Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations.

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize experimentally observed spindle shapes of giant vesicles in a uniform AC electric field.

Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations.

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize the experimentally observed spindle shapes of giant vesicles in a uniform AC field.

Electrostatic force on a spherical particle confined between two planar surfaces.

A charge-free particle in a uniform electric field experiences no net force in an unbounded domain. A boundary, however, breaks the symmetry and the particle can be attracted or repelled to it, depending on the applied field direction [Z. Wang et al., Phys. Rev. E, 2022, 106, 034607]. Here, we investigate the effect of a second boundary because of its common occurrence in practical applications. We consider a spherical particle suspended between two parallel walls and subjected to a uniform electric field, applied in a direction either normal or tangential to the surfaces. All media are modeled as leaky dielectrics, thus allowing for the accumulation of free charge at interfaces, while bulk media remain charge-free. The Laplace equation for the electric potential is solved using a multipole expansion and the boundaries are accounted for by a set of images. The results show that in the case of a normal electric field, which corresponds to a particle between two electrodes, the force is always attractive to the nearer boundary and, in general, weaker that the case of only one wall. Intriguingly, for a given particle-wall separation we find that the force may vary nonmonotonically with confinement and its magnitude may exceed the one-wall value. In the case of tangential electric field, which corresponds to a particle between insulating boundaries, the force follows the same trends but it is always repulsive.

Particle-surface interactions in a uniform electric field.

The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to be weakly conducting, so that that the leaky dielectric model applies. The Laplace equation for the electric potential is solved in bipolar coordinate system and the potential is obtained in terms of a series expansion of Legendre polynomials. The force on the particle is calculated using the Maxwell tensor. We find that in the case of normal electric field, which corresponds to a particle near an electrode, the force is always attractive but at a given separation it varies nontrivially with particle-suspending medium conductivity ratio; the force on a particle that is more conducting than the suspending medium is much larger compared to the force on a particle less conducing than the suspending medium. In the case of tangential electric field, which corresponds to a particle near an insulating boundary, the force is always repulsive.

Electrohydrodynamic assembly of colloidal particles on a drop interface.

A mathematical model to simulate the dynamics of colloidal particles on a drop interface in an applied electric field is presented. The model accounts for the electric field driven flow within the drop and suspending fluid, particle-particle electrostatic interaction, and the particle motion and rotation due to the induced flow and the applied electric field. The model predicts the formation of chains in the case of conducting particles or an undulating band around the equator in the case of dielectric particles. The model results are in agreement with recent experimental work. A study is presented on the impact of particle concentration and electric field strength on the collective motions of the particles. In the case of non-conducting particles, we find that in the presence of Quincke rotation, the amplitude of the undulations of the observed equatorial particle belt increases with particle concentration but decreases with electric field strength. We also show that the wavelength of the undulations appears independent of the applied field strength.

Mitochondria-rough-ER contacts in the liver regulate systemic lipid homeostasis.

Contacts between organelles create microdomains that play major roles in regulating key intracellular activities and signaling pathways, but whether they also regulate systemic functions remains unknown. Here, we report the ultrastructural organization and dynamics of the inter-organellar contact established by sheets of curved rough endoplasmic reticulum closely wrapped around the mitochondria (wrappER). To elucidate the in vivo function of this contact, mouse liver fractions enriched in wrappER-associated mitochondria are analyzed by transcriptomics, proteomics, and lipidomics. The biochemical signature of the wrappER points to a role in the biogenesis of very-low-density lipoproteins (VLDL). Altering wrappER-mitochondria contacts curtails VLDL secretion and increases hepatic fatty acids, lipid droplets, and neutral lipid content. Conversely, acute liver-specific ablation of Mttp, the most upstream regulator of VLDL biogenesis, recapitulates this hepatic dyslipidemia phenotype and promotes remodeling of the wrappER-mitochondria contact. The discovery that liver wrappER-mitochondria contacts participate in VLDL biology suggests an involvement of inter-organelle contacts in systemic lipid homeostasis.

Colloidal particle electrorotation in a nonuniform electric field.

A model to study the dynamics of colloidal particles in nonuniform electric fields is proposed. For an isolated sphere, the conditions and threshold for sustained (Quincke) rotation in a linear direct current (dc) field are determined. Particle dynamics becomes more complex with increasing electric field strength, changing from steady spinning around the particle center to time-dependent orbiting motion around the minimum field location. Pairs of particles exhibit intricate trajectories, which are a combination of translation, due to dielectrophoresis, and rotation, due to the Quincke effect. Our model provides a basis to study the collective dynamics of many particles in a general electric field.

