|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?|
|A wave of brightness propagating through a molecule.|
|This is from an actual presentation I gave at group meeting.|
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).
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.|
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.