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Register a new userMetastability of lipid necks via geometric triality
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Necks are features of lipid membranes characterized by an uniquley large curvature, functioning as bridges between different compartments. These features are ubiquitous in the life-cycle of the cell and instrumental in processes such as division, extracellular vesicles uptake and cargo transport between organelles, but also in life-threatening conditions, as in the endocytosis of viruses and phages. Yet, the very existence of lipid necks challenges our understanding of membranes biophysics: their curvature, often orders of magnitude larger than elsewhere, is energetically prohibitive, even with the arsenal of molecular machineries and signalling pathways that cells have at their disposal. Using a geometric triality, namely a correspondence between three different classes of geometric objects, here we demonstrate that lipid necks are in fact metastable, thus can exist for finite, but potentially long times even in the absence of stabilizing mechanisms. This framework allows us to explicitly calculate the forces a corpuscle must overcome in order to penetrate cellular membranes, thus paving the way for a predictive theory of endo/exo-cytic processes.
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Unravelling the physical mechanisms behind the organisation of lipid domains is a central goal in cell biology and membrane biophysics. Previous studies on cells and model lipid bilayers featuring phase-separated domains found an intricate interplay between the membrane geometry and its chemical composition. However, the lack of a model system with simultaneous control over the membrane shape and conservation of its composition precluded a fundamental understanding of curvature-induced effects. Here, we present a new class of multicomponent vesicles supported by colloidal scaffolds of designed shape. We find that the domain composition adapts to the geometry, giving rise to a novel antimixed state. Theoretical modelling allowed us to link the pinning of domains by regions of high curvature to the material parameters of the membrane. Our results provide key insights into the phase separation of cellular membranes and on curved surfaces in general.
Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate. A single lipid bilayer coats both colloids and substrate, allowing local lipid exchange between them, thus rendering the system thermodynamically open, i.e. able to exchange heat and molecules with an external reservoir in the neighborhood of the colloid. By reconstructing the Gibbs phase diagram for this system, we demonstrate that the free-energy landscape is directly influenced by the geometry of the colloid. In addition, we find that local lipid exchange enhances the pinning of the liquid disordered phase in highly curved regions. This allows us to provide estimates of the bending moduli difference of the domains. Finally, by combining experimental and numerical data, we forecast the outcome of possible experiments on catenoidal and conical necks and show that these geometries could greatly improve the precision of the current estimates of the bending moduli.
Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.
We re-examine previous observations of folding kinetics of compressed lipid monolayers in light of the accepted mechanical buckling mechanism recently proposed [L. Pocivavsek et al., Soft Matter, 2008, 4, 2019]. Using simple models, we set conservative limits on a) the energy released in the mechanical buckling process and b) the kinetic energy entailed by the observed folding motion. These limits imply a kinetic energy at least thirty times greater than the energy supplied by the buckling instability. We discuss possible extensions of the accepted picture that might resolve this discrepancy.
The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes in vivo is challengin
g because of the membrane complexity as well as the short time and small length scales involved. By contrast, in vitro model membranes with engineered curvature provide a versatile platform for this investigation and applications to biosensing and biocomputing. However, a general route to the fabrication of lipid membranes with prescribed curvature and high spatial resolution is still missing. Here, we present a strategy that overcomes these challenges and achieve lipid membranes with designed shape by combining 3D micro-printing and replica-molding lithography to create scaffolds with virtually any geometry and high spatial resolution. The resulting supported lipid membranes are homogeneous, fluid, and can form chemically distinct lipid domains. These features are essential for understanding curvature-dependent cellular processes and developing programmable bio-interfaces for living cells and nanostructures.
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