Rich, P., Liaw, H., & Lee, A. (2014). Large environments reveal the statistical structure governing hippocampal representations. Science, 345 (6198), 814-817 DOI: 10.1126/science.1255635
Have you ever felt lost and alone? If so, this experience probably involved your hippocampus, a seahorse-shaped structure in the middle of the brain. About 40 years ago, scientists with electrodes discovered that some neurons in the hippocampus fire each time an animal passes through a particular location in its environment. These neurons, called place cells, are thought to function as a cognitive map that enables navigation and spatial memory.
Place cells are typically studied by recording from the hippocampus of a rodent navigating through a laboratory maze. But in the real world, rats can cover a lot of ground. For example, many rats leave their filthy sewer bunkers every night to enter the cozy bedrooms of innocent sleeping children.
In a recent paper, esteemed neuroscientist Dr. Dylan Rich and colleagues investigated how place cells encode very large spaces. Specifically, they asked: how are new place cells recruited to the network as a rat explores a truly giant maze? Today, we huddle closely with Dr. Rich to whisper about his findings.
SP: Do you remember when and how you first learned about hippocampal place cells? Did your interest in the hippocampus burgeon immediately, or ripen like a stubborn avocado?
Not exactly, only that it was during my undergraduate studies. I was on a neuroscience degree course and there was quite a lot of cellular and molecular neuroscience. I was interested in the more cognitive aspects of neuroscience, but I wanted to still be studying the brain per se rather than psychology. The hippocampus and place cells seemed as though it had the higher-level cognitive aspects, but was still very much grounded to the physiology, to neurons and spikes. Some of the lecturers who taught were rodent hippocampal researchers, so I was exposed to a lot of the experimental and computational work on the hippocampus. It was also around that time that grid cells had just been discovered, so I think some of the excitement in the field trickled down to us undergraduates.
SP: The experiments in this paper required you to record from the brains of rats running through huge mazes, up to 48 m long. Where and how did you set this up?
DR: When we were planning this experiment, none of our normal lab rooms were large enough. One evening we wandered around prospective parts of the building, the back service corridors and such, asking “can we do it here?”, “where would we mount the cameras?” et cetera. Eventually we found a suitable space, the cage washing room in the animal facility. The trouble was that it was in full use during the week for cleaning animal cages; we were only able to use it on weekends. So, when we had an animal ready to go, we would have to set up the whole experiment just for the weekend. Starting Friday evening, we’d move everything down and set it all up, recording rig, cameras, cables, maze pieces, the lot. We ran the experiment all weekend then cleared the room in time for the start of work on Monday. Since we couldn’t really plan exactly how things would go, initially there were a lot of trips to the hardware store. We’d have some problem, and think “pipe clamps, we need pipe clamps!”, then go to the store to get pipe clamps, and by the time we got back there would be something else we needed! After the first few times we got the setup and teardown running smoothly, and then we were able to concentrate on running the experiment well.
SP: By looking at place cell recruitment in these big mazes, you discovered that the formation of place fields is an independent Poisson process with its rate drawn from a gamma distribution. In describing the gamma-Poisson process, you cite a book called On Random Processes and Their Application to Sickness and Accident Statistics by O. Lundberg. What's up with that book?
DR: Ove Lundberg was a Swedish mathematician who did some important work on Poisson processes. The major motivation of his work was in its application to the insurance industry. This branch of mathematics, known as risk theory, had actually been pioneered by his father Filip Lundberg.
Prior to Ove Lundberg, in the 1920s, British mathematicians Major Greenwood and Udny Yule had developed the gamma-Poisson model trying to understand the distributions observed amongst accidents in factory workers. They concluded that preexisting differences offered the best explanation for the differences they saw in the number of accidents each individual suffered. At around the same time, the Hungarian mathematician George Polya was working on different mathematical models that gave similar distributions. In these models individuals would start from an identical baseline, and the occurrence of an accident (or more generally an event) would increase the future likelihood of an accident for that individual. These types of model, which were framed in terms of drawing balls from an urn, became known as cumulative advantage or rich-get-richer models. Ove Lunberg was the first to show that these two mechanisms, preexisting differences or cumulative advantage, could actually give rise to the same stochastic process, even though the starting assumptions were very different.
I had been struggling with simulations of models in an attempt to distinguish between preexisting differences or a cumulative advantage mechanism in our data. When I found out that someone had solved the exact same problem, it was a crucial piece of information in interpreting our data.
The reference itself was actually a bit of a pain. Since it was a book, the journal wanted the whole title to be in the shortened reference list, which counted against our word limit. So we were always joking about how much it really needed to be in, because we could get another 10 words or so if we got rid of it. But it was an important piece of the puzzle, so it always stayed in.
