Over the last two days, six physicists have won Nobel Prizes, but just like last year, and the year before, etc, I missed out. Ah well, it could have been worse, at least actual biologists won the Nobel in Physiology or Medicine. Yesterday, three physicists changed the light bulb, forever, and were awarded the Nobel Prize in Physics. Today, three physicists saw smaller things than they should have been able to, and picked up the Nobel Prize in Chemistry. They won it for developing techniques for imaging with light, objects that are smaller than the wavelength of the light. The effect is illustrated in the figure up top of this post, on the left is a living cell imaged using a conventional microscopy — details are blurred by the size of light photons we are using to image the cell. On the right is the cell imaged using one of the techniques that got the prize. There you can see individual spots in the image, these spots are the locations of individual protein molecules .
The idea behind one of the techniques that won the Chemistry Prize is at heart quite simple — although there are some quite technical bits to get it to work that I’ll omit here. We start with the problem they solved. A photon of light is about 500 nm across, if it is green say, blue ones are a little smaller. This means that if you have perfect optics you can easily use green light to resolve two objects 500 nm apart. That is easy.
But cell biologists in particular want to resolve much smaller things: the nanomachines that run our cells are mostly tens of nanometres across, much smaller than a photon of green light. Even very large proteins, such as Dystrophin, the protein missing in people with Duchenne Muscular Dystrophy, is only about 100 nm long. So what happens if we try to use green light and microscopy to distinguish between one end of this protein and the other?
We are in trouble. Let us say that the two ends of the protein are at points A and B, 100 nm apart. If a photon actually originates from a point A, then indeed if our microscope has perfect optics it is more likely that we will see the photon as if it originated at point A, but because the photon is quite large, it is actually also possible that we will apparently see the photon coming from B. The ratio of the probability that the photon looks as if it came from point B, to the probability it looks like it came from point A is
relative probability ≈ exp[-(δ/(λ/2))²]
for points A and B a distance δ apart, and for λ = 500 nm the wavelength of light. If we put δ = 100 nm in this equation we see that probability that the photon looks to us to have come from the end it really did come from, is less than 20% higher than the probability it looks like it came from the other end. This is no good.
However, this is just one photon. What if you really blast the sample with lots of light and get many photons out? If point A puts out 1000 photons, then with each one 20% more likely to appear to have come from A rather B, then typically we get about 550 apparently from point A, and 450 apparently from point B. Production of photons is a random process so there is statistical uncertainty here, which the Central Limit of Statistics tells us is about √1000 ≈ 30. So we expect 550±30 photons apparently from A and 450±30 apparently from B.
The two sets of error bars do not overlap and we can be confident that the light is indeed coming from the end of the molecule at A, not that at B. Using many photons, we have resolved two points much closer together than the size of the photons themselves. A neat trick, which is why three physicists will be off to Stockholm.
Chance & Necessity 