About a new paper from my lab  on how membranes flow through water, featuring our shortest title ever!
For many years I’ve been interested in the physical properties of cell membranes, properties determined in large part by the underlying lipid bilayer. Bilayers are remarkable materials, and my research group has measured characteristics such as stiffness and viscosity in a variety of studies.
We became interested in a very simple question: how does a lipid membrane flow through water? Imagine a solid sphere of radius R, pulled through water:
If it’s small or slow, so the flow isn’t turbulent, the velocity (v) of the sphere is proportional to the pulling force (f):
f = 6 π η R v,
where η is the fluid viscosity. Imagine instead an air bubble moving through water, pulled perhaps by its buoyancy. Now,
f = 4 π η R v.
Note that what has changed is the number, 6 or 4.
Now imagine it’s a sphere of liquid. Again f is proportional to v, but the number, which I’ll call C, is something between 4 and 6, dependent on the viscosities of the sphere and the surroundings. The different Cs arise because of how fluid flows at the interface. C is 6, for example, at a “no-slip” interface, at which the fluid velocity must go to zero as we approach the solid surface.
Finally, imagine a sphere of lipid bilayer, rather like a cell. What’s its C? That’s the question we set out to answer. In addition to being fundamentally interesting (to us at least), this “C” comes up in analyses of flowing blood and suspensions of liposomes. (Liposomes are small spheres of lipid membrane, used for drug delivery and other applications.)
It’s widely assumed that C=6 for lipid bilayers. It has at times been speculated that perhaps C is less than 6, because lipid bilayers are not solids but liquids — two dimensional fluids. (References for these statements are in our paper.) There are theoretical arguments that C must be 6 for an ideal two-dimensional fluid, i.e. one that is infinitely thin or that can’t have any flow perpendicular to its surface.
Remarkably, however, no one had directly measured C.
Therefore, we set out to measure how lipid surfaces flow through water. Getting spheres of membrane is easy; we made giant lipid vesicles, spheres of lipid bilayer tens of microns in diameter. Rather than applying a force to them, which is difficult, we instead watched them do nothing, letting them simply diffuse, driven by thermal energy, suspended in a watery sea far from any wall or surface. The diffusion coefficient is directly related to the drag coefficient, and therefore C. (Below: a scan through such a giant vesicle.)
This required two key techniques. One is light sheet microscopy, which I’ve written about before (e.g. this and this) mostly in the context of our studies of the gut microbiome. Light sheet microscopy allows fast imaging of “slices” of a sample, in our case letting us track the central plane of a vesicle. Crucially for us, the vesicle can be floating deep in the interior of the imaging chamber, far from any wall that would alter its diffusive behavior. The second technique is accurate determination of vesicle position, which we do using Hough transformation and the symmetry-based algorithm I developed earlier. This sounds straightforward, but it took us a couple of years to get it to work. Graduate student Philip Jahl valiantly and tenaciously spearheaded the effort and performed all the experiments.
We measured the diffusion of solid spheres, and verified that C=6. We measured the diffusion of oil droplets, and verified that C was what it should be given their viscosity. We examined lipid vesicles and found C=6 ! (See the paper for uncertainties and other technical notes.)
Lipid bilayers, it seems, move through water like solids do. It is perhaps reassuring that the common assumption is correct.
Our methods pave the way for imaging-based studies of more complex hydrodynamic systems. For example: lipid bilayers can undulate, driven by thermal forces or by the activity of embedded proteins; what does this do to their flow properties? (I.e. What is “C” for a floppy, fluctuating membrane?)
I like the fact that we’ve measured a basic property of lipid membranes that had not been measured before. Admittedly, it approaches the border between “basic” and “obvious.” Reviewers at Physical Review Letters thought it crossed that border, but were fine with the paper being in the new sister journal Physical Review Research. Regardless of theory, Philip and I believe that experimentally pinning down the nature of membrane drag is in itself important even if the answer isn’t surprising from a theoretical perspective. Nature often doesn’t conform to theoretical ideals and experiment, fundamentally, is the arbiter of truth.
Another advantage of exploring something conceptually simple is that it enabled the shortest title of any article I’ve ever written — “Lipid Bilayer Hydrodynamic Drag.” Just four words! That will be a tough record to beat.
 Philip E. Jahl, Raghuveer Parthasarathy, “Lipid Bilayer Hydrodynamic Drag.” Phys. Rev. Research 2, 013132 (2020). https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.013132
— Raghuveer Parthasarathy, February 7, 2020