Switchable positioning of plate-like inclusions in lipid membranes: Elastically mediated interactions of planar colloids in 2D fluids

Diffusion, density, and defects on spheres

We simulate and model diffusion of spherical colloids of radius, a, on spherical surfaces of radius, R, as a function of relative size and surface concentration. Using Brownian dynamics simulations, we quantify diffusion and microstructure at different concentrations ranging from single particles to dense crystalline states. Self-diffusion and structural metrics (pair distribution, local density, and topological charge) are indistinguishable between spheres and planes for all concentrations up to dense liquid states. For concentrations approaching and greater than the freezing transition, smaller spheres with higher curvature show increased diffusivities and nonuniform density/topological defect distributions, which differ qualitatively from planar surfaces. The total topological charge varies quadratically with sphere radius for dense liquid states and linearly with sphere radius for dense crystals with icosahedrally organized grain scars. Between the dense liquid and dense crystal states on spherical surfaces is a regime of fluctuating and interacting defect clusters. We show local density governs self-diffusion in dense liquids on flat and spherical surfaces via the pair distribution. In contrast, dynamic topological defects couple to finite diffusivities through freezing and in low density crystal states on spherical surfaces, where neither exist on flat surfaces.

Shape equilibria of vesicles with rigid planar inclusions

Motivated by recent studies of two-phase lipid vesicles possessing 2D solid domains integrated within a fluid bilayer phase, we study the shape equilibria of closed vesicles possessing a single planar, circular inclusion. While 2D solid elasticity tends to expel Gaussian curvature, topology requires closed vesicles to maintain an average, non-zero Gaussian curvature leading to an elementary mechanism of shape frustration that increases with inclusion size. We study elastic ground states of the Helfrich model of the fluid-planar composite vesicles, analytically and computationally, as a function of planar fraction and reduced volume. Notably, we show that incorporation of a planar inclusion of only a few percent dramatically shifts the ground state shapes of vesicles from predominantly prolate to oblate, and moreover, shifts the optimal surface-to-volume ratio far from spherical shapes. We show that for sufficiently small planar inclusions, the elastic ground states break symmetry via a complex variety of asymmetric oblate, prolate, and triaxial shapes, while inclusion sizes above about 8% drive composite vesicles to adopt axisymmetric oblate shapes. These predictions cast useful light on the emergent shape and mechanical responses of fluid-solid composite vesicles.

Dynamics of giant vesicle assembly from thin lipid films

MOTIVATION

Giant unilamellar vesicles (GUVs), cell-like synthetic micrometer size structures, assemble when thin lipid films are hydrated in aqueous solutions. Quantitative measurements of static yields and distribution of sizes of GUVs obtained from thin film hydration methods were recently reported. Dynamic data such as the time evolution of yields and distribution of sizes, however, is not known. Dynamic data can provide insights into the assembly pathway of GUVs and guidelines for choosing conditions to obtain populations with desired size distributions.

APPROACH

We develop the 'stopped-time' technique to characterize the time evolution of the distribution of sizes and molar yields of populations of free-floating GUVs. We additionally capture high resolution time-lapse images of surface-attached GUV buds on the lipid films. We systematically study the dynamics of assembly of GUVs from three widely used thin film hydration methods, PAPYRUS (Paper-Abetted amPhiphile hYdRation in aqUeous Solutions), gentle hydration, and electroformation.

FINDINGS

We find that the molar yield versus time curves of GUVs demonstrate a characteristic sigmoidal shape, with an initial yield, a transient, and then a steady state plateau for all three methods. The population of GUVs showed a right-skewed distribution of diameters. The variance of the distributions increased with time. The systems reached steady state within 120 min. We rationalize the dynamics using the thermodynamically motivated budding and merging (BNM) model. These results further the understanding of lipid dynamics and provide for the first-time practical parameters to tailor the production of GUVs of specific sizes for applications.

Flower-shaped 2D crystals grown in curved fluid vesicle membranes

The morphologies of two-dimensional (2D) crystals, nucleated, grown, and integrated within 2D elastic fluids, for instance in giant vesicle membranes, are dictated by an interplay of mechanics, permeability, and thermal contraction. Mitigation of solid strain drives the formation of crystals with vanishing Gaussian curvature (i.e., developable domain shapes) and, correspondingly, enhanced Gaussian curvature in the surrounding 2D fluid. However, upon cooling to grow the crystals, large vesicles sustain greater inflation and tension because their small area-to-volume ratio slows water permeation. As a result, more elaborate shapes, for instance, flowers with bendable but inextensible petals, form on large vesicles despite their more gradual curvature, while small vesicles harbor compact planar crystals. This size dependence runs counter to the known cumulative growth of strain energy of 2D colloidal crystals on rigid spherical templates. This interplay of intra-membrane mechanics and processing points to the scalable production of flexible molecular crystals of controllable complex shape.

Complex motion of steerable vesicular robots filled with active colloidal rods

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system's geometrical and material properties, such as the aspect ratio and Péclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments.

Curvature-Mediated Forces on Elastic Inclusions in Fluid Interfaces

Heterogeneous fluid interfaces often include two-dimensional solid domains that mechanically respond to changes in interfacial curvature. While this response is well-characterized for rigid inclusions, the influence of solid-like elasticity remains essentially unexplored. Here, we show that an initially flat, elastic inclusion embedded in a curved, fluid interface will exhibit qualitatively distinct behavior depending on its size and stiffness. Small, stiff inclusions are limited by bending and experience forces directed up gradients of Gaussian curvature, in keeping with prior findings for rigid discoids. By contrast, larger and softer inclusions are driven down gradients of squared Gaussian curvature in order to minimize the elastic penalty for stretching. Our calculations of the force on a solid inclusion are shown to collapse onto a universal curve spanning the bending- and stretching-limited regimes. From these results, we make predictions for the curvature-directed motion of deformable solids embedded within a model interface of variable Gaussian curvature.