Programming Nonlinear Interfacial Mechanics of Synthetic Cells: Lipid Geometry and DNA Nanostructures

TL;DR

An analytical framework is established that captures the nonlinear elastic response of lipid-membrane-coated synthetic cells under micropipette aspiration and demonstrates that nonlinear interfacial mechanics can be programmed by altering the molecular geometry and effective dimensionality of adsorbed elements.

Abstract

Soft interfaces formed by lipid membranes are fundamental to living cells, synthetic cells, and membrane-based soft materials. However, a quantitative framework linking molecular organization with nonlinear interfacial mechanics remains elusive. Here, we establish an analytical framework that captures the nonlinear elastic response of lipid-membrane-coated synthetic cells under micropipette aspiration. Incorporating both area stretching and curvature bending enables the model to quantitatively reproduce the complete pressure-displacement response within the small-deformation regime. This approach reduces interfacial mechanics to two parameters: the in-plane area-stretching modulus and an out-of-plane bending-related term. Using this unified framework, we experimentally demonstrate that nonlinear interfacial mechanics can be programmed by altering the molecular geometry and effective dimensionality of adsorbed elements. The lipid molecular shape and curvature-dependent packing regulate in-plane stiffness, while DNA nanostructures, the other adsorbed element, introduce an orthogonal control axis via dimensionality: isolated motifs primarily enhance area stretching, whereas three-dimensional network architectures markedly reinforce bending resistance. Together, these results establish a general molecular design principle for programming interfacial mechanics and provide a quantitative foundation for engineering mechanically tunable synthetic cells and soft interfaces.

Figures (3)

• Figure 1: Analytical model for the deformation of membrane-covered spherical droplets during micropipette aspiration. (a) A droplet with radius $R$ is aspirated by a pipette with an inner radius $R_\mathrm{p}$ under a certain pressure difference $P$ between the external environment and the interior of the pipette. The resulting deformation in the aspirated region includes the surface stretching and bending due to the aspiration length $L$. Stretching and bending are characterized by an area-stretching modulus $K$ and a bending modulus $k$, respectively. (b) Two different molecular-level scenarios of the interface during surface stretching: (Top) When the lipid supply rate from the reservoir is sufficiently fast compared to deformation time, the interfacial tension $\gamma$ is maintained to be constant ($\gamma$=$\gamma_\mathrm{0}$), and (Bottom) when the supply rate is slow, the strain is constant (constant area-stretching modulus, $K$), but $\gamma$ varies with expansion ($\gamma$=$\gamma$($K$)). (c) Curvature change of the lipid membrane: (Top) The schismatic of the neutral surface of the lipid membrane with a thickness $h$ in the aspirated region inside the pipette. Curvature variations mainly arise in the aspirated spherical segment (purple) and the pipette edge (yellow). (Bottom) Considering the spontaneous curvature of lipids (curvature radius $R_0$), curvature changes from the initial $1/R_0$ to $1/R'$ in the aspirated spherical segment. (d) Two typical experimentally obtained $P$--$x$ curves (red; left: convex-downward, right: convex-upward) and their fits using our model based on Equation \ref{['eq:model']} (black solid lines) and the conventional fits with a constant $\gamma_\mathrm{0}$ (black dashed lines).
• Figure 2: Micropipette aspiration of droplets with different types of lipids. (a) A microscope image showing a droplet aspirated by a pipette with $R_{\mathrm{p}}=12$$\mu$m at an aspiration pressure, $P$. (b, c) Typical $P$--$x$ curves for droplets with each lipid (circles) and their fits using our model based on Equation \ref{['eq:model']} (black solid lines). (d) $K$ (left) and $\gamma_0+\tilde{k}$ (right) for each lipid droplets. PE shows the largest values both in $K$ and $\gamma_0+\tilde{k}$. ($n$ = 6, 7, 9 and 25 for PG, PC, PE and TAP, respectively). (e) Schematics illustrating lipid molecular geometry and their adsorption at the interface. PE has a relatively small headgroup cross-sectional area compared with its hydrophobic tails, i.e. inverted-cone geometry. PC, PG, and TAP possess comparable head and tail cross-sectional areas, i.e. cylindrical lipids. Upon adsorption onto a surface with a large radius of curvature, PE molecules are easily packed on the membrane with small headgroups, resulting in an increased surface number density compared with the other lipids. (f) Schematic illustration of the opposite dependence of $\gamma_0$ and $\widetilde{k}$ on interfacial adsorption. While increasing interfacial adsorption generally reduces $\gamma_0$, it simultaneously enhances $\widetilde{k}$. When the spontaneous curvature $c_0$ of the adsorbed molecules is larger, $\widetilde{k}$ is shifted to higher values. (g) $K$ (left) and $\gamma_0+\tilde{k}$ (right) for PE droplets at two different lipid concentrations. The absence of any significant change in either parameter indicates that the interfacial adsorption of PE is already saturated at 1 mM. (h) The curvature dependency of $K$ (left) and $\gamma_0+\tilde{k}$ (right) for PE droplets. Light gray dashed lines indicate the average values. The dashed line for $K$ is calculated using data with $1/R \gtrsim 0.02~\mu\mathrm{m}^{-1}$.
• Figure 3: (a) Schematics of hybridization of DNA with and without sticky ends by decreasing the temperature. The three different DNA oligomers form a Y-shaped dsDNA motif. In the presence of sticky ends, the Y-motif DNAs further hybridize to create a network structure, whereas motifs without sticky ends remain isolated. These nanostructures electrostatically localize beneath the membrane when encapsulated within lipid-coated droplets. (b) Typical $P$--$x$ curves for droplets with DNA nanostructures (circles) and their fits using our model based on Equation \ref{['eq:model']} (black solid lines). (c) $K$ (left) and $\gamma_0+\tilde{k}$ (right) for each DNA nanostructures (Y0 and Y4). For reference, the DNA-free values (--) obtained for 1 mM TAP in the previous section are also shown ($n$ = 25, 16 and 10 for --, Y0, and Y4, respectively). (d) Schematics of Y0 and Y4, which are confined in quasi-two-dimensional and three-dimensional configurations, respectively. Despite having the same total number of DNA motifs, the effective surface density of DNA motifs directly adsorbed at the interface is higher for Y0 than for Y4. (e) The average values of $K$ and $\gamma_0+\tilde{k}$ for Y0 and Y4 with those of different lipids (obtained from Figure \ref{['fig:2']}d). The error bars represent the standard error. A light gray line indicates the scaling relation, $\propto K^3$, expected from thin-film elasticity theory.