We investigate the stability of growing vesicles using the formalism of nonequilibrium thermodynamics. The vesicles are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a water{/}lipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium thermodynamics. This formulation allows the forces and fluxes relevant to the dynamic stability of the vesicle to be identified. The method is used to analyze the stability of a spherical vesicle against arbitrary axisymmetric perturbations. It is found that there are generically two critical radii at which changes of stability occur. In the case where the perturbation takes the form of a single zonal harmonic, only one of these radii is physical and is given by the ratio $2 L_p / L_γ$, where $L_p$ is the hydraulic conductivity and $L_γ$ is the Onsager coefficient related to changes in membrane area due to lipid accretion. The stability of such perturbations is related to the value of $l$ corresponding to the particular zonal harmonic: those with lower $l$ are more unstable than those with higher $l$. Possible extensions of the current work and the need for experimental input are discussed.
We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity …
Renormalized mechanics and stochastic thermodynamics of growing vesicles
The James Franck Institute, University of Chicago（芝加哥大学詹姆斯·弗兰克研究所）；Department of Chemistry, University of Chicago（芝加哥大学化学系）；Engineering Sciences and Applied Mathematics, Northwestern University（西北大学工程科学与应用数学系）
Biological membranes constantly change their shape in response to external stimuli, and understanding the remodeling and stability of vesicles in heterogeneous environments is therefore of fundamental importance for a range of cellular processes. One crucial question is how vesicles respond to external osmotic stresses, imposed by differences in solute concentrations between the vesicle interior and exterior. Previous analyses of the membrane bending energy have predicted that micron-sized giant unilamellar vesicles (GUVs) should become globally deformed already for nanomolar concentration dif…
In recent experiments, small, thick-walled vesicles with a narrow size distribution were formed from copolymers where the degree of polymerisation of the hydrophobic block, N_B, was significantly greater than that of the hydrophilic block, N_A. Using a mean-field theory, we reproduce several aspects of the behaviour of these vesicles. Firstly, we find a minimum in the free energy of the system of vesicles as a function of their radius, corresponding to a preferred size for the vesicles, when N_B is several times larger than N_A. Furthermore, the vesicle radius diverges as N_B is increased towa…
We investigate the electrostatics of a partially formed, charged spherical shell in a salt solution. We solve the problem numerically at the Poisson-Boltzmann level and analytically in the Debye-Huckel regime. From the results on energetics of partially formed shells we examine the stability of tethered (crystalline) and fluid shells towards rupture. We clearly delineate different regimes of stability towards rupture, where, for fluid shells, we also include the effects of bending elasticity of the shells. Our analysis shows how charging of the shell induces its instability towards rupture but…
Consider a closed lipid membrane (vesicle), modeled as a two-dimensional surface, described by a geometrical hamiltonian that depends on its extrinsic curvature. The vanishing of its first variation determines the equilibrium configurations for the system. In this paper, we examine the second variation of the hamiltonian about any given equilibrium, using an explicitly surface covariant geometrical approach. We identify the operator which determines the stability of equilibrium configurations.
Lipid nanotube-vesicle networks are important channels for intercellular communication and transport of matter. Experimentally observed in neighboring mammalian cells, but also reproduced in model membrane systems, a broad consensus exists on their formation and stability. Lipid membranes must be composed of at least two molecular components, each stabilizing low (generally a phospholipid) and high curvatures. Strong anisotropy or enhanced conical shape of the second amphiphile is crucial for the formation of nanotunnels. Anisotropic driving forces generally favor nanotube protrusions from ves…
Membrane budding has been extensively studied as an equilibrium process attributed to the formation of coexisting domains or changes in the vesicle area to volume ratio (reduced volume). In contrast, non-equilibrium budding remains experimentally widely unexplored especially when time scales fall well below the characteristic diffusion time of lipidsτ . We show that localized mechanical perturbations, initiated by driving giant unilamellar vesicles (GUVs) through their lipid phase transition, leads to the immediate formation of rapidly growing, multiply localized, non-equilibrium buds, when th…
Vesicles self-assembled from amphiphilic diblock copolymers exhibit a wide diversity of behavior upon electroporation, due to competitions between edge, surface and bending energies that drive the system, while different viscous dissipation mechanisms determine the timescales. These effects are manifestations of the varying membrane thickness d from what are essentially chemically identical molecules. For smaller d, we find large unstable pores and the resulting membrane fragments reassemble into vesicles within minutes. Vesicles with larger d form long-lived pores of nanometer dimension that …
Lipid bilayer membranes are the fundamental biological barriers that permit life. The bilayer dynamics largely participates in orchestrating cellular workings and is characterized by substantial stability together with extreme plasticity that allows controlled morphological/topological changes. Modeling and understanding the topological change of vesicle-like membrane at the scale of a full cell has proved an elusive aim. We propose and discuss here a continuum model able to encompass the fusion/fission transition of a bilayer membrane at the scale of a Large Unilamellar Vesicle and evaluate t…
Giant unilamellar vesicles (GUVs), are a convenient tool to study membrane-bound processes using optical microscopy. An increasing number of studies highlights the potential of these model membranes when addressing questions in membrane biophysics and cell biology. Among them, phase transitions and domain formation, dynamics and stability in raft-like mixtures are probably some of the most intensively investigated. In doing so, many research teams rely on standard protocols for GUV preparation and handling involving the use of sugar solutions. Here, we demonstrate that following such a standar…
We report a new and facile method for measuring edge tensions of lipid membranes. The approach is based on electroporation of giant unilamellar vesicles and analysis of the pore closure dynamics. We applied this method to evaluate the edge tension in membranes with four different compositions: egg phosphatidylcholine (EggPC), dioleoylphosphatidylcholine (DOPC), and mixtures of the latter with cholesterol and dioleoylphosphatidylethanolamine (DOPE). Our data confirm previous results for EggPC and DOPC. The addition of 17 mol % cholesterol to the DOPC membrane causes an increase in the membrane …
Vesicles prepared in water from a series of diblock copolymers and termed "polymersomes" are physically characterized. With increasing molecular weight $\bar{M}_n$, the hydrophobic core thickness $d$ for the self-assembled bilayers of polyethyleneoxide - polybutadiene (PEO-PBD) increases up to 20 $nm$ - considerably greater than any previously studied lipid system. The mechanical responses of these membranes, specifically, the area elastic modulus $K_a$ and maximal areal strain $α_c$ are measured by micromanipulation. As expected for interface-dominated elasticity, $K_a$ ($\simeq$ 100 $pN/nm$)…
Studies have shown that following exposure to particulate matter, the ultrafine fraction (< 100 nm) may deposit along the respiratory tract down to the alveolar region. To assess the effects of nanoparticles in the lungs, it is essential to address the question of their biophysicochemical interaction with the different pulmonary environments, including the lung lining fluids and the epithelia. Here we examine one of these interactive scenarios and study the role of supported lipid bilayers (SLB) on the fate of 40 nm fluorescent silica particles towards living cells. We first study the particle…
The square-gradient density-functional model with triple-parabolic free energy, that was used previously to study the homogeneous bubble nucleation [J. Chem. Phys. 129, 104508 (2008)], is used to study the stability of the critical bubble nucleated within the bulk under-saturated stretched fluid. The stability of the bubble is studied by solving the Schrödinger equation for the fluctuation. The negative eigenvalue corresponds to the unstable growing mode of the fluctuation. Our results show that there is only one negative eigenvalue whose eigenfunction represents the fluctuation that correspon…