Vesicle dynamics in uniform electric fields: squaring and breathing.

We computationally investigate the dynamics of a vesicle exposed to uniform DC or AC electric fields. We employ the two-dimensional boundary integral method in order to simulate vesicle deformation under experimental conditions where peculiar drum-like ("squared") shapes have been observed. The vesicle membrane is modeled as an infinitely thin, capacitive, area-incompressible interface, with the surrounding fluids acting as leaky dielectrics. Our simulations capture the "squaring" phenomenon, in which vesicles deform into rectangular profiles with corner-like regions of high curvature, as vesicles undergo dynamic transitions between oblate and prolate ellipsoidal shapes.

Continuum modeling of the electric-field-induced tension in deforming lipid vesicles.

We computationally investigate the deformation of a closed bilayer membrane (vesicle) in a DC electric pulse with a goal of understanding cell electroporation. The electric stresses exerted on the area-incompressible interface generate non-uniform tension that can exceed the membrane lysis tension and drive pore opening. Using the two-dimensional boundary integral method, we track the spatial and temporal evolution of the highest membrane tension. Our simulations highlight the dynamic nature of electrotension and, in contrast to the common assumption, a possibility of electroporation away from the poles.

The equilibria of vesicles adhered to substrates by short-ranged potentials.

In equilibrium, a vesicle that is adhered to a horizontal substrate by a long-range attractive, short-range repulsive force traps a thin layer of fluid beneath it. In the asymptotic limit that this layer is very thin, there are quasi-two-dimensional boundary-layer structures near the edges of the vesicle, where the membrane's shape is governed by a balance between bending and adhesive stresses. These boundary layers are analysed to obtain corrections to simpler models that instead represent the adhesive interaction by a contact potential, thereby resolving apparent discontinuities that arise when such models are used. Composite expansions of the shapes of two-dimensional vesicles are derived. When, in addition, the adhesive interaction is very strong, there is a nested boundary-layer structure for which the adhesive boundary layers match towards sharp corners where bending stresses remain important but adhesive stresses are negligible. Outside these corners, bending stresses are negligible and the vesicle's shape is given approximately by the arc of a circle. Simple composite expansions of the vesicle's shape are derived that account for the shape of the membrane inside these corners.

Moving boundary problems governed by anomalous diffusion.

Anomalous diffusion can be characterized by a mean-squared displacement 〈x(2)(t)〉 that is proportional to t(α) where α≠1. A class of one-dimensional moving boundary problems is investigated that involves one or more regions governed by anomalous diffusion, specifically subdiffusion (α<1). A novel numerical method is developed to handle the moving interface as well as the singular history kernel of subdiffusion. Two moving boundary problems are solved: the first involves a subdiffusion region to the one side of an interface and a classical diffusion region to the other. The interface will display non-monotone behaviour. The subdiffusion region will always initially advance until a given time, after which it will always recede. The second problem involves subdiffusion regions to both sides of an interface. The interface here also reverses direction after a given time, with the more subdiffusive region initially advancing and then receding.

Fluid flow beneath a semipermeable membrane during drying processes.

The dynamic interactions between a semipermeable membrane and a long, thin layer of liquid beneath it are investigated in the context of drying processes. The membrane separates two aqueous solutions of sugar, and the transport of water across the membrane is driven by concentration and pressure gradients across it. A model is formulated using a long-wave approximation that includes the effects of volume loss due to water transport across the membrane, the incompressibility and bending stiffness of the membrane, and the dynamical effects that arise owing to the viscous stresses generated by the fluid flow. This model is first applied to study the desiccation of a sessile vesicle that is clamped to a rigid substrate and then also to study the behavior of blisters on laminated substrates. For each problem, equilibrium membrane shapes are obtained and their bifurcation structures are described as the sugar concentration above the membrane is varied. It is demonstrated that a wrinkled membrane coarsens to lessen the frequency of wrinkles and that if the membrane is clamped symmetrically so that it meets the substrate at a nonzero angle, then the membrane favors an asymmetric shape as water is drawn out through it.

Vesicle electrohydrodynamics.

A small amplitude perturbation analysis is developed to describe the effect of a uniform electric field on the dynamics of a lipid bilayer vesicle in a simple shear flow. All media are treated as leaky dielectrics and fluid motion is described by the Stokes equations. The instantaneous vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. We find that in the absence of ambient shear flow, it is possible that an applied stepwise uniform dc electric field could cause the vesicle shape to evolve from oblate to prolate over time if the encapsulated fluid is less conducting than the suspending fluid. For a vesicle in ambient shear flow, the electric field damps the tumbling motion, leading to a stable tank-treading state.