PI(3)P-dependent contact formation between tubular ER membranes and early endosomes, resulting in the conversion of ER tubules into sheets, the inhibition of mitochondrial fission, and sustained oxidative metabolism. Our results unravel an important role for early endosomal lipid signaling in controlling ER shape and, thereby, mitochondrial form and function to enable cells to adapt to fluctuating nutrient environments.

Compartmentalizing and sculpting nanovesicles by phase-separated aqueous nanodroplets

Phase-separated liquid droplets inside giant vesicles have been intensely studied as biomimetic model systems to understand cellular microcompartmentation and molecular crowding and sorting. On the nanoscale, however, how aqueous nanodroplets interact with and shape nanovesicles is poorly understood. We perform coarse-grained molecular simulations to explore the architecture of compartmentalized nanovesicles by phase-separated aqueous nanodroplets, and their morphological evolution under osmotic deflation. We show that phase separation of a biphasic liquid mixture can form both stable two-compartment and meta-stable multi-compartment nanovesicles. We identify morphological transitions of stable two-compartment nanovesicles between tube, sheet and cup morphologies, characterized by membrane asymmetry and phase-separation propensity between the aqueous phases. We demonstrate that the formation of local sheets and in turn cup-shaped nanovesicles is promoted by negative line tensions resulting from large separation propensities, an exclusive nanoscale phenomenon which is not expected for larger vesicles where energetic contributions of the line tensions are dominated by those of the membrane tensions. Despite their instability, we observe long-lived multi-compartment nanovesicles, such as nanotubules and branched tubules, whose prolonged lifetime is attributed to interfacial tensions and membrane asymmetry. Aqueous nanodroplets can thus form novel membrane nanostructures, crucial for cellular processes and forming cellular organelles on the nanoscale.

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.

Lipid nanotubes: Formation and applications

Lipids, the fundamental components of cell membrane, play important roles in the whole cycle of cell life, thus attracting worldwide attention, owing to their physicochemical property and extensive use in the applications based on lipid assemblies. Compared with liposomes, lipid nanotubes (LNTs) usually possess unique properties, such as highly ordered structure, precise molecular recognition, and the possibility of substance transport, thus providing more potential applications in different research fields. However, until now, there are still quite rare cases of LNTs successfully employed in practical applications. Bearing this in mind and based on our own experience in this field, we summarized and discussed the recent progress of the fabrication approaches and representative applications of the LNTs in the past decade, which would potentially provide basic understanding and guidance towards their future development.

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff–Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a ‘phase diagram’ for its symmetric and broken-symmetry states.

From reversible to irreversible: When the membrane nanotube pearling is coupled with phase separation

Membrane nanotubes, which are ubiquitous in biology and act as channels maintaining transport between different cells and organelles, readily undergo pearling in response to external stimuli. Membrane nanotube pearling involves generation of heterogeneous curvature coupled with redistribution of membrane components that may interfere with the shape recovery of pearled nanotubes. However, the mechanism underlying such delicate process remains unclear and difficult to study at the molecular scale in vivo. By means of molecular dynamics simulation, here we investigate pearling of multi-component membrane nanotubes and reversibility through manipulating system temperature and osmotic pressure. With the equilibrium shape of membrane nanotubes controlled by the osmotic pressure, our results demonstrate that the process of membrane nanotube pearling can be reversible or irreversible, depending on the phase segregation state. For the pearled nanotube releasing high surface energy, different lipid components redistribute along the tube axial direction. Lipids with unsaturated tails prefer gathering at the high-curvature shrinking region, whereas the swelling region is constituted by saturated lipids forming the liquid-ordered phase of a higher bending rigidity. Such curvature sensitive phase segregation minimizes the system free energy by reducing both the membrane bending energy and line tension at the phase boundary. As such, the pearled nanotube fails to recover its shape upon retracting stimuli, suggesting irreversibility of the membrane nanotube pearling coupled with phase separation. Given importance of membrane nanotube pearling in various cellular activities, these results provide a new mechanism of controlling equilibrium shapes of membrane nanotubes in complex cellular environment.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

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.

