Search Results (5)

Cell membranes contain a variety of biomolecules, especially various kinds of lipids and proteins, which constantly change with fluidity and environmental stimuli. Though Helfrich curvature elastic energy has successfully explained many phenomena for single-component membranes, a new theoretical framework for multicomponent membranes is still a challenge. In this work, we propose a generalized Helfrich free-energy functional describe equilibrium shapes and phase behaviors related to membrane heterogeneity with via curvature-component coupling in a unified framework. For multicomponent membranes, a new but important Laplace–Beltrami operator is derived from the variational calculation on the integral of Gaussian curvature and applied to explain the spontaneous nanotube formation of an asymmetric glycolipid vesicle. Therefore, our general mathematical framework shows a predictive capabilities beyond the existing multicomponent membrane models. The set of new curvature-component coupling EL equations have been derived for global vesicle shapes associated with the composition redistribution of multicomponent membranes for the first time and specified into several typical geometric shape equations. The equilibrium radii of isotonic vesicles for both spherical and cylindrical geometries are calculated. The analytical solution for isotonic vesicles reveals that membrane stability requires distinct elastic moduli among components ($k_{\mathrm{A}}\ne k_{\mathrm{B}}$, ${\overline{k}}_{\mathrm{A}}\ne {\overline{k}}_{\mathrm{B}}$), which is consistent with experimental observations of coexisting lipid domains. Furthermore, we elucidate the biophysical implications of the derived shape equations, linking them to experimentally observed membrane remodeling processes. Our new free-energy framework provides a baseline for more detailed microscopic membrane models. Full article

Adhesion between a red blood cell and substrates is essential to many biophysical processes and has significant implications for medical applications. This study derived a theoretical formula for the adhesive force between a red blood cell and a bulk substrate, incorporating the Hamaker constant to account for van der Waals interactions. The derivation is based on a biconcave shape of an RBC, described by the well-known Ouyang–Helfrich equation and its analytical solution developed by Ouyang. The theoretical predictions align with experimental observations and the empirical spherical model, revealing a $F\propto D^{-2.5}$ relationship for biconcave RBCs versus $F\propto D^{-2}$ for spheres. While the current study focuses on idealized geometries and static conditions, future work will extend these findings to more complex environmental conditions, such as dynamic flow and interactions with plasma proteins, thereby broadening the applicability of the model. This work bridges foundational research in cell membrane mechanics with practical applications in hemostatic materials, platelet adhesion, and biomaterials engineering. The findings provide insights for designing advanced biological sensors, surgical tools, and innovative medical materials with enhanced biocompatibility and performance. Full article

Recent experiments have indicated that at least a part of the osmotic pressure across the giant unilamellar vesicle (GUV) membrane was balanced by the rapid formation of the monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Therefore, we investigated a possible osmotic role played by these daughter vesicles for the maintenance of osmotic regulation in the GUVs and, by extension, in living cells. We highlighted a mechanism whereby the daughter vesicles acted as osmotically active solutes (osmoticants), contributing an extra vestigial osmotic pressure component across the membrane of the parent vesicle, and we showed that the consequences were consistent with experimental observations. Our results highlight the significance of osmotic regulation in cellular processes, such as fission/fusion, endocytosis, and exocytosis. Full article

A recurring motif in soft matter and biophysics is modeling the mechanics of interacting particles on fluid membranes. One of the main outstanding challenges in these applications is the need to model the strong coupling between the substrate deformation and the particles’ positions as the latter freely move on the former. This work presents a thin-shell finite element formulation based on subdivision surfaces to compute equilibrium configurations of a thin fluid shell with embedded particles. We use a variational Lagrangian framework to couple the mechanics of the particles and the substrate without having to resort to ad hoc constraints to anchor the particles to the surface. Unlike established methods for such systems, the particles are allowed to move between elements of the finite element mesh. This is achieved by parametrizing the particle locations on the reference configuration. Using the Helfrich–Canham energy as a model for fluid shells, we present the finite element method’s implementation and an efficient search algorithm required to locate particles on the reference mesh. Several analyses with varying numbers of particles are finally presented reproducing symmetries observed in the classic Thomson problem and showcasing the coupling between interacting particles and deformable membranes. Full article

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. Full article