SP: We are conducting this interview within a helicopter zooming across middle America. Do your results tell us anything about how place cells might represent extremely large spaces, such as the view from this helicopter space shuttle? Does your model predict an upper limit on spatial representation in the brain?
DR: This is an interesting implication of our data; it gives us an idea of what strategies might be employed in the hippocampus to allow the representation of very large spaces. The logarithmic-like recruitment of cells suggests that the hippocampal representation is able to encode a large range of environmental sizes. Also the variation of each cell’s propensity may be a way in which the hippocampus may represent different environmental scales; for instance cells with few fields, spaced far apart allow a coarse localization of position, whereas those with more fields give the fine spatial resolution once you know roughly where you are.
From the model, we can predict the behavior of place cells in environment much larger than we examined. For instance, we can extrapolate the recruitment of cells as a function of environmental size; we can read it off and see where it hits 95% or 99%. Would that length be the “upper limit” of the representation? Not necessarily. Even with almost all cells recruited as place cells, there are a huge number of locations that could be coded uniquely across the population using certain types of combinatorial code. One would have to specify a particular code in order to begin to think about an estimate of capacity in this case.
SP: In your experiment, the rat is entering an entirely novel environment, and so does not know how large the maze is going to be. But if he did have some prior expectation about the scale or shape of the maze, how do you think this would affect the rate of place cell recruitment?
DR: It’s definitely possible that an expectation of environment size may modulate some aspect of the place field representation; it makes sense for the hippocampus to optimize coding given the available information it has. However an interesting aspect of the model we describe is that it seems to be able to cope quite well with environments of different sizes even with fixed parameters. This may be a mechanism used to cope with the inherent uncertainty in the world; you never know exactly how large or small a place will be, so you have to account for either possibility.
SP: Sensory systems also use logarithmic compression to efficiently compress the broad range of input signals into the limited bandwidth of neurons. For example, the retina encodes luminance signals across nine orders of magnitude. Do you think that the logarithmic recruitment of place cells might arise from logarithmic compression in the sensory circuits that provide contextual signals to the hippocampus?
DR: Hippocampal coding is invariant to the specifics of the sensory input, place cells do not respond in a simple manner to sensory stimuli, but rather seem to integrate from a wide array of information in order to respond to place per se. Given this higher-level representation and the number of processing steps potentially involved, I’m not sure that something such as stimulus intensity (which is coded logarithmically), would directly relate to the size of the environment explored (which corresponds logarithmic-like cellular recruitment). Although the similarities may represent a common neural optimization principle, for instance, as you suggest the efficient use of a limited channel.
SP: As a sci-fi connoisseur, you are probably familiar with Asimov's The Gods Themselves, in which scientists discover and interact with a universe that has very different physical laws from our own. In what ways is the hippocampus designed specifically for our 4-d universe, and how might it be modified to accommodate additional dimensions?
DR: How hippocampal function is adapted specifically for 3+1D environments is a tough question. One theory is that the hippocampus forms the basis of a cognitive map that allows navigation in space and also time. For instance as you go to pick up the dry cleaning, you remember that the traffic along your planned route will be bad at this time of day, so you think of a shortcut to get there faster. In order to perform such a navigational computation the hippocampus may have to draw on a geometric representation it has of space. We don’t really know how it actually does this however. Looking at differences between animals that navigate exclusively in 2 or 3 spatial dimensions would probably provide the best clues about how dimensionality is adapted for.
I don’t think we would be able to ever perceive higher spatial dimensions in the same way as we do for normal space and time. This is because there has been zero evolutionary selection of such abilities. I would guess that a system for the general n-dimensional condition would be more complex than a system for a special case, and so would be selected against during evolution; I think is likely that we are hard coded to our native dimensionality.
We might be able to get around such limitations by using some tricks. Anecdotally, humans can do pretty well in video games that employ different geometries (think Pacman exiting one side of the screen and coming back in on the other side, or teleportation mechanics in other games), so perhaps we are able to chuck complex unnatural environments into smaller independent sections that we are able to deal with. Another idea is that we could co-opt other systems in the brain. For instance, we are quite adept at navigating our high-dimensional social environments. Perhaps one could try and think about a high-dimensional space using social metaphor?
Another sci-fi classic, Flatland by Edwin Abbott Abbott, deals explicitly with this question, how one might comprehend spatial dimensions higher than one’s own. I won’t spoil the story, but will highly recommend it for anyone interested in these questions.
SP: Does it make you sad to think that plants have no idea where they are?
DR: I’m not that well-disposed to plants in general since a large hydrangea pushed in front of me in line in the post office recently, so no.
