Origin of gradients in lipid density and surface tension between connected lipid droplet and bilayer.

We combined theory and experiments to depict physical parameters modulating the phospholipid (PL) density and tension equilibrium between a bilayer and an oil droplet in contiguity. This situation is encountered during a neutral lipid (NL) droplet formation in the endoplasmic reticulum. We set up macroscopic and microscopic models to uncover free parameters and the origin of molecular interactions controlling the PL densities of the droplet monolayer and the bilayer. The established physical laws and predictions agreed with experiments performed with droplet-embedded vesicles. We found that the droplet monolayer is always by a few percent (∼10%) less packed with PLs than the bilayer. Such a density gradient arises from PL-NL interactions on the droplet, which are lower than PL-PL trans interactions in the bilayer, i.e., interactions between PLs belonging to different leaflets of the bilayer. Finally, despite the pseudo-surface tension for the water/PL acyl chains in the bilayer being higher than the water/NL surface tension, the droplet monolayer always has a higher surface tension than the bilayer because of its lower PL density. Thus, a PL density gradient is mandatory to maintain the mechanical and thermodynamic equilibrium of the droplet-bilayer continuity. Our study sheds light on the origin of the molecular interactions responsible for the unique surface properties of lipid droplets compared with cellular bilayer membranes.

Fat inclusions strongly alter membrane mechanics.

Neutral lipids (NLs) are apolar oil molecules synthesized in the endoplasmic reticulum bilayer upon diverse biological stimuli. NLs synthesized are released in the hydrophobic core of the bilayer. At a critical concentration, NLs condense by phase separation and nucleate a lipid droplet (LD). After an LD forms, a fraction of NLs can be present in the bilayer but at a concentration below that of the nucleation. Here, we study whether and how the accumulation of NLs alters a lipid bilayer's mechanical properties. In synthetic systems, we found that NLs proffer unusual bilayer stretching capacities, especially in the presence of negatively curved phospholipids. This impact becomes spectacular when an LD is contiguous with the bilayer and supplies it with NLs. The tested NLs markedly decrease the bilayer area expansion modulus and significantly increase lysis tension but had opposite effects on membrane bending rigidity. Our data unveil how NL molecules modify overall membrane mechanics, the alteration of which may be linked to pathologies or anticancer treatments targeting NLs.

SNARE machinery is optimized for ultrafast fusion.

SNARE proteins zipper to form complexes (SNAREpins) that power vesicle fusion with target membranes in a variety of biological processes. A single SNAREpin takes about 1 s to fuse two bilayers, yet a handful can ensure release of neurotransmitters from synaptic vesicles much faster: in a 10th of a millisecond. We propose that, similar to the case of muscle myosins, the ultrafast fusion results from cooperative action of many SNAREpins. The coupling originates from mechanical interactions induced by confining scaffolds. Each SNAREpin is known to have enough energy to overcome the fusion barrier of 25-[Formula: see text]; however, the fusion barrier only becomes relevant when the SNAREpins are nearly completely zippered, and from this state, each SNAREpin can deliver only a small fraction of this energy as mechanical work. Therefore, they have to act cooperatively, and we show that at least three of them are needed to ensure fusion in less than a millisecond. However, to reach the prefusion state collectively, starting from the experimentally observed half-zippered metastable state, the SNAREpins have to mechanically synchronize, which takes more time as the number of SNAREpins increases. Incorporating this somewhat counterintuitive idea in a simple coarse-grained model results in the prediction that there should be an optimum number of SNAREpins for submillisecond fusion: three to six over a wide range of parameters. Interestingly, in situ cryoelectron microscope tomography has very recently shown that exactly six SNAREpins participate in the fusion of each synaptic vesicle. This number is in the range predicted by our theory.

ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation.

