Hydrodynamic shear dissipation and transmission in lipid bilayers

Abstract

Vital biological processes, such as trafficking, sensing, and motility, are facilitated by cellular lipid membranes, which interact mechanically with surrounding fluids. Such lipid membranes are only a few nanometers thick and composed of a liquid crystalline structure known as the lipid bilayer. Here, we introduce an active, noncontact, two-point microrheology technique combining multiple optical tweezers probes with planar freestanding lipid bilayers accessible on both sides. We use the method to quantify both fluid slip close to the bilayer surface and transmission of fluid flow across the structure, and we use numerical simulations to determine the monolayer viscosity and the intermonolayer friction. We find that these physical properties are highly dependent on the molecular structure of the lipids in the bilayer. We compare ordered-phase with liquid disordered-phase lipid bilayers, and we find the ordered-phase bilayers to be 10 to 100 times more viscous but with 100 times less intermonolayer friction. When a local shear is applied by the optical tweezers, the ultralow intermonolayer friction results in full slip of the two leaflets relative to each other and as a consequence, no shear transmission across the membrane. Our study sheds light on the physical principles governing the transfer of shear forces by and through lipid membranes, which underpin cell behavior and homeostasis.

Keywords: intermonolayer friction; lipid bilayers; membrane viscosity; microfluidics; optical tweezers.

Fig. 1.

Interfacing lipid bilayers with optical tweezers. (A) Overview of the microfluidic device used for lipid bilayer formation and optical tweezers experiments. (B) Close-up view of one aperture within the microfluidic device with a lipid bilayer spanning across it. (C) High-magnification optical image of a lipid bilayer spanning across an aperture. (D) Schematic and (E) image of the experiment for measuring the drag force. (F) Schematic and (G) overlaid image sequence of the experiment for measuring flow transmission. (G) The red dashed arrow represents the direction of motion. The images were captured using a light microscope and overlaid with a time step of 22 ms between images. Yellow dashed lines are used at the edges of the apertures in E and G to help visualize the bilayer. (Scale bars: A, 5 mm; E and G, 10 $\mathrm{\mu }$m.)

Fig. 2.

Drag force and flow transmission for a sphere translating parallel to lipid bilayers. (A) Relationship between the coefficient of drag $C_{\delta }=\frac{D}{6\pi \mu Ua}$ and the distance $d$ from the lipid bilayer and solid glass wall. The model is from Eq. 1 (47). (B) Relationship between the flow speed $u^{-}$ at a distance $r=3.8\hspace{0.17em}\mathrm{\mu }\text{m}$ from the moving sphere and the translation velocity $U$ of the sphere. The model is from Eq. 2 (48). Error bars represent SDs from separate experiments performed on different membranes formed within different microfluidic devices.

Fig. 3.

Hydrodynamic model of lipid bilayers. (A) Schematic of the computational domain with a sphere of radius $a$ translating parallel to a lipid bilayer of thickness $2t_m$ with a velocity $U$ at a distance $d$ away. The domain is split into upper aqueous ${\mathbf{u}}^{+}$, upper lipid monolayer ${\mathbf{u}}_m^{+}$, lower lipid monolayer ${\mathbf{u}}_m^{-}$, and lower aqueous ${\mathbf{u}}^{-}$. (B and C) Velocity profiles for the $xz$ plane passing through the center of the sphere. (D and E) Velocity profiles for the $xy$ planes coinciding with the upper ${\mathbf{u}}_m^{+}$ and lower ${\mathbf{u}}_m^{-}$ monolayers. The velocities ${\mathbf{u}}^{\pm }$ and ${\mathbf{u}}_m^{\pm }$ are normalized by the translating velocity $U$ of the sphere. The profiles are for (B and D) ${\eta }_{\mathrm{m}}=2t_{\mathrm{m}}\eta =1.7\times 10^{-8}$ Pa$\cdot$s$\cdot$m and $b=3.4$ Pa$\cdot$s$\cdot {\mathrm{m}}^{-1}$ and for (C and E) ${\eta }_{\mathrm{m}}=1.9\times 10^{-10}$ Pa$\cdot$s$\cdot$m and $b=1.9\times 10^4$ Pa$\cdot$s$\cdot {\mathrm{m}}^{-1}$.

Fig. 4.

Numerical simulations of drag force and flow transmission for a sphere moving parallel to lipid bilayers. Contour plots representing how (A) coefficient of drag $C_{\delta }$ and (B) coefficient of transmission $C_{\tau }=\frac{u^{-}}{u^{-}{|}_{r=3.8a}}$ (where $u^{-}{|}_{r=3.8a}$ is given by Eq. 2) vary with monolayer viscosity ${\eta }_{\mathrm{m}}$ and interlayer friction $b$. (C) Isocontours of the coefficient of drag $C_{\delta }$ (dashed lines) and the coefficient of transmission $C_{\tau }$ (solid lines). The shaded regions represent the experimental values (averages and SDs from Fig. 2A and slopes and 95% CIs from Fig. 2B) for DPPC (black), DOPC (blue), and DOPC/DPPC (green).