Viscosity in two dimensions

lipid bilayer

Continuing my trend of belatedly writing short descriptions of papers my group has published, this one came out in May, describing a new approach we developed for measuring the viscosity of lipid membranes:

“Measuring Lipid Membrane Viscosity Using Rotational and Translational Probe Diffusion,” Tristan T. Hormel, Sarah Q. Kurihara, M. Kathleen Brennan, Matthew C. Wozniak, and Raghuveer Parthasarathy, Phys. Rev. Lett. 112, 188101 (2014). [Link]

Viscosity is one of the most important material properties of any fluid, characterizing its resistance to flow (or more technically, its response to shear stresses). We’re intuitively familiar with viscosity, observing for example how warm honey flows much more easily than cold honey. For water, oils, and many other three-dimensional fluids, viscosity is well-characterized, tabulated in books and databases. For lipid bilayers, however, the two-molecule-thick liquids (illustrated above) that make up cellular membranes, viscosity is poorly quantified. It’s hard to measure, especially because lipid membranes are essentially two-dimensional fluids, whose flow behaviors differ quite dramatically from their three-dimensional counterparts. Understanding lipid viscosity is important for understanding how structures in membranes like protein clusters and cholesterol-rich “rafts” move, how proteins can alter the fluid properties of membranes, etc. In addition, it’s just embarrassing that the state of our understanding of the lipid bilayer, nature’s most important two-dimensional fluid, lags so far behind that of three-dimensional fluids.

We therefore set out to develop a new and better approach to quantifying lipid membrane viscosity. Our method hinges on Brownian motion: the random jiggling experienced by all objects due to ever-present thermal energy. As Einstein explained over a hundred years ago, the magnitude of the random motion of a particle in a liquid is a function of the liquid’s viscosity; the greater the viscosity, the lesser the motion, a relationship that holds in any number of dimensions. In fact, if one knows the size of the diffusing particle and the temperature, measuring the “diffusion coefficient” (which characterizes the random motion) is sufficient to extract the fluid’s viscosity. One can take this approach to measuring membrane viscosity, attaching particles to a membrane and watching their Brownian motion, but one runs into a problem: the effective size of the diffusing object may be different than the particle size. As illustrated below, one can imagine a variety of geometries for the particle-membrane linkage:

membrane linkages

On the left, the effective size of the diffusing object is bigger than the particle size; on the right, it’s smaller.

We realized that in addition to the “translational” Brownian motion of particles (i.e. their meandering position), one can examine their rotational motion: the orientation of particles also shows diffusive behavior that also depends on particle size and fluid viscosity. Measuring both translational and rotational diffusion allows one to determine both the effective particle size and the viscosity. We came up with a way of making paired spherical tracer particles to link to membranes…

paired tracers

We can image these with fluorescence microscopy, and the pairs allow us to visualize their orientation:

Using this approach, we were able to measure lipid bilayer viscosity. Moreover, we were able to study what happens when a protein that’s involved in membrane deformation interacts with the lipid bilayer, discovering that it dramatically increases the two-dimensional viscosity — the first time such an effect has been reported.

We were very happy with how this project turned out. It was also gratifying to see that others liked it — it got chosen for a “synopsis” from the American Physical Society, one of just six for the week, and was also featured in a “research highlights” blurb in Nature Chemical Biology (?!).  By a great coincidence, a paper on granular materials from my neighbor Eric Corwin also got a synopsis in the same week!

Tristan Hormel, the first author on our paper, is a graduate student in my lab, working now on a very different (and better?!) way of revealing fluid properties of lipid membranes. Sarah Kurihara, the second author, was an excellent UO undergrad biology major; she’s now doing fascinating things as a Peace Corps volunteer in Lesotho. Her blog is here: http://sarahkurihara.wordpress.com/. (I recommend it.) Katy Brennan and Matt Wozniak were great summer undergrads in the lab, here as part of a REU (Research Experiences for Undergraduates) program.

As mentioned, we’re continuing to explore the fascinating fluid dynamics of lipid membranes. We’re also using particle motions to examine viscosity in other contexts, for example inside fish guts (really), which I’ll hopefully write about in the future.