Cells convert excess energy into neutral lipids that are made in the endoplasmic reticulum (ER) bilayer. The lipids are then packaged into spherical or budded lipid droplets (LDs) covered by a phospholipid monolayer containing proteins. LDs play a key role in cellular energy metabolism and homeostasis. A key unanswered question in the life of LDs is how they bud off from the ER. Here, we tackle this question by studying the budding of artificial LDs from model membranes. We find that the bilayer phospholipid composition and surface tension are key parameters of LD budding. Phospholipids have differential LD budding aptitudes, and those inducing budding decrease the bilayer tension. We observe that decreasing tension favors the egress of neutral lipids from the bilayer and LD budding. In cells, budding conditions favor the formation of small LDs. Our discovery reveals the importance of altering ER physical chemistry for controlled cellular LD formation.

Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer.

Lipid droplets (LDs) are cytosolic organelles that protrude from the endoplasmic reticulum membrane under energy-rich conditions. How an LD buds off from the endoplasmic reticulum bilayer is still elusive. By using a continuous media description, we computed the morphology of a lipid droplet embedded in between two identical monolayers of a bilayer. We found that beyond a critical volume, the droplet morphology abruptly transits from a symmetrical elongated lens to a spherical protrusion. This budding transition does not require any energy-consuming machinery, or curvature-inducing agent, or intrinsic asymmetry of the bilayer; it is solely driven by the large interfacial energy of the LD, as opposed to the bilayer surface tension. This spontaneous budding mechanism gives key insights on cellular LD formation.

Modeling the Kinetics of Open Self-Assembly.

In this work, we explore theoretically the kinetics of molecular self-assembly in the presence of constant monomer flux as an input, and a maximal size. The proposed model is supposed to reproduce the dynamics of viral self-assembly for enveloped virus. It turns out that the kinetics of open self-assembly is rather quantitatively different from the kinetics of similar closed assembly. In particular, our results show that the convergence toward the stationary state is reached through assembly waves. Interestingly, we show that the production of complete clusters is much more efficient in the presence of a constant input flux, rather than providing all monomers at the beginning of the self-assembly.

The physics of lipid droplet nucleation, growth and budding.

Lipid droplets (LDs) are intracellular oil-in-water emulsion droplets, covered by a phospholipid monolayer and mainly present in the cytosol. Despite their important role in cellular metabolism and growing number of newly identified functions, LD formation mechanism from the endoplasmic reticulum remains poorly understood. To form a LD, the oil molecules synthesized in the ER accumulate between the monolayer leaflets and induce deformation of the membrane. This formation process works through three steps: nucleation, growth and budding, exactly as in phase separation and dewetting phenomena. These steps involve sequential biophysical membrane remodeling mechanisms for which we present basic tools of statistical physics, membrane biophysics, and soft matter science underlying them. We aim to highlight relevant factors that could control LD formation size, site and number through this physics description. An emphasis will be given to a currently underestimated contribution of the molecular interactions between lipids to favor an energetically costless mechanism of LD formation.

Shape and energy of a membrane bud induced by protein coats or viral protein assembly.

Intracellular transport vesicles and enveloped virus production is mediated by the polymerization of proteins that form bi-dimensional curved and rigid structures, or "coats", on a membrane. Using the classical framework of fluid membrane elasticity, we compute numerically the shape and the mechanical energy of the membrane deformation induced by a coat at different stage of growth. We furthermore derive analytical approximate expressions for the membrane shape and energy. They are found to be very accurate when compared to numerical calculations. These analytical expressions should be useful when building a relevant model of coat polymerization kinetics. We also discuss some consequences of the membrane energy features on the coat assembly process, showing that at high tension a kinetically arrested state of incomplete assembly could exist.

A general theoretical framework to infer endosomal network dynamics from quantitative image analysis.

