Dynamic Bidirectional Coupling of Membrane Morphology and Rod Organization in Flexible Vesicles

Abstract

The ordering of rod-like particles in soft, deformable containers emerges from the interplay of anisotropic interactions, geometric confinement, and boundary compliance. This competition couples internal particle organization to container morphology and is central to biological processes such as cell motility, division, and encapsulation, in which cytoskeletal filaments confined by lipid membranes actively reshape cells. Using a minimal model combining experiments and simulations of colloidal rods encapsulated in lipid vesicles, we show that soft confinement drives a bidirectional coupling between internal order and vesicle shape. This interplay gives rise to a phase diagram in which elongated vesicles promote nematic alignment at lower packing fractions, whereas higher packing fractions induce smectic-like ordering that reshapes vesicles into plate-like morphologies with increased bending energy. Furthermore, by controlling vesicle volume and membrane area, we demonstrate that these boundary conditions enable reversible tuning of both vesicle shape and internal rod organization. This study establishes a promising route for dynamically controlling colloidal self-assembly in soft containers and for mimicking ordering in cell-like compartments.

Figures (5)

• Figure 1: Experimental and numerical model setup. (a) Composite confocal fluorescence images of the midplane of a spherical isotropic vesicle and a linear nematic vesicle. The vesicle membrane is shown in red, and the encapsulated silica rods in green. The inset shows a SEM image of a representative silica rod. Scale bars: 5 (confocal) and 1 (inset). (b) 3D reconstruction of vesicles from confocal fluorescence $z$-stacks. Image stacks were segmented using the LimeSeg plugin in FIJI (ImageJ) machado2019limesegschindelin2012fiji, enabling quantitative measurements of vesicle volume $V_\mathrm{ves}$, surface area $A_\mathrm{ves}$, and number of rods $N$. (c) Coarse-grained simulations in LAMMPS, consisting of rigid rods encapsulated within a meshless membrane. Isotropic, nematic, and smectic rod ordering is obtained by gradually decreasing the vesicle volume from an initially spherical, isotropic configuration. The rod color corresponds to their local nematic order $S_i$ (isotropic and nematic vesicles), and local smectic order $\tau_i$ (smectic vesicle).
• Figure 2: Phase diagram of rod order and vesicle shape as a function of packing fraction $\eta$ and reduced volume $\nu$, for vesicles encapsulating $N = 30$ rods with aspect ratio $L/D = 5$. Colored data points indicate simulation results, while numbered white markers correspond to representative experimental vesicles. The colors indicate the rod ordering: blue for isotropic, red for nematic, and green for smectic. The symbols denote the vesicle shape: circles for spherical, triangles for linear, and squares for plate-like vesicles. The background colors denote the approximate boundaries of the different rod ordering regimes, while the black dashed lines distinguish the spherical, linear, and linear/plate regions. Representative snapshots from both experiments and simulations are shown for different phases, corresponding to the numbered markers. The white region in the top-right corner is inaccessible, as spherical vesicles (high $\nu$) are geometrically incompatible with very high rod packing. The red-white dashed lines correspond to the volume and area modulation explored in Fig. \ref{['fig:VolumeChange']}. Scale bars: 5.
• Figure 3: Bending energy of the vesicle ($E_\mathrm{b}$) rescaled by the bending energy of a vesicle containing spheres ($E_\mathrm{b,sph}$). (a) Color map of the rescaled bending energy as a function of the vesicle's reduced volume $\nu$ and rod packing fraction $\eta$. Blue (red) color indicates low (high) rescaled bending energy. The black dashed lines correspond to different vesicle shape regions (Fig. \ref{['fig:phase']}) The red area corresponds to the coexistence region of linear and plate-like vesicles. Highlighted are the linear (triangle) and plate-like (square) morphologies from (c). (b) Histogram of the rescaled bending energy within the coexistence region, the gray (green) histogram corresponds to linear (plate-like) vesicles. (c) Representative simulation snapshots of a linear and plate-like vesicle with their corresponding bending energy annotated.
• Figure 4: Correlation between membrane curvature and rod ordering in smectic vesicles with different morphologies. (a–c) Confocal midplane cross-sections overlaid with the in-plane membrane curvature $c_\mathrm{plane}$, defined as the curvature of the two-dimensional vesicle contour in the imaging plane (red: high curvature; blue: low curvature), given for a smectic linear (a), sphere (b), and plate-like (c) morphology. Below each image, a representative simulation snapshot of a corresponding vesicle morphologies is shown. Scale bars: 5. (d) In-plane membrane curvature $c_\mathrm{plane}$, expressed in units of $1/R_\mathrm{ves}$, where $R_\mathrm{ves} = (3V_\mathrm{ves}/4\pi)^{1/3}$ is the vesicle radius, plotted as a function of the normalized arc length $l/P$ along the vesicle outline. Here, $l$ is the curvilinear distance measured along the two-dimensional vesicle contour and $P$ is the total contour perimeter. (e) Correlation between the position along the rod, $s$ (schematic inset), expressed in units of $L/2$, and the membrane curvature along the rod axis, $c_{\parallel}$ (see Methods), for linear (cyan), spherical (red), and plate-like (green) morphologies. Data represent averages over all rod segments within 1.5 of the membrane. Experimental and simulation results are shown by filled circles and open squares, respectively. For linear vesicles, rods near the vesicle tips and along the base exhibit distinct curvature responses; their mean behavior is indicated by the dashed line.
• Figure 5: Rod packing under controlled changes in vesicle volume and membrane area. From left to right, panels show the vesicle's configuration as the internal volume decreases (a) and membrane area increases (b). The top row shows experimental snapshots, while the bottom row illustrates simulated vesicles at comparable reduced volume $\nu$ and packing fraction $\eta$ (within 15%). For the membrane-area modulation experiments, $\nu$ and $\eta$ were estimated from 2D cross-sections (see Supporting Fig. S8). The values reported above each snapshot correspond to those used in the simulations. Scale bars: 5.