- PAR ID:
- 10233980
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 905
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein–protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn–Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane–protein interactions.more » « less
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The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the “spontaneous curvature” term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrich’s model. Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.
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We describe a method to determine membrane bending rigidity from capacitance measurements on large area, free-standing, planar, biomembranes. The bending rigidity of lipid membranes is an important biological mechanical property that is commonly optically measured in vesicles, but difficult to quantify in a planar, unsupported system. To accomplish this, we simultaneously image and apply an electric potential to free-standing, millimeter area, planar lipid bilayers composed of DOPC and DOPG phospholipids to measure the membrane Young’s (elasticity) modulus. The bilayer is then modeled as two adjacent thin elastic films to calculate bending rigidity from the electromechanical response of the membrane to the applied field. Using DOPC, we show that bending rigidities determined by this approach are in good agreement with the existing work using neutron spin echo on vesicles, atomic force spectroscopy on supported lipid bilayers, and micropipette aspiration of giant unilamellar vesicles. We study the effect of asymmetric calcium concentration on symmetric DOPC and DOPG membranes and quantify the resulting changes in bending rigidity. This platform offers the ability to create planar bilayers of controlled lipid composition and aqueous ionic environment, with the ability to asymmetrically alter both. We aim to leverage this high degree of compositional and environmental control, along with the capacity to measure physical properties, in the study of various biological processes in the future.more » « less
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Many intrinsically disordered peptides have been shown to undergo liquid–liquid phase separation and form complex coacervates, which play various regulatory roles in the cell. Recent experimental studies found that such phase separation processes may also occur at the lipid membrane surface and help organize biomolecules during signaling events; in some cases, phase separation of proteins at the membrane surface was also observed to lead to significant remodeling of the membrane morphology. The molecular mechanisms that govern the interactions between complex coacervates and lipid membranes and the impacts of such interactions on their structure and morphology, however, remain unclear. Here we study the coacervation of poly-glutamate (E 30 ) and poly-lysine (K 30 ) in the presence of lipid bilayers of different compositions. We carry out explicit-solvent coarse-grained molecular dynamics simulations by using the MARTINI (v3.0) force-field. We find that more than 20% anionic lipids are required for the coacervate to form stable contact with the bilayer. Upon wetting, the coacervate induces negative curvature to the bilayer and facilitates local lipid demixing, without any peptide insertion. The magnitude of negative curvature, extent of lipid demixing, and asphericity of the coacervate increase with the concentration of anionic lipids. Overall, we observe a decrease in the number of contacts among the polyelectrolytes as the droplet spreads over the bilayer. Therefore, unlike previous suggestions, interactions among polyelectrolytes do not constitute a driving force for the membrane bending upon wetting by the coacervate. Rather, analysis of interaction energy components suggests that bending of the membrane is favored by enhanced interactions between polyelectrolytes with lipids as well as with counterions. Kinetic studies reveal that, at the studied polyelectrolyte concentrations, the coacervate formation precedes bilayer wetting.more » « less
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