Osmotically Induced Shape Changes in Membrane Vesicles

Abstract

We develop a self-consistent free-energy framework in which membrane shape and osmotic pressure are determined simultaneously in a finite reservoir by minimizing bending elasticity and solute entropy. Solute conservation makes osmotic pressure a thermodynamic variable rather than an externally prescribed parameter, producing a nonlinear coupling between membrane mechanics and solvent entropy. This coupling modifies the classical stability condition for spherical vesicles: instability emerges from global free-energy competition rather than the linear Helfrich stability criterion. The resulting critical pressures differ by orders of magnitude from Helfrich predictions and agree with simulations for small and large unilamellar vesicles. The framework is relevant to cellular environments involving biomolecular condensate confinement as well as synthetic vesicles and the development of osmotic-pressure-driven encapsulation platforms.

Figures (9)

• Figure 1: A discotic membrane shape obtained from (a) variational shape calculation, and (b) CGMD simulations of lipid vesicles with hydrophilic head (red) and hydrophobic tail (green) groups in the presence of osmolytes (black). Panel (c) shows an axisymmetric shape in the $z(s), x(s)$ plane and the geometric parametrisation used to compute equilibrium vesicle configurations.
• Figure 2: Shape diagram in the $l u(0)-l^2 \lambda$ plane showing solutions of the scaled shape equations in the absence of osmolytes including (a) spheres (blue solid), (b) stomatocytes (green dash-dotted), (c) prolate and oblate shapes (orange dashed), and (d) $L3$ shapes red dotted. The $\bigstar$ indicates the point on the oblate branch, such that solutions of the shape equations to its left become unphysical, self-intersecting shapes.
• Figure 3: Free energy $F_T$ (in units of $k_B T$) as a function of the osmolyte number $N$ for different shapes (a) sphere (blue dots), (b) prolate (green dashed), (c) oblate (red dash dotted), and (d) stomatocyte (brown solid) showing a sequence of shapes that minimize the free energy. The free energy $F_T$ for $L3$ shapes (not shown) are much higher ($>1000 k_B T$). The $\bigstar$ indicates values of $N$ beyond which self-intersecting shapes appear in the oblate branch. Other self-intersecting solutions of higher energies are omitted. Inset: Shows $\bar{P}(V_I)$ for solutions in the oblate branch (orange solid) and the osmotic pressure $\Pi(\phi(V_I))/k_c$ for $N=2400$ (blue dashed) and $N=3000$ (green dash dotted). The intersections correspond to self-consistent solutions of the shape equations.
• Figure 4: A phase diagram obtained from CGMD simulations in the $\Pi-V$ plane, and the associated equilibrium vesicle shapes (panel (a)). The critical concentration at which a spherical vesicle becomes unstable is identified by calculating the asphericity parameter $\kappa^2$ is shown in panel (b), as a function of time $\tau$ for different osmolyte number $N$. For $N \lesssim 10^4$$\kappa^2 \approxeq 0$, and jumps to a finite value once for $N > N_c \approx 1.75\times10^4$ the mean shape is non-spherical.
• Figure 5: Schematic of an axisymmetric vesicle shape. The $z$-axis denotes the axis of symmetry, while $s$ is the arclength along the meridional curve $(x(s),z(s))$. The angle $\psi(s)$ between the radial direction and the tangent to the curve varies from $0$ to $\pi$ between the two poles.