Controlled division of cell-sized vesicles by low densities of membrane-bound proteins

The proliferation of life on earth is based on the ability of single cells to divide into two daughter cells. During cell division, the plasma membrane undergoes a series of morphological transformations which ultimately lead to membrane fission. Here, we show that analogous remodeling processes can be induced by low densities of proteins bound to the membranes of cell-sized lipid vesicles. Using His-tagged fluorescent proteins, we are able to precisely control the spontaneous curvature of the vesicle membranes. By fine-tuning this curvature, we obtain dumbbell-shaped vesicles with closed membrane necks as well as neck fission and complete vesicle division. Our results demonstrate that the spontaneous curvature generates constriction forces around the membrane necks and that these forces can easily cover the force range found in vivo. Our approach involves only one species of membrane-bound proteins at low densities, thereby providing a simple and extendible module for bottom-up synthetic biology.

Membrane fission of a cell into two daughters is a core ability of cell-based life. Here the authors show that in artificial cells division can be controlled by regulating membrane curvature using low protein density.

Modeling membrane nanotube morphology: the role of heterogeneity in composition and material properties

Membrane nanotubes are dynamic structures that may connect cells over long distances. Nanotubes are typically thin cylindrical tubes, but they may occasionally have a beaded architecture along the tube. In this paper, we study the role of membrane mechanics in governing the architecture of these tubes and show that the formation of bead-like structures along the nanotubes can result from local heterogeneities in the membrane either due to protein aggregation or due to membrane composition. We present numerical results that predict how membrane properties, protein density, and local tension compete to create a phase space that governs the morphology of a nanotube. We also find that there exists a discontinuity in the energy that impedes two beads from fusing. These results suggest that the membrane-protein interaction, membrane composition, and membrane tension closely govern the tube radius, number of beads, and the bead morphology.

Simulation of fluid/gel phase equilibrium in lipid vesicles

Simulation of single component dipalmitoylphosphatidylcholine (DPPC) coarse-grained DRY-MARTINI lipid vesicles of diameter 10 nm (1350 lipids), 20 nm (5100 lipids) and 40 nm (17 600 lipids) is performed using statistical temperature molecular dynamics (STMD), to study finite size effects upon the order-disorder gel/fluid transition. STMD obtains enhanced sampling using a generalized ensemble, obtaining a flat energy distribution between upper and lower cutoffs, with little computational cost over canonical molecular dynamics. A single STMD trajectory of moderate length is sufficient to sample 20+ transition events, without trapping in the gel phase, and obtain well averaged properties. Phase transitions are analyzed via the energy-dependence of the statistical temperature, T_S(U). The transition temperature decreases with decreasing diameter, in agreement with experiment, and the transition changes from first order to borderline first-second order. The size- and layer-dependence of the structure of both stable phases, and of the pathway of the phase transition, are determined. It is argued that the finite size effects are primarily caused by the disruption of the gel packing by curvature. Inhomogeneous states with faceted gel patches connected by unusual fluid seams are observed at high curvature, with visually different structure in the inner and outer layers due to the different curvatures. Thus a simple physical picture describes phase transitions in nanoscale finite systems far from the thermodynamic limit.

Enthalpy-driven self-assembly of amphiphilic Janus dendrimers into onion-like vesicles: a Janus particle model

Synthetic vesicles of amphiphilic Janus dendrimers are known as dendrimersomes. The understanding of the conditions and formation mechanism of dendrimersomes is meaningful for further controlling the structures. Herein, the characteristics of the self-assembly of amphiphilic Janus dendrimer/water solutions into unilamellar and onion-like dendrimersomes are studied by molecular dynamics simulations via a spherical single-site Janus particle model. The model with two distinct surfaces, one hydrophobic side and another hydrophilic side, describes the amphiphilic nature of Janus dendrimers. By reducing the dendrimers with complex architectures to be simple Janus particles, we investigate the concentration-dependent self-assembled structures as well as the enthalpy-driven formation process of onion-like dendrimersomes, in contrast to the entropy-mediated self-assembly of amphiphilic flexible chains. Three typical equilibrium morphologies including linear micelles, lamellar structures and vesicles are found upon varying the Janus balance and dendrimer concentration. It is observed that the dendrimersomes consisting of the dendrimers with neglectable molecular configuration entropy become very stable, which agrees well with experimental observation. Specifically, different from many lipidsomes and polymersomes which can spontaneously merge, the size of dendrimersomes will not increase through mutual fusion once the well-defined onion-like structure is formed. Moreover, the discharge of water is achieved by water diffusion in our simulations, instead of in the "peeling-one-onion-layer-at-a-time" fashion. Our study combined with the previous ones using flexible chain models could depict a complete picture of dendrimersomes in favor of their applications in drug and gene delivery.

