On second thought, don’t ask worms for directions

In my last post, I wrote about a remarkable recent paper reporting that C. elegans, the well-studied nematode worm, can sense magnetic fields. In a series of elegant experiments, researchers at UT Austin showed that C. elegans moves at a particular preferred angle to an applied field. Moreover, that angle matches the angle between the Earth’s magnetic field and the vertical at the place the worms are from, suggesting that the worms can use the field to navigate “up” or “down.” But:

My colleague Spencer Chang cleverly realized that there’s a puzzle here: orienting at some angle θ relative to the magnetic field will just point the worm somewhere along a cone centered on the field direction (see illustration, left). This cone touches the vertical, but only at one particular “azimuthal” angle. If we want to move along the vertical, knowing θ is not enough — the worm would also need some information about the azimuthal angle, and it’s hard to imagine what that information could be.

I’m somewhat embarrassed that I didn’t realize this when reading the paper. (I imagined this cone then, but blithely didn’t think more about it, assuming that somehow the cone “averages out” in the worm’s search. This is wrong.)

Thinking further, it’s even worse than it seems: if I calculate the average of the angle θ’ between a vector on the cone and the vertical (see figure, left), it’s greater than θ! (That is, <cos(θ’)> = cos^2(θ), so <θ’> is greater than θ, where <> indicates an average over the azimuthal angle. I’ll leave it to the reader to check my math.) Therefore moving randomly on a cone of angle θ to the field is a worse strategy than simply moving along the field direction, if one wants to be close to the vertical.

It seems like one of the following must be true of the worms’ field-assisted navigation:

1. The worms must have a (separate) mechanism for determining the azimuthal angle. (It’s hard to imagine this.)
2. The worms are really bad at orienting vertically. (Notably, they are moving one- or two-dimensionally in the experiments, so actual 3D vertical orientation wasn’t tested.)
3. The worms are not actually trying to orient vertically, so it’s fine that they do a bad job of it.
4. The worms have some additional mechanism for sensing up and down, perhaps one that (also) isn’t very accurate, and this in conjunction with the magnetic field sensing allows them to orient. One might suspect gravity, but the authors of this paper show that gravitational sensing seems to be absent.

In search of insights, I emailed the corresponding author, Jon Pierce-Shimomura, who very nicely wrote back. He’s certainly aware of how puzzling the worms’ behavior is. Not surprisingly, he advocates for #4 as being likely — I’d pick it also — and suggests that pressure or humidity might give other cues. Mysteries remain, but they’re amenable to further clever experiments, many of which are underway. Obviously, it would be great to watch the worms’ motion in a fully 3D environment, in which their paths, the field direction, and the “cone” of angles between the vertical and the field could all be known, to infer what their strategies for navigation are. This need not even be done live — I imagine that if one could map the “tunnels” the worms have dug through a gel, one could infer their orientational tendencies. Who knew that a creature with 1000 cells could offer such puzzles?