Mechanical instability generates monodisperse colloidosomes

TL;DR

We study monodisperse colloidal vesicles formed by mechanical instability of disk-like colloidal membranes assembled from virus-like rods. Using the Helfrich energy with edge tension and first-principles axisymmetric minimum-energy (AME) modeling, we predict a critical area $A^{*} = 4π(2κ + ar{κ})^2/γ^2$; measured κ ≈ 1200 k_B T, γ ≈ 200 k_B T/μm, κ̄ ≈ 20 k_B T yield $A^{*} ≈ 1840 μm^2$ and a vesicle diameter ≈ 24 μm, while gravity shifts the observed diameter toward ~36 μm. The AME metastability analysis shows the energy barrier vanishes at $A^{ abla} = 4790 μm^2 = 2.6 A^{*}$, predicting diameter ≈ 39.1 μm, in good agreement with experiments (36.1 ± 3.2 μm). They demonstrate gravity-controlled vesicle sizing by anchoring membranes to ceiling vs floor and show complete closure with centrifugal detachment, enabling scalable production of monodisperse, selectively permeable colloidosomes. Overall, the work reveals a universal, mechanically driven pathway for vesicle formation in fluid membranes and offers a programmable platform for membrane-based materials.

Abstract

Formation and rupture of vesicles is a fundamental process underlying diverse phenomena in biology, materials science, and biomedical applications. Vesicles form when the area of a growing disk-like membrane exceeds a critical value at which the edge and bending energies balance each other. Observing such topological transitions in lipid bilayers is a challenge because of their nanoscale dimensions and rapid dynamics. We study a scaled-up model of colloidal membranes assembled from rod-shaped colloidal particles. The unique features of colloidal membranes enable the real-time visualization of spontaneous closure driven by instability relevant to all membrane-based materials. First-principles theory quantitatively predicts the instability point for vesicle formation and intermediate membrane conformations during the disk-to-vesicle transition. The instability generates monodisperse, selectively permeable colloidosomes with size controlled by gravity and membrane thickness, providing a scalable and programmable platform for diverse applications.

Figures (15)

• Figure 1: Vesicle formation from growing membranes. a, Rod-like particles assemble by the depletion attraction (orange arrows), which is balanced by electrostatic repulsion (blue arrows). b, A surface-anchored membrane continuously grows through the addition of individual rods. The edge energy of a growing membrane increases and eventually exceeds the size-independent bending energy of a closed vesicle, which triggers a mechanical instability that drives spontaneous closure. c, Continuous growth of a ceiling-anchored membrane lying in the plane of the page. d, Numerous polydisperse membranes anchored to the ceiling. e, Perimeter length L and area A over time during growth. f, Total fraction of particles incorporated into membranes $f_\mathrm{assembly}$ over time. g, Transformation of a disk-like membrane into a closed vesicle takes about 30 minutes. Time is relative to the onset of instability.
• Figure 2: Kinetic pathways of vesicle formation a, Monodisperse vesicles and flattened membranes anchored to the ceiling. b, Distribution of vesicle diameters obtained via mechanical instability (red, $36.1 \pm 3.2\,\mu\mathrm{m}$, $N = 76$) and gravity inversion method (gray, $73.0 \pm 15.5\,\mu\mathrm{m}$, $N = 73$) adkins_topology_2025. c, 3D meshes from imaged membrane (top) and axisymmetric minimum-energy (AME) model predictions (bottom) for the same area and perimeter. Experimental times are from the instability onset. d, Radial mean-curvature profiles $K(r)$ from the experimental 3D mesh (red) and the AME prediction (blue) at the instability onset, compared with the spherical-cap (SC, green) model. Dots and shading denote the mean and 95% confidence interval. Inset: corresponding 3D mesh and AME surface illustrating the definitions of the radial distance and mean curvature. e, Time evolution of curvature profile $K(r)$ during early closure, overlaid with AME model predictions (solid lines). The colors correspond to the times in the inset, which shows the perimeter over time. f, Energy landscapes as a function of perimeter $L$ for three areas $A = 1840, 3260,$ and $4790 \,\mu\mathrm{m}^2$ (blue, green, and red). Filled squares and circles denote flat disks and closed vesicles, respectively. The black arrow indicates the energy barrier. The top images show the AME model predictions corresponding to triangular markers along the curves.
• Figure 3: Gravity and membrane mechanics controls colloidosome size. a, Time lapse of floor (blue arrows) and ceiling (red arrows) anchored membranes. Floor-anchored membranes exhibit instability earlier in the growth cycle. b, Size distributions for ceiling (red) and floor (blue) anchored membranes. Floor-formed vesicles have a smaller size ($32.1 \pm 1.9\,\mu\mathrm{m}, N = 72$). c, Due to the difference in the change in the vertical position of the center-of-mass, gravity impedes the formation of ceiling-anchored vesicles while assisting bottom-growing ones. d, Stability of the 3D vesicle versus 2D disks as a function of rescaled area $\hat{A} = A/A^*$ and $\rho_\mathrm{a} g (2\kappa + \bar{\kappa})^2 / \gamma^3$, calculated with the AME model. Open stable indicates the regime where disk-shaped membranes are energetically favorable, Open metastable indicates the regime where vesicles are energetically favored and disk-shaped membranes are metastable, and Closed stable indicates the regime where the barrier for the transition from disk to vesicle disappears. The red and blue dashed lines correspond to ceiling and floor-anchored 200-nm membranes. The green dashed line represents 315-nm membranes anchored to the ceiling. The yellow curve is the SC model prediction for the onset of the mechanical instability.
• Figure 4: Complete closure and large-scale formation of vesicles a, Induced by a 30-s lateral centrifugal trigger, the ceiling-anchored vesicle detaches and sediments. Blue arrow marks the open pore, which diffuses across the vesicle surface and closes by 27 min. b, Size distributions for anchored (red, $37.7 \pm 1.2\,\mu\mathrm{m}, N = 16$) and sedimented (blue, $38.4 \pm 1.5\,\mu\mathrm{m}, N = 16$) vesicles. c, Pore-centered cross-sectional views in the $xy$- and $xz$-planes. The dashed circles indicate the pore. d, Vesicle formation over two days under an oblique centrifugal force. Cross-sectional slices in $xy$-, $xz$-, and $yz$-planes reveal closed vesicles layered along the chamber wall. e, 3D cross-sectional views of the same sample from (d) after additional centrifugation along the $x$-axis. Dense vesicles accumulate along the chamber wall.
• Figure E1: Time evolution of axial fluorescence intensity profiles.a, Time-lapse 3D imaging of the growth of membranes, starting 3 hours after sample preparation. b, Mean fluorescence intensity in the $xy$-plane at each axial $z$ position. The profiles are color-coded by time (3--72 hours). Two distinct peaks are observed near the chamber floor and ceiling, corresponding to membrane growth and vesicle formation at the surfaces. c, Magnified view of the dashed region in (b). Nonzero intensity is also maintained in the mid-axial region between the two surfaces, indicating the presence of isotropically dispersed particles. Over time, the mid-plane intensity gradually decreases, accompanied by a corresponding increase near the ceiling and floor planes, indicating continuous recruitment of dispersed particles into membranes.

Theorems & Definitions (2)

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