Temperature-responsive self-assembled nanostructures from lysine-based surfactants with high chain length asymmetry: from tubules and helical ribbons to micelles and vesicles

Stimuli-sensitive self-assembled nanostructures are of great relevance for the templating of nanomaterials and the design of efficient systems for the controlled delivery of molecules. Amino acid-based surfactants often display such fascinating self-assembly due to a combination of molecular features such as critical packing parameter, chirality and H-bonding interactions. Herein, we focus on a family of newly synthesized double-chained alkylcarboxylates derived from l-lysine, and designated by 8Lysn, mLys8, with n, m = 12, 14 and 16, and 12Lys16 and 16Lys12, where the numbers represent the number of C atoms in each hydrocarbon chain. The effects of the chain length asymmetry and structural isomerism of the surfactants on their interfacial properties, thermal behavior and self-assembly in water were investigated by a comprehensive toolbox, including surface tension, DSC, imaging (light microscopy, SEM, TEM and AFM) and SAXS. All the surfactants below their Krafft temperature self-organize into tubular structures of various morphologies (flat structures, twisted and coiled ribbons and hollow tubes), forming hydrogels at low surfactant concentration. Upon the solubilization phase transition, micelles or vesicles are formed depending on the surfactant structure, and the tubule-micelle or tubule-vesicle transition is thermoreversible. A molecular-level rationalization of the observed self-assembly and phase transition features is put forth.

Formation of Autophagosomes Coincides with Relaxation of Membrane Curvature

Autophagy is an intracellular degradation process that employs complex membrane dynamics to isolate and break down cellular components. However, many unanswered questions remain concerning remodeling of autophagic membranes. Here, we focus on the advantages of theoretical modeling to study the formation of autophagosomes and to understand the origin of autophagosomal membranes. Starting from the well-defined geometry of final autophagosomes, we ask the question of how these organelles can be formed by combining various pre-autophagosomal membranes such as vesicles, membrane tubules, or sheets. We analyze the geometric constraints of autophagosome formation by taking the area of the precursor membranes and their internal volume into account. Our results suggest that vesicle fusion contributes little to the formation of autophagosomes. In the second part, we quantify the curvature of the precursors and report that the formation of autophagosomes is associated with a strong relaxation of membrane curvature energy. This effect we find for a wide range of membrane asymmetries. It is especially strong for small distances between both autophagosomal membranes, as observed in vivo. We quantify the membrane bending energies of all precursors by considering membrane asymmetries. We propose that the generation and supply of pre-autophagosomal membranes is one limiting step for autophagosome formation.

Membrane nanotube pearling restricted by confined polymers

Increasing evidence showed that membrane nanotubes readily undergo pearling in response to external stimuli, while long tubular membrane structures have been observed connecting cells and functioning as channels for intercellular transport, raising a fundamental question of how the stability of membrane nanotubes is maintained in the cellular environment. Here, combining dissipative particle dynamics simulations, free energy calculations, and a force analysis, we propose and demonstrate that nanotube pearling can be restricted by confined polymers, which can be DNA and protein chains transported through the nanotubes, or actin filaments participating in tube formation and elongation. Thermodynamically, nanotube pearling releases the membrane surface energy, but costs bending energies of both the membrane and the confined polymers. Following the mechanism, the pearling of nanotubes confining longer and stiffer polymers is more difficult as it costs larger polymer bending energies. In dynamics, nanotube pearling occurs by repelling polymers from the region of nanotube shrinking to that of swelling. Shorter polymers can be readily repelled owing to the unbalanced force exerted by the shrinking tube region, whereas longer polymers tend to be trapped at the shrinking region to retard the nanotube pearling. Besides the low surface tension maintained by lipid reservoirs kept in living cells, our results supplement the explanation for the stability of membrane nanotubes, and open up a new avenue to manipulate the shape deformation of tubular membrane structures for study of many biological processes.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