“You should do birthday parties!” — Year 2 at the Oregon Country Fair

kids gyroscope country fair

Like last year, several of us from the Physics Department manned a booth at the Oregon Country Fair, the long-running hippie / arts / music / performance / counterculture festival that occurs each year outside Eugene. I worked there today, which was lots of fun. Though our booth was mostly about energy — lots of hands-on demonstrations of converting it between various forms — I spent most of my time with the wheel shown above, spinning it and handing it to passers-by who I enticed to stand on a freely-rotating platform. Via the magic of conservation of angular momentum, tilting the wheel made the person and platform spin, and tilting it the other way induced the opposite rotation. It’s wonderful to feel the wheel “pulling” in different ways, and the demonstration (a classic one) was a huge hit. A few photos:

girl and wheel

people wheel IMG_0468

peace country fair

The girl above (“Peace”) spent at least an hour with our energy demos, putting together every combination of circuit imaginable. (She was great!)

In addition to being told that we had the coolest booth at the fair, I was also given the advice in the title of this post — something to keep in mind if the department is looking for some extra cash! (Kidding aside, there would probably be a good amount of demand for science-themed entertainment, at least in Eugene.)

Though everyone loved angular momentum, we ended on a low note, as the wheel caught on and broke a piece off a little girl’s necklace. (She was very sad.) I suppose we can’t make everyone happy…

The day also reminded me of changes being made to the MCAT exam that I learned about a few weeks ago. Short version: a lot of topics are being removed from the list of content that the MCAT will cover, because they’re not particularly useful for being a doctor. One of these that ranked poorly in polls is angular momentum. This makes sense — it’s hard to think of any biological relevance of it, though its importance for other areas of science and technology is profound — but if physics courses for life scientists follow the advice of medical schools, a lot of students will never learn about how something as simple as rotation connects to deep and universal principles of how nature works.

I’ll end with a few more fair pictures:

green man IMG_0462 cropyew are here IMG_0457 cropgiant hula hoop

 

Sasquatch is an alien! (A proof in three graphs)

This week’s Economist has a fascinating map of the number of UFO sightings per capita, by state:

UFO sightings map (The Economist)

When I saw this last Friday, it raised a few questions:

  • What’s up with Washington?
  • How well do UFO reports correlate with population density? (Do aliens have a fondness for sparsely settled, wide-open spaces?)
  • Could I use any of this for group meeting this past week, in which my and Eric Corwin’s labs were continuing our exploration of good graph design?

To answer the first two questions, and possibly the third, I downloaded the UFO sightings data from the National UFO Reporting Center — an entertaining site. Population data is easy to find from the U.S. Census Bureau. Here’s UFO sightings vs. Population Density:

UFOs and population density

It’s not a bad trend! Washington is clearly an outlier. (I colored Oregon green, by the way.)

My wife and I brainstormed various other variables against which to plot the UFO data — latitude? education level? Inspiration finally struck: Sasquatch!

Thankfully, the Bigfoot Field Researchers Organization tabulates Sasquatch sightings, making it fairly easy to plot UFO sightings per capita vs. Sasquatch sightings per capita (Oregon is yellow):

UFOs and Sasquatch

Eureka! (Washington, by the way, is the data point in the upper-right.)

It’s hard to avoid the conclusion that Sasquatch is, in fact, an alien.

How can I plot all these data together? I could make some unenlightening 3D plot, but another approach would be to revisit the UFO vs. population density data, but now color each point by the state’s Sasquatch sightings:

UFO_popdens_Sasquatch

Here, red to cyan is 0 to 9 per 100,000 people. (Yes, I should have a colorbar.) Since the Sasquatch scale is rather bottom-heavy, it’s nicer if I map the square root of the Sasquatch count onto the red-cyan color scale (X = Oregon):

UFO_popdens_sqrtSasquatch

Happy World UFO Day!

P.S.

[1] If anyone wants my simple but unimpressive MATLAB function that colors points in a 2D scatter plot by the values of a third array, here it is. It would be fairly simple to add a colorbar, better hue or value sweeps, etc. Alternatively, you could pre-calculate colors and call MATLAB’s “scatter” function.

