Measuring Membrane Viscosity in the Widening Gyre

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The lipid membrane surrounding every living cell is a complex structure that has inspired decades of research into its biological functions and material properties. It might seem that a property of lipid membranes as fundamental as viscosity would be well characterized and predictable. However, membrane viscosity has proven surprisingly challenging to measure. Approximate values and even relative viscosities in ordered and disordered phases have been published, but we still lack systematic measurements showing how the viscosities of complex lipid mixtures vary with their composition. For example, most experimental results suggest that viscosity of cell plasma membranes increase with cholesterol content, but predicting the magnitude of this increase is not possible.

These measurements are needed because viscosity governs important biological processes. Some of the earliest measurements of membrane viscosity are derived from the shape changes undergone by red blood cells as they are confined or deformed during their movement through blood vessels (1), indicating that the material properties of the plasma membrane are required to predict the dynamic response of a cell to environmental forces.

Viscosity comes into play in more dramatic events as well. Malaria parasites multiply inside red blood cells, then burst the cell to release parasites so that they can infect additional cells. During bursting, the cell membrane (along with the associated cytoskeletal network) porates and then rolls up to invert the cell and expel the parasite bodies. This rapid deformation involves large shear flows, and so the timescale is determined by the lipid viscosity (2).

At smaller length scales, viscosity controls the diffusion and transport of proteins and lipids embedded in the membrane. The theory of homeoviscous adaptation, motivated by the observation in multiple cells and organisms that lipid composition is actively adjusted after temperature or concentration changes in a way that maintains constant viscosity, is based on the expectation that membrane viscosity has a strong influence on protein and cell function (even if the precise mechanisms are not known).

Most biological lipid membranes are in a fluid state; in addition, they may extend microns or even centimeters in the membrane plane but are only nanometers thick. This unique quasi-two-dimensional structure, combined with the coupling between lipids and the surrounding water, creates experimental challenges in measuring and defining viscosity. Consequently, reliable data exist only for a rather limited number of different membrane compositions. Although there is general agreement on the magnitude of ordered and disordered phase viscosities obtained by different labs and techniques, the differences are still large enough to obscure the variation due to lipid composition. This makes it difficult to synthesize information into a coherent model of how lipid composition determines the material properties of membranes in cells.

In this issue of Biophysical Journal (3), Sakuma and colleagues introduce a novel method for determining membrane viscosity that overcomes many of the difficulties of previously available techniques. They have developed an exceptionally robust experiment, making it possible for the first time to map viscosity changes across many different membrane compositions.

Theirs is far from the first experiment measuring membrane viscosity. A common strategy is to measure the diffusion of very small tracers such as single fluorescent lipids. Methods such as FRAP, electron spin label resonance, and fluorescence polarization are referred to as measuring microviscosity because they reflect resistance to movement in the microenvironment surrounding individual probe molecules. The diffusion of small membrane inclusions is generally modeled by the Saffman-Delbrück equation. However, applying this equation requires determining the size of the inclusion, which is not straightforward for small, flexible molecules. Moreover, the model of the membrane as a continuous fluid does not necessarily apply on the length scales of single lipids. At even smaller length scales, conformational changes in rotor molecules have been used as a measure of viscosity. Measuring these quantities is important because the understanding of diffusion and conformational changes of small membrane components is biologically relevant. However, it is not guaranteed that the measured value of viscosity will be independent of the measurement technique unless the measurement encompasses collective motion involving large numbers of lipids.

In 1999, Dimova and co-workers performed a measurement by observing the sedimentation of a polystyrene microsphere attached to a giant vesicle (4). Challenges in interpreting this experiment arose from the similar sizes of the microsphere and the vesicle, as well as variation in the placement of the bead on the membrane. Similarly, Parthasarathy and co-workers found a range of apparent probe sizes when they tracked microspheres attached to black lipid membranes, reflecting variations in how the microspheres adhered to the membrane (5). In general, relatively large three-dimensional probes linked to 5-nm-thick membranes may behave in a way that reflects the properties of the probe and exactly how it is attached rather than intrinsic membrane properties. This can be avoided by imaging phase-separated membranes: domains of the minority phase are easily visualized and provide a probe for membrane position that is continuous with the membrane. This strategy limits the investigation to membranes occupying a phase coexistence region; however, this still encompasses a wide range of interesting compositions.