Electrostatic-Driven Dynamic Jamming of 2D Nanoparticles at Interfaces for Controlled Molecular Diffusion

Dynamically engineering the interfacial interaction of nanoparticles has emerged as a new approach for bottom-up fabrication of smart systems to tailor molecular diffusion and controlled release. Janus zwitterionic nanoplates are reported that can be switched between a locked and unlocked state at interfaces upon changing surface charge, allowing manipulation of interfacial properties in a fast, flexible, and switchable manner. Combining experimental and modeling studies, an unambiguous correlation is established among the electrostatic energy, the interface geometry, and the interfacial jamming states. As a proof-of-concept, the well-controlled interfacial jamming of nanoplates enabled the switchable molecular diffusion through liquid-liquid interfaces, confirming the feasibility of using nanoparticle-based surfactants for advanced controlled release.

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Membrane Nanotubes Increase the Robustness of Giant Vesicles

Giant unilamellar vesicles (GUVs) provide a direct connection between the nano- and the microregime. On the one hand, these vesicles represent biomimetic compartments with linear dimensions of many micrometers. On the other hand, the vesicle walls are provided by single molecular bilayers that have a thickness of a few nanometers and respond sensitively to molecular interactions with small solutes, biopolymers, and nanoparticles. These nanoscopic responses are amplified by the GUVs and can then be studied on much larger scales. Therefore, GUVs are increasingly used as a versatile research tool for basic membrane science, bioengineering, and synthetic biology. Conventional GUVs have one major drawback, however: they have only a limited capability to cope with external perturbations such as osmotic inflation, adhesion, or micropipette aspiration that tend to rupture the membranes. In contrast, cell membranes tolerate the same kinds of mechanical perturbations without rupture because the latter membranes are coupled to reservoirs of membrane area. Here, we introduce GUVs with membrane nanotubes as model systems that include such area reservoirs. To demonstrate the increased robustness of these tubulated vesicles, we use micropipette aspiration and changes in the osmotic conditions applied to phospholipid membranes doped with the glycolipid GM1. A quantitative comparison between theory and experiment reveals that the response of the GUVs is governed by the membranes' spontaneous tension, a curvature-elastic material parameter that describes the bilayer asymmetry on the nanoscale. Because of their increased robustness, GUVs with nanotubes represent improved research tools for membrane science, in general, with potential applications as storage and delivery systems and as cell-like microcompartments in bioengineering, pharmacology, and synthetic biology.

Scaffolding the cup-shaped double membrane in autophagy

Autophagy is a physiological process for the recycling and degradation of cellular materials. Forming the autophagosome from the phagophore, a cup-shaped double-membrane vesicle, is a critical step in autophagy. The origin of the cup shape of the phagophore is poorly understood. In yeast, fusion of a small number of Atg9-containing vesicles is considered a key step in autophagosome biogenesis, aided by Atg1 complexes (ULK1 in mammals) localized at the preautophagosomal structure (PAS). In particular, the S-shaped Atg17-Atg31-Atg29 subcomplex of Atg1 is critical for phagophore nucleation at the PAS. To study this process, we simulated membrane remodeling processes in the presence and absence of membrane associated Atg17. We show that at least three vesicles need to fuse to induce the phagophore shape, consistent with experimental observations. However, fusion alone is not sufficient. Interactions with 34-nm long, S-shaped Atg17 complexes are required to overcome a substantial kinetic barrier in the transition to the cup-shaped phagophore. Our finding rationalizes the recruitment of Atg17 complexes to the yeast PAS, and their unusual shape. In control simulations without Atg17, with weakly binding Atg17, or with straight instead of S-shaped Atg17, the membrane shape transition did not occur. We confirm the critical role of Atg17-membrane interactions experimentally by showing that mutations of putative membrane interaction sites result in reduction or loss of autophagic activity in yeast. Fusion of a small number of vesicles followed by Atg17-guided membrane shape-remodeling thus emerges as a viable route to phagophore formation.