Does STED really break the law?


Ernst Abbe, legendary German physicist of yore, defined the resolution of a microscope as a function of the ratio of the objective aperture radius to the working distance of the image object. Meaning that the closer the image object (the shorter the focal length) and the wider the objective lens is, the greater the resolution, all else being equal. It’s commonly referred to as “Abbe’s diffraction limit”-a fundamental, physical limit to our ability to form images with lenses. Wavelength plays into it too, and that’s why the longer wavelengths used in say, two-photon microscopy can only resolve different light sources over a longer distance.

I remember sitting in a neurology seminar last year, the topic was the imaging capabilities of STED (STimulated Emission Depletion) confocal microscopy-a superresolution technique-for living neurons. Immediately prior to the section where the method was described (a doughnut-shaped point-spread function photobleaches nearby fluorophores, preventing them from contributing to the intensity measurement at a given point) was a cartoon involving a police officer and some sort of criminal hijinks taking place. The title of the slide was something along the lines of “How to break the law.”

As one audience member was quick to point out, the fluorescence emission (from the middle of the doughnut-shaped stimulated emission PSF) still must travel back through the objective and all the other optics, convolving with the various transfer functions of the lens elements at every step of the way. How can this be said to be breaking the diffraction limit? I agree.

Because a confocal microscope is a scanning apparatus, it only illuminates and records a single point at a time. The illumination path has a point spread function just as in the imaging path, so normally a fairly large volume, capable of containing many fluorophores, is illuminated and contributes to the light brought to focus by the imaging path. By bleaching a large volume around surrounding the region of interest, the only fluorophores capable of excitation by the non-toroidal excitation PSF reside in this central volume. Although the PSF incident on the photodetector is still diffraction limited, the only fluorophores contributing to the signal are in that small, central, un-depleted volume.

I’m not convinced that this corresponds to superresolution, at least not without qualification. It certainly allows you to superlocalize the fluorophores, but resolution in microscopy is differentiating between two proximal light sources in space and, I think this is crucial, in time. So there is a time scale involved in STED, and all scanning methods, for which two objects can be resolved, as long as their movements are much slower than the scan. A highly dynamic process like cell membrane fluctuations would probably fall outside of the processes that could be imaged by STED. I think a more suitable term would be appropriate for this and similarly limited techniques.

I don’t make this claim simply because I’m catching my grumps early this year. I think the terminology is genuinely misleading. Consider the title of this paper: “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function” [1].
They demonstrate an interesting method for recovering depth in a widefield microscope, and they do pinpoint a dense population of fluorophores, some of which are only a few nanometres apart. But the fluorophores are effectively immobilized, and the entire imaging processing takes 450 seconds.
“Resolution” and “sensitivity” are two very different things, and under certain constraints you can use one to inform the other. The title in this case misleads the reader to assume that physical laws are being broken, which is not the case. In particular this mild misdirection will lead undergraduates and laypeople to misinterpret the claims of science. We should take efforts to avoid it, even if your rival is pulling in grant money with these sorts of “impossible” claims. After all, I’m sure that Ernst Abbe wouldn’t buy it.

[1]S.R.P. Pavani, M.A. Thompson, J.S. Biteen, S.J. Lord, N. Liu, R.J.Twieg, R. Piestun, W.E. Moerner. Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function. Proc. Nat. Ac. Sci. 106:9. (2009)

Note: The 3D localization of dense fluorophores they report, again by multiple rounds of partial photoactivation and photobleaching, was generated over 30 cycles of 30 exposures, each frame consisting of a 500 ms exposure. That’s over five minutes of acquisition time.

