18 July, 2008

Summer's almost gone...

For those that are interested, this is the grand result of my research this summer – a plot of the T1 relaxation time vs. Temperature for 4,4’-Dimethoxyoctaflurodiphenyl (“DMOFDP”).

It’s absolutely beautiful and mysterious.

Supposedly, plots like this are useful to biochemists for understanding how and why DNA and other nuclear ‘characters’ interact the way they do. For instance, it aides in figuring out why the molecules involved in DNA replication are shaped the way they are, and how their defects might cause diseases.

DMOFDP is an organic molecule with two aromatic rings surrounded by fluorine atoms and with two “rotors” pegged onto opposite ends. The rotors are just three hydrogen atoms bonded to a central carbon atom, which is attached to an oxygen. The three hydrogens “rotate” freely around the carbon when zapped with radio frequency light.

The important thing here is that the hydrogens (that are rotating) and the fluorines (which are attached to the rings in the middle) can exchange energy (since they are similar spin systems). By looking at the plot above, we can learn how much energy it takes to rotate the hydrogen rotors, and how much they interact with the fluorines.

We got the light blue points by pulsing the fluorine atoms, and the purple points by pulsing the hydrogen atoms. Where there are two purple dots (a light colored one above, and a darker colored one below) the hydrogens are interacting efficiently with the fluorines.

What do I mean by ‘interacting efficiently’? Imagine two empty tanks, side by side, connected by a valve that is either open or closed. One tank has a hole in the bottom. At the beginning of the experiment, you will fill one of the tanks, and record how quickly the water level drops. Now when you fill the tank with the hole in the bottom, how fast the water level drops depends on the size and shape of the tank, and the size of the hole. But if you open the valve to the other tank, the water will equilibrate between the two tanks immediately (at a fast rate) and then drop at a slower rate together. The tanks are the hydrogen and fluorine systems, and whether or not the valve is open affects whether or not they interact, or exchange energy.

This is all very exciting, since the current theory doesn’t explain such interactions at the temperatures shown in the plot. I’ll spend the next 7-8 months developing the theory and writing about it.


spencer said...

Hey, summer's not nearly over yet! I'd say we've got at least two months left.

This is pretty interesting stuff that I won't pretend to understand. But what kind of theory would you come up with to explain this? I mean, would it be based on quantum mechanics or something? Do you have to redo the whole system or just a part of it?

higgy said...

There's a classical and a quantum explanation for what's going on - the classical being long-winded but managable, and the quantum one being extraordinarily accurate and (as always) mind-bogglingly strange. I won't give you either.

For simplicity, pretend that if I 'zap' a certain type of molecule with a particular frequency of light, it will give off a considerable amount of light back (which I can detect). But ONLY if I zap it with that particular frequency.

In a sample, though, there are 10^23 molecules (give or take some). In such a statistical system, the 'particular frequency' mentioned above can vary as molecules can exchange a tiny bit of energy with each other depending on their close proximity. Basically, this means there's some spread in the light spectrum that comes into my detector.

It turns out that spread is a Lorentzian. Since the spread in frequencies of light detected is dependent on the proximity of the molecules (on a micro- scale), and one way of changing proximity is to vary the temperature, we can plot this Lorentzian as a function of temperature! Recall that the inverse of a frequency is a time, in this case "R". When plotted on a semi-log graph, it looks like a mountain with straight sloping sides and a rounded peak. That's what the graph in the picture is.

NOW, when there's different samples present, or if the molecules are packed in a particular way, they can interact and exchange energy in new and interesting ways. That can cause more than one curve to appear, and it tells us a lot about the structure and motion of the molecule. It gives us functional information.

So I'm essentially taking a theory that's very solid, and extrapolating it to a more complicated system. Understanding an established theory, and then pushing it a bit farther and figuring out how to 'fix' it is what makes physics so enjoyable.

higgy said...

And I should add that I don't think this post is necessarily appropriate as far as Debaser's usual content goes...

...but given that each point (or pair of points) on that plot took at least 2 hours of work (not including setting up and shutting down each day), I'm going to ignore the fact that it probably doesn't appeal to anyone outside the narrow field of study that is 'low frequency NMR relaxometry'.

spencer said...

I see. So there are various models (classical, quantum) of a simpler phenomenon and you're extending one of them to a more complex phenomenon?

I guess what I'm trying to ask is what this extending actually consists of (or, what do you mean by "theory"?). Is there a fixed model that explains every physical situation that you are applying to this specific situation? Or is "quantum mechanics" more of a general set of principals for developing models that you are applying to this particular phenomenon?

Cassady said...

Higgs, I've got to say that this, while completely beyond me, is also intensely interesting, and I'd like to hear you explain some of it in person.

higgy said...

Spence - good question.

Over a decade ago, the question people wanted to answer was, "How can we predict the rate at which a rotor moves given its placement on an immovable 'truck' of carbon atoms?"

To answer it, chemical physicists (and physical chemists) developed a model that took certain parameters (types of atoms present, distances between atoms, spectral density of radiation present..) and gave a single rotational rate.

About 3 years ago, Prof Beckmann (my advisor) investigated a new type of molecule whose only difference was the degree and type of interaction between the atoms on the rotor and the atoms on the 'truck'. He observed not one, but two rates in his experiments, and had to go back and modify the model to account for this.

When we began this summer, we were expecting 'my' molecule (DMOFDP) to produce two rates according to this modified model - and it did! - but in the wrong places. So, we have a half-dozen hypotheses to explain this on the table, and our goal now is to eliminate them one-by-one, and then modify the model again to account for this class of molecule.

How do classical and quantum 'theories' play into this? The "Model" I've been referring to (including the modifications made over the years) is comprised of axioms, principles, and results from 3 of the 4 main cornerstones of physics: Electricity/Magnetism, Quantum, and Statistical Mechanics. The Model simply consists of these applications of these principles.

So, to summarize - (1) the "Model" (here) is made up of principles from E&M, Quantum, and Stat Mech; (2) this "Model" originally only explained a very simply type of functional molecule, and so (3) it had to be modified to account for more complex molecules.

spencer said...

This is very interesting. In particular, it's interesting how obviously physics is not Popperian and is in fact a Kuhnian normal science. Theory comes after observation. There is a "core" of theory that cannot be contradicted, but many auxiliary hypotheses that can change to fit the facts. It's so much richer than pure falsificationism. I think a lot of people still think of the hard sciences as discovering immutable truths.

Ultimately, there does not seem to be much methodological difference between physics and the social sciences (i.e. economics).