DNA Waves: New paper in Physical Review E.

In June I submitted my latest paper to Physical Review E, and today it was published. I also uploaded a preprint to arxiv.org, and that free version can be found here. It is (probably) the last paper from my PhD work, which I wrote on-and-off in my spare time over the last year. Here, I'll briefly summarize what the paper is about.

A DNA molecule snaking its way through an array of cavities (which are separated by about a micron). The paper is about how "waves" appear to propagate along the DNA molecule.

As I've mentioned in some  other articles, my Ph.D. work was about the physics of DNA molecules trapped in cavities connected by a narrow slit. I was studying this both to better understand polymers in geometries using DNA as a model system, and to possibly develop genetic sequencing technology. The first paper I published on this was about diffusion through these cavities, and most of my Ph.D. I spent working on measuring the entropy loss involved in confining DNA. Towards the end I started working on a paper looking at how long it takes DNA to fluctuate from one cavity to another, which we described in terms of modes of a coupled harmonic oscillator system. That was published last summer.

From my two-pit fluctuations paper.

One day I did an experiment using much longer DNA than usual, and I noticed something cool: when you look at videos of the molecules, it looks almost like there are waves propagating back and forth along the molecule. I decided to investigate that, and that's what the paper was about.

Do you see the waves?

Looking at these movies you can sort of convince yourself that there are these transient waves, and a good way to look at how these things propagate over time is through a kymograph, which averages out one spatial dimension so you can see how the profile in the other dimension evolves over time. Doing this, you can see diagonal streaks of brightness, which are the propagating waves. You can see both positive waves, where excess DNA propagates between the pits, and negative waves, where paucity propagates, which are analogous to electron holes in a semiconductor. I also thought I could see evidence of waves reflecting off the end of the molecules, although that didn't make it into the final paper.

A wave of brightness propagating through a molecule.

The main way I analyzed the data was through correlation functions. A correlation function basically measures the probability that a deviation from the mean of one thing leads to a deviation from the mean in another thing. In my two-pit fluctuation paper, I was looking at the cross-correlation between the intensity in one pit and the other, and since DNA is just going from one pit to the other, if the intensity pit 1 deviates upward from the mean, it's very likely that pit 2 has deviated downward, so they are anti-correlated. At short time-scales this anti-correlation is strong, while at long time-scales it decays towards an uncorrelated noise floor.

This is from an actual presentation I gave at group meeting.

With two pits this is simple, but with a larger number it gets complicated. With three pits you have one-two, two-three, one-three, plus the autocorrelation functions one-one, two-two, and three-three. In general for N pits you have N(N-1)/2+N unique correlation functions, which provide a lot of information. My biggest molecule was in 15 pits, which would give 120 correlation functions. We decided to focus on correlations between neighboring pits: 1-2, 2-3, 3-4 etc. This would allow us to look at the process of DNA leaving one pit and going to the next one, then from that one to the next one, etc.

Basically what we observed was that any given point in time, neighboring pits were anti-correlated (as expected, because if there's more DNA in one pit it's less likely to be in another), and then that grew to a positive correlation at some later time (this is the propagation of the "wave": excess DNA in one pit at one time is more likely to be found in a neighboring pit at a short time later), and then a long-time decay (everything averages out due to random thermal motion).

Cross-correlation functions between different pit intensities. At zero time (A), they are anti-correlated because DNA in one pit is less likely to be in another. At a short time later (B), they are positively correlated, because the excess DNA at A is likely to have reached B at this time. At long times (C), random fluctuations bring correlation down to zero. This is the meat of the analysis.

This pattern was repeatably observable for all these large-N systems, which gave us a lot of data on how these waves propagate through confined DNA. We could also see something similar looking at next-nearest neighbors, and even next-next-nearest neighbors. The hard part was understanding all this data and what it was telling us about the underlying physics that lead to these waves. Presumably, such an explanation would allow us to predict what these correlation functions look like.

When the DNA molecule is at equilibrium, there is a certain length in each cavity (the ideal length balances its own self-repulsion and the entropy loss from the slits), and a certain tension in the strands linking each cavity. If, due to a thermal fluctuation, one cavity has an excess of DNA, the whole system gains some energy that is harmonic with respect to the excess length of DNA, and this excess is diminished as DNA is transferred to adjacent cavities through propagating changes in tension in the linking strands.