BACKGROUND: Endocytosis allows the import and distribution of cargo into a series of endosomes with distinct morphological and biochemical characteristics. Our current understanding of endocytic cargo trafficking is based on the kinetics of net cargo transport between endosomal compartments without considering individual endosomes. However, endosomes form a dynamic network of membranes undergoing fusion and fission, thereby continuously exchanging and redistributing cargo. The macroscopic kinetic properties, i.e., the properties of the endosomal network as a whole, result from the collective behaviors of many individual endosomes, a problem so far largely unaddressed. RESULTS: Here, we developed a general theoretical framework to describe the dynamics of cargo distributions in the endosomal network. We combined the theory with quantitative experiments to study how the macroscopic kinetic properties of the endosomal network emerge from microscopic processes at the level of individual endosomes. We compared our theory predictions to experimental data in which dynamic distributions of endocytosed low-density lipoprotein (LDL) were quantified. CONCLUSIONS: Our theory can quantitatively describe the observed cargo distributions as a function of time. Remarkably, the theory allows determining microscopic kinetic parameters such as the fusion rate between endosomes from still images of cargo distributions at different times of internalization. We show that this method is robust and sensitive because cargo distributions result from an average over many stochastic events in many cells. Our results provide theoretical and experimental support to the "funnel model" of endosome progression and suggest that the conversion of early to late endosomes is the major mode of LDL trafficking.

Kinetic regulation of coated vesicle secretion.

The secretion of vesicles for intracellular transport often relies on the aggregation of specialized membrane-bound proteins into a coat able to curve cell membranes. The nucleation and growth of a protein coat is a kinetic process that competes with the energy-consuming turnover of coat components between the membrane and the cytosol. We propose a generic kinetic description of coat assembly and the formation of coated vesicles and discuss its implication to the dynamics of COP vesicles that traffic within the Golgi and with the endoplasmic reticulum. We show that stationary coats of fixed area emerge from the competition between coat growth and the recycling of coat components, in a fashion resembling the treadmilling of cytoskeletal filaments. We further show that the turnover of coat components allows for a highly sensitive switching mechanism between a quiescent and a vesicle producing membrane, upon a slowing down of the exchange kinetics. We claim that the existence of this switching behavior, also triggered by factors, such as the presence of cargo and variation of the membrane mechanical tension, allows for efficient regulation of vesicle secretion. We propose a model, supported by different experimental observations, in which vesiculation of secretory membranes is impaired by the energy-consuming desorption of coat proteins, until the presence of cargo or other factors triggers a dynamical switch into a vesicle producing state.

Charged inclusion in nematic liquid crystals.

We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio Ze/R, where Ze is the charge and R is the radius of the particle. Numerical analysis shows the presence of defects around the particle for large Ze/R. They are nanometer-scale defects for microscopic ions. If the dielectric anisotropy is positive, a Saturn ring defect appears. If it is negative, a pair of point defects appear apart from the particle surface, each being connected to the surface by a disclination line segment.

Capillary attraction of colloidal particles at an aqueous interface.

We study the capillary forces arising from charged colloidal particles trapped at an oil-water interface. Since it is quadratic in the electric field, the electric stress acting on the interface cannot be written as the superposition of one-particle terms. Indeed, we find that the interfacial pressure is dominated by two-particle terms, which induce capillary forces involving one, two, three, or four particles. The dominant interaction is attractive and varies with the inverse cube of the particle distance.

Electric-field induced capillary interaction of charged particles at a polar interface.

We study the electric-field induced capillary interaction of charged particles at a polar interface. The algebraic tail of the electrostatic pressure of each charge results in a deformation of the interface u approximately r(-4), where r is the lateral distance. The capillary interaction of nearby particles is repulsive and varies as rho(-6) with their distance rho. As a consequence, electric-field induced capillary forces cannot be at the origin of the secondary minimum observed recently for charged poly(methyl methacrylate) particles at an oil-water interface.

Is there a dipolar interaction of like charges in thin aqueous films?

The dipole moment and the screened interaction of interfacial charges are discussed. We compare this interaction with that of parallel dipoles and show that the dipolar picture fails for charges in thin aqueous films.

Disjoining pressure of discrete surface charges on thin aqueous films.

The disjoining pressure of charged parallel interfaces confining an electrolyte solution is to a large extent determined by the screening clouds of the surface charges. We evaluate the pressure in terms of the number density sigma of discrete charges and film thickness d and find, at sigmad(2) approximately 1, a crossover from the well-known law P approximately sigma(2) to a linear behavior P approximately sigma. For the latter case, each surface charge results in strongly inhomogeneous pressure profiles at both interfaces.