The beauty of data

I was analyzing some results from a simple little experiment that I had done. The picture below is a recording of neural activity in the tail of a crayfish.

Notice the large, regular spikes? They start slow, speed up, and then slow down again. Those are from a single neuron: the tonic stretch receptor of a muscle receptor organ. This is a little sense organ that detect bending in the tail: the more it bends, the faster the neuron fires spikes. I've shown a recording of them in this journal before, because they were the first neurons I was able to record from in my lab.

You can see there are a few other neurons firing in this trace: a few bigger, most smaller. Using the marvels of computer technology, I can sort all of those by shape so that I'm left with just the one cell I'm interested in. In practice, it tends to miss a few spikes here and there, but in this case, it did a pretty good job.
Now I can focus in on just the response of the one, single neuron I'm interested in, shown in red.

Because this neuron fires all the time when stretched very consistently, the major thing we're looking for is, "How does that firing rate change?" Yes, I can see it gets faster and slower, but I'd like a bit more detail than that. I plotted the instantaneous frequency of the firing rate (spikes per second, calculated spike by spike rather than an average).

And I was shocked by what I saw.

Clearly, this neuron didn't just speeding up and slowing down once. It sped up, then went slower and faster several times, resulting in these distinct peaks in the firing rate. It wasn't visible in the initial trace, but was blindingly obvious when you did this simple analysis.

The shock wasn't just over realizing that the neuron's spiking was a bit more complex that I first though; the shock I felt was the shock of recognition. I looked at those dots, outlining a shape with the distinctive series of "scalloped" edges along the top. I'd seen that shape before. I'd seen it a few times in a recordings I'd made myself during my Ph.D. work. Mostly I had seen that shape in scientific papers by other authors, like these two traces here.

From Figure 1 in Wiens, T.J. 1993. J. Comp. Physiol. A 173: 435-444.

What that picture shows you are intracellular recordings from two muscle cells. A neuron is being stimulated by the experimenter (Ted Wiens, in this case), and the muscle cells are responding to each little puff of neurotransmitter that the neuron releases. (You can tell it's an old picture by the grid of dots visible in the second trace. This was probably photgraphed straight from an oscilloscope, which usually had a little grid to help you measure things. This was back in the dying days of analog neurobiology, before computers were fully integrated into neuro labs.) What's shown here is the muscle cells electrical response, but the amount of contraction -- the tension -- created by that muscle cell will closely parallel the electrical activity. Each peak of the trace above is the muscles response to a neuron firing once (in this case, the motor neuron fired four times).

But I wasn't recording from muscle. I was recording from a sensory neuron.

I put together what this trace was showing me in a flash. Somewhere in this preparation, a motor neuron was activated and firing action potentials. In fact, it's probably just a one motor neuron, because crustacean muscles have very few neurons to control their muscles. The motor neuron is firing, the muscle it's connected to is contracting. These little muscle twitches cause just a little tiny bit of tension, so slight that you can't even see the tail moving in the dish. But it's moving the tail just enough that the stretch receptor is picking up the tension, and reflecting the muscle's activity in its firing rate.

It was beautiful.

And because beauty should be shared, I went looking for someone to share it with. Because it was Saturday, not many people were in there office, but poor Chris had to bear the brunt of me geeking out over this trace. I did not feel guilty about this, since he was pulled me into his office and was waxing rhapsodic about some plant rust (fungal infection) or something a few days before.

It's beautiful to me not because it's any great discovery. I mean, neuron fires, muscle twitches, sensory system tells you "muscles twitching" is pretty basic stuff. No, I think what's beautiful is to see so directly this sensory neuron pick out what are, in all likelihood, the activity of single motor neurons is amazing to me. That, and the experience of looking at the data, having that rush of recognition and almost immediately knowing what's going on... It's exhilerating. It really is. It's pretty much what we scientists live for. Admittedly, we hope that sometimes it's on a larger scale: bigger data sets, more important experiments, things that push the envelope of knowledge, and so on. But even little moments like that are pretty special.

After the intital rush, I became interested in why this experience was so strong for me, and I think it has a lot to do with the immediacy of what I went through. I plotted the data, recognized the shape, and had an explantion in the space of a few seconds. I think this demonstrates just how important exploring and visualising data is. I'm a real admirer of Edward Tufte (last name pronounced "Tuft-ee"), and he talks a lot about this in his works. I wonder how many discoveries have been lost over time because people didn't have the right graph. For example, in this case, I was able to immediately recognize the shape because of the particular plot I chose. What if I had plotted the frequency not spike-by-spike, but averaging the firing rate every 0.1 seconds instead?

I don't find this graph as pretty as the one with just the dots, but I probably still would have recognized the shape. But what if I averaged the firing rate over every half a second instead of every tenth of a second? I would have seen this...

Clearly, a lot of information's been lost. I can tell something is contracting somewhere, but I can't see the exquisite sensitivity of the stretch receptor and how closely it seems to be tracking the muscle tension. So sampling at a higher frequency is better, right? Not necessarily. The original line graph (two above) took the average every 0.1 seconds; the one below takes an average every twentieth of a second...

Ack! That is one ugly graph! I might have recognized what was going on here, but I strongly doubt that I would have come to the conclusion that what I was seeing was beautiful. Even if I changed the line colour away from that gaudy pink.

And if I had plotted the exact same data not as a dots or a line, but as a bar graph of spike counts, I doubt I would have drawn any conclusions about what was going on besides the obvious (the neuron fired faster, then slowed down).

Incidentally, this is the same sampling rate as the first of the "pink line" graphs above: counting spikes every tenth of a second. Yet in one case, the graph reveals; in another, the graph conceals.

There are several lessons here. This example shows that creating a good graphic of the data is not a straighforward thing. "Show me the data" is a constant refrain among experimenters, but there will always be multiple ways to do that. If you don't take care in representing that data, particularly graphically, you will miss evidence for some very interesting things. And it also speaks to why a really good graph or image is so powerful: the immediacy. In this case, it was allowing me to see, in a measure of rate of one neuron, to trace the activity of two others -- and to see it, graphically, as clearly as if I had recorded from those other two cells.

Science is often about simplicity: the simplicity of realizing that what you thought were two different things are really the same thing. And I think that is why I experienced this small little set of nothing data as beautiful: in examining one thing, I saw another.