Measuring Lipid Membrane Viscosity Using Rotational and Translational Probe Diffusion

The two-dimensional fluidity of lipid bilayers enables the motion of membrane-bound macromolecules and is therefore crucial to biological function. Microrheological methods that measure fluid viscosity via the translational diffusion of tracer particles are challenging to apply and interpret for membranes, due to uncertainty about the local environment of the tracers. Here, we demonstrate a new technique in which determination of both the rotational and translational diffusion coefficients of membrane-linked particles enables quantification of viscosity, measurement of the effective radii of the tracers, and assessment of theoretical models of membrane hydrodynamics. Surprisingly, we find a wide distribution of effective tracer radii, presumably due to a variable number of lipids linked to each tracer particle. Furthermore, we show for the first time that a protein involved in generating membrane curvature, the vesicle trafficking protein Sar1p, dramatically increases membrane viscosity. Using the rheological method presented here, therefore, we are able to reveal a class of previously unknown couplings between protein activity and membrane mechanics.

Figure 1

Experimental setup. (a) Schematic of a membrane spanning an aperture. Fluorescent microspheres are associated with the membrane via a protein linkage, including some that are also bound with other microspheres to form the nonspherical tracers considered in the text. (b) Fluorescence images of one microsphere pair, separated by 0.3 sec. Both rotational and translational motion are apparent as the tracer thermally diffuses. The final image shows the best-fit center and orientation of the tracer. Scale: $0.123\mu \mathrm{m}/\text{pixel}$.

Figure 2

Diffusive behavior of tracers at DOPC bilayers. (a) Diffusion coefficients for motion parallel ($D_{\parallel }$) and perpendicular ($D_{\perp }$) to the tracer long axis. The best fit line, shown in red, has slope $B=1.03\pm 0.04$, indicating isotropic diffusion. (b) and (c) Translational and angular mean square displacements versus time for several tracers. The average is shown as a thick gray line, while a dotted line with $\text{slope}=1$ (expected for purely diffusive motion) is shown as a guide to the eye.

Figure 3

Effective inclusion radius and viscosity of a DOPC bilayer. (Main panel) Translational and rotational diffusion coefficients. Each data point is the average of 4 to 24 individual tracer measurements, with the error bars indicating the standard deviations. Decreasing inclusion radius size is indicated by progressively lighter shades of green. The curves are best-fit constant-viscosity contours determined by the SD (light green, solid), the HPW (dark green, solid), and NLP (dark green, dashed) models. (Inset) Histogram of effective tracer inclusion radii on log-linear axes. The bins correspond to the data points in the main panel, with radii obtained using the SD model, and placed such that the left-hand edge of the bin corresponds to the largest inclusion radius in its set. Though peaked near the microsphere radius of 100 nm, much larger inclusion radii are evident.

Figure 4

Membrane viscosity measured at different concentrations of the trafficking protein Sar1p on a log-log scale. The plot shows the mean and standard error of viscosity values determined by fitting individual paired-tracer diffusion coefficients to the HPW model, at each protein concentration examined. Inset: The effective radius for the same data, also on a log-log scale.