[2] If anyone wants an Excel file with all the UFO, population, and Sasquatch data, it’s here.

[3] The truth is out there!

UC vs. AirBnB

Amethyst radish -- Raghu Parthasarathy

Appallingly, the University of California system has just prohibited its employees from using AirBnB (and other peer-to-peer services) for business-related travel [link: Inside Higher Ed].

I’ve become a big fan of AirBnB [wikipedia]. For those unaware of it, it links people with rooms or apartments or houses to briefly rent out with people looking for a place to stay. It’s a great example of the internet facilitating both interaction and commerce, linking the excess supply (rooms) with demand (travelers) without the middlemen of hotels.

My family and I have used AirBnB for personal travel, but more often than this, I’ve used it for lodging during conferences. I’ve done this three times so far, and have each time been happy with it. I stayed a night in San Francisco during a computational image analysis meeting, for example, in an apartment in North Beach, walking to the meeting and wandering through one of my favorite areas. The cost: $84. Try finding a non-lethal hotel in San Francisco for that amount! It’s true that one sacrifices convenience a bit for AirBnB. It takes some effort to coordinate handoffs of keys, etc., and it’s not for everyone, or every occasion, but it can work well.

But: who cares if I dislike hotels, can put up with some risk, and like staying in interesting neighborhoods? The more important thing is that it saves money. Money for these meetings comes from my research grants. I and the people funding these grants (presumably) would prefer to spend this as much as possible on doing science; the hundreds of dollars I’ve saved by using AirBnB are hundreds of dollars that can go towards lab supplies, student salaries, equipment, etc., something that the administrators at the University of California should be encouraging, not shutting down. The decree comes from UC’s “Office of Risk Services,” which vaguely cites “insurance concerns.” The least risky action, of course, is to not travel and not work at all. Or better yet: all business-related travel could require a paid chaperone, looking out for pickpockets, oncoming traffic, and other dangers, further minimizing risk at the cost of wasted research funds. After all, the administration doesn’t benefit from its researchers saving money.

This is a short, quick post, so I included a just a small picture at the top: an amethyst radish, which I painted for a poster for a friend.

Next year, I’ll need a bigger cart

As mentioned a few weeks ago, a highlight of teaching this term was bringing in an elephant femur and a dog femur, to highlight the lack of simple proportionality between them. (The elephant’s femur is about 10 times as long as the dog’s, and 20 times wider.) Coincidentally, just a few days after this, researchers in Argentina reported the discovery of the largest dinosaur ever found [link; see also link, and link]:

ARGENTINA-PALEONTOLOGY-DINOSAUR

Museo Egidio Feruglio—AFP/Getty Images; copied from http://www.npr.org/blogs/thetwo-way/2014/05/18/313608255/a-giant-among-dinosaurs-discovered-in-argentina

Immediate after seeing the photo above, I wondered how its leg bones would compare to an elephant’s, so I wrote to the dinosaur’s discoverers.  They kindly replied with the femur dimensions:

Length (cm)                         Diameter (cm)

Dog                                        11.8 cm                                      0.85 cm

Elephant (“Tusko”)       107 cm (= 9x dog)                   16 cm (= 19x dog)

New Dinosaur                   240 cm (= 2.2x elephant)     34 cm (= 2.1x elephant)

It’s interesting to note that this dinosaur’s bones are about twice as long and twice as wide as the elephants. All other things being equal, this would point to the dinosaurs having less mechanical strength relative to their weight than elephants do. (Of course, all other things aren’t equal, and dinosaur enthusiasts spend lots of time thinking about tails, buoyancy in swamps, etc.) Still, it’s fascinating to think about!

I of course showed the picture, and the correspondence from Argentina, in class, which was fun. This was a few weeks ago. The course is over now, and I should recap it some time. Overall it went well — my evaluations this term are possibly my highest ever — but some parts were more successful than others. I’m a bit surprised, reading the comments, that no one mentioned the elephant femur. It’s hard to impress people these days. Next year I’ll have to drag in a dinosaur bone.