Because of the harmonic energy cost and my previous work mapping the two-pit system onto harmonic oscillators, the way I initially thought of the waves was in terms of a chain of harmonic oscillators, where a disturbance in one propagates down the chain as a phonon. It is a bit tricky to map this phenomenon onto a polymer in solution, because it is overdamped and effectively massless, so there is no momentum that is conserved. I spent a while trying to figure out the theoretical correlation function for an overdamped harmonic chain in thermal reservoir, and writing Monte Carlo simulations thereof, but that only got me so far.

One dimensional random hopping on an array. This model turned out to describe our system very well.

A simpler model turned out to work better: if you just imagine a bunch of Brownian random walkers on a one-dimensional lattice, each with some random probability of hopping in either direction at some rate, you can show that this system gives rise to collective motion which is exactly solvable and evolves in time in a way that looks like our observed correlation functions. In our system, we can treat the DNA as randomly fluctuating in either direction, but fluctuations are more likely in a direction that reduces excess DNA in a cavity, and that is essentially what the multi-hopping model is describing. A lot of the paper involves matching the predictions of the model to our observed correlation functions. It turned out to be different than I had initially envisioned it; I was originally thinking of it in terms of sound waves propagating through the molecule as tension perturbations.

I like this paper because it started out as an investigation of a neat phenomenon I happened to observe, and lead to something more systematic that we eventually understood in terms of some fairly fundamental statistical physics.  I'm glad the reviewers liked it too!

Update: this post was modified after the paper was published.

Do radioactive things glow?

In a lot of depictions of radioactive materials, there is a green glow that is emitted. This is so common the green glow itself is associated with radioactivity. Does this green glow exist, and if so, where does it come from?

This animated plutonium rod should not be confused with the inanimate carbon rod, which does not glow.

Radioactive materials such as uranium and plutonium do not, by themselves, glow. Pure uranium looks like a boring grey metal, and plutonium is slightly shinier. The glow associated with radioactivity originates from materials containing radioactive isotopes, but is due to electronic rather than nuclear transitions, similar to how certain materials glow under a blacklight. These materials can glow without an external power supply, because the atomic transitions can be excited by the radioactive decay. This is known as radioluminescence.

Radioluminescent materials were more common in the early 20th century, before it was understood how incredibly bad for you extended radiation exposure is. Clock faces often had dials painted with radium, so that they could be read in the dark. The luminescence was actually produced by zinc sulphide, which was activated to an excited state by the radium decay. Radioluminescent watches can still be purchased, but they use the safer tritium as an isotope.

Another common product was uranium glass, which was marketed as vaseline glass, apparently because it was the same colour as petroleum jelly was at the time. Once again, it is not the uranium producing the light, but the transitions excited by its decay.

Uranium glass glowing green.. The blacklight in the background is the main source of illumination.

Perhaps the most common radioactive green movie trope is plutonium, but plutonium is not used in radioluminescent compounds. It can appear to glow red, but that is due to a chemical reaction with oxygen (aka burning) rather than anything associated with radioactivity.

All of these heavy-element radioluminescent materials rely on alpha-decaying isotopes. Alpha particles tend to move slowly (compared to light) and are comparatively safe; alpha radiation can essentially be blocked by clothes, but if you inhale a piece of alpha-emitting dust you can be in serious trouble. The main scenario where radioactivity does produce a glow is not from alpha decay but beta decay*, typically in nuclear reactors. Nuclear reactors are often kept underwater, for cooling and for neutron shielding, and when emitted beta particles (electrons) exceed the speed of visible light in water, they emit Cerenkov radiation, which manifests itself as a blue glow (This is analogous to a sonic boom when something exceeds the speed of sound).

Cerenkov radiation from a nuclear reactor.

So just to summarize, radioactive materials do not emit light just because they are radioactive, but essentially act as a power source to make other things glow. Except nuclear reactors, those actually glow.

*Electrons are 1/7000th the mass of alpha particles, making them much faster at the same energy.

"What's the application?": Genetic sequencing and polymer physics

Long time no post. I wrote an article on PhysicsForums trying to explain a few of the applications of my field of research, and how they relate to some of the physics problems. Check it out!

https://www.physicsforums.com/insights/whats-application-polymer-physics-genetic-sequencing/