For every job, there is an appropriate tool. If you want to weigh yourself, you hop on the bathroom scales; if you’re looking to measure out some flour or sugar, you use a smaller version from the kitchen. Scientists in the lab have their own, hypersensitive scales, capable of measuring down to an individual thousandth-of-a-gram – but what if you need to go smaller than that?
Weighing individual cells – some of the tiniest things in the world – can require some outside-the-box thinking. So how have researchers managed it?
Turns out, there’s a few options.
Mathing it out
It was 200-odd BCE, and Archimedes had a problem. The new king, Hieron II, had commissioned a new crown from a smith – but he didn’t trust the finished product. He needed a way to figure out if the headpiece was pure gold, but – and this is important – without harming the crown in the process.
Of course, the rest is history. Archimedes had a bath and the original Eureka moment, streaked naked down the street, and invented his eponymous Principle: that when a body is immersed in a liquid, it experiences an upward force equal to the weight of the liquid displaced by the body.
Now, as ingenious as this breakthrough was, we’re not going to pretend it can be applied to things the size of a single cell. But with a little knowledge of physics, we can do something surprisingly similar.
“A resisting force is exerted on a body falling through a viscous fluid at rest,” begins a paper, now 70 years old and possibly the first to describe weighing a single, individual cell.
“If the body is a sphere and if the flow is streamlined, i.e., no turbulence or eddying occurs in the wake of the sphere, the force exerted by the fluid is expressed by the […] equation: F = 6πrnv,” the paper explains, “where r is the radius of the sphere, n the viscosity of the fluid, and v the rate of fall.”
Like the gold measurement technique that preceded it, this relationship is named for the guy who first worked it out: George Stokes, an Irish mathematician and physicist who served as the University of Cambridge’s Lucasian Professor of Mathematics 100 years before Stephen Hawking held the title. Stokes’ Law, as the equation is known, links the mass of a sphere falling through a fluid to its radius, speed, and the fluid’s viscosity – meaning if you know the latter three values, you can work out the initial one.
For the pair of microbiologists writing the paper, the cell in question was one of yeast. “The average weight of yeast cells in a cake is rather easily determined by weighing out a gram of yeast and counting the number of cells with a hemacytometer,” they admit, “but measuring the weight of an individual cell presents a different problem.”
So, instead, they tapped Stokes’ Law, dropping individual yeast cells into a one percent sugar solution with tightly controlled viscosity, temperature, and density. They filmed the cells sinking down through the liquid, timing precisely the speed of its fall; pairing that measurement with the liquid’s values and the cells’ diameters, they could math out the weights they wanted.
Averaging over close to 70 different cells, the weigh-in gave a yeast cell mass of around 79 picograms – that’s 79 trillionths of a gram – with measurements ranging from 24 to 192 picograms individually. That’s shockingly close to the kinds of measurements we obtain using cutting-edge technology today – not bad for a math equation invented 180 years ago.
Vibes-based
So far, so ingenious – but as useful as Stokes’ Law was, it wasn’t generalizable. Yeast cells are spherical – pretty much the perfect shape for math and physics – but others aren’t so easily geometrized. When researchers from MIT wanted to weigh the rod-like E. coli and B. subtilis cells in 2010, they needed to figure out an alternative method.
Their answer? Shake them up. “We used a suspended microchannel resonator (SMR) combined with picoliter-scale microfluidic control to measure buoyant mass and determine the ‘instantaneous’ growth rates of individual cells,” the team wrote in the resulting paper describing their efforts. “The SMR measures mass with femtogram precision.”
Basically, we’re talking about a tiny, hollow beam, fixed at one end and filled with fluid, which vibrates really, really quickly. As cells float through this fluid, their mass will change how fast and hard the beam vibrates – imagine how a spring’s motion changes if you hang a weight on the end for an idea of why.
From there, it’s just a case of measuring those differences in vibrations, and figuring out what weight would result in those numbers. It’s actually not all that different from how some of the simplest macro-size scales work: you take something boingy, add a mass that changes how much it boings, and then reverse-engineer what the weight of that mass must have been. Smart!
Blasting with light
Despite what movies, TV shows, and the occasional overconfident pick-up artist would have you believe, you can’t generally tell somebody’s weight just from looking at them – there’s simply too many variables. But scale the size way down, and the precision way up, and “eyeballing it” is a surprisingly effective way to work out how heavy a single cell is.
Okay, maybe that’s underselling it somewhat. The technique is actually known as “tomographic bright field imaging,” or TBFI, and it’s so complex that it took around six decades’ worth of theoretical work and engineering tweaks before finally being implemented in 2012 to weigh red blood cells.
Once implemented, though, it came with a bunch of advantages. TBFI doesn’t need any particular special instrumentation to perform: it “can be utilized with standard laboratory microscopes,” points out a writeup by Oregon Health & Science University (OHSU).
Then, “using wave propagation through semi-transparent materials, such as cells and engineered specimens, this software solution uses corresponding values of density within each pixel to determine quantitative measurements within an image,” the overview explains. “Providing 3-dimensional measurements allows for the quantitation of refractive index, dry mass, volume, and density as demonstrated by validation studies using polystyrene spheres and red blood cells.”
Overall, TBFI gave a weight of about 27 picograms for a red blood cell – which is good to know, but not the main point of the study.
“Our interest in developing this technique came from a need to interface with collaborators as a part of our funding and membership within the Physical Sciences in Oncology Centers,” explained Kevin Phillips, then a Research Assistant Professor and Postdoctoral Fellow at OHSU, at the time. “The establishment of these centers […] bring[s] physical scientists, engineers, and mathematicians in close working contact with cancer biologists and clinical oncologists with the ultimate goal of bringing about new ways of investigating, understanding, and hopefully treating cancer.”
So, while weighing a red blood cell is interesting, it’s useful more as a baseline for when things go wrong.
“[Our] team has been charged with the task of determining the physical properties of circulating tumor cells,” Phillips explained. “These cells are found in the blood of cancer patients – and will hopefully tell us something about how cancer spreads and how it responds to treatment.”
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