A soft, silky, scientific poster

I spent the past week at a fascinating conference on teaching at the interface of physics and biology: a mix of biophysics research talks, education talks, and combinations of the two. I presented a poster on my ‘biophysics for non-science majors’ course, which went over well. Perhaps its biggest impact was superficial, though: everyone (including me) loved the fact that it was printed on cloth. Thanks to a colleague who forwarded this link to a blurb on “the $25 scrunchable scientific poster,” which points out that the custom fabric printing site spoonflower.com will print any image, at 150 dpi resolution, on beautiful non-wrinkling fabric, I decided to give it a shot. I was delighted with the results — the poster looks great, and is simple to transport, folded and stuffed into a bag. No more poster tubes!

cloth poster

Plus, if you’re tired of questions, you can hide under it.

cloth poster blanket

 

The creation of the birds

The Creation of the Birds

“The Creation of the Birds,” by Remedios Varo

In general, there’s little or no correlation between the length of a eukaryotic organism’s genome and any other “obvious” characteristics, such as the creature’s overall size. Humans have a genome of about 3.4 billion base pairs; those of mice and giraffes are a bit smaller (2.7 billion base pairs), for example, and orangutans’ and guinea pigs’ are larger (about 4.0 billion base pairs) [1].  Many amphibians have gigantic genomes, 27 billion base pairs for the tiger salamander, e.g. The figure below, from the on-line version of Molecular Biology of the Cell, gives a nice glimpse of the scale of lots of organisms’ genomes. In general, genome size doesn’t mean much; it’s simply a relic of the accumulation of random bits of DNA, for example from viruses and transposons, over billions of years of evolutionary history.

Genome size

It turns out, however, that there are creatures for which genome size does matter. Suppose you’re an organism with a very fast metabolism –- your heart rate is high, you consume oxygen very rapidly, etc. Your ability to function may depend on the surface area of your red blood cells, since oxygen has to pass through the red blood cell membrane to be bound by hemoglobin. You might want, therefore, lots of small red blood cells rather than fewer large ones, since ratio of surface area to volume is greater for smaller shapes. For mammals, the desire for small blood cells shouldn’t generate evolutionary preferences about genome size, since our red blood cells don’t contain any DNA. In birds, however, the red blood cells do contain DNA. Flying is a metabolically costly activity — it takes a lot of energy to fight gravity. One might expect, therefore, that birds have small genome sizes, and indeed they do: about 1.3 billion base pairs, on average, compared to the mammalian average of 3.1 billion.

Should one believe this just-so story? If true, it would predict that (i) non-flying birds have larger genomes than flying birds, and (ii) hummingbirds, with the fastest metabolism of all the birds, should have the smallest genomes of all. Both of these are, in fact, true! As discussed in a neat paper from a few years ago [2], the average hummingbird genome size is 1.0 (+/- 0.01 s.e.) billion base pairs, much less than the avian average. I’ll leave it to the reader to explore (i), either via papers on the subject, or by exploring the genome size database in [1]. (The database is fascinating.)

I stumbled on all this while thinking about shape and scaling (for the class I’m presently teaching), and while reading a fascinating draft of a book on biophysical models and wondering whether there are exceptions to the lack of sense in animal genome sizes.

Of course, if I were designing a bird, I’d remove the DNA from red blood cells entirely, as is the case in mammals. But, no one asked me, and this provides yet another good illustration that evolution selects for traits that help organisms survive (like smaller genomes for birds), but doesn’t necessarily find “optimal” configurations. All this reminds me of the excellent painting by surrealist Remedios Varo, at the top of the post.

 

[1] All genome sizes are from the excellent http://www.genomesize.com (and references therein). Values (“C-values”) there are picograms of total DNA; on average, 1 pg is 0.978 x 10^9 base pairs.

[2] T. R. Gregory, C. B. Andrews, J. A. McGuire, C. C. Witt, “The smallest avian genomes are found in hummingbirds,” Proc. R. Soc. B Biol. Sci. 276, 3753–3757 (2009).  http://rspb.royalsocietypublishing.org/content/276/1674/3753