By considering the diffusion of micron-scale membrane areas that include large numbers of lipids, it is possible to measure viscosity as it is defined for continuum fluids, in terms of resistance to shear flows. Microscopic observations of micron-scale domain diffusion have yielded membrane viscosity estimates for a range of lipid compositions and temperatures (6). Multiple groups have used this method, tracking the movement of individual (minority-phase) domains to infer the viscosity of the majority phase, but it is also possible to assess the viscosity of the membrane as a whole. Hormel and co-workers showed that the correlated movement of two domains can yield a value that reflects the average viscosity of the two phases (7). Similarly, the dynamics of fluctuating domains near a critical phase transition can be analyzed to find a viscosity value in between the viscosities of the two phases (8,9).

Domain diffusion is due to thermal fluctuations; even larger-scale flows can be achieved by actively driving the system. Fluid membranes can circulate in response to flow in the surrounding fluid. If part of the membrane is prevented from flowing, this circulation creates shear in the membrane plane. Rather than observing the diffusion or fluctuations of phase-separated domains, they can be used as markers to visualize this type of larger-scale flow (10).

Sakuma and co-workers make use of a previously neglected geometrical feature of this membrane circulation. They use a micropipette positioned parallel to an immobilized vesicle to drive flow in one location, then observe the vortex flow that results in the rest of the vesicle (Fig. 1). Cleverly, they choose an observable that does not depend on the magnitude of the force, only that it is localized. The position of the vortex center depends only on three variables: the radius of the vesicle and the viscosities of the membrane and surrounding fluid. Qualitatively, when the viscosity of the membrane is small, then recirculating flows will be confined to the vicinity of the applied flow. This minimizes the volume of surrounding fluid that is displaced but results in large gradients in the membrane velocity. For larger ratios of membrane viscosity to surrounding fluid viscosity, the vortex centers will move apart as the flow spreads over the surface of the membrane. In the limit of infinite membrane viscosity, the vortices will be directly opposite each other, and the whole vesicle will rotate like a rigid sphere, although in practice this rotation is perturbed by the immobilizing micropipette. Sakuma et al. measured the position of the vortex center by utilizing a phase-separated membrane, in which preferential partitioning of a fluorescent probe provides a marker for membrane position. They tracked the trajectories of these domains, then determined the center of their orbits.

Figure 1.

A localized flow (large arrow) applied just above a lipid vesicle held on a micropipette causes the membrane to circulate. The position of the two vortices that form on the membrane surface is determined by the membrane viscosity. To see this figure in color, go online.

Another strength of this approach is its large dynamic range. Sakuma et al. were able to measure viscosities over more than two orders of magnitude. Other techniques, especially those reliant on thermal fluctuations, are more limited in the range of viscosities that can be measured. Achieving a large dynamic range allows for direct comparisons between disparate compositions using one method. Another positive feature of this method is that it measures flows that extend over tens of microns and consequently obtains the effective viscosity of the whole membrane. By choosing lipid compositions along a tie line, Sakuma and co-workers have contributed the most precise description to date of how the overall viscosity of a heterogeneous membrane varies with the area fraction of the two phases that make it up.

Their work brings a flood of new results to the field. Some of these results, such as a significant drop in viscosity near the critical point, contrast with previous determinations (8,9) and will require additional experiments for confirmation. Others, such as the trend in membrane viscosity with cholesterol content, should stimulate future modeling and simulation. The viscosity landscape mapped out by Sakuma and co-workers represents a significant advance to our understanding of membrane material properties and opens the door to more experiments and deeper understanding of both model membranes and living cells.

Editor: Markus Deserno.