Ender’s Game gets it wrong

You loved Ender’s Game, you read it young and considered the story and lessons within to be an important part of your development as a young adult. The loveable, relateable protagonist Ender is a misunderstood genius, destined to become an essential player in the survival of the human race. He was picked on and made fun of, constantly challenged by the pecking order. And all of this torment, from both authority and peers, arose because of his unique abilities as a human. Eventually he is vindicated by singlehandedly saving humanity from a perceived alien menace. Probably, you didn’t just like Ender, you wanted to be Ender, and thought you were two peas in a pod, gifted geniuses before your time. This is also why we like Peter Parker so much, and commonly described criteria for delusions in the Diagnostic and Statistical Manual of. Mental Disorders

But I’m not here to berate you for your literary preferences. I too loved Ender’s Game, identifying with the gifted and talented cast as a reflection of myself and my own cadre (for some reason, everyone considered themselves an Ender, never a Crazy Tom, Dink Meeker, Petra, or even a Bean). The audience as the protoganist is a common trait of tremendously succesful story franchises. Exemplia gratis: Harry Potter, Star Wars, The Matrix, etc., all involve a relatable character plucked from obscurity to “save the world,” blank masks ripe to be painted with our own faces.

A much more drastic feat of projection accompanies our personal escapisms in the story of Ender. The major plot driver of the story is a human projection of our centralized “insect” hierarchy on the Formics. In case you haven’t read or watched yet, the key to defeating the alien menace is to stomp the queen, shutting down the society from the top down. [Spoiler alert one sentence ago.] Once that happens, all the workers stop dead in their tracks like marionettes off strings. Fans of E.O. Wilson’s works and the concept of the superorganism will recognize that this isn’t quite how control plays out in a hive. Ants surely don’t consider themselves to be toiling in some Hymenopteran gulag. Instead, each individual is living out their dream job, which just so happens to be whatever form of labour is in short supply (though for bumblebees there is quite a bit of bullying involved in persuading workers to stay the line). Think Brave New World not 1984. In most cases, the queen is actively involved in negative feedback to repress rival queens among her offspring. This means that the destruction of the queen typically doesn’t destroy the colony’s ability to survive, for ants and many bees a new queen will be along shortly. And the executive control of the queen is almost non-existent. For many cases, it may be more accurate to think of the queen as toiling for the sake of the workers rather than the other way around. From a pure superorganism perspective, the queen is functionally the genitalia, where the workers are the organs, digits and nervous system of a body which just happens to consist of physically separate parts.

Ultimately in Ender’s Game the humans aren’t fighting the Other, they are fighting against their own reliance on central control as mirrored by the Formics. The Formics serve as a model of central authority across interstellar distances, and the vital trait that enables their society is faster than light telepathy. Not something real-world humans are likely to develop anytime soon. Ender empowers his lieutenants with tactical autonomy to overcome communication and planning lags from a central authority.

On balance, us humans are a bit like the Formics in our reliance on the human pseudo-superorganism and it’s technological appendages. Our society is increasingly ever-more reliant on science and technology, but the risk of technological and scientific literacy of most individuals falling woefully behind society as a whole is very real. If the societal infrastructure of the technical elite were destabilized or removed (stomping the queen), how well would society as a whole get along? How many of us have basic skills in coding or electronics (that’s a biased rhetorical: my undergraduate training was in electrical engineering). This is a real concern that doesn’t require the use of a D.R. device [doomsday weapon from the book] to be realized. If the role of science, technology, engineering, and mathematics in education, policy, and culture doesn’t maintain pace with our reliance on those fields for survival, we will face a very real crisis. If the worst scenarios predicted by planetary climatologists are realized, this crisis has already gained an awful lot of momentum. Confronted with problems progressing faster than our ability to deal with them, humans functionally become the unguided Formics of Ender’s Game. What a disheartening answer to Fermi’s Paradox*.

Note: there is plenty of discussion of author Orson Scott Card’s public bigotry available elsewhere on the internet. I deliberately avoid that entirely here.

*Fermi’s paradox: The universe is really big, with plenty of potential for life to develop and follow similar paths as on Earth. Why aren’t we constantly bombarded with wayward or directed radio communications from these civilizations? See Drake equation